"[Imagination is] that in virtue of which we say that an image occurs to us and not as we speak of it metaphorically." (Aristotle, "De Anima" III, cca. 350 BC)
"The faculty which grasps such concepts acquires intelligible forms from sense-perception by force of an inborn disposition, so that forms, which are in the form-bearing faculty and the memorizing faculty, are made present to [the rational soul] with the assistance of the imaginative and estimative [faculties]." (Avicenna Latinus [Ibn Sina], "A Compendium on the Soul", cca. 996-997)
"It seems that all perception is but the grasping of the form of the perceived object in some manner. If, then, it is a perception of some material object, it consists in an apprehension of its form by abstracting it from matter in some way. But the kinds of abstraction are different and their degrees various. This is because, owing to matter, the material form is subject to certain states and conditions which do not belong to [the form] by itself insofar as it is this form. So sometimes the abstraction from matter is effected with all or some of these attachments, and sometimes it is complete in that the concept is abstracted from matter and from the accidents it possesses on account of the matter."(Avicenna Latinus [Ibn Sina], "Liber De anima", cca. 1014-1027)
"Sometimes a thing is perceived [via sense-perception] when it is observed; then it is imagined, when it is absent [in reality] through the representation of its form inside, Sense-perception grasps [the concept] insofar as it is buried in these accidents that cling to it because of the matter out of which it is made without abstracting it from [matter], and it grasps it only by means of a connection through position [ that exists] between its perception and its matter. It is for this reason that the form of [the thing] is not represented in the external sense when [sensation] ceases. As to the internal [faculty of] imagination, it imagines [the concept] together with these accidents, without being able to entirely abstract it from them. Still, [imagination] abstracts it from the afore-mentioned connection [through position] on which sense-perception depends, so that [imagination] represents the form [of the thing] despite the absence of the form's [outside] carrier." (Avicenna Latinus [Ibn Sina], "Pointer and Reminders", cca. 1030)
"In the foregoing you will discover a very remarkable thing. God reserved the truth of things, which is the supreme truth, for Himself, but He conceded to His image the formation of images of things at whatever time." (Richard of St. Victor, "Benjamin Major" [aka "The Mystical Ark"], cca 1162)
"Logicians may reason about abstractions. But the great mass of men must have images." (Thomas B Macaulay, Critical and Miscellaneous Essays, 1840)
"Thus the man who is responsive to artistic stimuli reacts to the reality of dreams as does the philosopher to the reality of existence; he observes closely, and he enjoys his observation: for it is out of these images that he interprets life, out of these processes that he trains himself for life." (Friedrich Nietzsche," The Birth of Tragedy", 1872)
"We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality […]" (Ludwig von Bertalanffy, "General System Theory", 1968)
"The mapping from linguistic inputs to mental models is not a one-one mapping. So semantic properties of sentences may not be recoverable from a mental model. Reading or listening is typically for content not for form. People want to know what is being said to them, not how it is being said. [...] A mental model is a representation of the content of a text that need bear no resemblance to any of the text's linguistic representations. Its structure is similar to the situation described by the text." (Alan Granham, "Mental Models as Representations of Discourse and Text", 1987)
"The mental model, in turn, can be considered as a syntactic language of thought whose semantic interpretation is provided by the actual world. In this sense, a person's beliefs are true to the extent that they correspond to the world." (William J Rapaport, "Understanding Understanding: Syntactic Semantics and Computational Cognition", Philosophical Perspectives Vol. 9, 1995)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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Douglas T Ross - Collected Quotes
"Automatic design has the computer do too much and the human do too little, whereas automatic programming has the human do too much and...
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