"The true, which is identical with the divine, transcends our grasp as such. We perceive it only as reflection, parable, symbol, in specific and related manifestations. We become aware of it as life that defies comprehension, and for all that we cannot renounce the wish to comprehend. " (Johann Wolfgang von Goethe, "Essay on Meteorology", 1825)
"Here I am at the limit which God and nature has assigned to my individuality. I am compelled to depend upon word, language and image in the most precise sense, and am wholly unable to operate in any manner whatever with symbols and numbers which are easily intelligible to the most highly gifted minds." (Johann Wolfgang von Goethe, [Letter to Naumann] 1826)
"True symbolism is present where the specific represents the more general, not as a dream and shadow, but as a living momentary revelation of the inscrutable." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1826)
"In symbolical algebra, the rules determine the meaning of
the operations […] we might call them arbitrary assumptions, inasmuch as they
are arbitrarily imposed upon a science of symbols and their combinations, which
might be adapted to any other assumed system of consistent rules." (George Peacock, "Treatise of Algebra", 1830)
"Every natural fact is a symbol of some spiritual fact." (Ralph W Emerson, Nature, 1836)
"The science of algebra, independently of any of its uses, has all the advantages which belong to mathematics in general as an object of study, and which it is not necessary to enumerate. Viewed either as a science of quantity, or as a language of symbols, it may be made of the greatest service to those who are sufficiently acquainted with arithmetic, and who have sufficient power of comprehension to enter fairly upon its difficulties." (Augustus de Morgan, "Elements of Algebra", 1837)
"This principle, which is thus made the foundation of the operations and results of Symbolical Algebra, has been called 'The principle of the permanence of equivalent forms', and may be stated as follows: "Whatever algebraical forms are equivalent, when the symbols are general in form but specific in value, will be equivalent likewise when the symbols are general in value as well as in form." (George Peacock, "A Treatise on Algebra", 1842)
"A successful attempt to express logical propositions by symbols, the laws of whose combinations should be founded upon the laws of the mental processes which they represent, would, so far, be a step towards a philosophical language." (George Boole, "The Mathematical Analysis of Logic", 1847)
“The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.” (Augustus De Morgan, “Calculus of Functions”, Encyclopaedia of Pure Mathematics, 1847)
"Symbolism transforms the phenomenon into the idea, and the idea into an image in such a fashion that in the image the idea remains infinitely active and incommensurable, and if all languages were used to express it, it would still remain inexpressible." (Johann Wolfgang von Goethe, "Maxims and Reflections", [posthumous])
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