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" "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.
Robin George Collingwood (22 February 1889 – 9 January 1943) was an English philosopher, historian, and archaeologist. He is best known for his philosophical works including The Principles of Art (1938) and the posthumously published The Idea of History (1946).
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Knowledge as a past fact, as something dead and done with — knowledge by the time it gets into encyclopaedias and text-books — does consist of assertion, and those who treat it as an affair of encyclopaedias and text-books may be forgiven for thinking that it is assertion and nothing else. But those who look upon it as an affair of discovery and exploration have never fallen into that error. People who are acquainted with knowledge at first hand have always known that assertions are only answers to questions. So Plato described true knowledge as 'dialectic', the interplay of question and answer in the soul's dialogue with itself; so Bacon pointed out once for all that the scientist's real work was to interrogate nature, to put her, if need be, to the torture as a reluctant witness; so Kant mildly remarked that the test of an intelligent man was to know what questions to ask, and the same truth has lately dawned on the astonished gaze of the pragmatists. Questioning is the cutting edge of knowledge, assertion is the dead weight behind the edge that gives it driving force
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