Untitled1

Dedication iv
Foreword
Introduction 1
v
CHAPTER 1
Historical Panorama 4

CHAPTER 2
MACRO _ PHYSICS
Introduction: Conventional Approach to Science
and Physics 18

CHAPTER 3

The crucial question that will have to be answered is whether physics can truly be divorced from philosophy (which embodies logic, metaphysics, axiology as well as epistemology). Standard

CHAPTER

Historical panorama

physics deals with issues that are material as against spiritual ones. In other words, matter is decisive in nature and not spirit. This belief in matter as the stuff of which the universe is made is also tagged materialism as against the belief in ideas, spirit or God which is tagged idealism.

Mechanics as a discipline studies forces and the effects of forces on matter (or on things that are material). Material things occupy space and have weight. Given these characteristics of matter,

Despite the opposition and contradictions of some of Aristotle's theories in physics, his opinions held sway primarily because he enjoyed state power and protection like a latter day Isaac

CHAPTER

MACRO _ PHYSICS

Introduction: Conventional approach to science and physics

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

Dedication iv Foreword Introduction 1 v CHAPTER 1 Historical Panorama 4 CHAPTER 2 MACRO _ PHYSICS Introduction: Conventional Approach to Science and Physics 18 CHAPTER 3

The crucial question that will have to be answered is whether physics can truly be divorced from philosophy (which embodies logic, metaphysics, axiology as well as epistemology). Standard

CHAPTER

Historical panorama

physics deals with issues that are material as against spiritual ones. In other words, matter is decisive in nature and not spirit. This belief in matter as the stuff of which the universe is made is also tagged materialism as against the belief in ideas, spirit or God which is tagged idealism.

Mechanics as a discipline studies forces and the effects of forces on matter (or on things that are material). Material things occupy space and have weight. Given these characteristics of matter,

Despite the opposition and contradictions of some of Aristotle's theories in physics, his opinions held sway primarily because he enjoyed state power and protection like a latter day Isaac

CHAPTER

MACRO _ PHYSICS Introduction: Conventional approach to science and physics

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

Dedication iv
Foreword
Introduction 1
v
CHAPTER 1
Historical Panorama 4

CHAPTER 2
MACRO _ PHYSICS
Introduction: Conventional Approach to Science
and Physics 18

CHAPTER 3

MACRO _ PHYSICS

Introduction: Conventional approach to science and physics



	PHILOSOPHY OF PHYSICS ISBN *978-007-127-X* Copyright Ó Princewill Iheanyi Alozie, 2003 Second Edition 2004 University of Calabar Press *Printed by:* CLEAR LINES PUBLICATIONS 12 Bassey Duke Street, Calabar
PHILOSOPHY OF PHYSICS PRINCEWILL I. ALOZIE


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All rights reserved

No part of this book may be reproduced, stored in a retrieval system , or transmitted in any form or by any means, electronics, mechanical, photocopying, recording or otherwise without the prior written permission of the proprietor of the copyright. Princewill Iheanyi Alozie However, where part of this book is adapted, credit must be given to the author and original source, and the sense of the original source must not be distorted.
		DEDICATION

		This book is dedicated to my wife,Virginia Ifeanyi Phyllis Alozie (V.I.P.)


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FOREWORD		spirit (John 4:24) and not subject to theories and the fallibility of man. He is better experienced than imagined. You do not require a laboratory test or experiments to prove His existence. He is not `anthropomorphic and `male' as claimed by the philosopher. He can manifest Himself in any form to whoever He so wishes, as He did to Moses and to Saul of Tarsus. It is true that, this Jehovah chose to make Himself known first to the Jews and then to every other person who will believe in His Son Jesus Christ, who "When He ascended on high, He led captivity captive, and gave gifts to men. "And He Himself gave some to be apostles, some prophets, some evangelists and some pastors and teachers, for the equipping of the Saints for the work of ministry, for the edifying of the body of Christ (the church). "Till we all come to the unity of the faith and of the knowledge of the Son of God, to a perfect man, to the measure of the structure of the fullness of Christ", (Ephisians 4: 7-13). However, in reading through this beautiful research - based work by the philosopher, a physicist will be encouraged to appreciate physics the more and have the urge to contribute his own theory to the subject. In reading carefully through the text, the reader is likely to feel inner reawakening; a new spirit to become curious about ourselves, the earth, the oceans, space and much more. I have no doubt in my mind that this book will be found useful, relevant and pleasurable by science students and teachers as well as curious members of the general public. PROFESSOR EDET J. UWAH Professor of Physics University of Calabar, Calabar.

_For the non-scientist, the wonders of science hold endless fascination, while the scientist sees such as the very impetus for further strivings. But then, looking around our environment, a question could be posed: Why are science enthusiasts so few in number, when we are all increasingly depending on its application by way of technology, for our daily lives? Science in its natural state affects us all and indeed, the chief proponents of early scientific thought were themselves found in circles of natural thinkers - philosophers, because science then was simply a natural philosophy. The reality of our physical manifestation, including our environment, the suns, stars, planets, meteors etc, directly confront us to constantly inquire into the deep, to find out how we can enhance our knowledge and harness same to help explain the origin of the universe as well as our future and possible fate within the cosmological matrix. Archmedes' principle; Newtonian mechanics, laws of thermodynamics; the general theory of relativity, etc have, in terms of scientific knowledge and its application, brought us thus far, but our hunger for answers to, still some more, demands that we expect that Holy Grail: The theory of everything. This is the task which the current march of science should and ought to undertake. I believe The Philosophy of Physics is a brave attempt by Dr. Princewill Alozie in that direction. I do not intend to criticize your beautiful work. However, I have a different view on religion and physics. It is however very likely for any christian to disagree with the philosopher's statements in the last chapter of the book concerning God. I think there should be a demarcation between a concept and a fact. The God we talk about is not the conceptual god of the Greeks, but the actual living God whose name is JEHOVAH or YAWEH. He is a

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	CONTENTS			INTRODUCTION

				_The reason for writing this book is to reveal the closeness, or rather the inter-connection between physics and philosophy. A number of people in the society who could have become beacons in physics and mathematics had failed to embrace these basic science disciplines partly because the disciplines were presented as very abstract, formal or uninteresting enterprise. The philosophical and historical issues surrounding the various physical theories would invariably lead physicists to be a part of producers of new knowledge instead of just being content with the consumption of ready-made knowledge in physics. This book tries to show that all our knowledge in physics could be regarded at best, as tentative and useful under defined terms and circumstances. The book is designed in such a manner that it would be of interest to physicists, scientists in general, philosophers and lay persons. Symbols and formulas in the work could be ignored while reading by those who have no grasp of either logic or elementary mathematics. Such category of people will understand the arguments and the discussion in the work, despite such apparent lack of knowledge. The historical panorama covers in a brief manner, the diverse aspects of physics that would be discussed in the book. As the heading of the chapter suggests, this is done from purely historical, social and cultural perspectives. There are chapters dealing with macro-physics, micro-physics and the philosophies connected with them. The social, economic, mystical, political and religious implications of physical theories intersperse the work. There is however a
	Dedication iv Foreword Introduction 1 v CHAPTER 1 Historical Panorama 4 CHAPTER 2 MACRO _ PHYSICS Introduction: Conventional Approach to Science and Physics 18 CHAPTER 3 Logical Positivism and Physics 40 CHAPTER 4 Theory of Relativity 70 CHAPTER 5 Theories in Physics 85 CHAPTER 6 Micro-Physics 97 CHAPTER 7 Mathematics and Physical Theories 116 CHAPTER 8 Philosophies of Science 139 CHAPTER 9 Physics, Religion and the Society 174 Bibliography 180 INDEX 189 vii
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	chapter that briefly dwells on the social and religious import of physics. I am grateful to the staff and graduate students of the Physics Seminar Group with whom I have individually and collectively shared some of the ideas in this book. The seminar co-ordinator, Mr. Alfred Inyang who teaches quantum physics at the Physics Department together wit Dr. M. I. Umo and late Dr. Vincent Anyim of the Physics Department, were always ready and happy to discuss the philosophical issues in physics. Prof. Edet J. Uwah and Dr. Michael U. Onuu of the Physics Department had spent their valuable time reading the work and their comments have been of immense value. For instance, Prof Uwah drew my attention to the jumbled manner I referred to micro-particles. My graduate students and former students discussed with me during seminars and individually, the various aspects of this work. Some of these include Etorobong Godwin Akpan (who read carefully, the entire manuscript and detected some typographical errors), Christopher Akpan, John Edor, Enyimba Maduka, Dr. Macaulay Kanu, Dr. Ifechi Ndianefoo, Dr. Ochulor, Dr. K. Ojong, Dr. Emmanuel Eyo. Professor Asouzu, Drs. Ozumba, Uduigwomen, Ucheaga of the Department of Philosophy have at various times directly or indirectly discussed with me some of the views contained in this work. I am very grateful to all of them. I thank Messrs, James Crentsil, Akpan John and Ms Julie Onobo of the Clear Lines Publications for the various assistance rendered technically for the production of this work. I am also grateful to Miss Christy Nnana Jims for painstakingly typing the manuscript.			Another category of motivators for this work are non-professional philosophers. For instance, my friend and wife, Virginia Ifeanyi Alozie, though a chartered accountant by profession, constantly challenges some of my philosophical views. My daughters: Tobechukwu Chidimma and Uche Amarachi do unwittingly, provide me with topics for philosophy. My dear friends, Rev. Professor E. M. Uka (Religious Studies), and Prof Igbo Egwu of Public Health, (Unical), Prof S. N. Okiwelu (Zoology Department, Uniport; Mrs. Victoria I. Mbu and Chief A. U. Kanu, legal practitioners, belong to this category. I accept responsibilities for inadequacies that may still be found in this work. Princewill I. Alozie Department of Philosophy, University of Calabar, Calabar, Nigeria 9th February, 2004.

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			in a systematic way. Hegel's pre-occupation with the phenomenon of spirit did not make his philosophy acceptable to a number of the scientists of his time. Even social scientists had to re-formulate his dialectics in order to use his system of logic. Karl Marx, for instance, who accepted the Hegelian dialectical logic said that Hegel put dialectics upside-down. Marx reversed the position and put dialectics on a materialist as opposed to idealist or spiritualist foundation. It should be borne in mind that Hegel was a philosopher for the ruling class and of the crown. In the long run, his philosophy in general suited anti-people's policies; racist positions and anti-science posture. It is not surprising therefore that scientists almost unanimously opposed the Hegelian world-view. Added to the Hegelian factor was the over-burdening influence of religion; of kingly governance in the new nations of Europe. The kings of Europe, sometimes with the tacit approval of the papacy, ruled their subjects with iron hands. The philosophy which paved the way for the French revolution was therefore anti-monarchical and anti-religion in character. Saint-Simon and Aguste Comte fashioned the philosophy of science which bore the name, positivism and which relied on human intellect and experience as the guide to genuine knowledge. The sciences hooked on to empirical, inductive and deductive methods of acquiring knowledge and this became the new philosophy. This new philosophy was understandably intolerant of traditional metaphysics and philosophy in general and religion in particular. The crucial question that will have to be answered is whether physics can truly be divorced from philosophy (which embodies logic, metaphysics, axiology as well as epistemology). Standard
CHAPTER
	1
Historical panorama _Philosophy of physics discusses physics as a subject. In the distant past, physics, and indeed all knowledge came under the umbrella of philosophy. Major works on science were tagged, "natural philosophy." In England such great works were sometimes published by the Philosophical Transactions of the Royal Society. This is quite understandable, if we remember that the word, science _ scientia (in Latin), wissenschaft (in German), Nauka (in Russian), Amamihe or Mmuta (in Igbo) means knowledge. Knowledge has no boundary. In many respects, there are unimaginable connections between the various disciplines known to mankind. This situation continued to reign until the German philosopher, Hegel appeared on the scene. Hegel's philosophy of logic, or more appropriately, his principle of identity elevated a priori method of knowledge to a height that appeared to intimidate other methods. According to Hegel, a principle discovered as apriori was applicable not only to moral issues but also to human and physical domain. Hegel's logic, it must be admitted, was quite revolutionary in many ways. His dialectical approach to logic shook logicians up from the Aristotelian logical slumber. "Thesis, anti-thesis and synthesis" meant that there could always be other approaches to matters pertaining to logic. The sophists and some earlier philosophers in antiquity were quite aware of these approaches, but it was Hegel who re-presented these approaches

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	There were times when the Earth was regarded as the centre of the universe. The sun and all that existed in the universe was thought to be revolving around this centre. This Earth _ centredness is known as geocentric world-view. The geocentric world-view was supposed to have been replaced by the sun-centred world-view known as the heliocentric world-view. It does appear we may not easily dismiss all the theories emanating from a geocentric world _ view because of the emergence of a heliocentric world _view. Consider for a moment, the issue of gravitational force and the celestial bodies in the universe. Could we not imagine that some of these bodies attract or repel each other? If this is possible, as we believe it is, then the Aristotelian and Newtonian approaches to inertia have further potentials in cosmology and physics in general. If we remotely accept this possibility, then it leaves the floodgate open for pockets of truth about physical reality. We then arrive at a situation where geocentric and heliocentric world-views would both be true. This lands us in a contradiction at the surface value. However, given the concept of inertial reference frames, all laws of nature are the same in all inertial reference frames. The amusing aspect of this observation from a philosophical point of view is that geocentric or heliocentric reference frames would both be valid. We need to be reminded, that there is no big deal debating about the validity of geocentric versus heliocentric reference frames. The sun in our solar system is just one out of billions of suns in the universe. If we have billions of suns in the universe, then it is bordering on the absurd to dwell in an infinitesimal aspect of reality as if that aspect constitutes the whole. The law of inertia which is also Newton's first law of motion
				contains concepts which open the gate-way for contradictions. Mechanics as we know grapples with the motion of bodies in a given reference frame, as well as the causes of the nature of motion. Motion of bodies can be translational or rectilinear; rotational or curvilinear or chaotic; all in possibly uniform or non-uniform, accelerated or non-accelerated patterns. Aristotle as had been pointed out, was of the view that bodies change their position or move because of interaction with other bodies. At the macro-level of physical existence, it was difficult to sustain such a view. Technological development at a later period and issues connected with cosmology demanded a new approach to inertia and mechanics. It is possible that some aspects of the Aristotelian formulation will have to be re-visited or incorporated in quantum mechanics. Inertia and inertial reference frame For the purpose of macro-physics, Galileo Galilei formulated a partially workable understanding of inertia. Galileo, excluding external influences like gravitation, used thought experiment to arrive at the conclusion that bodies could move, not only uniformly in a straight line, but also uniformly in a circular form. Newton discarded the aspect of Galileo's formulation containing circular motion. Motion is usually in relation to a reference frame. There are frames of reference with respect to which all bodies which supposedly do not interact with others move uniformly in a straight line. These frames of reference are known as the inertial reference frames. What we will quickly notice is that there are numerous inertial reference frames. By implication, Galileo's formulation embodies a theory of relativity. The mathematical construction which

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	enables us to locate the relationship between the co-ordinates of bodies or particles in two different inertial reference frames at velocities of motion less than the velocity of light is known as the Galilean transformations. Inertial reference frames are bodies which do not interact with surrounding bodies and move uniformly in a straight line. Assumptions about the nature of space is brought into the picture immediately. Is space empty? Is it a vacuum? Physicists agree that space is not a vacuum. Space is not a solid either as Newton's theorems imply. If space is not empty and without impediments, then the concept of "straight line" does not hold. The shortest distance between two points would be a straight line if space were vacuum-like! This kind of difficulty about space led to the evolution of different types of geometries. Labachevsky's geometry is one such example. What emerges is that there would be "no bodies which do not interact with other bodies". Even if it has been argued that this Newtonian mechanics works out for our solar system, amendments had to be made on the concept of inertial reference frame. The first amendment was that known as Galilean transformations. According to Galileo's relativity principle, all inertial reference frames are equally justified. The Galilean transformations could be described as a marriage between Newtonian and Galilean mechanics which enables physicists to find the relations between the co-ordinates of a certain particle in two different inertial reference frames at velocities of motion much less than the velocity of light. Albert Einstein employed yet another contraption known as Lorentz transformation in the special theory of relativity. We note with pleasure that the concept of inertial reference frame	has been profitably utilized by natural philosophers like Aristotle, Newton, Galileo, Hendrik Lorentz, Albert Einstein and others in advancing the work of science. For instance, Newtonian mechanics has been used by people in the armament industry for the construction of rockets, missiles and nuclear war-heads; aerospace engineering and spaceship construction; automobile engineering; and chemical engineering, etc. At the same time, there are several advantages Einstein's approach to the concept of inertial reference frame (Lorentz transformation) has over Newtonian mechanics. We are told that Newtonian mechanics works because it handles phenomena at speed very much less than of light. At the logical level, there is a contradiction in the two mechanics. This is especially so, when Aristotelian classical logic is used. Following the laws of thought in classical logic, a thing is what it is: A=A. An amended "A" is no longer "A" but "An Amended "A" which is altogether a new entity. The laws of excluded middle and non-contradiction as well as that of identity hold sway in the various brands or systems of logic with the possible exception of dialectical quantum, fuzzy and four-valued logic. In classical logic, truth-value can be arranged as true or false. In fuzzy logic which is related to fuzzy set theory in mathematics, we have truth values like: True More or less true Rather true Not very true Not very false More or less false Rather false


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is composed could not be said to be the result of empiricism or experimentation. These pronouncements were partly echoes of past speculations on the subject-matter. Some of these pronouncements were rooted in the findings of ancient mystical and religious schools. We are not surprised that opposition to Aristotle's work and the contradictions would be great, considering the numerous, diverse sources of his scientific writings. The attempt to bring a dichotomy between the material content of the Earth and those of the heavens can help to illustrate a part of this point. Thinkers and scientists in his days did not all subscribe to the divine origin of the heavenly bodies or to the unmoved mover (Primum mobile). The Epicureans and the Stoics, were in many ways opposing schools. The Epicureans upheld the atomic theory of the universe and were opposed to Aristotelian religious coloration of matter. The Earth was regarded as the centre of the universe. The Stoics, on the other hand, dethroned the Earth and installed the sun as the centre of the universe. The Stoics and Epicureans de-emphasized divine origin of the universe, especially in their versions. The Stoics maintained that, all that was, reflected one origin. That origin was the sun. Human beings or other organisms were functioning according to the rhythms set in motion by the sun's absolute dictation. This sounds like the position of some scientists in the era of quantum mechanics; in an era when the micro-world and electro-magnetism were being injected into a yet to be universally accepted unified field theory. Despite the opposition and contradictions of some of Aristotle's theories in physics, his opinions held sway primarily because he enjoyed state power and protection like a latter day Isaac	Newton. To recapitulate, according to Aristotle, a thing left to itself will remain at rest. As for Isaac Newton, such an object will move in a straight line with uniform or constant speed. It therefore appears sometimes that political authority is needed for the advancement of some world-views. Science, contrary to some views, cannot be separated from the political atmosphere that nurtures it.




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CHAPTER
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MACRO _ PHYSICS Introduction: Conventional approach to science and physics _Science is a leading world-view today, among contending others. Science aims at explaining and understanding the universe in which we find ourselves, as well as fathoming the relationships that exist between phenomena. The ability to understand, explain and investigate the relationships in nature leads to predictive aspect of nature. What is known as science has always been with human-kind, although the methods, aims and achievements of science have been changing in time from place to place. Among many practitioners of science, there is the belief that the foundation of their enterprise is careful observation and description of facts about the world. We shall have a lot to say about the credibility of observation and fact assemblage as the core foundation of science. It has to be admitted with some qualifications, that the assemblage of facts and data plays important role in articulating explanatory statements, scientific laws and theories. Data is the recording of information in measurable units and numbers of objects or events. Data, like facts aim at providing bases for precise and reliable scientific statements. Scientific explanatory statements have different nomenclatures. Such statements are sometimes called hypotheses,
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principles, laws or theories, depending on the fulfilment of certain conditions. A hypothesis is a guess concerning the relationship between observed facts or guess about the interpretation or explanation of observed facts. It is assumed that a scientific hypothesis must be amenable and confirmable by an experiment. Karl Popper, a philosopher of science, is of the view that a hypothesis qualifies to be scientific if it is capable of being falsified. In the course of our discourse it would be evident that there is not a great demarcation between hypotheses, principles, theories and laws. A principle is supposed to be a hypothesis that has been confirmed through many precise experiments. A scientific law is like a principle but however covers a broader range of phenomena. A scientific theory is also broad-based explanation of reality, which could also help in some kind of prediction. What we have stated so far do not differ significantly from scientific models for example, that we find in the scientific enterprise. Computer simulations and models play important roles in science. In our discussion of science, you will infer why we have to be using these terms like hypothesis, theory and law interchangeably. As already pointed out, many scientists believe that the foundation of their occupation is careful observation and assemblage of facts from which hypotheses or theories are formulated. Observation here includes the workings of our sensory organs. This approach of making the sensory organs the fountain-spring of science has acquired the term, empiricism or positivism. In broad terms, following the hard fact or empirically-based science enterprise, we could divide science tentatively into: 1.Observation and human experience 2.Hypotheses and theories		3.Experiments. The division is tentative because observation and human experience will feature in some measure when theories and experiments would be discussed. The three tentative divisions are in reality inter- woven. Physics or the physical science will be our reference point throughout this work. Observation and human experience Observation, which is here, tied together with the functions of our senses of sight, smell, taste, touch, and hearing have played important roles, and still plays roles in our quest for making sense out of our physical environment. This physical environment includes the wind that is blowing across our house; the stones that litter the field, the water that is flowing in a nearby stream; the sun and moon with their effects on us, the computer, animals, plants and human beings, biosphere, motions, sensations, and much more. Our senses and experience enable us to identify and classify objects, just as we are enabled to form concepts and words. Concepts could be visible or invisible entities. Concepts and language become tools for the articulating of views and observations of the physical world. The objects and abstract entities have properties which enable us to differentiate them from one other. The stones littering our field could be composed of different substances or minerals. A stone could be a precious metal to a particular observer; an instrument or weapon to another observer; or a religious object to yet another observer. Definitions of terms do not often remove this kind of problem. The human sensory organs do not always register the same result concerning observed objects or phenomena. The

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	organs may be slightly defective, or outlandish; the observer may be immersed in cultural or learned responses to stimuli of the sensory organs. The effect of prejudice, indoctrination could be complicated by the effect of the environment, the observer and the observed phenomenon. The preparation of special instruments like the microscope, telescope, radio-telescope, etc., do not make observation flawless, despite such assertion by such scientists. The sophisticated instruments designed for observation were designed from the point of view of some assumptions and philosophies. The assumptions made in the construction of instruments do not rule out rival assumptions. Besides, there are numerous categories and terms in science that cannot be subjected to observation. Terms like "meson", "time", cannot be observed in the normal senses of observation. The claim that observation is a major foundation of science is further faulted by the fact that observation is not a neutral act. Observation is guided by theory of one type or the other. When an observer declares that a stone has been observed, there is an underlying theory of what it is to be identified as a stone. There would also be theories of what non-stones are! We should remember that observation, as a phenomenon is not strictly the business of physics. Non-the-less, physics cannot ignore the phenomenon known as observation. Observation is being studied by neurobiology, psychology in conjunction with philosophy. Advances so far in psychology and neurobiology do not encourage us to weigh observation heavily more than the other aspects of science. If we have been very critical of observation as a major plank on which science stands, it is because of the over-			blown picture given to it. There are levels in physics in which observation has blown the trail albeit with its theory-laden nature. Newtonian mechanics, Archimedes' principle, law of thermodynamics, and many more aspects of classical physics have made use of observation in ways that seem to mask other aspects of scientific breakthrough. Granted that observation might have played major roles in the establishment of these theories, laws and principles, we are at this level, dealing with insignificant aspects of the universe and reality. Empiricism or positivism in science humours itself with the ability to interpret, theorize and announce principles and laws that concern specific and discrete aspects of the universe or reality. Consider some well established principles in physics like Archimedean principle; Newtonian mechanics; laws of thermodynamics; classical and substantial part of relativistic physics for insight into the philosophy underlying such principles, theories and laws. Archimedes' principle The Archimedes' principle has been of great help in the ship-building industry. Even the descent and ascent of submarines obey this principle. Archimedes observed that if a body is immersed in fluid, that body would experience pressure of the fluid which would force the body vertically upwards. The resultant force which sends the object upwards is known as buoyant force. Submarines have enormous tanks filled with air. When the tanks pump out the air and refill same with water from the ocean, the submarine's weight is greatly increased. The increased weight causes the submarine to continue to sink or dive until a particular equilibrium is attained at
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	and body of air. The assumption is a correct one. Although the assumption is a correct one, it is equally correct to assume that the world or universe contains numerous micro-entities that are of great importance to science and humanity. Many of these micro-entities are hardly observable even with some microscopes or telescopes. In celebrating the exploits of scientists at the macro-level, we should always remind ourselves that there are numerous macro-entities in astronomy and astrophysics that we have not been able to observe and may never be in a position to observe. No person has been able to observe the whole universe, although we make scientific pronouncements concerning the nature of the universe. These pronouncements about the nature of the universe are usually referred to as informed predictions and guess work about reality. It is possible that in the long run, those scientific guesses about the universe turn out to be ludicrous. We also noted that the Archimedes' principle assumes that space is three-dimensional in nature. To this assumption must be added another assumption, which regards space as four-dimensional, even at macro-level existence of phenomena. Both assumptions appear to be correct, depending on the particular event or phenomenon under consideration. At some other levels, or under different circumstances, we may be hearing of six, eight, ten or more dimensions of space. Closely related to the issue of space is that of the geometry underlying Archimedes' principle. Euclidean geometry reigned for about two thousand years without any major successful challenger. This is not to say that Euclid was not challenged by his contemporaries. Despite such challenges, the politics of geometry during the period was in favour of Euclid. Even before Albert			Einstein, the non-Euclidean geometries had started to flourish. Einstein and Poincare, among others, popularized the non-Euclidean approaches to geometry. You will recall the axioms of geometry. These were regarded to be true for all times and in all situations. The successful challengers of those axioms showed that the question of proof was not a trivial and easy one. Conventionalism, psychologism, empiricism, intuitionism and various types of philosophy of mathematics busied themselves with this and other problems of truth, proof, and relevance. Archimedes' reliance on Euclidean geometry for the articulation of his principle is definitely a salutary aspect of observation and empiricism in science and society at large. Despite the few criticisms we have for observation and empiricism as the foundation of science, society and scientists cannot do without these approaches, especially in the information era when people are made to believe without observing; or when what is observed is given a slant that confuses and obliterates from the memory what was observed. Similarly, the existence of other equally valid geometries is a reminder that we have to be very accommodating in matters that deal with knowledge (epistemology) as well as matters concerning the nature of reality (metaphysics). Finally, the assumption of a static fluid in gravitational equilibrium is only relatively correct. In real life, there is no static fluid. Everything is in motion. Similarly, gravitational equilibrium makes sense in terms of other forces, since it is now known that other heavenly bodies have their respective force of gravity. It is in this regard that Bernoulli's and Pascal's principles are very relevant in understanding how the Archimedes' principle functions.


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	Archimedes' principle indeed handles a minute aspect of science in comparison with Isaac Newton's mechanics and other laws that bear his name. Let us examine how resilient Newton's physics will be as a possible champion of empiricism and its logical positivist derivatives. Newtonian physics Empiricism or positivism as a philosophy of science claims that reliable scientific, and indeed all indubitable knowledge derive from human experience. The human experience in this respect includes all variants of observation. As had been suggested earlier, it is believed that observation and data assemblage enable the scientist to formulate a hypothesis, which could be confirmed or negated by a crucial experiment. The logical positivists updated this approach by insisting that scientific hypothesis and theory ought to be formulated in the language of science, which is mathematical and logical in nature. We shall be saying more on the various shades of logical positivism after reminding ourselves first, of some of the basic contents of Newtonian physics. Sir Isaac Newton (1642-1727) was a very prominent mathematician and physicist of English nationality. He made remarkable impact in the sphere of calculus almost at the same time Leibniz produced his own version of calculus. In the area of planetary motion or orbits, Newton was probably trailing the achievement of the German astronomer and mathematician, Johannes Kepler (1571-1630) who gave us three laws that bear Kepler's name. In the area of mechanics, Newton relied on Galileo Galilei (1564-1642) the Italian astronomer, mathematician and physicist, for some significant aspects of the three laws of motion that bear Newton's			name. The Principia Mathematica was published in 1687 in which Newton stated the three laws of motion, as well as that of gravitation. Newton made very useful contribution in the area of optics. He was, however, not a very honest academician (Hawking, 1988). Newton's first law of motion Newton's first law of motion is also known as the law of inertia which is very much like Galileo's conclusion on motion. According to Newton's first law of motion: A body at rest continues to be at rest and a body in motion continues to be in motion at uniform velocity unless acted upon by an external force. Newton's second law of motion According to the second law of motion: A force acting on a body causes a change of momentum per second, proportional to the applied force and the momentum change takes place in the direction of the force. This second law could still be formulated thus: The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to the mass of the body. Newton's third law of motion This law is usually expressed as: To every action there is an equal and opposite reaction. For our purpose in this work we would state the third law thus: Whenever two bodies interact, the force exerted on one body is equal in size and opposite in direction to the force exerted on the other body. We shall briefly consider the content of these laws in a way that their philosophical components would easily be appreciated.
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Newton's first law of motion Newton's first law presupposes a body which is not affected by any external force. Such a body is considered to be a free body. It is fairly certain today that such a free body is mythical. Even as you are seated or probably walking, numerous forces are acting upon you. This includes atmospheric pressure, gravitational force, wind and forces of the elements, etc. We are often not aware of the forces at work, especially when there are counter-balancing forces. Newton's first law of motion however helps us to understand why the book on the table continues to lie there until made to move by a force. The law explains why a piece of rock, or football would continue to descend on a slope until it is stopped by something external. In aeroplane, you are advised to fasten your seat belt during take-off or landing. You are also advised to put on your seat belt in your automobile or car when in motion. The seat belt prevents you from flying forward in case of a sudden stoppage. While in a moving vehicle, the speed of the vehicle is the speed at which you move, it is also the speed of all macro-objects attached to the vehicle. This law, as had been noted earlier, is also referred to as law of inertia. It is a law of inertia because it describes the tendency of bodies to resist changes in motion. This tendency can be expressed as a lineal or vector quantity. From a technical angle, it means that such a quantity can be represented by a line that has both size and direction. Newton's first law could be articulated in terms of momentum, which is a vector quantity. The momentum of a particle, for instance, is defined as the product of its mass and velocity. Mass in this regard is simply a measure of the inertia of the body. The mass of a body is assumed to be the same notwithstanding the		location in the world, and is also assumed to be a constant that is measurable. Velocity, on the other hand, is the rate of change of displacement over the time taken for such displacement. Velocity = You will often find the above expression put in the language of calculus thus: V = Where s is the small change in displacement made in a small time t, the velocity is but expressed as V = In symbolic terms, the momentum, p, of a particle, which is the product of mass ,m, and velocity, v, would be: P = mv since Newton's first law suggests that in the absence of prevailing counter external forces, the momentum of a particle remains constant. In terms of momentum therefore, Newton's first law can be stated as P = P or P = {constant}. (Since a body at rest has velocity, v = o OR a body is in uniform motion, when velocity, v = constant). Now, this first law which is supposed to be a law of nature does not hold in all situations and in all places. Consider the book on a table, the football on the floor, the rock on the floor, all of which are situated in a stationary aeroplane or luxury bus or train coach. These objects will be at rest as long as the vehicles are stationary. As soon distance time

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as the vehicles accelerate at great speed, the objects will not move forward, but will drift backwards with speed. This clearly shows that the first law is not tenable or valid in all reference frames. The reference frames are known as inertial reference frames. It is only through observation of objects that are in motion that we are able to know inertial reference frames. This whole idea of inertial reference frame is thrown into confusion and mess when both the observer and the observed are in varying velocities in space. The very first law of motion has problems for empiricism and derivatives of logical positivism. Even the inertial reference frame on our planet earth appears to ignore the effect of the rotation and revolution of this planet. It means that a lot of thinking, theorizing and philosophizing come to play in our scientific laws. The equation or assertion that the velocity of a particle is always a constant (p=[constant]) would continuously need adjustment, depending on what is being considered. Second law Newton's second law of motion is considered a law of nature and at the same time defines force for us. Force, ordinarily, means a push or pull exerted on a body. The law expresses a relationship between net force, acceleration and mass in the change of motion. The concept of net force mentioned above could be illustrated with an imaginary wheelbarrow at our disposal. The wheelbarrow is loaded with 100kg bags of rice. On a well tarred, level road, you could push the wheelbarrow to a distance of 50 metres in 20 minutes time. The first law of motion suggests that you and wheelbarrow could continue on a uniform speed indefinitely unless there is an impediment or a hindering external force. The force you exert to		keep the wheelbarrow moving is necessary to balance the resisting forces of air resistance and tyre friction. The removal of the resistant forces of air resistance and tyre friction, for instance, would enable you and the wheelbarrow to continue moving at a constant velocity. The net force is the force you are applying on the wheelbarrow, minus the forces from air resistance and tyre friction. The net force is zero when you move at a constant speed in a straight line. The application of greater force on the wheelbarrow will unbalance the force by friction and air resistance. The greater force applied will give a net force greater than zero. The greater force will produce greater speed for both wheelbarrow and you. Less force will produce less speed. There is a relationship, therefore, between force and speed or acceleration. The acceleration increases or decreases proportionally according to the force applied. This proportionality is symbolically expressed thus: µ F or acceleration µ Force The symbol µ means "is proportional to." Now, if you double the load on your wheelbarrow to 200kg of rice, the acceleration of the wheelbarrow will be half the former value. Heavier load will get less acceleration and distance covered within the given time. Lighter load will give the reverse effect. We then say that the acceleration of a body is inversely proportional to its mass. This inverse proportionality relationship between acceleration and mass is expressed symbolically thus: or acceleration a When force is added in the relationship, we have something like 1 m 1 m


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	such instruments always express the correct value of what is measured. When we talk of correct value, we have assumed a standard measuring criteria. By convention, there exists such measuring standard. How our agreed standard will fare when we are dealing with entities of the micro-world and at high-energy levels would be another cause for concern. This second law can be expressed in terms of momentum. In doing so, the assumption that the mass of a particle is constant is maintained. From this assumption ma is converted into the following formula and calculus: The second law is then expressed as The assumption that the mass of a particle is constant, built into the calculus of the second law of motion is interesting in the light of the understanding that mass is a measure of inertia as well as the amount of matter an object or body has. We stop to wonder what matter and anti-matter will mean at various levels of consideration for the second law of motion. Very closely related to the existence of matter, anti-matter and mass is the relationship of mass and energy. This relationship is now contained in the famous Einstein's equation, E=mc² where c stands for speed of light. These observations about Newton's second law of motion are meant to show the limited nature of that law and to make allowance for other world views on nature.
force mass		OR	this: Acceleration a The consideration of this relationship between acceleration, net force and mass led to the articulation of the second law of motion thus: The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to the mass of the body. Newton's second law of motion can be derived from the above formula; to F a ma and then to F = ma. This law, like the first, has been confirmed to be accurate on many grounds. Engineers and astronomers have found the law very exciting and useful. We see the manifestation of this and the other laws in everyday life. Despite these sterling qualities, the law is not a universal one. It operates within an inertial reference frame. The points raised concerning inertial reference frame while discussing the first law of motion largely apply here too. The second law assumes that a single unit of force is operational. In reality you can find multiplicity of forces at work. This is supposed to have been taken care of by the principle of superposition of forces. By this principle, net force is interpreted to be the vector sum of the individual forces. This could be so if all the forces added necessarily behave alike and move all in one direction! There is also the problem of measurement of mass and force. Various sophisticated instruments have been devised for such measurements. Many scientists are very much satisfied with the results they get from such measuring devices. We have our doubt if force mass OR 33
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Third law The first law considers what happens to an object when the net force or resultant force is zero. The second law considers what happens when the resultant force is not zero. The third law considers how the forces are produced through interactions and what follows from such interactions. Let us once more consider the approximate wordings of the law. Whenever two bodies interact, the force exerted on one body is equal in size and opposite in direction to the force exerted on the other body. This law is very explicit about two bodies and the result of their interaction. A quantitative relationship is given in this law about each given pair of bodies. In the example of the wheelbarrow we considered in the previous law, there is a reaction from the wheelbarrow in response to your pushing. When a ripe mango fruit falls to the ground the force of gravity pulls on the mango while the stellar gravitational force like that of the sun and moon will be pulling at the mango fruit. The reaction from the sun is apparently insignificant because of the enormous size and distance of the sun. This law could be expressed in terms of momentum thus: whenever two objects exert forces on one another, the resulting changes of momentum are of equal magnitudes and opposite directions. What is significant about this law and other laws by Newton on dynamics is that objects in space as well as space itself have absolute definite character. Closely related to this absolute nature of space is the notion entailed by these laws of motion that time is absolute. It is further assumed by the laws that space is three-dimensional. Let it be restated here that Newtonian dynamics clearly implies the relativity of space, although he is said to shy away from such an implication because that would mean denying the existence		of an absolute God [Hawking,18]. The three laws of motion are closely related to Newton's law of gravitation. This law states that: Every object in the universe is attracted to every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distances between them. This law is very much in use in every day life. Astronomers and astrophysicists do attest that the law of general gravitation is very valid. A number of the calculations on gravitation and many other aspects of Newtonian mechanics are based on the assumption that the sun of our solar system is more or less stationary. Perhaps, the presence of the other solar systems would make such an assumption untenable. Even the three dimensional approach to the geometry of space would encounter problems if measurements are made to include the sun! Such a measurement is possible only if we proceed beyond the sun, stationing the measurer on other suns! The interesting thing about the discussion is that astrophysicists are not only considering a non-static galaxy, but now discussing multi-galaxies and an expanding universe. If the universe is actually expanding, then Newtonian physics, and even Einsteinian physics would be grappling with a very complex and intractable problem, it would mean that the uncertainty phenomenon common at the micro-level of physical existence is facing planets, galaxies and the entire universe. We gather from all these that Newtonian laws break down at the micro-level as well as at the macro-level of the cosmos in astrophysics. There is however another theory that does not support the expanding view of the universe. This is the steady state universe

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theory or hypothesis. Even the steady state universe theory also admits of expanding galaxies and the continuous creation of new matter and new galaxies. If this is the real situation, there is indeed nothing steady about such a universe that is in perpetual flux. Yes, a universe will always exist by this theory. But the universe will not necessarily be the same. The steady state universe theory was to be a comforter for those who were scared by the idea of an expanding universe which entails a universe that loses heat and matter; a universe that will collapse into a black hole and cease existing. The idea of an end and a beginning of the universe is implied by another theory known as the Big Bang theory or hypothesis. The Big Bang hypothesis sounds like the Christian Bible idea of the creation and an end of the world. The details are definitely different. It should be very discomforting for adherents of deterministic positivist science (with the weapons of observation) to be faced with rival theories on almost every aspect of the scientific endeavour. Rival theories abound on both specific and universal phenomena. Let us consider some aspects of light for example as proposed by Newton. Isaac Newton, before the publication of his Principia Mathematica that contained most of his laws on mechanics and gravitation, had written on light and colours. In his particle or corpuscular theory of light, Newton asserted that the straight - line travel of light could be better understood as small particles of matter that travelled at great speed from a source of light. Particles of light are supposed to obey the Newtonian laws of motion. When we talk of light, we are having in mind light from the sun, moon, stars, fluorescent tubes, electric bulbs, etc. Light is		reflected, refracted, dispersed, diffracted, polarized and also has characteristics known as interference. All these properties of light do not suggest a single theory for an explanation. The Newtonian particle or corpuscular theory of light was confronted almost at the same time in 1600's by Christian Huygen's wave theory of light. Despite the existence of these two rival theories of light, the scientific community of the time, preferred Newton's particle theory of light, principally because of the influence and authority of Newton and the role of the English state in promoting the work of their citizen. The Dutchman's wave theory of light had to wait until the beginning of 18 00 to be recognized. The wave theory of light reigned undisturbed until Albert Einstein resurrected the corpuscular theory of light in a modified form. Although the wave theory was confirmed to be correct, there were a number of problems about light it could not solve. These problems include the photoelectric effect and black body radiation. The photoelectric effect is the movement of electrons as a result of energy acquired from light. The photoelectric effect is put in use through transforming solar energy into electric energy. The black body radiation is the light emitted from hot objects. Max Planck in experimenting on black body radiation discovered that light emitted from such hot objects had a fixed amount of energy. He was of the view that energy from vibrating molecules are in certain amount of quanta. Planck was thus associated with what is known as quantization of energy. Einstein used Planck's quantum concept of energy, and applied it to the solution of photoelectric effect. Einstein was of the view that the energy in light could be carried from place to place by particles whose energy depended on the wavelength of the light. Einstein called this particle of light -energy photons.

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	The situation as of now is that both the wave theory of light and particle theory of light are accepted by scientists. Attempts have been made to combine the two theories of light as one. The last is yet to be heard about the theory of light. Despite this lack of clear knowledge of the nature of light, very important scientific theories assume a total knowledge of the nature of light! When scientists speak very confidently about the speed of light as a constant, we wonder if this degree of certainty covers all regions of space and the nebulous universe! It is suggested here that our inability to measure speed of light in some areas of the cosmos, coupled with the difficulty or near impossibility of completely apprehending and explaining reality, should impel us to regard our pronouncements on this subject as tentative. Empiricism and various shades of logical positivism played vital roles in establishing the two competing theories of light. The two competing theories have been unified into one, using a term, "wavicle" for that purpose. The eminent physicist, Arthur Eddington provided the word, wavicle. In terms of empiricism, wavicle cannot be pinned down and measured with any degree of certainty. There are lots of mathematical assumptions about this wave-particle duality. The assumptions are being faced with Heisenberg's uncertainty principle of the micro-world. We shall now examine another brand of positivism, known as logical positivism, in relation to physics.


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CHAPTER		embroiled in dispute over the theory of meaning. The dispute over theory of meaning meant establishing the status of logical atomism, observation statements, verificationism, operationism, phenomenalism and confirmationism. The meaning of these terms will be discussed shortly. It has to be stated that logical positivism grappled with the problem of explanation, prediction, causation, statistical laws and the hypothetico-deductive model of science. Theory of meaning and logical positivism Some of the early logical positivists were of the view that scientific statements or our everyday language are compound statements or concepts which could be reduced to simpler ones through the provision of appropriate definition. According to this approach which is also known as logical atomism, a concept like "Force" would have to be defined and reduced to the indivisible components of such a word or notion. The equation, Force=mass x acceleration (F=ma) would appear to satisfy this logical atomist approach. In this equation representing Newton's second law of motion, mass and acceleration are left undefined. The scientist could proceed to define "mass" as a measure of the inertia of a body and "acceleration" as a change of velocity per unit time. You will still be left with some undefined terms like "measure", "inertia", "velocity", "time" and so forth. What is becoming clear is that we could continue without end seeking for the indivisible component of a concept. It is also assumed that there will be meaning invariance as we continue to look for, and possibly find the indivisible element of our concept, statement or theory. This assumption is mistaken, as the equations, F=ma and E=mc² will readily show. Mass in the two equations are not operating at the same level and context.
	3
LOGICAL POSITIVISM AND PHYSICS
Introduction _In the 20th Century, the empiricism of Francis Bacon, St. Simon and Auguste Comte transformed into logical positiv ism. The word, positivism is traced to Auguste Comte, but the actual term, "logical positivism" started taking shape in Austria. A group of scientists formed a kind of philosophical club known as the Vienna Circle, the sole purpose of which was to discuss various aspects of science, especially the foundations. The circle or club was established in Vienna hence the name Vienna circle. The circle was interested in demarcating science from non-science. Considering the prolonged turmoil in society encouraged by religious politics, economics and philosophy, these great minds thought that it was necessary to distance science from metaphysics which bestraddled religion and philosophy of the period. Mathematics and logic which was regarded as the language of science had to be the conveyor of scientific theories. The works of Leibniz, Frege, Boole, Bertrand Russell and Alfred Whitehead united mathematics with logic. Mathematical logic, based on the works of Aristotle, Boole, Russell, etc., and geometry based on Euclid, were still powerful tools. These logical and mathematical tools later on got formidable challengers. The presence of the special theory of relativity, general theory of relativity and quantum mechanics however, served as stimulants and catalysts to the logical positivists and their philosophy. Historically, logical positivism was

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There is need to find a way of making sense of our scientific theories. In the history of philosophy, the following types of truth, among many others, are known: logical truth, analytic truth, synthetic truth. In logical truth context, statements have meaning because of their conformity to logical or mathematical form and logical constants. In the statement: "Galileo's principle of relativity is related or not related to Einstein's theory of relativity"; the logical constants in the statement are "is", "or", "not". The word, "is" is existential and affirmative, "or" is a disjunction, while "not" is a negation. These are also found in mathematics. Any other statement could fill in the gap or place of "Galileo's principle of relativity" and "Einstein's theory of relativity." The first part of the statement could be represented by any symbol, say, P while the second part of the statement concerning Einstein could be represented by the symbol Q. We will thus have P or not Q. Anything or idea could be fed into the symbols P and Q. Constants remain what they are. Some symbols for constants can take the form: V for "OR" (L, &, .,) for and; ( -, ~,) for negation;® for implication; º for equivalence. There are more and very many variations for these mathematical or logical constants. When we state that 2 + 3 = 5 we should realize that the answer to that addition could change if we are considering rain clouds, rain drops, goats and yams. In mathematics as in logic, we give content to the variables of language forms. Logical truth will not make much meaning in the questions: F=ma or E=mc² if we do not explore some extra logical means to resolve, at least partially, the problems of meaning of the undefined terms in our scientific theories. While recognizing the role of the formal aspect of the theory, the question of assigning meaning will be explored by semantics. This will be examined under the heading:
		analytic truth. A statement is analytically true when the essence is elicited from the meanings assigned to the descriptive terms as well as the logical form. Semantics demands that we know of our theory, the physical object or property, it is supposed to represent. Without this semantic pre-requisite, physical theories may sound more or less like fairy tales. Meanings have, no doubt, been assigned to the above theories: F=ma; and E=mc². That the meanings assigned are not all encompassing is evidenced by the fact that numerous interpretations have emanated from those formulae. Analytic truth Analytic truth is a part of what is usually known as analytic philosophy. This branch of philosophy developed basically because it was assumed that the problem of philosophy arose from conceptual confusion that could be resolved through careful examination and reduction of statements into the least indivisible components. Since the main object of analysis was concept or statement, the trend shifted to language analysis. This latter trend is now known as linguistic philosophy. Bertrand Russell, G.E. Moore; and Wittgenstein were leaders in the trend of linguistic philosophy. This analytic approach at its best, has been described as mere tautology. The reason for such a conclusion is that a statement like 4+4=8 is a repetition of 8 in 4+4. Nothing new has been added, it is argued. It is even argued that there is no need for the dichotomy between logical truth and analytic truth. Williard V.O.Quine and some other philosophers were even of the view that the dichotomy between analytic philosophy and synthetic approach to truth is indefensible. Godfrey Ozumba correctly observed that "Quine, with his rejection
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	their physicist colleagues, that sense-data are the immediate object of all sensory perceptions. This was the view of many members of the logical positivists in the Vienna circle. Rudolf Carnap for example introduced what he called protocol sentences as a foundation for reporting indubitable and incorrigible report of immediate sense experience, which would form the basis of all other knowledge. Otto von Neurath who also belonged to Vienna circle and one of the founders of logical positivism made use of protocol sentences but in a slightly different sense. For Neurath, protocol sentences represent reports of particular observations of the physical world, which would form sets of basic, but not incorrigible sentences. These logical positivists who strove to demarcate science from non-science; and fought tirelessly against the presence of metaphysical elements in scientific theories, believed that scientific knowledge will be increasing progressively and cumulatively. Any new piece of solid, indubitably-based empirical knowledge will be added to the stock-pile of existing body of knowledge. Observation statements as proposed by the logical positivists are of limited value in the development of physics. Newtonian physics which is said to be exceedingly empirical, cannot claim to have recorded protocol sentences and sense-data in the everyday meaning of such terms, and of the various components of Newtonian mechanics and Newtonian physics in general. In astronomy and astrophysics, a substantial claim and theories on this realm cannot all be claimed to have emanated from observation and sense-data. Conjectures, assumptions and religious world-view becloud some of these physical theories. The kinetic molecular theory makes some doubtful assumptions about ideal gas, yet the result of calculations based on such an ideal gas has yielded equivalent result to the first			law of thermodynamics. The kinetic molecular theory operates on micro-world level but within the sphere of Newtonian mechanics. Science, even at Newtonian standard would have ground to a halt if an insistence is made for the adoption of "observation statement" only in the construction of theories. Observation statements do play some role in another aspect of logical positivism known as verificationism. Verificationism and operationism Verificationism is a theory of meaning and truth which insists that in order to admit that a statement is true, there should be justification for such an admission. The logical positivists initially regarded a proposition as being meaningful if there is an empirical justification for admitting such a proposition as being true. There had been several shifts in the meaning of verificationism. The current approach is to regard verificationism as a theory of truth which regards propositions as true if there are proofs or other such reasons for accepting the veracity of the propositions. As we are aware, proof in mathematics could be very formal and in reality could be very much inclusive. Kurt Godel endeavoured to demonstrate that pure mathematics is not complete since we cannot conclude a proof by using only principles within the system. Godel's publication of his incompleteness theorem in mathematics came at the heels of David Hilbert's efforts to show that mathematics did not contain paradoxes and contradictions. Godel in another publication showed how mathematics could be finite and so provable or decidable. The solution to the problem of proof boils down to agreement or convention. You decide what constitutes the proof.
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				represents the predicate of the judgment. In the judgment." All submarines obey Archimedes' principle," All submarines" constitutes the subject, while "obey Archimedes' principle" constitutes the predicate. I is a particular affirmative judgment with the structure: "Some S are P." E is a universal negative judgment with the structure "No S is P" O is a particular negative judgment with the structure, "Some S are not P." We could present all that we have been saying about judgments, including the relations between S and P in tabular form. In doing so, we shall also use some symbols of logical constants or connectives we had noted earlier, and would include symbols involving quantities known as quantifiers. Symbols "(")" is a universal quantifier while symbol "( $ )" is an existential quantifier. The brackets and other symbols have the same meaning as in mathematics. We should also note that logic as used here could be sentential (SL) or predicate (PL) in form.
	science as it is known today. Quantum mechanics, molecular biology, quantum chemistry, nuclear physics, etc, would be eliminated from science topics. It is not surprising that some members of logical positivism beat a saving retreat! The logic in logical positivism We have so far outlined some of the features of logical positivism. There is need to have an understanding of what is meant by logic in the context of discussing logical positivists' usage of the term in philosophy of science. Logic, generally, could be understood as the subject which develops systems and principles of drawing inferences as well as evaluating arguments. There are basically two types of arguments that are of interest to the logical positivists. These are deductive and inductive arguments. Modal logic, three-valued logic are modifications of deductive and inductive logic in one form or the other. An argument in logic is a group of judgmental statements, one or more of which (the premises) are claimed to provide evidence or reasons to believe, one of the others (conclusion). The word "judgment" will be used interchangeably with proposition, sentence and statement. There are different types of propositions or judgments. We have judgments of properties; judgments of relations; judgments of existence (existential); categorical judgments. Judgments could be universal in character. Judgments could be affirmative or negative in nature; or quantitative and qualitative in character. A combination of some of these classifications of types of judgment could give us the following four characteristics using the letters A, I, E, and O: A is a universal affirmative judgment. The structure of such a judgment is usually "All S are P" where S represents the subject of the judgment and P
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Judgements or propositions

Laws of thought in formal logic

The edifice of formal logic which we are discussing is built on a foundation known as laws of thought. These laws of thought are considered immutable and true under all circumstances. These laws are abstract in character, and include the law of identity, the law of non-contradiction, the law of excluded middle and the law of sufficient reason. Aristotelian logic has only three laws of thought, but the fourth law of sufficient reason was supplied by Leibniz. These laws are used in the various rules of inference and are universal in their application in everyday life. Although it has been stated that the laws of thought are abstract in character, it must be realized that the source of abstraction is concrete. A house is a house by convention. A piece of sandstone will be recognized as such. To enhance intelligible communication among people it is important that meanings and essences are stable and consistent. The expression of the laws in abstract forms enable the laws to be used the way mathematical entities like 4+4=8 would be used. The symbolic expression for these laws of thought are as follows:

a º a expresses law of identity expresses law of non-contradiction, expresses law of the excluded middle. Let us consider each of the laws in greater detail in the context of physics.

The law of identity

In the process of reasoning, every concept and judgment must be used in the same meaning. This is how the law of identity is usually formulated. "A" as a concept remains "A". A is A. Professor Chike Obi is Professor Chike Obi. Professor Chike Obi is a professor of mathematics. So, when the name is mentioned, we think of the

FORMULA OF JUDGMENT

RELATIONS BETWEEN

S AND P

IN PREDICATE AND MATHEMATICAL LOGIC

TYPES OF

JUDGMENT

UNIVERSAL

AFFIRMATIVE

PARTICULAR

AFFIRMATIVE

UNIVERSAL

NEGATIVE

PARTICULAR

NEGATIVE

DENOTATION

S^- P^-

TRADITIONAL

LOGIC

ALL S are P

(S a P)

Some S are

(S / P)

No S is P

(S e P)

Some S are

(S o P)

P⁺

a L a

S^- P^-

P⁺



	mathematician and professor with that name. Concept, object should be identical to itself. The law of identity enables us to delimit the field of discourse and subject-matter under question. The law of identity ensures that concept substitution or thesis substitution is not employed to bring about confusion and lack of clarity in communication. The law of identity could be expressed mathematically as A º A. In mathematics, we use equality signs, sign of equivalence of sets; in theory of algorithms there are identities of letters arrived at through abstraction of identification. The equality in the expression A º B is symmetrical in the sense that A º B is the same as B º A. The equivalence expression could be transitive in the sense that A º B and B º C then A º C. The axiomatic rule of replacing an equal with an equal becomes handy with equalities. In physics, as in reality, absolute identity hardly exists. Even in mathematics, there are some modification which renders equalities non-equivalent. In set theory, there are still some unresolved issues which cast doubt on the claim that all the sets regarded as equal are indeed equal. Remember the paradox of set theory where it is being asked whether the set of all sets is a member of that set. Despite claims by some mathematicians that paradox has been sorted out through theory of types and the like, doubt persists as regards the claim of such resolution. In the physical world of plant kingdom, the green plant uses chlorophyll in the leaves and with the aid of radiant energy from the sun which is combined with water and carbon dioxide produces more foliage, wood and oxygen. The physical chemical way of putting what happened in words could be:			Energy +Carbon dioxide+Water = Wood+ Oxygen. A word equation for the reverse of photosynthesis described above will be oxidation which is the reverse of photosynthesis. Such word equation will be Oxygen + Wood = Carbon dioxide + Water + Energy. Although we have given a positive word equation with the sign of equality, burning of the wood could be a process when photosynthesis is not taking place, but appropriately for our example, the wood is consumed by combustion to release carbon dioxide, water and energy. The sign of equality does not imply equality in the existence form of the plant and the elements as they appear to us. In thermodynamics, our equation for the first law has the equality sign thus: E = Q - W. This equation which gives the idea of conservation of energy and the idea that the change of internal energy (E) equals the input of heat (Q) and work (W) enables us to predict the behaviour of physical systems like steam engines, automobile engines, carnot engine and the concept of entropy. This led, as expected, into the second law and third law of thermodynamics. Considering the equation of the first law with the ensuing definition of entropy placed side by side with Rudolph Clausius' theorems of reversible and irreversible cycles, we will realize that the sign of equality means nothing for our universe that contains the internal energy. The formulation of the second law of thermodynamics which says that an engine operating in a cycle cannot transform heat into work without some effect on its environment implies that the total thermodynamic measure of disorder (entropy) of the universe continually increases. The natural process is for a state of order containing the internal energy (E) to

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degrade into a state of disorder with a corresponding increase in entropy. In an era of the new ideology called globalization, we would want to know what happens to our universe. The available energy of the universe is gradually diminishing, and with time the universe would approach a limit of maximum disorder known as the heat death of the universe. This heat death resembles in some way the Christian Biblical picture of the second end of the universe through fire or fiery consummation. The important thing for us here is that equality at the long run in our thermodynamic equation is neither symmetrical, transitive, nor even reflexive. A is not necessarily A in the cases discussed.

The law of identity is not always timeless. In the example of a physical human being called Professor Chike Obi, the laws of identity will be useful and correct if it is realized that at childhood, Chike Obi was not a professor of mathematics. The identity of a Chike Obi, the professor of mathematics is only valid within a specific time-frame. Even within that time - frame, Chike Obi was also the leader of a political party known as the Dynamic Party of Nigeria. Specificity of a phenomenon, event or an object is essential within space and time to enable the law of identity to be properly operational.

The law of non-contradiction

The law of non-contradiction says that "two opposing judgments may not be true at one and the same time and in one and the same relation." The law does not permit us to assert that this is an electric bulb and at the same place and time assert the opposite view that this is not an electric bulb.

In symbolic form, this law is represented as a judgment and its

negation, thus: a and not-a more appropriately it is written as a - a OR ( a a). This law is very useful in everyday communication. It enhances clarity of thought and expression.

In real life, it is possible to have these contradictory formulations of the law. The empiricists and logical positivists insist on confirmation, verification, sense-data criteria, etc for the acceptance of a scientific judgment as meaningful and true. By this position, false perception of a phenomenon should not be accepted as truth. If two blind men who have never seen or known about an elephant are led to an elephant. One such blind man feels and touches the massive body-frame of an elephant and declares that the elephant is like the wall of a house. The other blind man feels and touches the massive leg of an elephant and declares that the elephant is like a tree trunk, from the empiricist and logical positivist position, we ought to admit the declaration of these blind men as correct, true and scientific. But as we are all aware, the elephant is more than what these men have declared. In terms of pursuit of universal truth, we are not far from the behaviour and declaration of the blind men!

If we take an example in physics, we will appreciate the possibility of having contradicting judgments co-existing in science. Light is a very common phenomenon. We all appear to know what light is. When we move into the discipline of physics, it will be obvious that light is considered as a particle and as a wave. The word "wavicle" is supposed to represent such an understanding. Einstein called the particle-like energy packets in light, photons. Arthur Holly Compton is said to have confirmed experimentally the particle-like behaviour of photons. In the process of experimental confirmation, Compton reasoned that since the energy of the photon



is a reduction of energy implies an increase of wavelength. Max Born discovered the probability interpretation of wave in which the probability for the presence of photon is proportional to the intensity of wave. In terms of the law of non-contradiction, it is not permitted to assert that light is photon and light is not photon simultaneously. Alternatively, it should not be simultaneously asserted that light is wavelike and not wavelike at the same time. But the reality of physics at the moment clearly accepts this contradictory assertions about the nature of light. What is very damaging for empiricism and logical positivism is that photons cannot be seen or directly made available for verification or confirmation. The probabilistic interpretation of quantum waves by Max Born eventually led to the confirmation of Werner Heisenberg's uncertainty relations. We are told that at the atomic level, the quantum uncertainties are often so immense that it is completely meaningless to speak of the position or momentum of a wavicle at the same time. For a phenomenon you cannot directly see, you are further informed that location of position and momentum is bathed with uncertainties. To talk of law of non-contradiction is definitely irrelevant. The logic here moves away from Aristotelian deductive certainties to inductive probabilities and uncertainties. Similarly when multi-valued logic is operative, the law of non-contradiction does not apply. The law of excluded middle According to Aristotle, there cannot be any intermediate position between contrary statements, but of one thing we must either assert or deny. The law is reformulated thus: Of two contradictory judgments, one is true, the other is false, and a middle value does not E = hv = hc / l		exist. In everyday communication it is important to be definitive as much as possible. In the statement: This is a university or not a university; This is a country or not a country; it is possible to affirm one of the statements or judgments in each of the contradictory claims after a clear understanding or definition of what is meant by university or a country. The law of excluded middle is expressed in symbolic form thus: a v - a where the symbol "v" stands for "OR" and "a" stands for any variable. This law, as valuable as it is, like the other laws of thought, faces some difficulties in terms of predictive capacities in science. Prediction is about the future. The judgment, that it will rain very heavily in the month of December next year, cannot have a truth-value of "true" or "false." If our knowledge of the heavenly bodies could be described as perfect, and the use of sophisticated meteorological instruments could be made available to our excellent meteorologists, we may still not be sure that our prediction will not be neutralized by some unforeseen factors in the firmaments. Human disturbances for example, of the atmosphere, ionosphere and troposphere could alter our prediction. Our judgment about rain falling heavily during next December will be at best, probable. There are however some predictions made by Newtonian physics as well as Einstein's theory of relativity that have been exceedingly accurate. The accuracy of our predictions depend on the object or phenomenon in question, as well as the sophistication and standard of our knowledge in the relevant field. There are situations when we may never know if our prediction could be correct. So, we have as expectation, the response "Not known"; "Probably true"; "Indeterminate"; "No idea," etc.

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In such instances, the law of excluded middle fails to function. The situation becomes more problematic in the realms of quantum mechanics. Quite a lot of calculations in this area are statistical and probabilistic in nature. It is within this sphere that we have indeterminacy or uncertainty relations. In the micro-world as well as in the familiar macro-world, we are not always examining two variables and two possibilities. There could be many variables and many possibilities. What this means is that the law of excluded middle would not apply in such considerations. In mathematics we came across the notion of diffused algorithms and diffused sets as well as the concept of computer simulation in cybernetics all designed to handle such indeterminate and multi-valued approach to knowledge. Logic has also developed three-valued logic and multi-valued logic for the purpose of handling such phenomena. Attempts are being made recently to popularize what is known as quantum logic. The law of sufficient reason This law as had been pointed out was introduced by the logician, mathematician and philosopher, Leibniz. The law says; " every true thought should be sufficiently substantiated." There is no agreed method of symbolizing this law. Some logicians make use of the following symbols: a b. There is an objection to this method that arises from the paradox of material implication in two-valued logic. In two-valued logic, a b will have the truth-value as true even when "a" and "b" are both false; or "a" is true and "b", false. It would appear that the respectability of the symbolic form would be enhanced if the modal notion of necessity is added to the two variables "a" and "b". This will however make the approach		resemble the law of identity. In whatever form this very important, but often neglected law of thought is presented, it is still faced with all the problems associated with two-valued logic. The implication is that criticisms which follow two-valued logic will also apply to the law of sufficient reason as formulated. Deduction and traditional logic We have noted that the law of thought which underlines Aristotelian traditional logic is deductive in character. Majority of the members of logical positivist school made use of deductive inference and traditional logic in their approach to science. Aristotle's (384-322 BC) logic is syllogistic in character. A syllogism is a logical system with three judgments, two of which serve as evidence "or premises" while the last serve as the conclusion which flows from the evidence. We have already outlined four types of categorical judgments represented with the letters A.E.I,O. Each of these judgments have three terms known variously as: major term (predicate of the conclusion) minor terms (subject of the conclusion) middle term (middle ground between the two). Syllogisms have standard forms which are made up of mood and figure. The validity or invalidity of a standard form is determined by mere inspection of the form. This is one reason it is called formal logic. The mood of a syllogism is made up of the letter names of the judgment or proposition. These are A,E,I,O. A judgment or statement with an "A" for major term , minor term, and middle term will have a mood that is AAA. The figure of syllogism (categorical) is determined by the middle term in the premises. There are four figures possible. You check this out by using S for

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B. Rules of premises

4). It is not possible to draw any conclusion from two negative premises.

5). If one of the premises is negative, then the conclusion should also be negative.

6). It is not possible to draw a conclusion from two particular premises.

7). If one of the premises is particular, the conclusion must be particular.

The rules in traditional Aristotelian logic, coupled with developments brought about by logicians and mathematicians like Gottlob Frege (1848-1925), George Boole (1815-64), Alfred North Whitehead (1861-1947) and Bertrand Russell (1872-1970) to mention a few, expanded the coast of natural deduction in both sentential logic and predicate logic. At this stage of development, deductive inference was harmonized with mathematical methods of arriving at conclusion. This harmonization brought with it, specific rules of inference. We shall simply present about eighteen (18) rules of inference that formal logic uses. It must be added that these rules are in use in modal logic. We are presenting these rules to enable readers who are not conversant with formal logic to appreciate what is meant when any of the rules is mentioned.

Rules of inference

1 Modus ponens (MP) 2. Modus tollens (MT)

p ® q p ® q

subject of the conclusion, P for predicate of the conclusion, M for middle term. The four possible figures are as follows:

1 2 3 4

M P P M M P P M

S M S M M S M S

S P S - P S P S P

Given the fact that there are four kinds of categorical judgments, (A,E,I,O) and three judgments in a syllogism, there will be (4x4x4) 64 possible moods. Four different figures will give us (4x64=256) 256 different forms of categorical syllogism. Some of these forms are now of historical importance only. Some of the rules in syllogism are still important even till the present moment.

Some rules of categorical syllogism

A. Rules of terms

In each syllogism there must be only three

terms.

2) The middle term should be distributed at least in respect to one of the premises.

3). A term which is not distributed in the premises cannot be distributed in the conclusion. If this rule is violated the terms

of the conclusion would say more than the term of the premises.



3). Hypothetical syllogism (HS) 4).Disjunctive syllogism (DS) p ® q p v q 5). Constructive dilemma(CD) 6). Simplification (Simp) (p ® q) L(r®s) 7). Conjunction (Conj) 8). Addition (Add) P Axiom of replacement: Within the context of a proof, logically equivalent expressions may replace each other. 9) De Morgan's rule (DM) -(p L q) º (-p v -q) -(p v q) º (-p L -q) 10) Commutativity (Com): (p v q) º (q v p) (p L q) º (q L p) 11) Associativity (Assoc): [p v (q v r)] º [(p v q) v r] [p L (q L r)] º [(p L q) L r] q p q ^		12) Distribution (Dist):[p L (q v r)] º [(p L q) v (p L r)] [p v (q L r)] º [(p v q) L (p v r)] 13) Double negation(DN): P º - - P 14) Transposition (Trans) (p®q) º (-q® -p) 15) Material implication (Impl.) (p® q) º (-p v q) 16) Material equivalence (Equiv.)(p º q)º[(p®q)L(q® p)] (pºq) º [(pLq) v (-pL-q)] 17) Exportation (Exp): [(pLq) ® r] º [p® (q®r)] 18) Tautology (Taut) p º (p v p) p º (p L p) Formal logic and scientific explanation We have endeavoured to highlight some of the features of empiricism and logical positivism in general. In addition, we have endeavoured to show what we mean by logic as it concerns most of the discussion among logical positivists. Logic for this group is formal in character. It is this formal logic with all the tainting of Aristotelianism that logical positivists use in their conception of scientific explanation. There is a reigning doctrine which states that science enables us to have understanding and complete insight into the nature of the structure and processes which make up reality. The understanding that is derived from the model of explanation provided by logical positivism is exceedingly limited and in some cases questionable.


	64		65



Carl Hempel was one of the logical positivists who developed a sophisticated concept of scientific explanation. His model was based on deductive reasoning, and could be formulated thus: 1. All gases expand when heated. 2. Methane is a gas. 3. Methane expands when heated. The above expression could be rendered symbolically thus: 1. 2. Ga Premises 3. Ha Conclusion This model posits that if there is a law governing a particular phenomenon, anything that belongs to the same class as the said phenomenon, will necessarily be affected by the governing law. Thus, since all gases expand when heated, it follows that methane will necessarily expand when heated. Scientific explanation is effected by subsuming a phenomenon under a law of nature. This model of scientific explanation is sometimes referred to as deductive - nomological model or covering law model of scientific explanation. As we can observe, there is a law of nature, condition fulfilling that law, and conclusion that doubles as the explanation. The usual schema for the model is: L₁ ……………… L_n C₁ .………………C_n Explanan E Explanandum event.		The evidence becomes the explanan while the conclusion becomes the explanandum (or that which is to be explained). This model, by assuming the structure of deductive inference, has also assumed that the process of reducing phenomena to symbols and evolving an adequate syntax are unproblematic. This model of scientific explanation is far from achieving its objective. What the model is implying is that knowledge of the law of nature is necessary for any scientific explanation to take place. The individual and general conditions in the deductive system serving as premise or evidence may be the requirement for the establishment of a scientific law. Robert Boyle's assertion that, " if the temperature is constant, then the product of pressure and volume must remain constant as a given amount of gas is compressed or expanded" was the outcome of some processes and investigation that were guided by some theories. These theories sorted themselves out through experiments, trial and error method of theorizing, experimenting, and confirming. The formal logical approach, by convention is only apparently satisfactory, given certain objections by some philosophers of logic and mathematics. What is to be explained is already assumed and is present as one of the premises. Both the initial condition, the law and background knowledge often may need some re-examination, amendment or even abandonment. In the example of "all gases expand when heated", the ideal gas law is a conglomeration of laws which include Boyle's law, Gay - Lusac's law/Charles law of diffusion, and many more. The kinetic theory of matter, including gases, was developed with some of these laws and assumptions about the nature of matter. We now know that the ideal gas law does

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		not operate absolutely under all circumstances. It does not apply, for instance, when temperature is on Kelvin's scale absolute zero. We are also informed that the ideal law does not apply in situations when gas may liquefy or solidify as the case may be before the absolute zero temperature could be reached. We are also aware that material substances which interest scientists and logical positivists, exist in solid, liquid or gaseous forms depending on temperature and pressure. For instance, iron, tungsten and silicon carbide become gases at temperature exceeding 20000c, while oxygen, ammonia, and carbon dioxide are gases at living room temperature. Besides, the assumptions behind the kinetic theory and ideal gas are quite spurious. The deductive - nomological model of explanation is in no position to be aware of all these relevant comments about the law, which is the pillar of the model. The model is faulted on philosophical ground as well as on scientific ground. The model is yet to give a convincing argument why it thinks that "Ga" which is the premise following must necessarily be Ha in reality. The formulation may suffice for gases like methane and carbon dioxide at low temperatures. When what is considered is the metal iron converted into a gas at exceedingly high temperature, that kind of gas will definitely not conform to behaviour of ideal gas. Scientific explanation is a more complicated matter than the formal logical approach to the issue. Carl Hempel realized this difficulty when he opened the gate to inductivist approach. But his inductive approach can easily fit into a deductive model, given his kind of probability approach to induction. The case for and against inductive inference and probability calculus will be explored later in this work. It is however, interesting that the logical positivists used the model they ®		constructed for scientific explanation and also as a model for scientific prediction. According to this claim, ability to use the deductive logic to induce new or novel facts is the same as prediction. This position of theirs on explanation and prediction is known as symmetry of explanation and prediction. The interest for us lies in the realization that one concept or deductive theory is serving two purposes: explanation and prediction. Theory surfaces not only now, but all along the logical positivist position. Observation is clothed in theory; experiment and confirmation is theory-laden; theory and laws compete with other theories and laws. The numerous problems confronting logical positivists brought about some re-organization, retreat and total escape from their camp. We shall examine some other schools in philosophy of science after having an overview of relativistic and quantum physics.

				)
" (G	H


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		of special relativity. The developments in physics pointed to the conclusion, very much acceptable to Albert Einstein, that there is no special frame of reference known as the ether, specially positioned in a reference frame to have the velocity of light with the value c (which used to be 3.00 x 12¹⁰/ cm /sec, but the adjusted standard of metre and of speed of light since 1983 is now c=2.99792458 x 10⁸ metres per second). Considering mechanical phenomena and attendant inertial frames, Einstein was convinced that all frames in uniform translation with respect to each other seemed to be equivalent, since the propagation of light, measured in any direction, is equal to the same value, c. In 1905 Albert Einstein (1879-1955) made a revolutionary proposal in a general hypothesis that affects all laws of physics. This revolutionary hypothesis is the principle of relativity. The principle states that "all the laws of physics are the same in all inertial reference frames." This revolutionary principle led Einstein into choosing one out of two time-honoured principles: Galilean transformation on which Newtonian mechanics and gravitation relied or Maxwell's equation that is contrary to Newtonian laws. In order to appreciate why Einstein's principle is revolutionary, we need to consider the Galilean transformation in classical physics a little further. We also need to re-evaluate Galilean transformation in the light of electromagnetic theory as well as ponder over the consequences of the Michelson - Morley experiment on Einstein's theory. Classical physics holds that laws of mechanics are the same in all inertial reference frames. By the laws of mechanics in classical physics, it is assumed that electromagnetism, electricity, magnetism, and optics will benefit from this law of mechanics stipulating that
CHAPTER
	4
Special theory of relativity _Empiricist and logical positivist philosophy of science dwelt and settled basically on sense-data, verification, theory-free observation and the like because classical physics provided the disciplinary support for such an approach. By classical physics, we mean fields as broad as Newtonian mechanics, solid and fluid mechanics, Archimedes' principle, Maxwell's theory of electromagnetic field, thermodynamics and the kinetic theory of gases. Our examples and illustrations have been, so far, concentrated within the field of classical physics. We shall notice that relativistic physics and quantum physics will demand a different orientation and world-view in respect to philosophy of science in general and of physics in particular. The theory of relativity impels us to overhaul and change completely our notion of space and time, on which classical physics is based. Quantum physics invites us to consider the abandonment of the notion that nature is continuous. It was to the credit of Albert Einstein that he considered the features of Newtonian mechanics; the problems of inertial reference frame; the Galilean transformation and classical mechanics; the Galilean transformation and electromagnetic theory and the Michelson-Morley experiment on the velocity of light and issues concerning a supposed ether frame before formulating his principle THEORY OF RELATIVITY

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70

these are the same in all inertial reference frames. The speed of light as deduced from the law of electricity and magnetism violates these time-honoured laws of mechanics. Light is known as an oscillating electric and magnetic disturbance propagating through space. The speed of light as optics teaches us is 3.00 x 10⁸ m/s in all reference frames. But the Galilean addition law for velocity holds that the speed of light ought not be the same in all reference frames.

Galilean transformation and classical physics

The basic assumption here is that motion is relative, since the values of the velocity and acceleration of a particle depend on the frame of reference in which these quantities are measured. Suppose we have two observers in two different but adjoining reference frames, and a diagram or graph plotted to specify the two different reference frames. The first reference frame could be distinguished by the symbols x', y', z' and t'. If there is motion of particle in respect to these reference frames which could be hypothetically shown in two sets of co-ordinates, the values of the motion when measured will be different. This conforms to the assumption that motion is relative. This relativity of motion has something unique, in that the co-ordinates obtained in one reference frame are geometrically related to those obtained in the other reference frame by a transformation formular known as Galilean transformation.

In the Galilean transformation, the assumption is that time is absolute. A measured value of time in the co-ordinates will be t'=t. In a new reference frame with a constant velocity "v" with respect to the first frame of reference, the relationship between the sets of co-ordinates ( , y, z, t) and (x', y', z', t) will be:

' = - ut

y' = y

z' = z

t' = t

These four equations together make up the Galilean transformations. These equations are built on the intuitive assumption that time and length are absolute. These Galilean transformations and their assumptions of absoluteness of time and length form the foundation of Newtonian physics. Both the Galilean transformations and Newtonian physics are applicable whenever we are dealing with velocities which are small compared with the speed of light. Velocities that approximate speed of light require a different transformation.

The equations for velocity and acceleration of Galilean transformations could be derived from the equation above (x¹ = x - ut) by differentiation. The velocity of particle x¹ relative to particle x² would then become:

This means that v' = v - u.

In essence, the velocity of x' relative to x is just the difference between the velocities of x' and x² relative to u.

Similarly, the acceleration of x' relative to x is

(if and only if dt = dt')

dx¢

dt¢

dx¢

a¢ = = = (V - U) - - O

dv¢

V¢ = = = (x - ut) = - U

This means that a' = a.

We thus deduce that the acceleration of x' measured in the two reference frames are identical. The implication is that acceleration is absolute and does not depend on the reference frame. Our daily experiences in life support the results of the Galilean transformation computation which conform to laws of Newtonian mechanics.

Indeed, Newtonian mechanics asserted that all inertial reference frames in uniform translation with respect to each other are equivalent as far as mechanical phenomena are under focus. This assertion invokes another supportive assertion which states that: No mechanical phenomena can be used to differentiate between inertial frames. This means that it is impossible through mechanical means or experiment to prove that one of the frames is in a state of absolute rest while others move in respect to it.

Galilean transformation and electromagnetic theory

We had indicated earlier that Newtonian mechanics with the accompanying Galilean transformations do not hold for phenomena like electricity, magnetism or phenomena whose velocities approximate the speed of light. We wish to consider further the behaviour of electromagnetic phenomena when Galilean transformation is applied.

A changing magnetic field induces an electric field while a changing electric field in turn induces a magnetic field. James Clerk Maxwell ((1831-1879) established the law describing this induction effect of electric fields. He unified the laws of electricity and magnetism in a single law now referred to as Maxwell's equations. These Maxwell's equations essentially modified Ampere's law which

asserts that: The integral of B around any closed mathematical path equals µo times the current intercepted by the area spanning the path,

We shall not bother ourselves with the complicated mathematical components of this law and all the laws constituting Maxwell's equation.

These are the basic laws which make up Maxwell's equation:

Gauss' law for electricity

Gauss' law for magnetism

Faraday's law

Maxwell - Ampere's law

(where I, is steady current; B is magnetic field; mo is permeability constant; Q is charge; eo is permittivity constant; f, is electric flux; E is electric field and Id = eo is displacement current).

e t



	mechanical phenomena were concerned if they were inertial frames; but in regard to electromagnetic phenomena they were not equivalent. For electromagnetic phenomena there was only one frame of reference, the ether frame, in which the velocity of light was equal to "c". There was also the Michelson-Morley experiment towards the second half of the 19th Century. The Michelson-Morley experiment The Michelson-Morley experiment which was conducted in 1887, was designed to demonstrate the existence of the special frame of reference called the ether frame, and to determine the motion on the Earth with respect to that frame. The experiment was elaborate, meticulous and sophisticated. At the end of their experiment, they came up with the following declaration of result: The velocity of light is the same when measured along two perpendicular axes in a reference frame which probably, is moving relative to the ether frame in different times of the year. With the survey of physics at the end of the 19th Century, it became obvious that Einstein's principle of relativity was indeed revolutionary. Given that Maxwell's equations and the laws for the propagation of light were included in laws of physics referred to in the declaration that "all the laws of physics are the same in all inertial reference frames," he made a second postulate which states that: The velocity of light is independent of the motion of its source. (Alternatively, the velocity of light (in vacuum) is the same in all inertial reference frames. (The standard value for speed of light is: c = 3.0 x 10⁸m / s)).			The second postulate means invariance of the speed of light. This invariance of speed of light requires our abandoning our fixed and intuitive notions of length and time. In order to demonstrate the appropriateness of this invariance of speed of light with regard to different reference frame, physicists and mathematicians usually construct reference frame with co-ordinate grids and synchronized clocks. The clocks are synchronized from a master clock situated at the origin of the co-ordinates. This is done by sending out a flash of light from a point exactly midway between the clock at the origin of the co-ordinates and other clocks. The two clocks are synchronized if both show exactly the same time when the light from the midpoint reaches them. Einstein defined simultaneity as follows: Two instants of time t₁ and t₂ , observed at two points x₁ and x₂ in a particular frame, are simultaneous if light signals simultaneously emitted from the geometrically measured midpoint between x₁ and x₂ arrived at x₁ at t₁ and x₂ at t₂. In Einstein's theory, simultaneity does not have an absolute meaning, independent of the spatial co-ordinate, as it does in Newtonian mechanics and classical physics. Simultaneity is relative in relativistic physics. Time is relative not only when comparing synchronized clocks and light signals, but also in clocks and light aboard a spaceship. The clock on board a spaceship suffers from time dilation. This means that the rate of the moving clock is slow compared with the rate of identically manufactured clocks at rest on Earth. Time dilation is not only in relation to clock on the Earth as measured by the clocks on the spaceship. Time dilation in relativistic physics is symmetrical.


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Length is also relative in relativistic physics. This is so because the length measurement of a moving body depends on simultaneity. Since simultaneity is relative, so is length. The length of a body measured in the reference frame of the Earth is shorter than the length measured in the reference frame of the spaceship. Just like in time dilation, length contraction is symmetrical. A body at rest on the Earth will experience contraction when measured by instruments on board a spaceship. The contraction effect applies only to lengths along the direction of the spaceship. Lengths perpendicular to the spaceship are not affected.

The Lorentz transformations

The Lorentz transformations express the major characteristics of relativistic space and time. The diagram used in illustrating the Lorentz transformations is known as Minkowski diagram or space-time diagram. The following equations make up the Lorentz transformation.

y' =y

z' = z

There is another form of the Lorentz transformations which is useful in transforming from the primed frame to the unprimed frame. This is an algebraic solution of the above type of Lorentz transformations:

c²

t' + X V

y = y'

z = z'

The Lorentz transformations perceive space and time symmetrically. A change of reference frame mixes the space and time co-ordinates of an event. What is a pure space interval or a pure time interval in one reference frame becomes a mixture of both space and time intervals in another reference frame. In the words of H.Minkowski, "henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Relativistic momentum and energy

The special theory of relativity has touched virtually all aspects of Newtonian physics. For instance, there is a totally new approach to momentum and energy that differs from Newtonian approach.

We recall that the momentum of a particle of mass 'm' and velocity 'v' is

P = mv

The Galilean transformation for velocity is

V' = v - u

While the Galilean transformation equation for the momentum is

P-' = mv' = mv - mu = P - mu

t' + X V



	The difference between the old reference frame and the new reference frame is only a constant quantity which is independent of the velocity, v of the particle. Even the non-relativistic transformation formulae for the law of velocity and for the law of momentum correspond to each other. However, the following relativistic formula for momentum has been established: When the speed of the particle is small in comparison with the speed of light, the non-relativist formula holds sway. At exceedingly high speeds, the relativistic momentum becomes infinite as the speed of the particle approaches the speed of light. This relativistic physics would affect kinetic energy, and thus the formula derived for the relativistic kinetic energy is The relativistic kinetic energy becomes infinite as the particle approaches the speed of light. This formula also suggests that it is impossible for any particle to attain the speed of light, since it is impossible to supply a particle with an infinite amount of energy. The special theory of relativity did not reckon with the effect of gravitation. When eventually the special theory of relativity was applied to the classical theory of gravitation, Einstein had to modify some of the postulates of the special theory in order to obtain what he called the general theory of relativity.			The general theory of relativity In 1915 Albert Einstein established the general theory of relativity. He observed that gravity is different from other known forces, since it is affected by curved nature of space-time. Space is curved or warped because of the distribution of mass and energy in it. This idea of curved space differs from the conventional idea of a flat space. By the known laws of motion, the heavenly bodies like the Earth ought to move in straight lines. But this is not possible because of the curved nature of space-time. Einstein pointed out that if space is correctly perceived as four - dimensional instead of the three-dimensional conception, we shall discover that the Earth still moves in a straight line. The nature of space-time makes us think that planetary bodies, including the Earth move in circular orbits, from a three - dimensional point of view. It is important to note that there are not great differences between the predictions concerning the orbits of our solar system as presented, respectively by both Einstein and Newton. Light in the general theory of relativity no longer appears to travel in straight line, but is bent or curved by the force of gravity in a curved space-time. The general theory of relativity followed some predictions of the special theory of relativity. This is noticeable, for instance, in time dilation or slowing down of time, when light approaches a large body like the Earth. Space and time in general theory of relativity are not pure and isolated, but rather integrated with matter in a dynamic way. Force or movement of a body in a curved space-time affects the curvature of space-time while the force or movement of a body is affected, in turn, by the curvature of space-time. The Big-Bang hypothesis, the


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existence of black holes, singularities and implied expansion of the universe could be deduced from the general theory of relativity.
	CHAPTER

			5
		THEORIES IN PHYSICS
		Overview _We started this book by presenting a traditionalist view of what science is and how it operates. In that perspective, it was said that observation, hypothesis and theory formulation and experimentation are some of the key aspects of science. When people make an observation, they formulate a hypothesis that pretends to explain and predict the phenomenon observed; therefore experiments are conducted to either confirm or discard the hypothesis. The hypothesis that has been confirmed several times graduates to become a theory. In this section, we shall further emphasize what had already been pointed out in the section dealing with empiricism and logical positivism that no meaningful observation can be made without a guiding theory. Furthermore, it will be noted that experimentation is done within a framework of theory. The existence of a particular theory presumes the existence of competing theories. With unfolding position that we cannot actually confirm a theory to be true, we could have a situation that a supposedly confirmed theory suffers major amendment. In this regard, theory and hypothesis could indeed, become synonyms and we shall treat the concept as such in this work. The significant dimension of this section is that theories of physics would be presented the way the specialists see them. This means that there will be a difference from the general approach of the mainstream philosophers of science. In order to
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can move with speed approaching the velocity of light and radio waves.

The theory - statement contains mathematical notions like : magnitude; directly proportional; inversely proportional; square of the distance; direction of the force; line. The equation for the Coulomb's law clearly presents the mathematical symbols in relation to the assumed data and empirical content of the theory. The magnitude of the force that a particle of charge "q' " exerts on a

particle of charge "q" at a distance "r" is F =

Where `K' is constant.

Expressing the direction of force vectorially, use is made of the unit vector "r" directed from the charge q' to the

charge q.

The vector equation of the law has the advantage of giving both the magnitude and the direction of force. The electric charge is measured in Coulombs (C) which corresponds to the numerical values in SI system of units as follows:

Charge of proton, e

e=1.60x10^-19c

Constant = 8.99x10⁹N.m²/C²

But the constant is usually stated thus:

Constant =

The quantity o is called the permittivity constant, and has the following numerical value:

e0 =8.85x10^-12C²/(N.m² )

r²

One coulomb is the amount of electricity charge that a current of one ampere delivers in one second.

We shall examine Ampere's and Gauss' laws. But before then, we have to observe that the theory under discussion has made room for experiments and proof. The proof in this context is both mathematical and experimental or empirical.

Gauss' law (for electricity).

This law is a mathematical restatement of the Coulomb's law. Mathematical physicists say the Gauss' law is easier to calculate than is the case with Coulomb's law. This Gauss' law assumes the hypothethical syllogistic form: if… then…

The law states:

If the volume within an arbitrary closed mathematical surface holds a net electric charge Q, then the electric flux

through the surface is , that is

But this equation is frequently expressed thus:

There is yet another law for calculating magnetic force but which in many ways have the same mathematical structure as in Gauss' law for electricity. This law is known as Ampere's law.

According to this law "the integral B around any closed mathematical

r²



	path equals µo times the current intercepted by the area spanning the paths, Ohanian discussed and illustrated these laws very well (Ohanian, 1989:574, 612). In the two equations, E is for electricity while B is for magnetism. These equations and their mathematical formulations are very close to vector field theory. The vector field theory in mathematics deals with scalar and vector functions in Euclidean three-dimensional space. This theory upholds the invariant properties of scalar and vector functions or properties that do not depend on the coordinate representation. The underlying assumption for this vector field theory is that in nature, there are no special reference frames. The references that are in use are just useful instruments for carrying out calculations. Gauss was one of the mathematicians who championed this approach to mathematics. Some of the topics that interest those interested in this theory include, among others, invariants; scalar and vector functions; continuity of scalar and vector functions; gradient; line integrals of gradient; independence of the path; regions and their boundaries; the divergent theorem; Stokes' formula; line integral in space; etc. This particular formulation of Gauss on electricity leans heavily on his conception of regions and their boundaries or surfaces and their boundaries. Smoothness and orientability are some of the relevant properties. Gauss was able to use this mathematical instrument to deduce much of what is known in Coulomb's law. Ampere's law made use of some of these kinds of mathematical devices, which include integrals, differential equations, sequences
		ad series among others to arrive at his conclusions. These physical theories in their mathematical forms are deductive. We have already explained what we mean by this under deductive inference in logic. These mathematical constructions are also axiomatic in nature. What is very interesting about the laws in electricity and magnetism so far discussed is that these laws featured in Maxwell's equations. Maxwell's equations in full is known as Maxwell-Ampere's law. As had been pointed out earlier, the law is made up of Gauss' law for electricity; Gauss' law for magnetism; Faraday's law and Maxwell-Ampere's law. In some significant way, the Maxwell-Ampere's law is a modification of all the other laws of electricity and magnetism. In terms of representation of reality, we could say that Maxwell-Ampere's law better does that as far as electromagnetic phenomena are concerned. The mathematical formulations of physical theories lend themselves to the procedures of formal proof. Although we are interested here in physical theories we should remember that mathematics had its own theories too. Mathematical theories, whether they are about infinite series, linear differential equations, partial differential equations, algebra and geometry of vectors, field theory, probability, or numerical analyses have some common features. These mathematical theories are presumably devoid of any fixed "empirical reality." This is probably designed to make mathematics a rigorous way of reasoning. It has been argued in some quarters, that mathematics is an abstraction of reality. This is partly correct. But the total picture of the origin of mathematics must also be traced to imagination and


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A resolution to the confusion that could be generated by thinking of the dichotomy between stochastic and non-stochastic models of physical reality; inductive and non-inductive model of perceiving physical reality; reductionist models of classical/relativistic physics and quantum physics, can be resolved as conceiving these apparent dichotomies as different sides of the same coin. Micro-particles are found in macro-objects. Macro-objects are modelled after micro-entities! Who really can say, if the nature of the universe would not warrant us to perceive our macro-entities as micro-entities! Our planet Earth could look like a micro-entity in the midst of the immensity constituting the universe. If this view is possible, then the demarcation between classical/relativistic physics and quantum physics pales into insignificance. Physical or empirical contents of theories in physics are useful, provided we do not make a fetish of either the theories or the data of the theories. Data collection in physics makes sense only with an accompanying scientific theory or notion. If this is not the case, it will be difficult to differentiate the collection of materials by a small child or mad person from that of our physicist! The issue of one data contradicting the other in another theory would not have become an issue if there were no mutual relationship between data, empirical content of a theory and the theory itself. Physical theories are usually built on models just as the architects conceptualize a building or an edifice in a model. We shall appreciate the empirical content or lack of such content further after reviewing the position of physics in the micro-world (in quantum physics).
	CHAPTER
		6
	MICRO-PHYSICS
	_Micro-physics could be said to have been inaugurated in the year 1900 when Max Planck offered a solution to the problem of black body radiation. A black body is a body that absorbs and emits wave-length and temperature. Such a body would appear black when viewed from outside. Radiation in physics is the dissemination of energy from a source. The energy is disseminated as the inverse square of the distance from the source in the absence of absorption. The term, 'radiation' is applied to assorted kinds of particles like protons, neutrons, etc, to electromagnetic waves, x-rays, radio waves, ultraviolet, infrared, -rays, etc. Radiation of electromagnetic waves is experienced by all bodies, whether hot or cold. Animal and human beings are also sources of radiation. Very hot bodies radiate electromagnetic waves that are visible with our naked eyes whereas very cold bodies radiate electromagnetic waves that could be detected with specialized instruments. You could recall occasions when you sensed that somebody has approached you closely from behind, despite the fact that the approaching person was noiseless in the act. You could also sense the presence of another person in a very dark room, even if the person perceived or sensed in the darkroom stays motion-less and noiseless . Kitaigorodsky argues that this sensing of feeling takes place because the person feeling or sensing has a very highly ¡


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	are also continuous. The electromagnetic waves of such a body is also assumed to be continuously absorbed. Lord Rayleigh (formerly known as John William Strutt, 1842-1919) reviewed the work done on black bodies by Boltzman, Wein and Planck's earlier results. Rayleigh in 1900 suggested a modification of those results based on what is known as partition of energy (equipartion theorem) which states that every mode of vibration should be alike favoured. The equipartion concept was treated independently by Clerk Maxwell, Lugwig Boltzman and Josiah Willard Gibbs using their understanding of the theory of probability to produce statistical mechanics. The equipartion theorem statistically stated says that "each translational or rotational component of the random thermal motion of a molecule has an average kinetic energy of , when the total average rotational kinetic energy is KT. Following the method of calculation adopted, the energy of all the molecules taken together is NkT. There is need to emphasize two points here for the purpose of subsequent discussion on the philosophy of physics. The first point is that the calculations on molecules made the assumption that all molecules have the same speed. This is farther from the truth, since some molecules which the mathematical physicists have settled for, do not tell us all the truth about molecular speed or distribution. What has been said about distribution of molecular speed also applies to the notion of equal distribution of energy in radiation. The second point to note is that the ideal black body which would absorb all and reflect none of the radiation falling upon it at a temperature that would not destroy it, does not exist. Black bodies are physical abstractions and are non-existent! This explains the				resort to laboratory type of an isothermal enclosure, which is a spherical cavity, blackened inside and completely closed except a narrow slit on the side. We have to keep these two assumptions about energy, molecules and physical reality in mind when reflecting the truth of physics. Rayleigh, however, made use of the results based on this artificial black body to make his own contribution on the subject. Given the notion that the energy flux of the radiation coming from the hole in a cavity is directly proportional to the energy density of the radiation inside the cavity, Rayleigh decided to consider and calculate the radiation inside the cavity. Rayleigh's calculations and formula agreed fairly well with experimental data involving long wavelengths, but did not agree for short wavelengths. Rayleigh's formula and calculations were assessed by Sir James Jeans who sensed the connection of Rayleigh's formula with equal distribution of energy, laws of classical thermodynamics and electrodynamics. In other words, the concept of temperature now extended to electromagnetic waves. A modified formula known as Rayleigh - Jeans law was established. This new formula showing the calculation of the density of electromagnetic radiation, , for a narrow range of frequencies is where v is the cavity volume, w is the light frequency, c is the speed of light, T is the temperature in Kelvin's and KB is the Boltzman constant approximately equal to 1.4 x 10^-16 erg/k. KB converts degrees into ergs, that is, gives temperature in energy units. We are told that the Rayleigh-Jeans law fits well with experimental data while considering low-frequency radiation, but fails to account for whole

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	radiation spectrum of all frequencies (Kaganov, 1981:78). This means that classical theory of black body radiation was unable to explain the experimentally observed spectral energy distribution. Attempt to use the Rayleigh - Jeans classical approach to black body radiation produced what the physicists call absurd results, since the total energy radiated is infinite. Put differently, the calculations gave reasonable results at the long-wavelength end of the black body spectrum, but infinitely large energy output at the short-wavelength end of the black body (Kaganov, 78). Max Planck conceptualized a model of an ideal black body as a large number of atomic oscillators that emit and absorb electromagnetic waves. By Planck's calculation, he assumed that the energy of E, of an atomic oscillator could have discrete values of E=O,hf, 2hf, 3hf, 4hf, etc. This means that the only permitted values of the energy "E" are E=0, hf, 2hf, 3hf, 4hf,.... All other values of the energy are forbidden. The energy "hf", known as energy quantum, is sometimes written, thus: "hv". The integer "n" is also known as the quantum number of the oscillator. Thus, Planck assumed that E = nhf, where n=0, 1,2,3,4, …………. and where n is a positive integer, f is the frequency of vibration (in Hertz), and h is a constant. Planck's constant has been calculated to have a value of h=6.6260755 x 10^-34 J.S. The energies with discrete values do not have energies between these values. If an energy system has only certain definite values, and nothing in between, the energy is regarded as quantized. There is an element of thermodynamics in Planck's approach to the solution to the problem of black body radiation. In essence, he started from classical physics and later veered onto modern physics with his quantization postulate. Planck's idea or model of black body radiation prepared the way for the consideration of electromagnetic energy as a collection of packets of discrete amount of energy. As has been stated above, the energy of a packet is said to be equal to hf.			Albert Einstein seized upon this idea and made another bold move by specifically stating that light consists of packets or descrete energy? which he called photons. Einstein made this statement in connection with the phenomenon known as the photoelectric effect. According to this phenomenon, when light shines on a metal surface, it tears off electrons from the atoms in the metal and sends them flying off. These electrically charged particles or electrons from the metal cause electrical current to flow. These electrons that are ejected with the aid of light are also known as photoelectrons. Light in essence produces an electric current. This is what the photoelectric effect is all about. The photon model of light also implies that photon has energy. The photoelectric effect is used or applied in various modern electrical appliances. The automatic elevator (lifts) doors are glaring examples. You will notice a beam of light at a point or edge of the door. When that beam of light gets in contact with a metal surface at the other segment of the door; the current flows, causing the door to close. However, if a person enters the lift or elevator before the door closes, the elevator door will move backwards and open without closing. It closes only when there is no interruption in the flow of current. The photoelectric effect is also used in a type of burglar alarm. In the burglar alarm appliance, a beam of light passes across a room before hitting the metal surface within an appropriate phototube. An ultraviolet light which is usually invisible to the naked eye is used. Whenever an intruder passes through the beam, the light intensity drops at that moment. The momentary drop of current in the photoelectrons is transmitted electronically in a way that it activates an alarm. The photoelectric effect is equally used in


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	the production of motion pictures with their requisite soundtracks. Some aspects of the photoelectric devices are used in certain modern communication equipment. Einstein was able to conjecture, based on the photoelectric effect, the entire nature of light and subsequently of physical reality. Physicists of his time, including Max Planck, thought of light as made of waves in the tradition of Thomas Young who popularized the wave theory of light. Instead of swimming along with the popular theoretical current of light as an electro-magnetic wave, Einstein jumped into an entirely different stream of thought, that maintained that light is made up of particles, despite the fact that photoelectric effect and the photon nature of light were to be confirmed several years later after 1905, precisely by 1923. Arthur H. Compton, and Peter Debye, a Dutch, independently predicted in 1923, the scattering of photons from another particle- the electron. Compton conducted an experiment on scattering based on the theoretical assumption that light is made of particles. The experiment was successful and is said to confirm the particle nature of light. At the moment the particle nature of light was being confirmed experimentally, a French graduate student, Prince Louis de Broglie in 1923 postulated that since light waves could exhibit particle-like behaviour, particles of matter should equally exhibit wave-like behaviour. De Broglie stated that the wavelength of a particle is given the same relation that applies to a photon. The equation of De Broglie's wavelength would appear in this form: where h is Planck's constant and P is the magnitude of the relativistic momentum of the particle and is now known as the de Broglie's wavelength of a particle.			De Broglie's hypothesis was confirmed experimentally in 1927 by Clinton J. Davisson and Lester H. Germer working together; and George P. Thomson working independently. Erwin Schrodinger from Austria got acquainted with De Broglie's electron waves or matter-waves hypothesis. This type of approach was then referred to as the wave-particle duality or simply, wavicle. Schrodinger perceived electrons as patterns of standing waves (not spherical objects); and those standing waves are "quantized" as particles in a discontinuous manner. He formulated an equation based on such a perception, which the electron wave shape would have to obey if the electron was part of the hydrogen atom. He used his equation to deduce the light spectrum of hydrogen. This finally settled or confirmed the point that electrons are also waves. Waves as well as particles are in relative motion. Realization of this simple fact of motion of particles and waves means that micro-physics would be having a corresponding mechanics. We recall that at the macro-level of physical reality, Newtonian mechanics was very much available to account for the laws of motion. In Newtonian mechanics, for instance, the motion of a body or a particle under the action of a force is described by the second law. Newton's second law of motion states: "A force acting on a body causes an acceleration which is in the direction of the force and has a magnitude inversely proportional to the mass of the body." This second law of motion is represented symbolically in any of these forms:


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	The Greek sigma å represents vector sum of net Force applied to Mass (m) and Acceleration (a). By this second law and its formula, the initial position (or initial coordinate) and the initial velocity are specified; and the position and velocity of a body (in particle) at any next instant can be found. The precision and extreme determinism that we find in classical physics of Newton evaporates in quantum physics. Describing the position of a particle in physics is an up-hill task. This difficulty in applying classical mechanics of Newton to particles or waves in motion opened the gate for another type of mechanics. De Broglie's wavelength replaced later by Schrodinger's wave equation were important steps in the establishment of quantum mechanics. In quantum mechanics, the behaviour and motion of group or myriads of particles is the focus, instead of an individual particle. It is true that Erwin Schrodinger perceived electrons as standing waves, he was not sure of what was waving. Since he was sure something was waving, he called that thing a psi-function or a wave-function. This wave function is represented thus: y (x,y,z,t,). In the psi-function, three variables determine the position of a particle (x,y,z), and the forth is time, t. The wave- function has been described as an inherently complex function. We are also informed that the value of an inherently complex quantity cannot be measured with an actual physical instrument. There is an understanding among physicists that there should be no attempt to attribute to wave-functions a physical existence like sea waves. Wave-functions are simply computational devices which are significant only in the context of Schrodinger's theory. The wave-function is not found in Heisenberg's theory, yet both theories are the same in	the final analysis. The interpretation of the meaning and significance of de Broglie - Schrodinger wave-function was quite problematic initially. Schrodinger regarded the wave as the wave of matter and not just particle. This interpretation was rejected by Max Born who regarded the de Broglie - Schrodinger wave-function as indicator of the probability of finding an electron at some point in space. The waves are waves of probabilities. The probabilistic interpretation of Schrodinger's wave-function meant the abandonment of determinism in quantum physics. Indeterminism or uncertainty principle became the watch word for this new approach to physical reality. This uncertainty principle comes out more sharply in Werner Heisenberg's matrix quantum mechanics. The interpretation of the value or significance of the Schroedinger wave-function as a mere mathematical device further reveals the relationship between mathematics, physics and physical theories. We shall discuss this relationship between mathematics and physical reality in great details in a section of this work. For now, we wish to examine the contribution of Werner Heisenberg who provided an alternative approach to quantum mechanics at about the same time as did Schroedinger. Werner Heisenberg studied literature, Greek philosophy - especially Plato and the atomists, mathematics and physics among other subjects studied by German students. Working under Arnold Sommerfeld, Heisenberg completed his doctoral work (Physics) in 1924. The conceptual and idealistic world-view of Plato was superimposed on atomist philosophy. Following Platonian world of forms,
y



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	Heisenberg perceived atoms in physics in functional, relational and abstract forms in terms of energy transmitted. The energy emanating from an atom was perceived as an array of mathematical numbers. He was able to calculate atomic processes using these arrays of mathematical numbers, which were later identified as mathematics of matrices. A matrix (plural, matrices) is a collection of numbers or algebraic symbols (variables) arranged in a rectangular form with rows and columns. Sometimes, a whole matrix can be assigned a specific symbol. There are different types of matrices. Significant differences exist in mathematical operations on matrices as against simple numbers. For instance, simple numbers like 7 and 6 submit to the commutative law of multiplication like 7 x 6 = 42. The order of the multiplication does not alter the result obtained. In algebra, 7x6=6x7 can be represented symbolically as A.B=B.A or AB=BA This is another example of the commutative law of multiplication. If we assume that B and A have the following elements: then (1) (2)	What this hythothetical example has shown is that in matrix multiplication, the commutative law does not hold. This aspect of matrix algebra constitutes some problems for the claim that all mathematics is reducible to formal logic. The problem also excites the doubt whether we can really reduce all reality to mathematics. Physics of the macro-world, and indeed of classical level makes use of terms like "position", particle", "momentum", "mass", velocity". Physical variables which describe the motion of bodies, including that of a particle are simple numbers. This means that the variables used in classical physics to describe position and momentum of a particle would obey commutative law. This is so, because simple numbers are used. In the micro-world or in quantum physics, we are dealing with infinitesimals, pockets and packets of matter and atom, discrete matter that is also related to other bits of matter. More importantly, micro-physics presents us with situations in which it is impossible to talk of the position and momentum of a particle with absolute certainty. Physicists mostly agree that it is more sensible to talk of the likely position (location) and behaviour of a group of micro-particles. Matrix algebra was considered more appropriate for the development of quantum mechanics. Heisenberg, Max Born, Pascual Jordan, Paul Dirac and Wolfgang Pauli developed matrix quantum mechanics out of Heisenberg's initial conceptualization of atoms as arrays of numbers. This matrix quantum mechanics, which has the wave mechanics as a viable alternative, is both regarded either as quantum mechanics or quantum theory. The uncertainty principle in quantum mechanics is difficult to swallow in the light of the reality of the macro-world. At the



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heels of the uncertainty relations comes the principle of complementarity, both of which constitute the Copenhagen Interpretation of quantum mechanics. The reality of the macro-world and of classical physics is that the laws of classical or Aristotelian logic (especially the laws of thought) are sacrosanct. A house is a house with definite, verifiable location. A ball is a ball and could be caused to move to another identifiable location. Our sensory perception and experience with events and objects compel us to accept the truth-value of "true" or "false" as the anchor of classical logic. Similarly, we are attracted by Newtonian mechanics by the ease with which such classical mechanics can be demonstrated or proved to be demonstrated or proved to be correct. Furthermore, we are used to perceiving reality in three co-ordinates (dimensions) and time. Space and time are here regarded as separate entities. Quantum mechanics challenges all these approaches of perceiving reality. Instead of knowing something by observing it, quantum mechanics suggests that something is not there, until you observe it. This sounds strange. There are consequently many kinds of interpretations to quantum theory. Two such interpretations include the "Copenhagen interpretation" and the "many worlds interpretation." The Copenhagen interpretation of quantum theory The Copenhagen interpretation of quantum theory, revolves principally round Heisenberg and Bohr. Heisenberg developed the uncertainty relations in which we cannot simultaneously establish both the position and momentum of a particle in motion. The		uncertainty relations of Heisenberg is equivalent to Bohr's indeterminacy principle. Heisenberg resorted to probabilistic approach in the determination of future motion of particles or an object. Bohr, on his own part, developed the concept of complementarity. Complementarity was used by Bohr for the encouragement of the admission of the contradictory positions in quantum theory. For instance, the wave and particle picture of light exclude each other. For Bohr, the wave picture complements the particle picture of light. Furthermore, we are aware that the uncertainty relations specifies that we cannot simultaneously know the position or velocity of a particle. For Bohr however, the knowledge of the position of a particle is complementary to the uncertainty relations and the principle of complementarity both constitute the Copenhagen interpretation of quantum theory. The name "Copenhagen" is used because Heisenberg, Bohr, and Pauli and a few others exhausted themselves in the town of Copenhagen trying to find a suitable interpretation of quantum theory. In the words of Werner Heisenberg, the interpretation of quantum theory starts from a paradox. Any experiment in physics, whether it refers to the phenomena of daily life or to atomic events, is to be described in the terms of classical physics. The concept of classical physics forms the language by which we describe the arrangement of our experiments and state the results. We cannot and should not replace these concepts by any others. Still, the application of these concepts is limited by the relations of uncertainty. We must keep in mind this limited range of applicability of the classical concepts while using them, but we cannot and should not try to improve them (Heisenberg, 1991). The paradox and difficulties of quantum theory are not very

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obvious from the mathematical representation of the theory. It is at the observation and empirical levels that these difficulties are very clearly manifested. For instance, when the question: What happens really in an atomic event? is asked, the answer to such a question is deduced through observation by a mathematical probability function. The probability function is a dual statement of both tendencies and facts. What happens between one observation and another cannot be described. According to Bohr, it is wrong to think that the task of physics is to find out how nature is. Physics is concerned with what we can say about nature. Physics, and indeed science, concerns itself with certain aspects of the world. Solids, liquids, molecules, solar radiation, electricity, engines, motion, and billions of phenomena could be studied by physics and science in general. These phenomena and objects studied are indeed insignificant as far as the whole universe is concerned. Quite often, the influence and position of the scientist in the whole process of such study are ignored. In quantum theory, experiments are often needed to establish the usefulness of the theory. The experiment which is backed by some theories in the first instance, requires some theoretical interpretation. Heisenberg tells us that the theoretical interpretation of an experiment requires three distinct steps. These steps are: (1) the translation of the initial experimental situation into a probability function; (2) the following up of this function in the course of time; (3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function. The first step is taken with the full understanding that the uncertainty relations are present. We are required, well before the		experiment, to describe the arrangements for the experiment. This very first step of experiment in quantum theory will be mingled with various aspects of classical physics. The experimental apparatus, the measuring device and the language used in describing the experiment would, very likely, be tainted with elements of classical physics. It is important to realize that the results of the experiments, the phenomena or objects studied are in contact with other parts of the world. The measuring instruments are made from substances in the world as well as the experimental instruments. What this means is that the uncertainties of the macro-world, the uncertainities of the micro-world, combine with the uncertainties of the whole world. Observation in quantum theory is of clusters or clouds of events and not of an event or a particle. The probability function of the theory contains these additional uncertainties. In all, however, the probability function contains the objective element of tendency and subjective element of incomplete knowledge. Observation plays an important role in quantum theory. Unlike the case in classical physics, observation cannot be predicted with certainty. What is more, observation cannot be continuous without interval. The probability function arising from observation is discontinuous. The discontinuous change in observation and in our knowledge gives support to the notion of the quantum jump in quantum theory. We can summarize the Copenhagen interpretation of Bohr and Heisenberg by saying that quantum theory of relativity is statistical and opposed to determinism and objectivity, as we know


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it. Copenhagen interpretation makes the point that it is meaningless to talk about the physical properties of quantum entities without precisely specifying the experimental arrangement by which we intend to measure them. Quantum reality is in part an observer-created reality, and human intention influences the structure of the physical world. In the words of Max Born, "the generation to which Einstein, Bohr, and I belong was taught that there exists an objective physical world, which unfolds itself according to immutable laws independent of us; we are watching this process as the audience watches a play in a theatre, Einstein still believes that this should be the relation between the scientific observer and his subject," (Pagels, 1982). Despite the difficulties and controversies over the interpretation of quantum theory, a lot of new grounds have been broken, using the quantum theory as the foundation. These new fields which have been developed on the basis of quantum theory are in the areas of the theory of electrical conductivity; quantum theory of solids, band theory of solids, quantum chemistry, molecular biology and many more areas. The scientific enterprise appears to be advancing and giving birth to new technologies despite some difficulties with popular logic, metaphysics, epistemology and axiology. Newtonian physics was very useful in technological advancement despite the fact that there were competing parallel approaches to logic, and to other areas of philosophy and physics. The same can be said of relativistic physics of Einstein. Modern physics has raised the question about the truth		of physics in terms of the nature of reality. It has also raised the issue of how to unite all these schools of physics, which have helped solve numerous problems for technology.

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				sciences in St. Louis. The paper predicted that no velocity will exceed the speed of light; the relativity of time and also the consistency and appropriateness of Michelson-Morley result and Fitzgerald- Lorentz contradiction (French, 80). From the above account, it is easy to conclude that Poincare's principle of relativity is almost identical with that of Albert Einstein. The major criticism of Poincare's principle of relativity is that he made references to "fixed" and "moving" systems. If this is a fault in terms of theory of relativity, we must similarly note a kind of fault in Einstein's theory of relativity in terms of quantum mechanics. Einstein, as is well known was aware of the issues in quantum theory, and indeed was one of the founders to a significant extent. Yet, Einstein had co-ordinates, clocks, clocks in the box and deterministic categories in his physical orientation. From the point of view of quantum mechanics and its Copenhagen interpretation by Neils Bohr and Heisenberg, and from that of Stephen Hawking who aims at joining Einstein's theory of relativity, quantum mechanics and electro-thermodynamics into a unified field theory, Einstein's approach will definitely appear inadequate. What is being suggested here is that neither Poincare nor Einstein could be said to have arrived at the final truth about physical reality. The apparent difference between the paths pursued by Poincare and that of Einstein was further magnified by Einstein himself in the article, "Geometry and Experience." In that article, Einstein made a summary of what he considered to be Poincare's conception of geometry. According to that summary, "geometry (G) predicates nothing about the behaviour of real things, but only geometry together with the totality (P) of physical laws can do so. Using symbols, we may say that only the sum of (G) + (P) is subject
CHAPTER
		7
	MATHEMATICS AND PHYSICAL THEORIES
	_The battle of ideas over the nature of reality in physics was also replicated in mathematics. The debate concerning the relationship of mathematics with physics even became very crucial with the formulation of the special theory of relativity of Albert Einstein - a physicist, and Henri Poincare - a mathematician, almost at the same time. Poincare's several achievements in physics seem to suggest that physical discoveries could be made through mathematics. It must be quickly added that there are physicists who differentiate Poincare's approach to the special theory of relativity from that of Einstein. This differentiation, in my view is only relatively justifiable. It is partially justifiable at the level of special theory of relativity. When we move into the atomic or sub-atomic level, the differentiation takes a more complicated form. According to Silvio Bergia, Poincare had been working on various aspects of theory of relativity between 1895 and 1904 (French, 1979). These aspects included the criticism and final rejection of the concept of ether, the concept of space-time and his conclusion that absolute motion for the Earth is impossible; and the principle of relativity which stipulates that "…the laws of physical phenomena must be the same for a `fixed' observer or for an observer who has a uniform motion of translation relative to him: so that we have not, and cannot possibly have any means of discerning whether we are, or are not, carried along in such a motion" (Whittaker). Poincare is said to have made these predictions in a paper he delivered to an international congress of arts and

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to experimental verification. Thus (G) may be chosen arbitrarily and also part of (P); all these laws are conventions. All that is necessary to avoid contradiction is to choose the remainder of (P) so that (G) and the whole of (P) are together in accord with experience. Envisaged in this way, axiomatic geometry and the part of natural law which has been given a conventional status appear as epistemologically equivalent", (Einstein,1921, MCMLIV). In the same breath, while applying the above characterization of geometry to Reimannian metric of the four-dimensional space-time continuum, Einstein is of the view that the question of whether this continuum has a Euclidean, Reimannian or any other structure is a question of physics proper which must be answered by experience. Interestingly, Einstein realized that his interpretation of geometry breaks down when applied immediately to spaces of sub-molecular order of magnitude. Despite this realization he found some role for Euclidean interpretation or what he called attempts to ascribe physical meaning to the constitution of elementary particles. The insistence on experience by Einstein for the assessment of mathematical postulates is useful for physics. The little difficulty here is that experience could be either at the macro-level or micro-level of physical existence. Mathematics, including geometry at the macro-level of physical existence, are number-oriented. Even when infinities are discussed at that level, the orientation is number- oriented. Probabilities also follow the same numerical pattern. At the micro-level of physical existence, a resort could be made to matrices. We have made reference to matrices earlier while introducing microphysics. It was pointed out that some physical phenomena or events cannot be adequately described or represented with real		numbers, but with diffusion or generalization of numbers known as matrices. These diffused or generalized numbers are arranged in rows or columns with distinct rules for addition and multiplication. A matrix is an arrangement of elements with no numerical value. To appreciate the place of matrices in quantum theory we would give two more different ways of understanding matrices. For instance, let G be a field and n, m be two integers > 1 (greater than or equal to 1). An array of elements in G, of the type a₁₁ a₁₂ a₁₃ …….a_1n a₂₁ a₂₂ a₂₃ …… : : : : : : : : : : am₁ am₂ am₃ ………a_mn is called a matrix in G. This matrix can be denoted by (aij), i=1,…..,m and j=1,…,n. we call this an m x n matrix (or marix of order m x n). It has m rows and n columns. In the above example, the first row is (a₁₁, a₁₂, a₁₃ ….^a1n) and the first column is a₁₁ a₂₁ . . . . am₁ a_ij similarly denotes the element of the matrix (aij) lying in ith row and jth column and we call this element as the (I,j)th element of the matrix.
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					be trying to find out which of the particles is elementary. More important to our discussion of Einstein's view on geometry and mathematics is that S-matrix theory is based upon events, and not upon things. It is concerned with events in the sense of individual things happening during the collision process. It is not concerned with individual particle, but with arrays of particles. Geometry as perceived by Einstein will definitely not be appropriate in the discussion or calculations at the sub-atomic level of physical existence. Einstein as earlier stated realized this himself, but was caged by the deterministic world-view. This was the possible way of characterizing Einstein's view on mathematics, after realizing that he wrote: "It is true that this proposed physical interpretation of geometry breaks down when applied immediately to spaces of sub-molecular order of magnitude." It is important to observe that Poincare's perception of mathematics does not differ significantly from that of Einstein. Henri Poincare was of the view that the formalized system of geometry and the laws of geometry were not statements about reality at all, but arbitrary conventions about how to use such term as "straight line" and "point". If we compare this with Einstein's position in the said article where he stated as follows: "Insofar as geometry is certain, it says nothing about the physical world; and insofar as it says something about our physical experience, it is uncertain. Further more, Einstein continues: "The progress attained by axiomatic geometry consists in the clear separation of the logical form from the factual and intuitive content. According to axiomatic geometry, only the logical- formal is the object of mathematic; but not the intuitive content that is connected with the logical -formal…. The statements about physical objects
			aA
	cA


				The second way of understanding matrices is through the addition and multiplication process. Thus: whereas the multiplication of similar arrays of numbers would involve the product of all elements of intersecting rows and columns. This second example of matrices have two rows and two columns. There are different types of matrices. These include square matrix; null or zero matrix, diagonal matrix; triangular matrix, identity matrix and scalar matrix. It is easy to observe that arithmetic, algebra and geometry among other forms of mathematics, are involved in matrices and operations with matrices. This is not surprising, as the Irish mathematician William R. Hamilton (1805-1865) developed a method of organizing data of all sorts into arrays, or mathematical tables known as matrices. Heisenberg used this matrix mathematics in the calculations he made while experimenting with particle collision of high-energy in particle physics. The collisions necessarily would result in the scattering of particles. This is why the word, scattering matrix had been adapted. The scattering matrix is also shortened in the form S-matrix. The S-matrix can be represented in diagrammatic form together with the particles. The S-matrix diagram can be rotated. It is said that all of the particles represented in an S-matrix diagram are defined in terms of each other. The implication of this way of perceiving particles is that we should no longer aA
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	has been locked by the claims of traditional logic: the principles of science are either Apodictic truth [logical conclusion synthetic a priori) or Assertoric truth [facts of sense observation]. Poincare, taking his inspiration from the work of Lobachevski and Reimann, pointed out in the particularly significant case of geometry, that another solution is possible: the principles maybe simple arbitrary conventions… However, far from being independent of our minds and nature, they exist only by a tacit agreement of all minds and depend strictly upon the factual external conditions in the environment in which we happen to live (Frank, 88). If we consider the latter part of the quotation a bit further, we could quickly flash our minds on the burning issues of particle physics where there is no distinction between empty, as in "empty space" and not-empty, or between something and not-something. In the words of Gary Zukav, the world of particle physics is a world of sparkling energy, forever dancing with itself in the form of its particles as they twinkle in and out of existence, collide, transmute and disappear again (Zukav, 1979:213). The subjective aspect of Poincare's philosophy of mathematics could be detected in Neils Bohr's principle of complementarity. Bohr developed this concept to explain the wave-particle duality of light. The particle nature and the wave nature of light are mutually exclusive, although both are complementary nature of light. Investigation into how light can be particle and wave even though these are exclusive qualities, revealed that the particle and wave characteristics are not properties of light! They are properties of our interaction with light. Depending upon our choice of experiment, we can cause light to manifest either particle-like properties or wave-like properties. If we choose to demonstrate the wave-like characteristics of light, we can per			form the double - slit experiment which produces inference. If we choose to demonstrate the particle-like characteristics of light, we can perform an experiment which illustrates the photoelectric effect. We can also cause light to manifest both wave-like properties and particle-like properties by performing Arthur Compton's famous experiment (Zukav, 116). Very much related to the principle of complementarity of Bohr, is the uncertainty principle of Heisenberg. According to Heisenberg, there are limits beyond which we cannot measure accurately, at the same time, the processes of nature. The limits do not arise because of defective measuring apparatus or because of the minute size of what is being measured. The point made by Heisenberg is that we cannot observe a phenomenon without changing it. The physical properties which we observe in the "external" world are enmeshed in our own perceptions not only psychologically but ontologically as well (Zukav, 323). This means that: the concepts "external", and "internal" are related in a real and fundamental way. What is "external" apparently depends, in a vigorously mathematical sense, upon what we decide "internally". This sounds like the conventionalism of Poincare. Poincare however, does not belong solely to the conventionalist school in the philosophy of mathematics. He is said to have paid great attention to and followed Jean - Baptiste - Joseph Fourier's dictum that: "the profound study of nature is the most fecund source of mathematical discoveries" (Bell, 1937,538). He was of the view that logic has very little to do with mathematical discovery or invention. Mathematical discovery comes with previous assiduous


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study and thought at both the conscious and sub-conscious levels. He coupled his philosophy of mathematics with the psychology of mathematical creation. In this way, he appears to be the forunner of Thomas Kuhn and his gestalt shift in philosophy of science. Poincare perceived mathematical discovery as aesthic creation. It has been stated that Poincare coupled his philosophy of mathematics with the psychology of discovery. It may be necessary to emphasize that the problems in philosophy of physics are very much present in philosophy of mathematics. As a result, there are numerous schools in philosophy of mathematics. These schools include logicism, formalism, Intuitionism, Platonism, and Conceptualism. These schools could be divided into two groups depending on the assumed origin of mathematical truth and mathematical entities. The first group will belong to those who are of the view that mathematical truth and mathematical entities are discovered but not created or invented. The second group is the direct opposite of the above group, and do believe that mathematical truth, entities, proofs, etc, are all human creations and are also a part of our cultural heritage (Barow, 1988). Platonism broadly represents the school which believes that there exist mathematical concepts and truth beyond the human level. The business of mathematicians is to discover such truths and concepts. This view is sometimes linked with the popular view that says "God is the supreme and ultimate mathematician." It does happen that schools which ought to be far from Platonism make use of Platonism at some critical points. Thus, logicism believes that all mathematics is reducible to logic. Logic in this sense, is the rules for correct reasoning and for drawing appropriate inferences. The meaning of the word, "correct", and "appropriate" has never been sat	isfactorily arrived at. Although logic is supposed to be the creation of human beings, some mathematicians of the logicist school claim that since human beings are created by God, all human creations are directly or indirectly creations of God. The intricacies, uncertainties and problems of such claims and counter-claims about the divine origin of mathematics and logic are beyond the scope of this work. In the same vein, schools like "formalism" and "intuitionalism" sometimes are interpreted in platonic undertones. The other broad school is conceptualism. Conceptualism states that all that we find in mathematics is human creation and culturally derived. Just as in platonism, you would discover that some adherents of conceptualism share some view with logicism, intuitionism and formalism. Formalism in the philosophy of mathematics is associated with the mathematician, David Hilbert. It is however more appropriate to state that names like Gottlob Frege and Bertrand Russell were also involved in the establishment of formalism in some respects. Formalism makes use of formal language and formal system. Formal languages are used in logic, mathematics, computer designs and computational devices. A formal language has what is known as primitive symbols together with what is known as formation rules. The formation rules tell us what can be regarded as a well-formed formula. An examination of formalism as a philosophy of mathematics has to grapple with the fact that there are indeed two principal types of formal systems of logic. These are: a) axiomatic system and b) the natural deductive system. The axiomatic system, as had been earlier stated is built on the assumption that there are self-evident truths that need no further

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proofs. It is later to be established that such blind belief in the truth of axioms need not be so. However, the axiomatic system is a sub-set of the well-formed formulae. The elements of this sub-set are the axioms and the theorems of the system. Given the assumed infallibility of axioms, they are specified at the outset. On the other hand, theorems are derived from axioms following transformation rules provided by the system. There is an obvious difficulty in a further assumption that an axiom can also be called a theorem, since it can be derived from itself. This difficulty was to be highlighted by Bertrand Russell's paradox on the set theory. The axiom system is generally perceived as a set of meaningless symbols and strings or symbols, that provide specific rules concerning how to formulate new strings from given ones. Interpretation of a system in formal logic is done by assigning meaning to the hitherto meaningless symbols in the well-formed formulae. According to Gottlob Frege (1848-1925), formal systems have an intended interpretation such that their theorems are considered as necessarily true statements. Frege made the bold move of stating that the concepts of mathematics had to be defined in terms of logic, and that the theorems of mathematics are indeed truths of logic. This appears to follow the footpath of another German mathematician and philosopher like himself known as Gottfried Wilhelm Leibniz (1646-1716). Leibniz was an encycloepaedic, erudite, deep thinker known by philosophers as a representative of rationalism. His writing covered such diverse fields as physics, medicine, mathematics, politics, linguistics, history, and much more disciplines. Leibniz tried to reduce everyday language and logic into symbolic forms. This eventually was construed to mean that		everything that is, could be mathematicised. That was indeed a very bold move, although we are aware that his programme was unrealizable for the very simple reason that there are issues and notions that are beyond the realms of mathematics in the sense that mathematics is understood by many mathematicians. Frege, who borrowed a lot from Leibniz, proceeded to reduce arithmetic to logic. He did not seem to include geometry in this reductionist programme of his. That had to wait for David Hilbert (1862-1943) in his Foundation of Geometry in which he laid the foundations of an axiomatized formal system. It was Bertrand Russell and Alfred North Whitehead who systematically tried to show that all mathematics can be reduced to logic. This they did in their joint work: Principia Mathematica (1910-13). It is interesting to observe that Bertrand Russell who helped to popularize the work of Frege to the English speaking audience, was also the person who pointed out the inconsistency in Frege's logic. Frege's logic makes the assumption that every predicate determines a class. Russell in 1902 pointed out to him that the assumption is inconsistent, since it leads to the paradox concerning the class of classes that do not contain themselves as elements. This teriffic blow on Frege's programme by Russell's did not prevent Frege's programme from forming an important cornerstone for the philosophy of language. The natural deductive system as distinct from the axiomatic formal system discussed above, is again made up of primitive symbols, formation and basic rules of inferences. Axioms are clearly ruled out of this system. In the interpretation of the natural deductive system, the rules of interpretation can be understood to be valid inferences, and conclusions that emerge and they do not depend on

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assumptions that are necessarily true statements as found in the axiomatic system. When cracks, contradictions or paradoxes were spotted in mathematics - the language of science - David Hilbert worked tirelessly to expunge those contradictions or paradoxes from mathematics. The results of such efforts appeared in his book, Foundations of Geometry, (1899). Formalism as a philosophical approach to mathematics was thus firmly established by Hilbert, as had been stated. Hilbert's Foundation of Geometry; Russell's and Whitehead's Principia Mathematica received a devastating shock by another mathematician known as Kurt Godel (1906-78) in an article of 1931 entitled "On Formally Undecidable Propositions in Principia Mathematica and related systems." According to the theorem in the article, every formal arithmetic is incomplete in the sense that there exists a sentence (in the language of the first-order predicated calculus) which expresses an arithmetical truth and yet is not provable within the system. As we can recall, a formal system is made up of a set of axioms and a range of rules that enable theorems to be derived from the axioms in a formal way without reference to meaning. What is needed in the formal system is the effective definition of the axiom sets and the corresponding rules of derivation. The rules must include a mechanical method for deciding membership of the set, and corresponding method for deciding in any particular case, whether the method and rules have been appropriately applied. Given the rules and definite steps to be taken within the system, it means that the class of formulae is enumerable or countable. Computers make use of this formalist approach to generate all and		only the derivable formulae, any one of them in a finite amount of time. Kurt Godel demonstrated that given any consistent system (like the one used by the computer) an arithmetically true sentence can be formed which is not derived from the system. David Hilbert's formalist plan to exchange arithmetical truths with that of derivability in a formal system was shattered by Kurt Godel's undecidability theorem. We could observe some elements of conventionalism in Poincare's and Einstein's sense in the formalist stratagem. Conventionalism in the sense that there are laid down rules which are agreed upon for decisions of matters in mathematics. The other philosophy of mathematics which was very popular at the time of formulation was intuitionism. Intuitionism has so many meanings. It could stand for the anti-empiricist philosophy of sir William Hamilton - a Scottish philosopher, (1788 - 1856). Hamilton's philosophy was greatly influenced by Immanuel Kant's philosophy. Hamilton canvassed the view that categorical propositions in logic should be reformulated in such a way that the object and subject should all have quantifiers. E.g. (All S is P) should become: (All S is all P). This approach was not popular among logicians and was consequently abandoned. In addition to Hamilton was William Whewell (1794 - 1866) as a major source of intuitionism. Whewell was an outstanding physicist, philosopher of science and great in many other intellectual fields. He too was greatly influenced by Kant. According to Whewell, geometry and Newtonian mechanics are necessary truths. He was also of the view that there is need to incorporate several known laws of science from different fields into a single, more comprehensive


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theory. In his approach, appears to be fashionable today in the thrust for a unified quantum fields theory. In his days, John Stuart Mill lambasted Hamilton and Whewell as anti-empiricists and referred to them as intuitionists. We are more interested in the intuitionism championed by L.E.J. Brouwer (1881-1966). This special interest is due to the fact, that Brouwer, like Hilbert, was responding to the series of mathematical and logical paradoxes during the first quarter of the 20th Century. Whereas David Hilbert reacted by developing an axiomatic formal system, Brouwer took recourse to a constructivist theory of mathematics. By this constructivist, intuitionist approach to mathematics, natural numbers are the primary objects of mathematical knowledge. This mathematical knowledge are brought into being by human thought, and do not have independent existence as postulated in platonism. Following Brouwer's reasoning on mathematics, some mathematical propositions are neither true nor false. This goes against the popular grain in logic which recognizes the law of excluded middle. One of the reasons for Brouwer's approach was the controversy at the time on the status of infinites and finite domains in mathematics. Since infinity is unattainable from a mathematical standpoint, Brouwer postulates that we should make-do with finite domains in our mathematical constructions. As a result of these approaches, intuitionist logic was developed by Rend Heyting in 1930. In this strand of logic, conjunction (&) (Ù), disjunction (V), implication (®) (É), and negation (~) are all taken as primitive. There are eleven axioms, and two rules of inference: uniform substitution of variables and modus ponens for implication. This intuitionist logic does not include the law of
		excluded middle (Pv - P) and one half of the law of double negation (- - P® P). This had led to the rejection of proofs that combine reductio ad absurdum with double negation. As a result, mathematical theorems that cannot be proved by other means have to be abandoned. This has helped in making intuitionism less attractive to many mathematicians. Nevertheless, some aspects of intuitionism, feature in mathematics today. A study of various philosophies of mathematics will reveal that those philosophies often cross their boundaries to the ones they criticize. This happens because mathematics, like physics, is a human creation. Mathematics changes with time and in places, depending upon numerous variables. Mathematics, being a human creation is also a cultural phenomenon. Given the cultural background of mathematics, absolute truth and absolute objectivity may not exist even in mathematics. Richard Feynman, an eminent professor of theoretical physics had endeavoured to show the relationship between mathematics and physics. According to this physicist, "mathematics is a language plus reasoning; it is like a language plus logic." Now, it happens that there exist many languages and many types of logic. Even an attempt to symbolize language did not leave us with one uniform language. Computer programming which has utilized symbolic language that is enmeshed in formal logic of some sorts has given rise to diverse computer languages and programmes. Even his assertion that we are going to quote now does not help matters. If anything, the quotation only shows that there are different types of mathematics. According to him, "Everybody who reasons carefully about anything is making a contribution to the knowledge of what happens when you


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think about something, and if you abstract it away and send it to the Department of Mathematics they put it in books as a branch of Mathematics," (Feynman, 1965:45). He agrees that in mathematics, you can start in different places, and that if "various theorems are interconnected by reasoning, there is no real way to say 'these are the most fundamental axioms', because if you were told something different instead, you could also run the reasoning the other way." Reasoning here is given a unilineal approach. In reality, you could reason in a deductive manner. In this case, you come up with certainties as conclusions. You may also reason inductively and this could give you probabilistic conclusions. You may reason dialectically in which case, certainties may reverse to uncertainties which could be resolved into a new certainty. If we are reasoning about array of events, we may have to abandon the three modes of reasoning outlined above. The creators of quantum theory realized this when recourse was made to matrices. Quantum logic is an attempt to show that there is an entirely different way of perceiving physical reality. Despite Feynman's wonderful contributions in quantum theory and in computation, his philosophy of mathematics is of the conservative and traditional strain. According to this conservative view of the relationship between mathematics and physics, "mathematicians are only dealing with the structure of reasoning, and they do not really care about what they are talking about. They do not even need to know what they are talking about, or, as they themselves say, whether what they say is true… but the physicist has meaning to all his phrases. That is a very important thing that a lot of people who come to physics by way of mathematics do not appreciate. Physics is not mathematics, and mathematics is not physics. One helps the
		other. But in physics you have to have an understanding of the connections of words with the real world" (Feynman, 55). This quotation has the various characterization of mathematics by Albert Einstein as we have examined above. This view of mathematics fails to account for the fact that Poincare arrived at the special theory of relativity through mathematics and not necessarily through physics. But more fundamentally, discussion of the principle of complementarity and Copenhagen interpretation of quantum theory had revealed that the phrase "understanding of the connection of words with real world" contains a new metaphysics, epistemology and logic. The arrogance of an all - knowing, deterministic classical physics was made to give way to a sober, quantum relativistic, more embracing world-view and physics. Richard Feynman was very much aware of the problems of classical physics as well as of quantum theory. This is why it is puzzling that he strove to make a sharp distinction between physics and mathematics. To show that his philosophy of mathematics is out of tune with his philosophy of physics, we need to quote Feynman at a greater length. He realized that knowledge of all the fundamental laws of physics does not amount to much in nature, since the real world is tied up in multiplicity of complexities of varying hierarchies. These complexities and hierarchies include entities like mass of atoms, protons, neutrons, electrons, waves, storms, sun spot, star, etc. In his own words: "As we go up in this hierarchy of complexity, we get to things like muscle twitch, or nerve impulse, which is an enormously complicated thing in the physical world, involving an organization of matter in a very elaborate complexity. Then come things like 'frog'. "And then we go on, and we come to words and concepts like 'man',


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and 'history', or 'political expediency', and so forth, a series of concepts which we use to understand things at an ever higher level. "And going on, we come to things like evil, and beauty, and hope… "Which end is nearer to God; if I may use a religious metaphor. Beauty and hope, or the fundamental laws? I think that the right way, of course, is to say that what we have to look at is the whole structural interconnection of the thing; and that all the sciences, and not just the sciences but all the efforts of intellectual kinds, are an endeavour to see the connections of the hierarchies, to connect beauty to history, to connect history to man's psychology, man's psychology to the working of the brain, the brain to the neural impulse, the neural impulse to the chemistry, and so forth, up and down, both ways. And today we cannot, and it is no use making believe that we can, draw carefully a line all the way from one end of this thing to the other, because we have only just begun to see that there is this relative hierarchy. "And I do not think either end is nearer to God. To stand at either end, and to walk off that end of the pier only, hoping that out in that direction is the complete understanding, is a mistake. And to stand with evil and beauty and hope, or to stand with fundamental laws, hoping that way to get a deep understanding of the whole world, with that aspect alone is a mistake. It is not sensible for the ones who specialize at one end, to have such disregard for each other… the great mass of workers in between, connecting one step to another, are improving all the time our understanding of the world, both from working at the ends and working in the middle, and in that way we are gradually understanding this tremendous world of interconnecting hierarchies," (Feynman, 125-6). This latter view of Feynman accommodates the view of
		Einstein and of Poincare on mathematics. It is also because of this kind of view that I earlier stated that the problems found in philosophy of mathematics surfaced also in philosophy of physics. They are not only closely related, the two are inter-woven. At this level of understanding nature and reality, we have to be at least tolerant of philosophical schools in mathematics like platonism, conceptualism, logicism, formalism, intuitionism and many other such schools. The better position may be that each of these schools would express minute portions of mathematical and physical reality. We are encouraged to take this viewpoint from the background of the history of physics and of mathematics. The history of physics can be said to have passed through phases resembling platonism and conceptualism. The statement: "God created Heaven and Earth", is both physics and religion but could be characterized as either solely physics or solely religion. It depends on who does the characterization. Similarly, the Big Bang hypothesis of the origin of the universe could be given a physicalist interpretation or a religious interpretation. Physics has moved from creationism platonism) to empiricism/positivism and the certainty or determinism this entails, to relativism of Einstein and to the uncertainties in quantum theory. Similarly, in mathematics, we could move from God the creator of mathematics (platonism) to the certain and deterministic periods of Cantor, Frege, Hilbert. From this period we witness the onslaught of Godel's undecidability or incompleteness and completeness theorems on the claims of certainty and truth in mathematics. Then the realization that there are phenomena in nature that cannot be described in the normal number notions, led to the exploration of Hamilton's matrices. Matrices coupled with uncertainty principles in physics has led to the establishment of a kind of logic known as quantum


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logic. All these rub off on philosophy of science - and of physics in our special case. We shall see how these tendencies show up in a selected philosophies of physics. In this regard, we shall not be repeating the points already made in the book, History and Philosophy of Science (Alozie, 2001). Let us start with Karl R. Popper's effort in this direction.
			CHAPTER
					8
		PHILOSOPHIES OF SCIENCE
		Karl Popper's philosophy of science _Sir Karl Raimund Popper (1902-94) was an Austrian philosopher who fled his country to New Zealand and later to Britain because of the hounding and killing of his former communist colleagues. His status as a refugee from the Nazi persecution of communists and later an emigrant, coloured his writings in philosophy. His philosophy and logic could be said to be situational. Popper used this kind of statement while describing Darwinism as a philosophy. In the Poverty of Historicism, Popper referred to Darwinism as an application of the logic of situations. According to his usage of the phrase "logic of situations" if we want to know why somebody is doing a particular thing or is holding a particular view or propounding a theory, we should see the action or theory as a response to the problem being confronted (Popper, 1957). It is therefore misleading to talk of Popper's philosophy of science, or of any kind of philosophy. In short, Popper has no consistent philosophy. In philosophy of science, Popper is of the platonist hew. In politics and social science, he is critical of platonism. In the Logic of Scientific Discovery, Popper is a determinist and against induction in any form. In some other works of his, he admits probabilities and indeterminism in science although for different kinds of reasons other than the indeterminism of quantum theory. He writes about truth and verisimilitude yet, he

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admits that we will be unable to recognize truth when such is before us. He is against relativism in science, yet his writing suggests that relativism in knowledge should be encouraged. Rationality of science Karl Popper believes that there is nothing more rational than the method of critical discussion, which is the method of science (Popper, 1972: 27). He also says the same thing in his Conjecture and Refutation that the growth of our knowledge, our way of choosing between theories, in a certain problem situation makes science rational (Popper, 1963:69). The conviction that science is a rational enterprise drives Popper to seek demarcation criteria that will distinguish science from non-science. This conviction and quest for demarcation criterion is further re-inforced by the belief that the aim of science and philosophy is, or ought to be the search for truth. This view was expressed in several parts of his book, Objective Knowledge, (Popper, 1972:40,191,319). Given Popper's strong tie with skepticism or fallibilism, and a strong aversion to induction, it is difficult to fathom how the demarcation between science and non-science could be achieved. Popper's fallibilism, anti-induction, and his falsificationism pose serious problems not only for the demarcation project, but also for the claim that science is rational and truth - seeking. The demarcation of science from non-science is a feature Popper shares with the positivists. This positivist hangover from positivism and logical positivism is well expressed by Popper in his Logic of Scientific Discovery. According to him, the first task of the logic of knowledge is to put forward a concept of empirical science, which draws a clear line between science and metaphysical		ideas (Popper, 1968:38 - 9). Theories or ideas are scientific if they are framed in falsifiable ways. Statements or ideas that cannot be subjected to falsification are regarded by Popper as metaphysical. He soon discovered that there are so much in science which are metaphysical. He changed gear by admitting that metaphysics is important in science. The demarcation project, and his whole methodology of science is built on logic and mathematics, although this is not always very explicit. According to Popper in Conjecture and Refutation, logic is the organon of criticism, given the fact that proofs in logic and mathematics enable us to identify rules of inference that are valid within specific languages. Empirical science should have its theories formulated in such a way that a false conclusion from a valid inference will demonstrate the falsity of the premise. Logic in this view, gives the grounds for falsificationism (Popper, 1963,1969:64). Also in his Objective Knowledge, Popper looks upon logic as the theory of deduction or of deviability. He says that we should, in the empirical sciences, "use the full or classical or two-valued logic. If we do not use it but retreat into the use of some weaker logic - say the intuitionist logic or some three-valued logic... then we are not critical enough (Popper, 1972:305). This limited perception of logic by Popper has also contributed to the various issues he was unable to grapple with satisfactorily in philosophy of science. These include falsificationism and issues of truth. Falsificationism is the concept which holds that scientific theory should be put to a test, and if the theory or hypothesis fails the test or is refuted, such a theory or hypothesis is abandoned. For Popper, the scientist starts his work with a particular problem in
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view. He designs tentative theory that would solve the given problem. Subjection of the tentative theory to serve tests would lead to elimination of errors in the theory. At this state when errors have been eliminated, the problem in view would have been solved, except that such solution gives birth to another problem. In essence, there is no permanent solution to a problem. This is in perfect agreement with a fallibilist posture in which all knowledge claims are provisional and in principle revisable. And even if we hold fallibilism to mean that although we are sure that some of our propositions are true and certain, it is possible that some of them are false, the Popperian schema of problem (P') ®Tentative Theory (TT) ® Error Elimination (EE) ® Problem (P²) ---- P³…. Pⁿ will still hold. The problem for demarcation and falsification arises when Popper's anti-inductivist stance is invoked. Popper imbibes David Hume's condemnation of induction on the grounds that we wrongly make generalizations from the past to the future, or generalizations from what we have experienced, to what we have not experienced. As Anthony O' Hear correctly observes, scepticism about induction can seem curiously perverse. It says that we have no grounds for thinking that the future will be like the past, but it actually gives no reason for thinking that the future will be different in any given respect (O' Hear, 1980:19). The evaluation of what he calls empirical content, the corroboration of theory, testing of theories, falsification of theories, are in large measure, inductive enterprises. Even his doctrine of verisimilitude which means nearer to the truth, or the truth-content of a theory minus its false-content are evidently exercises in induction. Popper realizes this, although as characteristic of him, he hardly comes out boldly to correct his former positions on any matter.		He writes in an ad hoc manner, depending on the situation he is facing. In Popper's words, "there is a probabilistic, though typically non-inductivist argument which is invalid if it is used to establish the probability of a theory being true, but which becomes valid (though essentially non-numerical) if we replace truth by verisimilitude. The argument can be used only by realists who not only assume that there is a real world, but also that this world is by and large more similar to the way modern theories describe it than to the way superseded theories describe it… Moreover, it only establishes a probability of verisimilitude relative to its competitors (and especially to its predecessors). In spite of this, there may be a "whiff" of inductivism here… (Popper, In: Schlipp 1974: 1192 - 3). Even if Popper fails to admit a "whiff" of inductivism in his methodology and conception of science, it will be strange to admit the role of probability in science without recourse to inductive reasoning. Popper wished to avoid this kind of embarrassing conclusion by now writing of "essentially non-numerical" probability. This does not help his case, since we know that matrix algebra that handles more complicated phenomena in quantum theory is inductive and probabilistic. Induction has many faces, but the essential nature is the same. There are other problems with Popper's approach to science. These include the hatred for definition; the claims that all descriptive terms are dispositional; his controversial or unacceptable views on basic statements, conventionalism, realism and instrumentalism, probability, indeterminism and relativism in science. On the problem of meaning and definition, Popper explicitly said he is never interested in what he called the problem of meaning, which he describes as a verbal problem and a pseudo - problem

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(Popper,1969: 40). He did not bother about the possible identification of meaningful statements which could be counterposed to meaningless statements. A verification theory of meaning would obviously expose the bogus claims of some scientific theories. Partly for this reason, Popper busied himself advancing reasons why definitions could be avoided. Definitions admittedly have enormous problem in epistemology and logic. Despite these problems, definition has been known to play some important role in both communication and understanding at some levels. Deductive logic which Popper uses has some of its terms defined. What is more, if Newton failed to define force, or some of the concepts in the various theories and laws he developed, it is difficult to comprehend how Newtonian physics would be understood by anybody. Mathematics which physics uses is usually flooded with definitions. It is however true that there are always some terms that are never defined. The undefined terms could change our total perspective when attempts are made in examining the significance of those undefined terms. The paradoxes found in mathematics and some of the developments or revolutions in mathematics could be linked with survey of undefined terms by mathematicians. These developments or revolutions did not discard the use of definitions, but continued to make use of them, while noting the limitations. It is however puzzling to find out that a philosopher who has been passing judgment on other philosophical systems; who believes that the aim of science is the pursuit of truth; who believes in the explanatory power of science, is not interested in meaning and definition. The position of Popper on meaning and definition is sufficient to regard his writing on any issue as mere fiction with no value to the real world of physics as acclaimed by professionals. Unfortunately, there are many more		problems like this. Popper's claims that all descriptive terms are dispositional is a plausible one. However, in the light of his realist, rationalist stance on science, there will not be any justifiable reason for demarcating science from non-science; or for regarding science as being more rational than any other intellectual or spiritual endeavour. He was brought to this position by his opposition to those who claim that verification is a scientific theory and that observational experience is sufficient for establishing certainty and truth. In the Logic of Scientific Discovery (Popper, 1968:95) and in Conjecture and Refutation (Popper 1969:387), Popper made the interesting point that: "Here is a glass of water" which cannot be verified by any observational experience. The reason is that the universal terms which occur in this statement('glass, water') are dispositional: they denote physical bodies which exhibit a certain law-like behaviour." By saying that universal terms are dispositional, Popper means that such terms are hypothetical or theoretical. Such terms are theory-ladden. In the case, "Here is a glass water" it has to be affirmed that indeed there is a glass not a transparent plastic. This means we will be grappling with theories of the nature of glass and related entities. Similarly, we will have to quickly consider theories related to water. Even the term, "Here" could mean "take" or could be an existential category. In either case, the existence or non-existence of 'glass' and 'water' need some approval and confirmation. We recall that there are terms in mathematics and physics that do not represent any tangible object. Could the expression: "Here is a glass of water' belong to such non-existent category? Again, this turns out to be a theoretical question. Given all these myriad of theoretical

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expressions in the proposition: 'Here is a glass of water', it does not make sense to settle only for the one observational experience which is just one theory, while ignoring the other theories. All the theories have equal status. I agree entirely with Popper on this score, since there is a sense in which Einstein's theory of relativity together with quantum theory make allowance for abandoning privileged positions in space and time and encourage the relational perspective of space - time as well as the abandonment of determinism in the Laplacean framework. But the inconsistent nature of Popper's whole philosophy made him have some theoretical terms with privileged positions. An example is what he calls "basic statement". Basic statements are testable hypotheses, or singular existential statements which record the occurrence of observable events in space and time and which serve as tests of general theories. Although basic statements are testable hypotheses, they need not be tested, since they are accepted for some purpose as not being in need of further testing. Basic statements are characterized by the agreement to accept them as such, not necessarily because of the availability of convincing evidence, or of superior argument. "The empirical basis of objective science has thus nothing 'absolute' about it. Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being (Popper, 1972:111).		Basic statements are in many ways like the axioms we come across in mathematics. In physics, as in science generally, basic statements are very crucial. Popper articulated the importance of basic statements in this way: "From a logical point of view, the testing of a theory depends upon basic statements whose acceptance or rejection, in its turn, depends upon our decisions. Thus, it is decisions which settle the fate of theories… this choice is in part determined by considerations of utility", (Popper, 1972:108 - 9). The two quotations from the Logic of Scientific Discovery taken together, will make us wonder why much fuss is made about science from epistemological point of view. Truth as has been pointed out is provisional and unattainable. It has been argued in many quarters - and I share the same view - that it is technology that makes science look very superior. Technology could be developed and has been developed despite the controversies in science. It is indeed possible to separate science from technology. The problem that could confront such separation today is the fact that science is now defined with technology as an implied term of such definition. Furthermore, it is disturbing that an enterprise that lays no claim to an encompassing truth should denigrate psycho-analysis, Marxism as scientific disciplines. Similarly, religion, mysticism and a significant aspects of world-view of the traditional African, ought to have appreciable space in matters epistemological from Popper's unintended philosophy of science. Popper admits dogmatism, infinite regress, and psychologism in science. For this, he adopts the 19th Century German philosopher's trilemma. The German philosopher in question is Jakob Friedrich (1773 - 1846). Fries' trilemma is an anti - foundationalist argument

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(sometimes referred to as Munchhausen trilemma in which he postulated that any argument purporting to establish an ultimate basis must be defective since it is bound to lead to an infinite regress or to a logically vicious circle. But to assume an ultimate foundation without argument is arbitrary. Fries asserts that there are three options available. One option is to accept some statements dogmatically. The second option is to attempt to justify such statements. But the justification of these statements through reasoned argument, commits us to the view that statements can be justified only by yet other statements, and hence to an infinite regress of justifications. The third option is that we can break out the net of language without being reduced to dogmatism, because there are some statements which can be directly confronted with perceptual experience. Popper calls this third option psychologism. He adopts the three elements of Fries trilemma: dogmatism because we decide to accept certain statements as basic; the infinite regress because we could test them further if we wanted to and because being unproven, they can be seen as having need for further testing; psychologism because, in Popper's terms, experience may motivate, but never justify, our decisions regarding basic statements (O' Hear, 1980:74). The resolution of this trilemma by fusing all the salient elements appears a little untidy. Dogmatism features in religion, mysticism, astrology, politics. Thomas Kuhn in his Structure of Scientific Revolution has made provision for dogmatism or conservatism within the paradigm before a revolutionary change. Imre Lakatos had argued that falsified theories should not be thrown away, but should be conserved. This too amounts to some dogmatism. Feyerabend had also shown that such trends exist among scientists. If dogmatism is		co-joined to infinite regress and psychologism, we could legitimately ask, as Feyerabend had consistently asked what is great about science? The admission of some role for metaphysics, dogmatism, psychologism, infinite regress, the inability to successfully conduct the demarcation of science from pseudo-science (or non-science), and the view that there are no such things as crucial experiments makes me wonder why O' Hear will still support Horton's former view that change through empirical testing differentiates "conservative and empirically closed systems such as African magic from science" (O' Hear, p.111; Horton, 1967, 1982). It should be stated that when Robin Horton wrote that piece in 1957, it was quite revolutionary. He tried to show similarities and dissimilarities between Western science and African science which he called African thought. He has substantially revised his views, and is happily married and settles in Nigeria. At the time Horton wrote, everything about Africa was regarded as fetish, with no iota of relationship with western science. With developments in quantum theory, cosmology, and astrophysics, it is rather retrogressive to stick on to deterministic, infallible, cumulative picture of science. The picture of science is not improved with the admission by Popper that there is some kind of conventionalism in his philosophy. We came across conventionalism while discussing Einstein's and Poincare's philosophy of mathematics. The same conventionalism has surfaced in Popper's philosophy. Popper's conception of conventionalism is different from such views as commonly met in philosophy of science and philosophy of mathematics. In mathematics, conventionalism involves systems of symbols or entities to which practioners agree on the meaning or

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significance of such symbols. They also decide on procedure that will result to what can be admitted as proof. Truth or falsity of the symbols or entities are not necessarily very important for conventionalism. The same approach applies in physics. Set of propositions in physics are put together in a logical structure such that some logical truth not necessarily based on empirical truth, could be deduced. For Popper, the correspondence theory of truth as developed by Alfred Tarski together with Popper's theory of verisimilitude and basic statements gives an entirely different picture of conventionalism. According to Popper's version of conventionalism, scientific theories are human creation. In physics for instance, the physicist formulates theories which are foisted on nature. The physical theories are mere logical, artificial structures, built around our conception of the world, and deciding that such an artificial, logical creation conforms to our scientific world. Instruments for measurement and methods of observation are very important in this particular conventional scheme. If observation or experiments fail to confirm our view of the world or fails to confirm our scientific theory, the conventionalist would most probably examine the instruments or question the method of observation. If the instruments are in order and the method of observation satisfactory, the conventionalist would probably spew new theories known as "ad hoc" that will explain the discrepancies between theory and observation. This way of looking at scientific theory makes it look unfalsifiable. And if Popper is a conventionalist, it means that he has also destroyed the falsifiability criterion of science he advocates. Popper is aware of the danger of this conventionalist 'stratagem' as he calls it. His response is that 'ad hoc' hypothesis is not necessary.		What is needed is abandon the falsified theory, formulate a new falsifiable one which should be subjected to test. Karl Popper illustrates his understanding of being a conventionalist stratagem with the discovery of the planet, Neptune by Adams and Leverrier. From the point of view of Newtonian astronomical physics, the orbit of Uranus appeared eccentric, when the principles of Newtonian astronomic physics were applied to an initial set-up that included the positions and masses of the sun, Jupiter and Saturn and the mass of Uranus. It has been pointed out that Neptune was discovered because the eccentricity of Uranus's orbit was explained not in terms of the failure of Newtonian principles, but on the grounds that there was an extra-Uranian planet interfering with Uranus's orbit. Adolf Grunbaum had shown that Popper's use of the term 'ad hoc' could be applied to a major aspect of falsificationism - the content increase of hypothesis. Grunbaum, taking on Popper on his own falsificationist terms, has shown that quite a lot of the Popperian examples and hypotheses are unfalsifiable (Grunbaum, 1976 BJPS, 27, pp.329 - 62). Grunbaum is nevertheless a disciple of falsificationism. He uses the Bayes's theorem as an anchor for his brand of falsificationism. Bayes's theorem in probability theory was developed by a Clergyman the Reverend Thomas Bayes' (1702 - 61). According to this theorem, the probability of A given B is equal to the probability of A multiplied by the probability of B given A (the 'likelihood' of B), divided by the probability of B. This is usually taken to mean that evidence confirms hypothesis. But there can be no confirmation of hypothesis that is probabilistic or inductive, and upon which Popper has assigned a zero value to what is known as the 'prior probability'

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of the evidence and of the hypothesis. For instance, let A represent the hypothesis, and B represent the evidence. The degree to which the hypothesis is confirmed by the evidence (that is the probability of A given B) is given by the 'prior probability' of the hypothesis (that is, the probability of A) multiplied by the 'likelihood' of the evidence divided by the 'prior probability' of the evidence (that is the probability of B). Those who use the Bayesian theorem in this way, including Grunbaum, forget that an evidence which is probabilistic can neither confirm nor falsify any hypothesis or theory (Grunbaum, 1976, pp.213 - 52). In general terms, Grunbaum was quite critical of Popper's position in philosophy of science. A more devastating criticism of Popper's conventionalism and falsificationism was delivered by a former disciple of Popper, Imre Lakatos. First, Lakatos did show, using several examples in physics and some other science disciplines, that falsified theories are not abandoned but often brought back to active participation in the formulation of new and probably superior theories. As regards Newtonian astronomical physics and scientific theories, Lakatos argues correctly, I think, that "even if experiments could prove experimental reports, their disproving power would still be miserably restricted: exactly the most admired scientific theories simply fail to forbid any observable state of affairs." This is why a prestigious theory of celestial mechanics propounded by Newton could not account for a new planet - Uranus. He argue from the history of science perspective that Newtonian mechanics cannot be said to have been falsified as a result. What is more, there is no physical theory that could be regarded as perfect and which does not contain some anomalies. Aristotelian, Galilean, Newtonian, Einsteinian		physics as well as the various theorems in quantum theory have clear signs of incompleteness in terms of comprehension of the essence and laws of physical reality. Lakatos made the important observation that if we decide to pursue the Popperian criterion for demarcating science from non-science (and metaphysics), then we certainly end up in complete skepticism, since this approach will render all science as practised irrational metaphysics which ought to be discarded. He was attacking what he called 'dogmatic falsificationisms'. We shall here reproduce in greater details, the tirade Lakatos poured on dogmatic falsificationism - his former school: "Scientific theories are not only equally unprovable, and equally improbable, but they are also equally undisprovable… The collapse of dogmatic falsificationism under the weight of fallibilistic argument brings us back to square one. If all scientific statements are fallible theories, one can criticize them only for inconsistency. If scientific theories are neither provable, nor probabilifiable, nor disprovable, then the skeptics seem to be finally right: science is no more than vain speculation and there is no such thing as progress in scientific knowledge (Lakatos, 1970 :103). This kind of outlook was alarming for Lakatos and so he proceeded to reconstruct Popperian model which will bring science to logical and psychological greatness and respectability. This he tried to do by advocating the elimination to a very minimum level elements of conventionalism in Popper's falsificationism while holding on to testability and confirmation of theories. In addition, he made the important point that it is mistaken to consider falsification in terms of single theory. In truth, at each time, the scientist is grappling with many theories. The term "proliferation of theory" better describes the arrays of theories considered when dealing with any single

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scientific problem. Such consideration of arrays of theories led him to the formulation of what he called the Methodology of Scientific Research Programme (MSRP). The MSRP will have a hard core, and periphery. There is a protective belt and so forth. This MSRP is modelled after a kind of fruit - say a palm fruit. Progress is made when the scientist moves from one research programme to a newer, more fruitful one that has better explanatory and better predictory power. How to identify elements of the research programme and when to decide it is time to consider a research programme as degenerating or progressing was an open - ended issue. The arguments against Popper's falsificationism and methodology of science, would lead to a democratic anarchic methodology of science. But the emotional attachment to the western concept of science makes him work desperately to concoct what he thinks, will bring epistemological and methodological grace to science. The attempt to give science this glorious picture, ended up in gross failure. That Lakatos did not succeed has been rigorously argued by Paul Feyerabend in his classical book: Against Method. It also explains why the book was dedicated to Imre Lakatos, whom Feyerabend referred to as "a friend and fellow anarchist." Thomas Kuhn (1922 - 1996) responded differently to the problems of science. Drawing heavily from history of science, Kuhn highlights the conservative and dogmatic nature of science at what he calls the paradigm level. The paradigm, although given several interpretations, basically represents the learned behaviour, values, notions of scientists. The community of scientists works within this learned, conservative, dogmatic framework, perceiving science and the world from this perspective or paradigm.		This dogmatic aspect of science features in Popper's critical rationalism, in Lakatos methodology of scientific research programme and amongst positivists and logical positivists who perceived growth in science as a cumulative exercise engrossed with the assemblage of indubitable, certain scientific truths. But Kuhn goes beyond this dogmatic level to show that the accumulation of puzzles and eventual solutions to nagging puzzles would usher in a new revolutionary stage that represents a new paradigm. In a new paradigm, the world-view of scientists would differ from the previous paradigms. The differences would be so fundamental that different paradigms cannot be compared. If concepts acquire entirely different connotation and world-view there is no basis for comparing paradigms. The implication of revolution in science for epistemology is that truth in science is not eternal. It changes from paradigm to paradigm. Popper's view on truth, despite his notion of verisimilitude, does have a similar characteristic. Since the model developed by Lakatos has the Popperian touch, he automatically incorporated the culture or world - view of not bothering about truth. Paul Feyerabend also dispensed with the notion of truth. Given the proliferation of theories within any given paradigm and given the historical, cultural and situational origin of scientific theories, it is obvious that truth has to be conditional and relative. Dogmatism among many scientists and philosophers make them regard the conditional and relative qualification to truth with extreme hostility. This need not be so. The realization that these apparently conflicting and diverse ways of perceiving physical reality could be harmonized would be the beginning of a new kind of progress in science and human society at large. This means that the world-views

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of the mystics, religious bodies, cultural entities like the Igbos, Yorubas, Akan, Budhists, Shintos; political ideologies as diverse as capitalism, socialism, fascism, democracy have to be considered from a holistic integrative standpoint. This is difficult from the standard, popular philosophical practice; but possible from some other philosophical and scientific paradigms. We shall discuss in another chapter this non-popular, non - standard viewpoint which makes an alternative philosophy of physics possible. For now, we shall consider Popper's views on instrumentalism and realism. We shall show that Popper's views here as in other aspects of his writing bring out the eclectic and anarchic nature of his philosophy. Instrumentalism and realism Instrumentalism is the philosophical tenet which states that scientific theories or theories of any type are not, strictly speaking, true or false, but are to be regarded as tools for making predictions. John Dewey (1859 - 1952) who was one of the proponents of instrumentalism also referred to this school variously as pragmatism, and experimentalism. Some adherents of positivism as well as some adherents of pragmatism see theories as instruments necessary for predictions; or for moving a set of data from one theoretical framework to another. The problem here is that what is regarded as instrument could be faulty or misleading. Similarly, a probably faulty instrument could probably lead to a prediction of nothing! This is almost certain to occur if we are dealing with unobservable entities in physics. Karl Popper's general ambivalence and tendency towards anarchism in philosophy of science is clearly manifested in his handling of instrumentalism and realism. In one breath, he is against		instrumentalism. At another breath he espouses instrumentalism. His understanding of realism makes the instrumentalism which he criticizes appear as a synonym. According to him, an instrument raises no claim to truth, and so cannot be falsified in the sense in which a theory which does raise such claims can be falsified (Popper, 1982 : 103). Instrumentalism which he described as 'uncritical'; 'irrational' and 'objectionable' has been used by the church in history against the rising popularity of science. But elsewhere in his Objective Knowledge, he asserts that "theories are true or false and not merely instruments. But they are of course instruments also;… (Popper, 1972:80). Truth in this case is tied up with the correspondence theory of truth, correspondence with the facts. Scientific theories are of human origin as had been pointed out several times. He recognizes this human origin of scientific theories and modifies the similar Kantian position thus: "Our intellect does not draw its laws from nature, but it tries - with varying success - to impose upon nature laws which it freely invents (Popper, 1969:191). Since human beings and their creations are fallible, the theories they invent will also be fallible. Popper is aware of this and he shows this when he writes that a good explanatory theory is always a bold anticipation of things to come. It ought to be testable, and capable of being shown to be true;…" (Popper, 1972 p.264). It is easy to perceive that Popper's view of scientific theories is instrumentalist in nature. Theories are not only human inventions, they are saddled with the problems of relativity of truth. It is necessary to emphasize that Popper never regarded himself as subscribing to the idea of relativity of truth. Indeed he claims to be a realist, and asserts that the question of whether our man-made theories are true or not, depends upon real facts; real facts which

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are , with very few exceptions, emphatically not man-made (Popper, 1972 :328). Now, our observations and even the experiments conducted by scientists are guided by theories. Theories can never be proved to be true no matter the number of confirming experiments, he tells us. It is difficult to appreciate how the scientist will know "real facts" when this knowledge will be clothed in theoretical terms. The instrumentalist implication of the way he thinks theories should be used brings in the problem of proliferation of theories. One such problem is the criteria to be used in selecting one out of possibly numerous competing theories as the one representing "real fact." The realization of such a difficulty made Popper to declare himself a realist. Thus, he declares, "our theories which guide us in setting up our experiments and in the interpretation of their results have of course always been our inventions: they are inventions or products of our 'consciousness'. But that has nothing to do with the scientific status of our theories which depends on factors such as their simplicity, symmetry and explanatory power, and on the way they have stood up to critical discussion and to crucial experimental tests; and on their truth (correspondence to reality), or nearness to truth (Popper, 1982:41). He puts consciousness in quotes, as if consciousness which plays major role in theory formulation is not the kind of psychological consciousness he has in mind. Factors like simplicity and symmetry are as perceived by the human mind. There is nothing dictating that scientific theories must be simple. Reality is not necessarily simple. We may decide to reduce complex, complicated phenenomena to a simple picture of theory. What applies to our use of simplicity also applies to our use of symmetry.		In the universe in which we live symmetry is continuously broken. Whatever symmetry that existed in the universe is said to have been at the time of the Big Bang phenomenon - at a period of immense or intense energies when life did not and could not exist. This symmetry existed probably during the first nanoseconds of the Big Bang which is said to be the origin of the universe and the origin of time! This is the prevalent doctrine among many physicists and cosmologists. Given this scenario, the artificial reduction of theories and reality to symmetries may not reveal the 'real facts.' Explanation and crucial experiments as handled by Popper do not save his realism from anarchic tendencies. This is particularly so, if we remember that his brand of realism is tagged "critical." We can then call it critical realism or critical rationalism. In this regard, Mario Bunge's Philosophy of Physics follows the same trend of critical realism (Bunge, 1973 p.86). Some of the critical comments on this school would therefore cover both Popper and Bunge. The aim of science is to find satisfactory explanation of phenomena as the critical realists attest. Given that, all knowledge is theory-impregnated, including the concepts used for explanatory purposes, it becomes quite problematic to discuss explanation in a satisfactory way. The explanan and explanandum are all immersed in theories. Some arbitrariness will be introduced at some point to resolve this dilemma. Without such arbitrary approach, the scene is ready for anarchism. It has also been pointed out that this kind of approach does not permit crucial experiments to give decisive verdicts. What we find is that idealism has been decorated with linguistic philosophy, which pretends to recognize the empiricist perception of reality. This cock-tail type of philosophy takes into the concoction, some aspects of logical positivism. Let us examine

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how critical realism fares in physics in more concrete ways. Quantum theory happens to be the area where much of the battle in philosophy of physics has been raging .The principle of complementarity together with the uncertainty principle which forms the Copenhagen interpretation of quantum theory is the principal target of attack from Popper's and Bunge's realism. These philosophers are upset because subjectivism has been introduced into physics . Mario Bunge asserts that the Copenhagen doctrine is scientifically and philosophically untenable because it is inconsistent and not thoroughly physical (Bunge,1973 p.88). The difficulty these philosophers are battling with is not trivial. Physics is about reality. And reality is concrete ,like the table upon which I am writing. Quantum mechanics or quantum theory is dealing with the micro-world that cannot be treated or observed like my table. Now ,if quantum theory is about physical reality, it should be expressed in a non-committal, impersonal objective manner, devoid of the feeling and ideas of a human knower. The nature of the micro-world which includes unobservables like electron, photon, gluons, quarks, neutron, proton, neutrinos; exotic quanta like charmed particles, matters and anti-matters, etc, makes it a bit ridiculous to think that we can package our understanding of the micro-world the way it is done at the macro-world. This is not to suggest that there are no conceptual problems in macro-physics. By convention, the conceptual problem in macro-physics are swept under the carpet . The consistency demanded by Bunge is not justified by the history and practice of physics. Aristotelian physics is not exceedingly consistent with the physics expounded by Galileo and Netwon. Nor would we justifiably assert that Newtonian physics is		very consistent in its entire ramification, with the relativistic physics of Einstein. Quantum theory is inconsistent with the other physics from the point of view of deterministic physics of Newton and Einstein. Despite these inconsistencies, deterministic aspects of physics are very fruitful for technological purposes. Indeed, it is problematic to make use of terminologies belonging to classical physics for phenomena in quantum theory. We could be consoled that the language of physics, which is mainly mathematical, abounds with inconsistencies, apart from the mathematical paradoxes hinted at earlier. Euclidean geometry is definitely inconsistent with non-Euclidean geometry. Conceptional problems in statistical mechanics, in randomness, theories of probability and in theories of chaos further demonstrate inconsistencies in mathematics and therefore in mathematical physics. Yet, physics fruitfully advances irrespective of such inconsistencies. The same kind of fruitful inconsistencies abound in logic: Aristotelian versus non-Aristotelian logic. Critical realists like Mario Bunge and Karl Popper with critical rationalism, have found it impossible to abandon earlier doctrine of a solely material, determinate world for a partly non-material, indeterminate physical reality. Quantum theory's new doctrine that the properties of quantum objects or entities can only be ascertained if we first specify the experimental arrangement by which we intend to measure the quantum objects, implies that, quantum physical truth is in part an observer-created truth. For instance, in the wave and particle nature of light, it cannot be said that light is both wave-like and particle-like at the same time. Light manifests wave-like or particle-like characteristics, depending upon the experimental approach of the physicist. It appears irritating for

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Mario Bunge that in quantum theory, human thought and intention influence the structure of the physical environment. The anger against Copenhagen interpretation is further fuelled by Heisenberg's assertion that: "The atoms or the elementary particles are not as real; they form a world of potentialities or possibilities rather than one of things or facts." (Heisenberg, 1971). Bunge's assertion that the Copenhagen interpretation is not thoroughly physical, addresses views like that of Heisenberg. However, the realization that physicists have tentatively formulated a working theory, that combines Einstein's theory of relativity with quantum theory, has rendered Bunge's criticism antiquated, unnecessary and wrong. The union of theory of relativity and quantum theory has yielded quantum field theory. Despite the problem of fusing quantum with field, this new approach explains the interaction of the quantum in diverse areas simultaneously. The quantum can both be here and there; this and that simultaneously. Physical reality is no longer just things and facts, but non-substantial field of potentialities, probabilities or possibilities. Karl Popper's realism is overloaded with falsificationism, verisimilitude, anti-induction, etc. In terms of quantum theory, Popper changes gear from his anti-inductivist stand to a probabilistic position. It is common knowledge that statistical results are inductive. He maintains that quantum mechanics is a statistical theory. His realist stand is articulated thus: "There is no reason whatever to doubt the realistic and objective character of all physics. The role played by the observing subject in modern physics is in no way different from the role he played in Newtons' dynamics or in Maxwell's theory of electric field: The observer is, essentially the man who tests the theory" (Popper, 1972 :304). He continues this		line of thought by stating that quantum mechanics is not an abstract physical formalism but a theory of something very concrete: a theory of atoms, a theory of their structure as possessing a positively charged nucleus and shell structure of negative electrons that explain, in principle, very concrete properties of the chemical elements (Popper, 1982 :11). He applies a device in logic known as the fallacy of the straw man. This fallacy is committed when the opponent's argument is distorted for the purpose of easily destroying the distorted argument. In Popper's case, he then says that quantum theory has done away with the wave-particle perception in the principle of complementarity when Max Born interpreted the square of the wave amplitude as a probability for finding the particle was accepted. He writes of the incompleteness of quantum mechanics; and proceeds to show how many new particles have since been discovered; and how the theory had now encompassed not only the commutation relations, Heisenberg's uncertainty relations, Pauli's exclusion principle; but has added quantum electrodynamics, quantum field theory and even quantum chromodynamics (Popper, 1982,:13). The issue at the time is not the discovery or postulation of new elementary particles, but the inability to measure position and momentum simultaneously. The argument of both Popper and Bunge on quantum theory breaks down at the point where theory of relativity is coupled with quantum theory under the name, quantum field theory. By a complex process and reasoning, the stage was ready for the emergence of the phenomena known as quark and black hole. Quarks are particles named by Murray Gell-Mann who discovered or proposed the existence of the particle in 1963/4. For this, he was awarded a Nobel

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Prize in 1969. Also at about the same time in 1964 another physicist, George Zweig independently came to the conclusion of the same type of particle which he called "aces." Since Zweig's position was not widely known, or rather not published, the name "quark" is used in physics. According to the quark theory, all the known particles that interact via the strong nuclear force - hadrons - could be obtained out of simple combinations of three particles together with their anti-particles. There are thus, a number of types of quarks. These include at least six of what physicists call flavours. These are designated up, down, strange, charmed, bottom, and top. In symbolic form these are respectively: u, d, s, c, b, t. The quark configuration is changing due to the works of physicists like Sheldon Glashow, Sam Ting, Burton Richter and others. It is now being suggested that the quark scheme would require at least eighteen (18) quarks (6 flavours each in 3 colours) and 18 anti-quarks plus a number of particles called gluons which serve to carry the force binding the quarks together (McCusker, 1990 :1003); Gershtein & Logunov, 1981 : 488-9). With these proliferation of hadrons, quarks, leptons, electrons, neutrinos, etc.; and the situation in high-energy particle physics in which particles sparkle with enormous energy among themselves, bouncing in and out of existence; collide, transmute and disappear; it is meaningless to talk of fundamental or elementary particles. Given the nature of quarks, it could be postulated that what we may eventually consider to be "elementary" could be a composite smaller particles. It is important to note that nobody has yet seen a free quark. But physicists believe that quarks exist! Experiments with quarks and anti-quarks, matter and anti-matter by causing them to collide, have		established a reliable method of creating new forms of matter. The search for elementary particle has come to a dead end. This dead end has given rise to the search for a theory that will unite both the micro-world and the macro-world physics. The results of the search are the emergence of unified theories in physics. We had earlier hinted at the attempt made to integrate the theory of relativity with quantum theory under the new name of quantum field theory. Although "quantum" and field are contradictory phenomena, the idea of quantum field theory has yielded some positive experimental results. Quantum field theory coupled with Bell's theorem will necessarily lead to the conclusion that all parts of the universe are interconnected. John Bell's inequality theorem was about the concept of hidden variables. Einstein had objected to quantum theory on the grounds that it promotes indeterminism in physics. Einstein also noted that distant events cannot instantaneously influence local events without any mediation. This second assertion of Einstein concerned local causality, which should not be violated. It is further suggested by some physicists that the indeterminacy principle exists so far, because all the facts about physical reality are not yet known. When these facts, or hidden variables are known it will be possible to be very determinate and precise about physical reality. The mathematician and physicist Von Neumann devised a mathematical proof to show that there cannot exist such hidden variable. John Bell showed that Von Neumann's proof did not concern quantum theory and was therefore irrelevant. Bell put forward a mathematical formulae which showed that the local causality condition was violated by the quantum theory and that the hidden variable exists. This brings the issue to a non-local, non-objective reality which entertains the

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idea of action-at-a distance in physics. Physicists opposed to quantum theory and its Copenhagen interpretation were alarmed that mysticism and telepathy have been admitted into physics. This they argued, was because the mystics' claim that all parts of the universe are instantaneously interconnected. Furthermore, telepathy has been shown to exist, that is, it has been verified. Bell's mathematical inequality theorem suggests the following approaches to physics: (1) At the so-called fundamental level of physical reality, the separate parts of the universe are connected in an intimate and immediate way, (2) If the statistical predictions of quantum theory are correct, then some of our customary opinions about the universe are faulty. (3) Some of the consequences of quantum theory also affect the macro-world. Telepathy, clairvoyance, psychokinesis, bioenergy, mysticism are all parts of reality. More will be said of this shortly. It is appreciated that the grand unified theories (GUT) implies that matter is a passing phase in the evolution of the universe, and that the super-symmetry theories suggest that the universe may have evolved in ten dimensions. These ten dimensions have degenerated to four remaining dimensions, which now account for all the four available forces. Despite the problems attendant upon these field theories, grand unified theories and the like, one thing is significant: physics in its deterministic and indeterministic moods cannot explain or account for some aspects of reality. Given this scenario in physics, relativism, indeterminism, probabilistic and possibilistic tendencies in the interpretation of physical theories cannot be wished away. These are parts and parcels of realistic physical perception of the universe. These tendencies are not only present at the atomic and sub-atomic aspects of physics.		They are also present at very large aspects like in astrophysics and cosmology. The Newtonian physics we discussed ealier can no longer be the appropriate model for the whole of reality. With the emergence of theory of relativity and quantum theory, mass is no longer associated with a material substance. Following upon this realization, particles (of particle physics) are now conceptualized as bundles of energy instead of elementary substances that resemble dust, sand, or static three-dimensional objects. High-energy particles are now better conceptualized as four-dimensional, dynamic models or entities in space-time continuum. Developments in astrophysics have shown that the much-revered theory of relativity is not a complete theory, since it failed to account for the physicist how the world started off, but did predict that all physical theories including itself, break down at the beginning of the universe. Meanwhile, one of the problems Einstein and opponents of the Copenhagen interpretation of quantum theory articulated, is that quantum theory is incomplete. Einstein argued that quantum theory cannot explain and describe the whole of reality. Astrophysics has returned the same verdict on theory of relativity. The grand unified theory we hinted at earlier (union of quantum theory and theory of relativity) did not include the force of gravity (Hawking, 55; 84). Stephen Hawking, working on the physical phenomenon known as "black hole" realized that quantum theory and general theory of relativity affect each other. Astrophysicists and cosmologists had developed many models of the universe. In Einstein's general theory of relativity, he described how gravity works everywhere and at all times, except at the moment when the universe

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was minute or infinitesimal. At this atomic or particle level, Hawking reasoned that the theory of relativity and quantum theory should be applicable to the universe. Although it is true that the general theory of relativity deals with macro-objects like planets, stars, galaxies, etc; and quantum theory deals with atoms, particles, anti-particles, quarks, etc; these two major theories converge at the infinitesimal sub-atomic level. In Einstein's cosmology, the universe was static, but contained a new concept of "anti-gravity" force which did not come from any source. He also asserted that the universe has an in-built capacity to expand in such a way that there will be a balance of attraction of matter that will result in a static model. The Russian physicist and mathematician developed a mathematical model which explains the non-static nature of the universe. The physicist was Alexander Friedman. Friedmann arrived at the conclusion of a non-static universe from two assumptions. The first is, that the universe looks identical in whichever direction we look. The second is that the first assertion would be true even if we were observing the universe from anywhere else. Also, another Russian, George Gamov (a former student of Alexander Friedmann) suggested that the early universe must have been very hot and dense, glowing with white-hot. It should also be stated that the Friedmann model of the universe has produced three possible interpretations. The first is the expanding universe interpretation. The second is the steady state universe interpretation. The third is the contraction universe interpretation. Of the three, the most preferred by physicists is the expanding universe model. The very hot and dense beginning suggested by George Gamov fits into the Big Bang hypothesis of the origin of the universe. When the hypothesis of the		Big Bang is married onto the expanding model of the universe, the second law of thermodynamics suggests that the universe would have a thermal death. This would be so, the reasoning suggests, because the Earth will be losing heat and energy without replenishment. Stephen Hawking postulates that contrary to such reasoning, the universe has no beginning in time; and that space-time has no boundary; and no causation as in quantum theory. In the words of Hawking: "The boundary condition of the universe is that it has no boundary. The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE" (Hawking, 144). Hawking suggests that God has no role in the universe. Now, Hawking's hypothesis or theory cannot be proved to be correct or false. He realizes this when he stated that "we could never be quite sure that we had indeed found the correct theory, since theories cannot be proved" (Hawking, 178). Given the all - embracing nature of Hawking's hypothesis - a theory of everything - his hypothesis is incomplete. He admits that there are problems or questions concerning the universe to which he has no solution or answer. According to him, "although science may solve the problem of how the universe began, it cannot answer the question: Why does the universe bother to exist? I do not know the answer to that (Hawking, 1993 p.90). There is therefore a need for theories that are holistic in nature. The English mathematician and logician, Alan Turing writing on a topic: "Can a Machine Think?" has, among other things, made a case for extra-sensory perception. Extra-sensory perception includes the following phenomena : Telepathy, clairvoyance precognition, and psychokinesis. Turing observed that "these disturbing phenomena

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seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy is overwhelming" (Turing, 1991p.512). It may be necessary to consult the following works in order to be aware that there exists enormous evidence for the reality of extra-sensory perception: Lawrence Leshan's The Medium, the Mystic and the Physicist; Shiela Ostrander's and Lynn Schroeder's Psychic Discoveries: Behind the Iron Curtain ; Jeffery Mishlove's The Roots of Consciousness (Psychic Liberation Through History, Science and Experience; and Thelma Moss' The Probability of the Impossible (Scientific Discoveries and Explorations in the Psychic World), to mention just a few. The mathematician, physicist and philosopher, Bertrand Russell in Mysticism and Logic has characterized the features of mysticism. Before doing so, he showed the elements of mysticism in a number of early scientists, especially in antiquity. Bertrand Russell's list of scientists with elements of mysticism in their work must be up-dated a bit to include Pythagoras, Theophrastus Bombastus von Hohenheim - also known as Paracelsus, John Dee, Johannes Kepler, Wilhelm Leibniz, Isaac Newton, and many more in the modern era, (Mishlove, 1975). According to the characterization of Bertrand Russell, mysticism has the "belief in the possibility of a way of knowledge which may be called revelation or insight or intuition, as contrasted with sense, reason, and analysis, which are regarded as blind guides leading to the morass of illusion." The second characteristic of mysticism is its belief in unity and its refusal to admit opposition or division anywhere. The third feature of mysticism, according to Russell, is the denial of the reality of time. The fourth and last feature of mysticism, Russell		asserts, is the belief that all evil is mere appearance, an illusion produced by the divisions and oppositions of the analytic intellect. Mysticism does not maintain that such things as cruelty, for example, are good, but it denies that they are real: they belong to that lower world of phantoms from which we are to be liberated by the insight of the vision (Russell, 1925). These features of mysticism are found in the writing and utterances of modern physicists. On ways of knowledge of the mystic, the physicist shares the same view. From Albert Einstein through Sir Arthur Eddington, Werner Heisenberg, Alfred North Whitehead to Stephen Hawking there is the view that empiricism and sensory perception can never give a true picture of reality or nature. For instance, Einstein argues that, "since, however, sense perception only gives information of this external world indirectly, we can only grasp the latter by speculative means (Einstein, 1958). Alfred North Whitehead says something that covers the four characteristics of mysticism. According to him, "the new view is entirely different. The fundamental concepts are activity and process… nature is a theatre for the inter-relations of activities. All things change, the activities and their interrelations… In the place of the Aristotelian notion of the procession forms, it (the new physics) has substituted the notion of the forms of process (Whitehead, 1934 :36). On unity and the illusion of division anywhere, Einstein is quoted as saying he found his theory of relativity because he was so strongly convinced of the harmony of the universe (Reichenbach (1959), 253: In Schilpp). In another place Einstein and Infeld wrote: "Throughout all our efforts, in every dramatic struggle between old and new views, we recognize the eternal longing for understanding, the ever-firm belief in the harmony of our world …" (Einstein &
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Infeld, 938, 1966 :296). Heisenberg in turn classifies modern science …not into different groups of objects but into different groups of connections… the world thus appears to be a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole (Heisenberg, 1958 : 107). On the mystics' denial of the reality of time there are corresponding views by eminent physicists. Louis de Broglie put it this way: "In space - time, everything which for each of us constitutes the past, the present and the future is given in block, and the entire collection of events, successive for each of us which forms the existence of a material particle is represented by a line, the world line of the particle. Each observer, as his time passes, discovers, so to speak, new slices of space - time which appear to him as successive aspects of the material world, though in reality the ensemble of events constituting space - time exists prior to his knowledge of them" (de Broglie: In Schlipp, 1959 :114). Stephen Hawking puts the matter in a way very similar to that of the mystics. According to Hawking, "…the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations…what we call real is just an idea that we invent to help us describe what we think the universe is like." According to him, "a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds (Hawking, 1988:147). On the assertion that, the belief that all evil is mere appearance, an illusion produced by the divisions and oppositions of the analytic intellect, the theoretical physicist, Henry Margenau has a parallel from science: "In my view…natural science contains no normative		principles dealing with ultimate goals; physical reality is the quintessence of cognitive experience and not of values… To know physical reality is to know where to look when something is wanted or needed to be seen; it is to be able to cure when a cure is desired, to kill when killing is intended. But natural science will never tell whether it is good or bad to look, lacks the premise of an 'ought'," (Margenau, 1950:326). With the quotations from physicists of the modern era, it is easy to notice the correlation between mysticism and physics. We should also remember that there are religious mystics. The Muslims and the Christians have their respective mystics. Some Christian mystics have turned into church founders and the establishers of what could be termed "church exploitative industries." Modern physics has implications for religion, economics and politics.


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			an aboriginal, eminently real, transcendent creator, at whose imposed will it obeys, is the fallacy which has infused tragedy into the histories of Christianity and Mohammedanism." Whitehead again appropriately observed that "when the Western world accepted Christianity, Caesar conquered; and the received text of Western theology was edited by his lawyers", (Whitehead, 1929, 1957: 519). This God was, or is anthropomorphic in nature, and was made to belong to a particular people, despite the assertion that God is of the universe. This God is a male who can be made to be angry and lead some parts of humanity to war. This God resembles the Greek gods of antiquity. Modern physics invites religious people to conceive reality (and probably the God concept) as embracing the whole of the universe. If God is one with the universe, it is logical to ascribe a particular quality or predicate to not God. Following Stephen Hawking's A Brief History of Time: (God and) the universe has no beginning and no end! A universal God would not have to interfere in the day-to-day affairs of the universe. If the uncertainty principle and theory of relativity are acceptable, then probability and the inter-relatedness of different sections of the universe has to be accepted. And I think that these theories have to be accepted. If for no other reason, for the fact that these theories have been vindicated by series of technological devices using them. Accepting these theories does not mean that the theories represent the whole of reality. To a large extent, scientific theories and theories about God are human creation. Since human beings are fallible, allowances should be made for the fallibility of our theories of God as well. This is an invitation for dialogue among religious groups and for
CHAPTER
		9
PHYSICS, RELIGION AND THE SOCIETY

Relevance of modern physics to religion _Modern physics changed the deterministic world-view to a combination of determinism and indeterminism of individual; specific entities or events. The dethronement of singularities and rabid dogmatism in relation to scientific laws has a direct consequence on religion. Also the realization that scientific theories are human creation which may not necessarily be proved to be true is of great significance. Furthermore, the concept of space - time continuum, the view that the universe is timeless and without boundary, and the view that ensembles, fields and events are simultaneously inter-related in the universe are some of the features of modern physics. The first hammer falls on the religious view of God as the unmoved mover. This emanates from the ultimate and elementary basis of the universe. Alfred Whitehead has also traced the idea of the "unmoved mover" to Aristotle. The element of the unmoved mover can be found in Newton's first law of motion. In theological and ancient cosmological parlance, the 'unmoved mover' is an all-powerful, omniscient, authoritative creator of the world. The laws of this God must be obeyed and deviants are severely punished. Whitehead has also pointed out that the notion of God as "eminently real" is a favourite doctrine of Christian theology. As Whitehead correctly observes, "the combination of the two into the doctrine of

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the accommodation or tolerance in matters religious and scientific. The Newtonian and anthropomorphic conception of God had led many to supplication and prayer to God for favours. In a football match, for instance, two opposing teams will be praying that God favours their team! A universal being or God that accedes to such prayer will cease to be universal. Similarly, a benevolent God of love as a doctrine has the difficulty of explaining evil as conceptualized in Christian theology. As Einstein has pointed out, if such an Almighty God punishes offenders, the implication is that God is judging and punishing himself as the creator of such offender (Einstein, MCMLIV : 59). Indeed, it strikes me as strange that God will allow Africans, for instance, to be subjugated and dehumanized by other human beings and a God of love will be watching. Now, it has to be stated that anthropomorphic God leads necessarily to atheism. This is the type of God Nietzsche declared is dead. Mysticism, science and Marxism have to be incorporated in any form of religion that will have to be relevant today and in the period ahead. In the sphere of economics, and politics, the Newtonian physics re-inforces authoritarianism and rabid materialism. The result is capitalist economy, dictatorship, gross abuse of human rights, wars, colonization, and neo-imperialism. Even some interpretation of Marxism is tainted with Newtonian and Laplacean determinism. An uncreative and dogmatic Marxism is bound to crumble. Yet, Marxism as an economic framework, is the theory that will save mankind from self-destruction. The logic of capitalist economy is the maximization of profit by the few who control the means of production and distribution.		This maximization of profit drive which leads to war of conquest and annihilation of people fails to realize that an act in one part of the globe necessarily affects other parts equally. The conquest (pacification) and partitioning of Africa in Berlin did not bring peace to those who ravaged Africa. Instead of peace, world wars took place. The exploitation of people of the third world and the terrorizing of their citizenry through economic and political agents have led to further terrorism world-wide. The degradation of the environment in particular parts of the globe, has led to environmental problem the world over. It is not unlikely that the quest for material wealth could lead to the temptation of wiping out a whole race. Such a mad attempt would definitely lead to the wiping out of the human race. Lessons in molecular biology, history, ecology, psychology, economics and sociology suggest that the current trend of globalization on a capitalist and dictatorial platform will eventually spell the doom of mankind if not reversed to a humanitarian platform. Conclusion We divided physics into two tentative parts: Macro - physics and micro - physics. Physics has been shown to follow some traditional methods in cognition, formulation of theories and carrying out of experiments. The dichotomy between "facts" and theory was in vogue at an earlier period in the development of physics. The physics of Aristotle, Archimedes, Galileo and Newton had been shown to be adequate as far as the domain of operation is concerned. In other words, physics at the macro-level has limited application. The theory of relativity of Einstein maintained some features of macro-physics but revolutionized concepts of space, time, gravity and cosmology. In terms of determinism as a concept, Einstein's

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physics can be grouped with macro-physics although Einstein contributed to the establishment of quantum theory. Logic was explored and the conclusion was reached that Aristotelian logic had reigned for about two millennia because of its utility as a compass for valid reasoning. However, it was noted that there were areas of intellectual endeavour in which Aristotelian logic together with the laws of thought did not apply. Other forms of logic were suggested in such situations. The symbolic logic in use is a combination of Aristotelian, Boolean and sometimes, modal logic. A different type of logic making use of some of the symbols of traditional logic is suggested for quantum theory. Such an alternative logic, known as quantum logic has already been developed, despite the trail of criticisms following its formulation. Entirely different types of logic will continue to spring up. In the sphere of mathematics, the various philosophies of mathematics were examined. The conclusion is that no one philosophy of mathematics is to be regarded as complete. In geometry, for instance, Euclidean geometry was found not to be very adequate for the theory of relativity. Non-Euclidean geometry that was developed earlier came to the rescue. In algebra, the scatter matrix played the role useful in quantum theory. The paradoxes in mathematics coupled with Godel's incompleteness theorem drew the attention of physicists to the fact that mathematics is not physics, but more like artistic creation. In the area of philosophy of science, many schools were surveyed either directly, or for some, indirectly. Empiricist/logical positivist school, rationalist, realist and critical realist/critical rationalist schools were examined and found to capture only partial aspects of the scientific enterprise.		Even the historical, sociological and revolutionary approaches to the philosophy of science turned out to be partial reflections of what goes on among working scientists. Indeed, it is dialectical materialism that could qualify to be the proper representative of the school known as realism. This school makes use of dialectical logic and adheres to Vladmir Ilich Lenin's model in which he defined matter as "a philosophical category denoting the objective reality which is given to man by his sensations and which is copied, photographed and reflected by our sensations, while existing independently of them", (Lenin, 1977:114). This school believes that reality is knowable through scientific method alone. This is the problem with this particular school. Other forms of cognition are left out. What is required is to have a holistic approach to reality. In this regard, modern physics will have to incorporate the gains of classical, macro-physics into the theory of relativity and quantum theory. Like Fritjof Capra the theoretical high - energy physicist observed, "science as a whole would be complemented by the intuitive ways of poets, psychics, mystics and many other equally valid approaches. This approach will be the justification for a hard-core physicist becoming a religious leader, mystic or politician.


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INDEX

Motion of bodies 11, 15

MSRP 154

Munchhausen trilemma 148

Nebulous universe 39

Newton's laws of motion 28

Newtonian mechanics 12, 36, 74

Non-static universe 168

Observation statement 45

Permeability constant 75

Phenomenalism 41, 48

Photoelectric effect 38, 103

Photoelectrons 103

Photons 38, 57, 103

Physical theory 86, 92, 96

Platonism 126, 137

Possibilistic logic 14

Positivism 5, 19, 140

Precognition 169

Primum mobile 16

Protocol sentences 46

Psychologism 26, 148

Quantisation of energy 38

Quantum chromodynamics 163

Quantum field theory 165

Quantum logic 60, 134

Quantum mechanics 40, 60, 106

Quarks 7, 164

Radiation 97

Rayleigh - Jeans law 101

Relativistic momentum 81

Relativistic physics 79

Religious mystics 173

Scalar functions 90

Scalar matrix 120

Sense - data 45, 49, 70

Grand unified theories 166

Gravitational equilibrium 24, 26

Gravitational force 10

Hadrons 164

Hegel, F., 4

Heliocentric 9

Inertial reference frame 11, 72

Instrumentalism 94, 156

Intuitionism 26, 126

Judgements of existence 50

Kinetic energy 82

Kinetic molecular theory 46

Kinetic theory of matter 67

Labachevsky's geometry 12

Laws of thought 53

Linguistic philosophy 43

Logical atomism 41, 45

Logical positivism 39, 41, 50

Logical truth 42

Lorentz force 76

Lorentz transformations 13, 80

Lucretius 6

Macro-particles 96, 109

Marx, K., 5

Maxwell's equation 71, 77, 91

Mass 29, 41

Materialism 6

Mathematical theories 91, 93

Matrix quantum mechanics 107

Mesons 7

Metaphysics 5, 24, 40

Michelson - Morley experiment 70, 78

Micro-entities 96

Modal logic 50

Modus ponens 63, 132

Momentum of particle 29, 81

Absolute zero 45, 68

Acceleration 33, 41

Almighty God 176

Ampere's law 74, 89

Analytic truth 42

Anti-empiricists 132

Anti-gravity force 168

Anti-matter 49

Apodictic truth 124

Archimedes' principle 22, 25, 51

Aristotle 9, 15

Assertoric truth 124

Astrophysics 36, 167

Atomic theory 6

Axiology 5, 114

Axiomatic geometry 118, 121

Big bang theory 37, 137

Black body radiation 38, 99, 102

Black holes 84

Categorical judgements 50

Categorical syllogism 62

Christian bible 37

Christian mystics 173

Christian theology 174, 176

Clairvoyance 169

Classical physics 70

Commutative law of multiplication 108

Comte, A. 5, 40

Confirmationism 41

Constructive dilemma 64

Copenhagen interpretation 110, 113, 135, 162

Corpuscular theory of light 37

Coulomb's law 76, 87

Curved space - time 83

Cybernetics 60

Darwinism 139

Deductive logic 144

Deductive - nomological model 66, 68

Democritus 6

De Morgan's rule 64

Diagonal matrix 120

Dialectical quantum 13

Double negation 65

Early universe 168

Egyptian civilisation 6

Einstein's equation 34, 42

Einstein's theory of relativity 15

Electromagnetic theory 70, 74, 77

Electrostatic force 87

Empiricism 26

Entropy 45, 55

Epicurus 6

Epistemology 5, 26

Equipartion 100

Ether 77

Fallibilism 14

Falsificationism 140, 153

Faraday's law 76, 91

Four-valued logic 13

Fundamental particles 164

Fuzzy logic 14

Fuzzy set theory 13

Galilean transformations 12, 70, 77

Gauss' law 75, 89

General theory of relativity 40, 83

Geocentric 10

Globalisation 56

Gluons 7

God of love 176

189

190



Set theory 54 Simultaneity 79 Singularities 84, 174 Special theory of relativity 70, 82 Speed of light 39, 79 Square matrix 120 Steady state universe 168 Stefan - Boltzman law 99 Stoke's formula 90 Structure of reasoning 134 Sub-atomic level 116 Syllogism 61 Synthetic truth 42 Telekinesis 98 Telepathy 166, 169 The theory of excluded middle 58, 132 The law of non-contradiction 58, 56 The law of sufficient reason 60 Thermodynamics 44, 55 Theory of meaning 41 Three - dimensional space 90 Three -valued logic 50 Time dilation 79 Traditional African 147 Triangular matrix 120 Two-valued logic 60 Undecidability theorem 131 Unified field theory 117 Universal God 175 Unprimed frame 80 Vector 29 Vector field theory 90 Velocity 30, 77 Verificationism 41, 47 Vienna circle 40, 46		Wave theory of light 38, 104 Wavicle 39, 57 Zero matrix 120


	191

physics deals with issues that are material as against spiritual ones. In other words, matter is decisive in nature and not spirit. This belief in matter as the stuff of which the universe is made is also tagged materialism as against the belief in ideas, spirit or God which is tagged idealism.

This materialistic world-view relies on the atomic theory. The atomic theory was well developed in the mystery school of ancient Egypt. With the collapse of the black Egyptian civilization and the ascendance of Greek and subsequent European civilization, there is hardly any mention of ancient Egypt as the originator of the atomic theory.
The atomic theory was developed in a culture that was ruled by mystics, religious leaders and technocrats. The atomic theory could not, under such circumstance, be divorced from philosophy. Democritus who transported the atomic theory to Europe was not in any intellectual position to elaborate on the many aspects of the theory.
The atomic theory had been expounded also by Epicurus and Lucretius in antiquity. Scientists like Galileo, Boyle and Newton made use of the atomic theory in their scientific investigation. Materialism as the foundation of the sciences gained further ground when it was articulated that matter could exist in gaseous, liquid and solid forms. It is therefore not surprising that contributions to the development of physics came from chemistry, engineering, mathematics and biology. The atomic theory was developed by John Dalton in the field of chemistry. Although some of the conclusions of Dalton may now be said to be faulty, he made great strides in chemistry of his time. According to Dalton, everything is made of atom which is not divisible. By the1920s the atom was said to be

made up of electrons orbiting a nucleus which is itself made up of protons and neutrons. Today, we have a deluge of fundamental particles, which include protons, neutrons, electrons, neutrinos, quarks, gluons, mesons, and many others that are approximately 100 in number.
The new interpretation of the meaning of atom implies that we now have two brands of physics to deal with: physics at the MACRO-LEVEL of existence and physics at the MICRO-LEVEL of existence. If physics is studying reality, will there be any justification to have two or more answers to a question about any particular phenomenon? Should we discard all that Galileo, Newton, Einstein and their contemporaries did in the light of developments in particle physics? Where should the exploits of mystics and spiritualists be located in the body of knowledge of events that are material? Attempts will be made to address some of these questions in this book. We shall start by reminding ourselves of some of the theories of physics at both the macro and later the micro levels.

Macro-level physics
We shall examine theories at the macro-level of physical existence in a random manner that will cover some topics in mechanics, heat, light, sound, electricity, energy. Although similar terminologies and concepts are sometimes used for certain phenomena at the macro and micro levels of physical existence, the meanings are not always static.
Mechanics as a discipline studies forces and the effects of forces on matter (or on things that are material). Material things occupy space and have weight. Given these characteristics of matter,