On Symbols (1940-1949)

"Symbols have a trick of stealing the show away from the thing they stand for." (Henry S Haskins, "Meditations in Wall Street", 1940) 

"We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for […] The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for." (Hermann Weyl, "The Mathematical Way of Thinking", 1940)

"Nothing is harder to understand than a symbolic work. A symbol always transcends the one who makes use of it and makes him say in reality more than he is aware of expressing." (Albert Camus, "The Myth of Sisyphus", 1942)

"[The power of understanding symbols] issues in an unconscious, spontaneous process of abstraction, which goes on all the time in the human mind: a process of recognizing the concept in any configuration given to experience, and forming a conception accordingly." (Suzanne K Langer, "Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art", 1942)

"It is generally agreed that thought employs symbols such as written or spoken words or tokens; but it is not generally considered whether the whole of thought may not consist of a process of symbolism, nor is the nature of symbolism and its presence or absence in the inorganic world discussed." (Kenneth Craik, "The Nature of Explanation", 1943)

"My hypothesis then is that thought models, or parallels, reality - that its essential feature is not ‘the mind’, ‘the self’, ‘sense-data’, nor propositions but symbolism, and that this symbolism is largely of the same kind as that which is familiar to us in mechanical devices which aid thought and calculation." (Kenneth Craik, "The Nature of Explanation", 1943)

"Thus there are instances of symbolisation in nature; we use such instances as an aid to thinking; there is evidence of similar mechanisms at work in our own sensory and central nervous systems; and the function of such symbolisation is plain. If the organism carries a ’small-scale model’ of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise […]" (Kenneth Craik, "The Nature of Explanation", 1943)

"Thus we do not try to prove the existence of the external world – we discover it, because the fundamental power of words or other symbols to represent events [...] permits us to put forward hypotheses and test their truth by reference to experience. [..] A particular type of symbolism may always fail in a particular case, as Euclidean geometry apparently fails to represent stellar space; but if all types of symbolism always failed, we should be unable to recognise any objects or exist at all." (Kenneth Craik, "The Nature of Explanation", 1943)

"Without falling into the trap of attempting a precise definition, we may suggest a theory as to the general nature of symbolism, viz. that it is the ability of processes to parallel or imitate each other, or the fact that they can do so since there are recurrent patterns in reality." (Kenneth Craik, "The Nature of Explanation", 1943)

"Man has [...] discovered a new method of adapting himself to his environment. Between the receptor system and the effector system, which are to be found in all animal species, we find in man a third link which we may describe as the symbolic system." (Ernst Cassirer, "An Essay on Man", 1944)

"A mathematician is not a man who can readily manipulate figures; often he cannot. He is not even a man who can readily perform the transformations of equations by the use of calculus. He is primarily an individual who is skilled in the use of symbolic logic on a high plane, and especially he is a man of intuitive judgment in the choice of the manipulative processes he employs." (Vannevar Bush, "As We May Think", 1945)

"Figures and symbols are closely connected with mathematical thinking, their use assists the mind. […] At any rate, the use of mathematical symbols is similar to the use of words. Mathematical notation appears as a sort of language, une langue bien faite, a language well adapted to its purpose, concise and precise, with rules which, unlike the rules of ordinary grammar, suffer no exception." (George Pólya, "How to solve it", 1945)

"For, in mathematics or symbolic logic, reason can crank out the answer from the symboled equations -even a calculating machine can often do so - but it cannot alone set up the equations. Imagination resides in the words which define and connect the symbols - subtract them from the most aridly rigorous mathematical treatise and all meaning vanishes." (Ralph W Gerard, "The Biological Basis of Imagination", American Thought, 1947)

"When one analyzes the pre-conscious step to concepts, one always finds ideas which consist of 'symbolic images'. The first step to thinking is a painted vision of these inner pictures whose origin cannot be reduced only and firstly to the sensual perception but which are produced by an 'instinct to imagining' and which are re-produced by different individuals independently, i.e. collectively [...] But the archaic image is also the necessary predisposition and the source of a scientific attitude. To a total recognition belong also those images out of which have grown the rational concepts." (Wolfgang Pauli, [Letter to Markus Fierz] 1948)

"Belief has its structures, and its symbols change. Its tradition changes. All the relationships within these forms are inter-dependent. We look at the symbols, we hope to read them, we hope for sharing and communication." (Muriel Rukeyser, "The Life of Poetry", 1949)

"However obvious these facts may appear at first glance, they are actually not so obvious as they seem except when we take special pains to think about the subject. Symbols and things symbolized are independent of each other; nevertheless, we all have a way of feeling as if […] there were necessary connections." (Samuel I Hayakawa, "Language in Thought and Action", 1949)

"Men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite, which dislocate all mathematical operations." (Arthur Koestler, "Crossman", 1949)