“We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking.”

— R. G. Collingwood

Source: The Principles of Art (1938), p. 268

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R. G. Collingwood 16

British historian and philosopher 1889–1943

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“Language in its original imaginative form maybe said to have expressiveness, but no meaning. About such language we cannot distinguish between what the speaker says and what he means… Language in its intellectualized form has both expressiveness and meaning. As language, it expressed a certain emotion. As symbolism, it refers beyond that emotion to the thought whose emotional charge it is… The progressive intellectualization of language, its progressive conversion by the work of grammar and logic into a scientific symbolism, thus represents not a progressive drying-up of emotion, but its progressive articulation and specialization. We are not getting away from an emotional atmosphere into a dry, rational atmosphere; we are acquiring new emotions and new means of expressing them.”

R. G. Collingwood (1889–1943) British historian and philosopher

Source: The Principles of Art (1938), p. 269

“But how can we avoid the use of human language? The… symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.”

Tobias Dantzig (1884–1956) American mathematician

p, 125
Number: The Language of Science (1930)

“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 (1884–1939) American linguist and anthropologist

As cited in: Geza Revesz, The Origins and Prehistory of Language, London 1956. footnote pp. 126-127; As cited in: Adam Schaff (1962). Introduction to semantics, p. 313-314
Language (1921)

“Ebbinghaus: Language is a system of conventional signs that can be voluntarily produced at any time.
Croce: Language is articulated, limited sound organized for the purpose of expression.
Dittrich: Language is the totality of expressive abilities of individual human beings and animals capable of being understood by at least one other individual.
Eisler: Language is any expression of experiences by a creature with a soul.
B. Erdmann: Language is not a kind of communication of ideas but a kind of thinking: stated or formulated thinking. Language is a tool, and in fact a tool or organ of thinking that is unique to us as human beings.
Forbes: Language is an ordered sequence of words by which a speaker expresses his thoughts with the intention of making them known to a hearer.
J. Harris : Words are the symbols of ideas both general and particular: of the general, primarily, essentially and immediately; of the particular, only secondarily, accidentally and mediately.
Hegel: Language is the act of theoretical intelligence in its true sense, for it is its outward expression.
Jespersen: Language is human activity which has the aim of communicating ideas and emotions.
Jodl: Verbal language is the ability of man to fashion, by means of combined tones and sounds based on a limited numbers of elements, the total stock of his perceptions and conceptions in this natural tone material in such a way that this psychological process is clear and comprehensible to others to its least detail.
Kainz : Language is a structure of signs, with the help of which the representation of ideas and facts may be effected, so that things that are not present, even things that are completely imperceptible to the senses, may be represented.
De Laguna: Speech is the great medium through which human co-operation is brought about.
Marty: Language is any intentional utterance of sounds as a sign of a psychic state.
Pillsbury-Meader: Language is a means or instrument for the communication of thought, including ideas and emotions.
De Saussure: Language is a system of signs expressive of ideas.
Schuchardt. The essence of language lies in communication.
Sapir: Language is a purely human and non-instinctive method of communicating ideas, emotions and desires by means of a system of voluntarily produced symbols.”

Géza Révész (1878–1955) Hungarian psychologist and musicologist

Footnote at pp. 126-127; As cited in: Adam Schaff (1962). Introduction to semantics, p. 313-314
The Origins and Prehistory of Language, 1956

“By the logical syntax of a language, we mean the formal theory of the linguistic forms of that language -- the systematic statement of the formal rules which govern it together with the development of the consequences which follow from these rules. A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for examples, the words) or to the sense of the expressions (e. g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed.”

Rudolf Carnap (1891–1970) German philosopher

Source: Logical Syntax of Language, 1934/1937, p. 1

“We have to build the spiritual world out of symbols taken from our own personality, as we build the scientific world out of the symbols of the mathematician.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Source: Science and the Unseen World (1929), Ch. VIII, p.82

“There is no need in these mathematical days to defend the use of symbolism. It is regarded by many schools of modern thought as the only safe form of language. Wittgenstein treats symbols as something more than conventional signs, and regards them as corresponding in some way to the reality to which they refer. He would probably accept Gurdjieff’s dictum that:

Symbols not only transmit knowledge but show the way to it.

Even though other thinkers deny any objective reference to symbols, no one questions that symbolism has a power beyond that of ordinary language. It is different with the language of myth. This is despised by superficial thinkers, but the greatest philosophers have known its value.”

John G. Bennett (1897–1974) British mathematician and author

Gurdjieff’s All and Everything (1950)

“The fiction of an ideal language composed of pure atomic statements is as metaphysical as the fiction of Laplace's 'spirit'. Scientific language, with its ever growing equipment of systematic symbol formations, can by no means be regarded as an approximation to such an ideal language.”

Otto Neurath (1882–1945) austrian economist, philosopher and sociologist

Source: 1930s, "Protocol Statements" (1932), p. 91

“Science does not speak of the world in the language of words alone, and in many cases it simply cannot do so. The natural language of science is a synergistic integration of words, diagrams, pictures, graphs, maps, equations, tables, charts, and other forms of visual and mathematical expression… [Science thus consists of] the languages of visual representation, the languages of mathematical symbolism, and the languages of experimental operations.”

Jay Lemke (1946) American academic

Jay Lemke (2003), "Teaching all the languages of science: Words , symbols, images and actions," p. 3; as cited in: Scott, Phil, Hilary Asoko, and John Leach. "Student conceptions and conceptual learning in science." Handbook of research on science education (2007): 31-56.

“Mathematicians may flatter themselves that they possess new ideas which mere human language is yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations of their minds.”

James Clerk Maxwell (1831–1879) Scottish physicist

"Thomson & Tait's Natural Philosophy" in Nature, Vol. 7 (Mar. 27, 1873) A review of Elements of Natural Philosophy https://archive.org/details/elementsnatural00kelvgoog (1873) by Sir W. Thomson, P. G. Tait. See Nature, Vol. 7-8, https://archive.org/details/nature7818721873lock Nov. 1872-Oct. 1873, pp. 399-400, or The Scientific Papers of James Clerk Maxwell, p. 328. https://books.google.com/books?id=lzlRAAAAYAAJ&pg=PA328

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R. G. Collingwood 16

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