The Limitations of Science

Scientific method, as we see from the work of its founders, Copernicus, Kepler, Galileo, began by quite consciously and deliberately selecting and abstracting from the total elements of our experience. From the total wealth of impressions received from nature these men fastened upon some only as being suitable for scientific formulation. These were those elements that possess quantitative aspects. Between these elements mathematical relations exist, and these men were convinced that mathematics is the key to the universe. It is interesting, in view of its immense importance, to know how they came by this belief, for it was by no means a general persuasion. It was not part of the dominant Aristotelianism of their time. It seems to have been in part due to an innate prejudice, very proper to born mathematicians, and in part to the neo-Platonic philosophy that was prevalent, at that time, in South Europe. This philosophy contained important pythagorean elements, and gave to the mathematical aspects of the universe a much more exalted position than they occupied in the current Aristotelian outlook.

Copernicus became acquainted with this philosophy during his stay in Italy, and also with the fact that some of the ancient Greek philosophers had put forward the hypothesis that the earth was in motion. Being led, in this way, to take the sun as his centre of reference, Copernicus found, as we have already said, that a great harmony was bestowed on the motions of the heavenly bodies.

With the incorrect ideas of dynamics prevalent at the time, Copernicus's theory was open to grave objections. As a physical explanation of phenomena it was certainly no better than the Ptolemaic theory. Nevertheless, Copernicus was confident that its superior aesthetic charm would be sufficient to commend it to mathematicians.

This expectation was justified ...Kepler ...shows how greatly the aesthetic charm of the new theory appealed to him. To the mind of Kepler, however, the claims of the theory were greatly reinforced by the dignified position it gave to the sun, for Kepler, in a vague and mystical fashion, was a sun-worshipper...

Kepler had a preconceived idea as to the sort of thing the universe is. He did not approach the facts with the docility and lack of prejudice that is proper to the ideal scientific investigator. His deepest conviction was that nature is essentially mathematical, and all his scientific life was an endeavour to discover nature's hidden mathematical harmonies. Galileo, also, had no doubt that mathematics is the one true key to natural phenomena. It was this persuasion that gave these men their criterion for selection amongst the total elements of their experience. They confined their attention to those elements amongst which mathematical relations exist.

Bodies, for instance, have for their measurable aspects size, shape, weight, motion. Such other characteristics as they possess were regarded as belonging to a lower order of reality. The real world is the world of mathematical characteristics. In fact, our minds are so constructed, Kepler said, that they can know nothing perfectly except quantities.

With Galileo this separation of the mathematical from the other qualities became a perfectly clear and definite doctrine. Kepler had supposed that the non-mathematical qualities actually did belong to bodies, but that they were somehow less real. Galileo went further than this, and stated that the non-mathematical properties are all entirely subjective. They have no existence at all apart from our senses. Thus colours, sounds, odours and so on exist, as such, wholly in our minds. They are, in reality, motions of some kind or another in the external world, and these motions, impinging on our senses, give rise to these sensations of colour, sound, and so on. It is the mind that peoples the world with the songs of birds, the colours of the sunset, etc. In the absence of mind the universe would be a collection of masses of various sizes, shapes, and weights, drifting, without colour, sound, or odour, through space and time...

We are not here concerned to discuss the validity of this division into primary and secondary qualities, but merely to show the role it played in the formation of the scientific outlook. We may mention, however, that it has been attacked, philosophically, in two ways. It has been denied, on the one hand, that the primary qualities are any less 'subjective' than the secondary qualities. Each of these arguments denies that primary qualities are any more 'real' than secondary qualities although it may be true that only the primary qualities are susceptible of mathematical treatment. But the Galilean doctrine, which became part of the general scientific outlook, maintains that the primary qualities alone are real – the others are in some sense illusory.

With this reduction of the real world to colourless, soundless, odourless bodies in motion, the notions of space and time underwent a profound change. To the medieval philosophers the temporal process was the transformation of potentiality into actuality. The purpose of everything was to reach a higher state of being, culminating in union with God. The whole of the past up to the present moment, was the ground already won, as it were. As the process goes on until the final culmination is reached, when time stands still. We see how different this notion of time is from the mathematical time, introduced by Galileo. Time, as it appears in science, may be likened to an ever-moving mathematical point. The present moment, which has no finite duration, is merely a boundary point between a vanished past and a non-existent future. Time, conceived in this way, can be represented very simply mathematically as a straight line, successive points on the line representing successive instants of time. This conception has hitherto proved quite adequate for the needs of science, and has therefore been generally adopted. Philosophically, however, it has brought in its train a host of unsolved puzzles, and there can be little doubt that anew conception of time will have to be formulated. Even science itself is now giving hints that this may be necessary.

With this change in the notion of time comes a corresponding change in the notion of cause. When all things were regarded as moving towards union with God, then union with God was regarded as the final cause of all change. This cause of a process was to be found in the end towards which it tended. The reason why things happened was to be found in the purpose the happening served. With the new notion of time the future, being non-existent, had no influence on present happenings. The cause of anything happening now was to be found in its immediate past. Further, all that really happens are motions -motions of the constituent particles of the bodies forming the real world. And these motions are themselves the products of preceding motions. Galileo also believed that there are 'forces,' which are revealed by motions, but as to the nature of force he refrained from speculating.

We see that the scientific outlook, as presented by Galileo, constitutes a really amazing revolution in thought. The vivid world of the medievalist, a world shot through with beauty and instinct with purpose, a world having an intimate relation to his own destiny and an intelligible reason for existing in the light of that destiny, is dismissed as an illusion. It has no objective existence. The real world, as revealed by science, is a world of material particles moving, in accordance with mathematical laws, through space and time.

The early creators of science did not assume that this real world was also purposeless. Although God was no longer invoked as the final cause of phenomena, He was still given an important role as the initiator of the whole process. But, having made matter with its properties, He then left the world to develop according to the laws of mathematical necessity. In course of time it came to be considered unnecessary to invoke God even for this purpose, and the way was clear for thorough-going materialism. That this doctrine was made plausible by scientific researches is the greatest possible testimonial to the 'humanistic' importance of science. We have seen what the medieval outlook was in essentials. The essentials of the materialistic outlook may be given in the words of Bertrand Russell:

'That man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspiration, all the noon-day brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins. - all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand.’ (J.W.W. Sullivan:  The Limitations of Science, A.D. Peters).