The methodology of Science vs Metaphysics

THE METHODOLOGY OF SCIENCE AND METAPHYSICS

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THE METHODOLOGY OF SCIENCE AND METAPHYSICSGeorge Mpantes mathematics teacher www. mpantes. gr

Abstract .

The methodology of science

Positivism

Metaphysics

Pythagorean philosophy of numbers

The methodology of scienceIn the book the evolution of scientific thought, Abraham D 'Abro presents the methodology of science (Physics) from its first steps, from Galileo and Newton, until today. He claims that this methodology is the message for each meaning we ascribe to the world from the perspective of science. The natural philosophy is finally a philosophy of science and through the methodology of science, it breaks off all contact with the traditional philosophy, which D 'Abro rejects as it tries to interpret the results of physics with the arbitrary ways of an unskilled ....Clifford in his popular essays , voices the scientific attitude with increased emphasis when he writes: the name philosopher , which meant originally lover of wisdom , has come in some strange way to mean a man who thinks it his business to explain everything in a certain number of large books. It will be found , I think, that in proportion to his colossal ignorance is the perfection and symmetry of the system which he sets up; because it is so much easier to put an empty room tidy than a full one . these opinions prove that there exists a definite misunderstanding between scientists and philosophers; a misunderstanding which might easily have been avoided had philosophers possessed a proper realization of their inevitable limitations when discussing scientific matters. The simplest way to approach the source of the trouble appears to be to anlyse the methods of scientists and ascertain in what respect they differ from those of philosophers..Greek philosophers, metaphysicians, a-priorists, neo-realists and all the -isms have no reason to natural philosophy, which reaches its perfection through the theories of mathematical physics... it arises that the distinction between idealism and realism is purely academic in science, for our rule of action will be the same whichever of the two opposing philosophies we may prefer...we must agree that the theoretical physicists must be called philosophers, they are the philosophers of the inorganic world , as the pure mathematicians might be called the philosophers of abstract relations..The "method" is, claims D 'Abro, the only thing we can discuss about all questioning of philosophers, the scientists continue completely independently of the philosophers, and the scientific branch is faithfully following its own methodology, which is associated with philosophical views of the majority of physicists and mathematicians .Through a variety of examples from the development of theoretical physics, essentiallyan overview of the entire of physics, (mechanics, field theories , etc. phenomenological theories) establishes the central dogma of scientific methodology that it consists in coordinating and linking together in a rational manner a number of experimental facts , with the maximum of simplicity. By a rational way we mean primarily according to the rules of logic. As for the criterion of simplicity , which enable us to select one co-ordination rather than another ,it appears to be linked with our valuing of the expenditure of effort. Thus even a dog finds it simpler to enter a house by the front door rather than clamber in through the back window...In the more elementary cases , the procedure is one of commonplace , logical and inductive reasoning; but in the more advanced cases the process is exclusively mathematical. Nevertheless, as the methods of co-ordination are essentially the same in all cases , the mathematical ordinations , in view of their greater clarity , can be studied to advantage as typical instances in this respect.As for the problem of knowledge it appears necessary to approach it by the usual method of scientific investigation:

Knowledge is a construct or co-ordination in which our sensations enter merely as fundamental elements; judgment and interference enter into knowledge. For instance when as a result of our visual and tactual sensations we recognize that a table is there before us , we are claiming knowledge. But visual and tactual impressions by themselves do not constitute knowledge. . so we should recognize priority to the awareness of the senses than in so-called direct revelations of perception ...This theory for empirical origin of knowledge, is applied to our understanding of space, time, matter, motion, atomism of matter and light, etc., and gives us the sense of reality.The reality for science says D 'Abro, has a special meaning, which is produced of our scientific knowledge about the world, that is determined by the methodology of science and not disclosed elsewhere.

.but this reality, once again, is nothing but the expression of the simplest co-ordination of facts: no genuine metaphysical reality is implied. If we discard the criterion of simplicity , we may conceive of our world as many different ways as we please. For example the double bending of a ray of light , and Mercurys motion , would be accounted for by a modification of the Newton law of gravitation ..

The co-ordination of methodology consolidates the difference between the substance and structure of the world, and science to yields the second with the logical co-ordinations of methodology. The co-ordination can not assign the substance, it is simply a co-ordination. Science does not explain , it describes! The substance may change in nature , yet no difference will be perceived ; but if the relationships are modified , a new world will divulge itself to our observation.For the reality of substance .the mathematical equations are nothing but relations , and from initial relations all we can deduce are other relations. In other words , our equations can never yield us more than we originally put into them. It follows that were all relationships in nature to be preserved and the substances change , no observable difference could be detected; and we should never be able to differentiate between a whole class of worlds identical in structure but differing in substance. .If, then, we discard the procedure of the mystic , or of the metaphysician who claims a knowledge that cannot be submitted to the control of experiment , we must recognize that substance escapes us completely and that our knowledge of the real word can at best reduce to a skeleton or structure.

For the reality of structure which the metaphysician would defend (quite aside from the reality of substance) presupposes his a priori belief in the inevitable simplicity of nature. But simplicity is, after all, but an expression of human appreciation. So the structure, is our construction and we can not identify reality with the structure that we gave it. The reality is defined by the simplicity of our co-ordination not the supposed simplicity of nature. Nothing is assumed a priori, and this pragmatic sense of reality is that of the methodology of science. Boyle said, "I do not want stories about the truth of reality, only consistent theories" and the Larmor the laws of nature are, after all, but laws of mind" and

...I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism , where they are under our control, to the intangible heights of a priori . this is particularly true in our concepts of time and spaceEinstein

.. Of course the type of reality which we have been branding as elusive is the absolute reality , the true being of the metaphysician. The scientist also appeals the word reality but he employs it in a different sense. For him, reality is identified with simplicity of co-ordination , and he states his view explicitly, realizing full well that a reality of this type is far from being absolute and that is essentially pragmatic. It is for reasons such as these that the vast majority of scientists are agnostics in heart , not on account of any a priori predilection , but because a proper understanding of the limitation of scientific Knowledge leaves them no other alternative , refusing as they do to accept the Knowledge of the mystic of metaphysician as of any significance whatsoever. But scientific agnosticism must not be confused with that extreme form of idealism which denies the existence of any world apart from consciousness. It merely contents itself with stating that the objective world of science is nothing but the embodiment of the simplest co-ordination of sense impressions , for which some unknowable supra-intelligible world is assumed to be responsible..What is the program of the pragmatism that characterizes the scientific reality? What it consists the value of scientific knowledge?

It consists of the provision which can yield for the evolution of natural systems, 'nearby'. The quantitative reduction favors the mathematical investigation which 'runs' cognitive development and create forecasts. This generates the impression-the assumption that mathematical analysis is applicable to the physical world (mathematical hypothesis). This case could bring us a 'metaphysical' meaning to our world, but D 'Abro, removes this version (mathematical hypothesis).Here we must recall that however mysterious it may seem , nature appears to be amenable to mathematical investigation and to be governed by rigid mathematical laws , at least to a first approximation . So far as scientists are concerned , this belief is not the outcome of religious or philosophical presuppositions. Rather is a belief which is forced upon our minds by the triumphs of theoretical physics, the first grand example Newtons celestial mechanics. But a closer microscopic survey might prove that this appearance of mathematical purity and simplicity in nature was due to our crude macroscopic survey of phenomena. For instance, if the conditions are sufficiently chaotic , the chaos will generate simplicity when we view things from a macroscopic standpoint; it is only when we wish to view things microscopically that the chaos appears and mathematical methods become impossible. .So finally what is the nature of a scientific theory?

So, the methodology of physics defines the concept of the reality of science, a 'becoming into being' , but all this is a reality for specialists, who will speak about it coldly and objectively, without the warmth of a meaning, plan, or purpose, without qualities, without any poetic relationship with man - unknowable supra-intelligible world - a meaningless becoming which is to be there, and tending nowhere. But this is the only knowledge that helped man in his survival and his dominance of nature.Obviously (continues D Abro) there is nothing in the nature of an explanation in a scientific theory. Phenomena are not explained; they are merely interconnected , or described in terms of their mutual relations. As a matter of fact , there is no cause to be surprised at this failure of science to explain phenomena, the failure arises not from the limitations of science ,but from the limitations of the human mind itself. All we can ever do is to interpret A in terms of B , and B in terms of C. However far we go, we can never avoid an ultimate unknowable agent.Thus the Greeks wondered why the earth did not fall. An explanation was soon forthcoming. The giant Atlas holds it on his shoulders. But what, then , prevented the giant Atlas from falling together with the earth he was carrying? The nether region on which he stands gave him a support. This is as far as the explanation went , for no theory seems to have been advanced explaining why the nether regions did not fall with the Atlas and the earth.

We might consider more scientific examples; but we should find that the case is always the same. A is described in terms of B, B in terms of C, and so on. Consider the phenomenon of gravitation. Does any one really imagine that Newton and Einstein has ever attempted to explain gravitation? To say that gravitation is a property of matter or a property of space-time in the neighbourhood is just as much of an explanation as to say that sweetness is a property of sugar; for in last analysis , what is matter, what is space-timw? If we say that matter is an aggregate of molecules , atoms, electrons, protons, what of it? What are electrons? what are protons? We can only confess our complete ignorance and while attempting to reduce the number of unknown fundamental entities to a minimum , content ourselves with describing the properties which appear to characterise them and the relations that appear to connect them. Clearly, those who seek explanations will find no comfort in science. They must turn to metaphysics..Well what do we do with reality? We describe a behavior, pieces of it , fromA to B, "essentially setting up traps" in affairs of reality, trying to handle making small steps toward knowledge. So just as manipulated the numerical series in the first investigations of infinity. Now we can say as epilogue that the natural philosophy is the philosophy of the methodology of science. Nothing is assumed a priori, and this pragmatic sense of reality is hidden in the methodology of science, the essence of our reality escapes us completely, all that we hope to know is the structure, but the structure, viz the simplicity in co-ordination etc, is our discovery and we can not identify reality with the structure we gave it, the world is unknowable . There is no ultimate reality, the reality is the scientific image we construct for it. An example of metaphysics: the Pythagorean doctrine .

This text of D 'Abro is the epitome of positivism as described in the books of philosophy:....... The process of thinking of man passed three stages, three situations, the theological, the metaphysical and the positivism. Metaphysics has no place, because it seemed to be vain to ask for principles, substance, purpose in things . The human science must be limited to the phenomena, to study with the intention to find their own laws, in order to predict and to dominate, to benefit from the beneficial and avoid harmful. Our knowledge ensures the power over nature as it had been thought up by Bacon and the English empirical. The most remarkable of the problems dealt philosophy will find their effortless and natural solution in the sciences. This is the meaning of positivism (Theodoridis).But the metaphysical questions never end, and always follow the discoveriesof science, as science was born by the metaphysical searching. The men we now call scientists once called philosophers, and we know that Newton, the father of the scientific method, apart from mathematics and physics dealt with alchemy and theology, and the study of history in relation to the prophecies (David Ruelle).

This deep root of metaphysics is revealed very clearly in the comment of Heisenberg

In this connection , one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all-in spite of the fact that these sentences produce some kind of picture in our imagination; e.g the statement that besides our world there exists another world ,with which any connection is impossible in principle , does not lead to any experimental consequence , but does produce a kind of picture in the mind . Obviously such a statement can neither be proved nor disproved. One should be especially careful in using the words reality, actually etc., since these words very often lead to statements of the type just mentioned...

Such a world, an invisible world of our mind, is the world of mathematics in the case of the Pythagoreans, this world exists in minds of many scientists until today. Today many people of science are Pythagoreans.

THE PYTHAGOREANS .What is the metaphysical view of the mathematical hypothesis?

There is un unspoken hypothesis which underlies all the physical theories so far created, namely that behind physical phenomena lies a unique mathematical structure which is the purpose of theory to reveal. According to this hypothesis , the mathematical formulae of physics are discovered not invented, the Lorentz transformation , for example ,being as much a part of physical reality as a table or a chair. ( RELATIVITY: THE SPECIAL THEORY J.L.Synge p.163)

This "unspoken hypothesis" is a metaphysical hypothesis , the survival of the Pythagorean doctrine that "everything is number", which nowadays is read "everything is mathematics"Indeed we read the same sentence as above (Synge) written seventeen centuries ago:

.. The causal approach to nature consists in positing mathematical things as causes from which the objects in the perceptible world arise. The Pythagorean belief was that only what was possible in mathematics was possible in the structure of nature , and nothing could exist that implied a mathematical impossibility.Iamblichus 4o century BC.. The doctrine that the number is the essence of all things, past through the prism of countless philosophical currents, remains the central idea of Western science, the necessary key of its coordination . And one more thing: the fact that this key opens many locks, has praised many times but has not been explained (Berlinsky)Besides, when Galileo proclaimed the great scientific revolution of the West, saying that the book of nature is written in the language of mathematics, again formulated the same Pythagorean dictum, since mathematics is the manipulation of numbers.The number is the first principle says Pythagoras, "something that can not be defined, incomprehensible, and encompassing all the numbers." (Berlinsky)The Pythagoreans were never able to explain what they meant when they said that the number is the essence of everything... Pythagoreans, as they are called, devoted themselves to mathematics; they were the first to advance this study, and having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being -- more than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunity -- and similarly almost all other things being numerically expressible); since, again, they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modeled after numbers, and numbers seemed so be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. (Aristotle Metaphysics, I, 5)

The origins of this doctrine may be in the Eastern influence. Having traveled to Egypt and Babylon, Pythagoras might have been influenced by numerology, which deals with numbers and mystical relations among them, that was common in these two regions.The core of the Pythagorean doctrine is that number is the essence of things, and more translated the mathematical design of nature, indeed very attractive! We can understand every thing by numbers only as every object has a number that is characteristic to it. Philolaus (fourth century B.C.), a member of the Pythagorean school, is reported to have said that all things which can be known have number; for it is not possible that without number anything can either be conceived or known.[Heath, p. 67].Indeed throughout science, discoveries were made after accepting areality as a natural equivalent of a mathematical object. The waves of Hertz approached first by mathematics, and without the mathematical work of Green Stokes etc., the Maxwell field would not get physical subsistence. Dirac actually approached the relativistic electron as a mathematical object and discovered the positron. Yet many believe that this mathematization of physics today, is its most important tendency, and may ultimately be the last. How mush can we accelerate hadrons at CERN; they wonder. How we shall approach reality beyond these limits? Only with the numbers of Pythagoreans? But we must not forget the ultimate unknowable agent of the scientific explanation!After the Pythagoreans the most influential group to expound and propagate the doctrine of the mathematical design of nature was the Platonists, led, of course , by Plato. From here the distance until to the ideal world in which there were absolute and ultimate truths is very small. The later Pythagoreans and the Platonists distinguished sharply between the world of things and the world of ideas that is the inevitable termination of the metaphysical doctrine everything is numberBut if we compare the description of D'Abro on the methodology of science, namely the role of mathematics, given on pages 2, 3, this role is far from any structure and substance of metaphysical status, viz i n t h e m s e l v e s . Okey we can describe the structure with mathematics , but structure is but an expression of human appreciation (simplicity). On the other hand we can fabricate a mathematical model for any object of our fancy. Our mind constructs the structure before the mathematical model, (intuitionism) this model is our way of expression , as the words for poets. Behind the supposed mathematical design of nature is hidden the grand apparent operational definition of concepts which is supported from measuring, so from numerical indications. For positivists, mathematics is a free creation of human mind, having their own methodology, and may describe, or may not, some results of the domain of experience. Mathematics is an hypothetical truth. They install axioms and produce theorems: and so what? In 19O century , we had construct a mathematical model of the ether, which is expelled from physics, It is not a physical object , although it has a mathematical model.

So finally there are two worlds for humans, the invisible world of Pythagorean (mathematics) and the visible world of senses, which worlds are not related. The model of Heisenberg is in front of us in the case of Pythagoreans. If we believe in the unseen world we are metaphysicians, if not we are positivists.

"... At all times there have been opposite tendencies in philosophy, and it would not seem that these differences are nearing any settlement The reason is presumably that men have different minds and that these minds cannot be changed. Men do not agree because they do not speak the same language and because some languages can never be learned.Poincare

So there is no hope to expect agreement between positivists and metaphysicians. Sources .The evolution of scientific thought A.D Abro DoverMatire a Pense Changeux-Connes Infinity Ascent. A short story of mathematics David Berlinsky, Chance and Chaos David Ruelle T 1955

Janus Arthur Koestler George Mpantes mathematics teacher

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. These are the most critical reports about the philosophy of science. Cantor said that in the level of Knowledge, there is a principle of conservation: the principle of conservation of ignorance! (my comment)

This ultimate unknowable agent of the scientific explanation, is usually interpreted by metaphysics! (Pythogorean metaphysics)

Heisenberg: The physical principles of the quantum theory; University of Chicago, 1930; p.15