"Mathematical science has been at times embarrassed with contradictions and paradoxes; yet they are not to be imputed to imaginary symbols, rather than to any other symbols invented for the purpose of rendering demonstration compendious, and expeditious. It may; however, be justly remarked, that mathematicians, neglecting to exercise mental superintendance, are too prone to trust to mechanical dexterity; and that some, instead of establishing the truth of conclusions on antecedent reasons, have endeavoured to prop it by imperfect analogies or mere algebraic forms. On the other hand, there are mathematicians, whose zeal for just reasoning has been alarmed at a verbal absurdity and, from a name improperly applied, or a definition incautiously given, l have been hurried to the precipitate conclusion, that operations with symbols of which the mind can form no idea, must necessarily be doubtful and unintelligible." (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)
Symbolisms transform the experience into an· idea, and an idea into an image, so that the idea expressed by the image remains always active and unattainable and, even though expressed in all languages, remains unexpressible. Allegory transforms an experience into a concept and a concept into an image, but so that the concept remains always defined and expressible by the image. (Johann Wolfgang von Goethe, Maximen und Reflexionen., 1809-32)
"The imagination […] that reconciling and mediatory power, which incorporating the reason in images of the sense and organizing (as it were) the flux of the senses by the permanence and self-circling energies of the reason, gives birth to a system of symbols, harmonious in themselves, and consubstantial with the truths of which they are the conductors." (Samuel T Coleridge, "The Statesman's Manual", 1816)
"An idea, in the highest sense of that word, cannot be conveyed but by a symbol." (Samuel T Coleridge," Biographia Literaria", 1817)
"Generally speaking, symbol is some form of external existence immediately present to the senses, which, however, is not accepted for its own worth, as it lies before us in its immediacy, but for the wider and more general significance which it offers to our reflection. We may consequently distinguish between two points of view equally applicable to the term: first, the significance, and, second, the mode in which such a significance is expressed. The first is a conception of the mind, or an object which stands wholly indifferent to any particular content; the latter is a form of sensuous existence or a representation of some kind or other" (Georg W F Hegel, "Ästhetik" Vol. 2, 1817)
"Everything that takes place is a symbol. In representing itself perfectly it suggests what lies beyond. In this reflection extreme modesty and extreme pretentiousness seem to me combined." (Johann Wolfgang von Goethe, 1818)
"The symbol. It is the thing without being the thing, and yet the thing: an image concentrated in the mirror of the mind and yet identical with the object. How inferior is allegory by comparison. Though it may have wit and subtle conceit, it is for the most part rhetorical and conventional. It always improves in proportion to its approach to what we call symbol." (Johann Wolfgang von Goethe, "Addenda on the Paintings of Philostratus", 1820)
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