This paper presents Chapter XII (section 6) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.
The paragraphs of original material are accompanied by brief comments in color, based on the present understanding. Feedback on these comments is appreciated.
The heading below links to the original materials.
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“What is Mr. X?”
In the light of these considerations let us now see what we can make of the question, What is Mr. X? I must undertake the inquiry single-handed; I cannot avail myself of your collaboration without first answering or assuming an answer to the equally difficult question, What are you? Accordingly the whole inquiry must take place in the domain of my own consciousness. I find there certain data purporting to relate to this unknown X; and I can (by using powers which respond to my volition) extend the data, i.e. I can perform experiments on X. For example I can make a chemical analysis. The immediate result of these experiments is the occurrence of certain visual or olfactory sensations in my consciousness. Clearly it is a long stride from these sensations to any rational inference about Mr. X. For example, I learn that Mr. X has carbon in his brain, but the immediate knowledge was of something (not carbon) in my own mind. The reason why I, on becoming aware of something in my mind, can proceed to assert knowledge of something elsewhere, is because there is a systematic scheme of inference which can be traced from the one item of knowledge to the other. Leaving aside instinctive or commonsense inference—the crude precursor of scientific inference—the inference follows a linkage, which can only be described symbolically, extending from the point in the symbolic world where I locate myself to the point where I locate Mr. X.
Just like there is a continuum of substance there is also a continuum of knowledge.
One feature of this inference is that I never discover what carbon really is. It remains a symbol. There is carbon in my own brain-mind; but the self-knowledge of my mind does not reveal this to me. I can only know that the symbol for carbon must be placed there by following a route of inference through the external world similar to that used in discovering it in Mr. X; and however closely associated this carbon may be with my thinking powers, it is as a symbol divorced from any thinking capacity that I learn of its existence. Carbon is a symbol definable only in terms of the other symbols belonging to the cyclic scheme of physics. What I have discovered is that, in order that the symbols describing the physical world may conform to the mathematical formulae which they are designed to obey, it is necessary to place the symbol for carbon (amongst others) in the locality of Mr. X. By similar means I can make an exhaustive physical examination of Mr. X and discover the whole array of symbols to be assigned to his locality.
The knowledge symbolically represents what is there (the substance). This knowledge can be carried around and exchanged.
Will this array of symbols give me the whole of Mr. X? There is not the least reason to think so. The voice that comes to us over the telephone wire is not the whole of what is at the end of the wire. The scientific linkage is like the telephone wire; it can transmit just what it is constructed to transmit and no more.
It will be seen that the line of communication has two aspects. It is a chain of inference stretching from the symbols immediately associated with the sensations in my mind to the symbols descriptive of Mr. X; and it is a chain of stimuli in the external world starting from Mr. X and reaching my brain. Ideally the steps of the inference exactly reverse the steps of the physical transmission which brought the information. (Naturally we make many short cuts in inference by applying accumulated experience and knowledge.) Commonly we think of it only in its second aspect as a physical transmission; but because it is also a line of inference it is subject to limitations which we should not necessarily expect a physical transmission to conform to.
It is difficult to symbolize the substance in all its aspects. Furthermore, the interpretation of that symbolization depends on the filters the other mind may be using.
The system of inference employed in physical investigation reduces to mathematical equations governing the symbols, and so long as we adhere to this procedure we are limited to symbols of arithmetical character appropriate to such mathematical equations.* Thus there is no opportunity for acquiring by any physical investigation a knowledge of Mr. X other than that which can be expressed in numerical form so as to be passed through a succession of mathematical equations.
* The solitary exception is, I believe, Dirac’s generalisation which introduces g-numbers (p. 210). There is as yet no approach to a general system of inference on a non-numerical basis.
Mathematics is used to bypass the filters that may interfere with interpretation of symbols, but mathematics itself may act as a filter.
Mathematics is the model of exact inference; and in physics we have endeavoured to replace all cruder inference by this rigorous type. Where we cannot complete the mathematical chain we confess that we are wandering in the dark and are unable to assert real knowledge. Small wonder then that physical science should have evolved a conception of the world consisting of entities rigorously bound to one another by mathematical equations forming a deterministic scheme. This knowledge has all been inferred and it was bound therefore to conform to the system of inference that was used. The determinism of the physical laws simply reflects the determinism of the method of inference. This soulless nature of the scientific world need not worry those who are persuaded that the main significances of our environment are of a more spiritual character. Anyone who studied the method of inference employed by the physicist could predict the general characteristics of the world that he must necessarily find. What he could not have predicted is the great success of the method— the submission of so large a proportion of natural phenomena to be brought into the prejudged scheme. But making all allowance for future progress in developing the scheme, it seems to be flying in the face of obvious facts to pretend that it is all comprehensive, Mr. X is one of the recalcitrants. When sound-waves impinge on his ear he moves, not in accordance with a mathematical equation involving the physical measure numbers of the waves, but in accordance with the meaning that those sound-waves are used to convey. To know what there is about Mr. X which makes him behave in this strange way, we must look not to a physical system of inference, but to that insight beneath the symbols which in our own minds we possess. It is by this insight that we can finally reach an answer to our question, What is Mr. X?
Limitation of mathematics lies in the limitation of symbols being used to describe the substance. Therefore, mathematics cannot be wholly relied upon. Logic of consistency, harmony and continuity is necessary to prepare the symbols for mathematical application.
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