On Language (1920-1929)

 "We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections. (Niels Bohr, 1920)

"Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of a system of voluntarily produced symbols." (Edward Sapir, "Language", 1921)

"The essence of language lies, not in the use of this or that special means of communication, but in the employment of fixed associations (however these may have originated) in order that something now sensible - a spoken word, a picture, a gesture, or what not — may call up the 'idea' of something else. Whenever this is done, what is now sensible may be called a 'sign' or 'symbol', and that of which it is intended to call up the 'idea' may be called its 'meaning'. This is a rough outline of what constitutes 'meaning'." (Bertrand Russell, "Analysis of Mind", 1921)

"[…] mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediaeval slowness of the syllogisms expressed in our words." (Charles Nordmann, "Einstein and the Universe", 1922)

"Translating mathematics into ordinary language is like translating music. It cannot be done. One could describe in detail a sheet of music and tell the shape of each note and where it is placed on the staff, but that would not convey any idea of how it would sound when played. So, too, I suppose that even the most complicated equation could be described in common words, but it would be so verbose and involved that nobody could get the sense of it." (Edwin E Slosson,"Chats on Science", 1924)

"Once a statement is cast into mathematical form it may be manipulated in accordance with [mathematical] rules and every configuration of the symbols will represent facts in harmony with and dependent on those contained in the original statement. Now this comes very close to what we conceive the action of the brain structures to be in performing intellectual acts with the symbols of ordinary language. In a sense, therefore, the mathematician has been able to perfect a device through which a part of the labor of logical thought is carried on outside the central nervous system with only that supervision which is requisite to manipulate the symbols in accordance with the rules." (Horatio B Williams, "Mathematics and the Biological Sciences", Bulletin of the American Mathematical Society Vol. 38, 1927)

"The most general definition of a function that we have reached in modern mathematics starts by fixing the values that the independent variable x can take on. We define that x must successively pass through the points of a certain 'point set'. The language used is therefore geometric […]." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)

"A precise language awaits a completed metaphysics." (Alfred North Whitehead, "Process and Reality: An Essay in Cosmology", 1929)

"Thought is prior to language and consists in the simultaneous presentation to the mind of two different images." (Thomas E Hulme, "Notes on Language and Style", 1929)