Christopher Dawson on laws of mathematics

Gavin Ardley’s Marvellous Perception of the Nature of the Modern Sciences

 

Part One (b): Christopher Dawson sums it up

 

 

by

 

Damien F. Mackey

 

 

 

 

“If the laws of mathematics are simply the creation of the human mind,

they are no infallible guide to the ultimate nature of things. They are a conventional technique which is no more based on the eternal laws of the universe than is

the number of degrees in a circle or the number of yards in a mile”.

 

Christopher Dawson

 

 

 

 

 

The insightful words of Christopher Dawson (d. 1970) here seem to me closely to echo the sentiments of Dr. Gavin Ardley, in his masterpiece, Aquinas and Kant. The Foundations of the Modern Sciences (1950), who wrote in his Chapter III (“The Nature of Modern Physics”):

 

The Classical, or Realist, Theory of Modern Physics

 

The classical writers on scientific method, men like John Stuart Mill, and the English empiricists generally, took it for granted that modern physics was, like ancient physics, endeavouring to discover the nature and functioning of the physical world about us. Only, they believed, it was doing it much more successfully than was the ancient and medieval physics. They saw the change that came over physics in the days of Galileo as a change occasioned by increased attention to observation and experiment. They accused the Aristotelians of paying too little attention to observation and too much to a priori notions. Liberation from the medieval straight-jacket, and careful experiment and measurement, coupled with the powerful instrument of mathematics, was believed to be the reason for the great strides forward in physical science from Galileo onward.

Physics was thus regarded as a truly empirical science. The physicist was supposed to observe uniformities in Nature and to generalise these into laws. Some varied this a little by pointing out that physicists take hypotheses and then put them to the test of experiment. If experiment verifies the hypothesis then we have discovered a valid law or theory of physics. By these means, it was believed, were discovered such laws and principles as Newton’s Laws of Motion and the Law of Universal Gravitation, the Conservation of Energy, the Wave Theory of Light, the Atomic Theory of Matter, and so on.

Physics was thus held by these philosophers and logicians to be slowly wresting out the secrets of Nature, to be steadily unfolding before us the constitution of the physical world. The uniformity of Nature is revealed in the true laws of physics, and renders them immutable.

Physics is subject at every turn to the test of experiment, and anyone can upset a theory simply by showing that some observation is contrary to it. Thus physics abhors authority and anything that smacks of the a priori. Consequently the modern physicist reviles the old Aristotelian physicist who, he believes, was bound hand an foot by authority and a priori notions.

By this slow empirical advance, it was believed, there was built up this great edifice of modern physics; an edifice which today occupies one of the most prominent positions in our intellectual horizon, while in practical applications it has transformed daily life by surrounding us with a countless multiplicity of instruments and amenities.

Although the classical empiricist logicians were not all agreed on what was, precisely, the scientific method, yet on the general picture they were unanimous. [Footnote: See further Ch. XI, on Scientific Method.]

 

The Eddingtonian Theory

 

Nevertheless there has long been a minority which has held other views about the nature of physics and scientific method. In recent years these views have pushed their way more and more to the fore. The revolt has been rather tentative up to the present, but in this chapter we will extend it further and develop its consequences.

The John the Baptist of the Movement was Immanuel Kant. In more recent times the principles were revived by Poincaré.

[Footnote: Some account of the various transitional theories will be found in later chapters, notably in Ch. XVIII in the Section on Modern Physics and Scholastic Philosophy.] But the new interpretation has received its greatest impetus from the works of the late Professor Eddington, who gave a most elegant expression to what others had long been struggling to articulate. The new approach is based on the mode of acquiring knowledge in experimental physics. It pays little attention to what the physicist says, but much attention to what he does. It looks away from the world to the activity of the physicist himself. To Eddington and his school of thought, the laws of physics are subjective, arbitrary, conventional, dogmatic, and authoritarian. This is, of course, precisely the reverse of the classical theory which believes the laws to be supremely objective. But the new theory holds that the laws of physics are not the laws of Nature but the laws of the physicists. The laws of physics are always true, not because they represent uniformities of Nature, but simply because the physicist never lets them be untrue.

Newton wrote in the Principia that ‘Nature is pleased with simplicity and affects not the pomp of superfluous causes’. The classical empiricist logician would heartily endorse this dictum, although he might be puzzled if asked how he knew it to be true. But the alternative view would insist that it is not Nature which is pleased with simplicity, but the physicist. Whether Nature is pleased with simplicity or not we cannot tell, at least not within the province of experimental science. But we know that the physicist is pleased with simplicity and will exercise all his ingenuity to achieve it. The simplicity of the laws of physics, then, tells us much about the physicist, but nothing immediately about Nature.

This reorientation towards physics can be expressed very neatly by using the parable of Procrustes, and saying that physics is a Procrustean bed. Procrustes lived in ancient Greece. He was a brigand who terrorised Attica until finally he was vanquished by Theseus. Now Procrustes had a bed, and it was his practice to make travellers conform in length to that bed. If they were too short he stretched them out until they fitted, and if they were too long he chopped of their legs until they were the right length.

This is a parable of what the physicist does with Nature. He makes Nature conform to what he wants, and having done so announces that he has discovered a law of Nature: namely that all travellers fit the bed. Hence it is that the laws of physics are always true. It is because the physicist makes Nature conform to them. He runs Nature out into moulds, so to speak. A law of physics is not something discovered in Nature, but something imposed upon Nature.

In brief, physics is a put-up job. The physicist puts it all in implicitly at the beginning, and then draws it out explicitly at the end. Physics is manufactured, not discovered. Eddington puts the matter in his own inimitable style. [Footnote: Eddington, A. S.: The Philosophy of Physical Science (Cambridge, 1939), p. 109.]

[End of quotes]

 

 

Christopher Dawson wrote, in Progress and Religion (Sheed and Ward, 1938, p. 236), concerning mathematics and the universe:

 

The rise of modern physics was closely connected with a transcendental view of the nature of mathematics derived from the Pythagorean and Platonic tradition. According to this view, God created the world in accordance with numerical harmonies, and consequently it is only by the science of number that it can be understood. ‘Just as the eye was made to see colours’, says Kepler, ‘and the ear to hear sounds, so the human mind was made to understand Quantity’. (Opera 1, 3). And Galileo describes mathematics as the script in which God has written on the open book of the Universe. But this philosophy of mathematics which underlies the old science, requires a deity to guarantee its truth. If the laws of mathematics are simply the creation of the human mind, they are no infallible guide to the ultimate nature of things. They are a conventional technique which is no more based on the eternal laws of the universe than is the number of degrees in a circle or the number of yards in a mile. ….