On Abstraction (-1699)

"[Arithmetic] has a very great and elevating effect, compelling the soul to reason about abstract numbers, and rebelling against the introduction of visible or tangible objects into the argument." (Plato, "The Republic", cca 375 BC)

"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a few observations." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)

"The exact kind of language we employ in philosophical analyses of abstract truth is one thing, and the language used in attempts to popularize the subject is another." (Marcus Tullius Cicero, "De officiis" ["On Duties"], cca.44 BC)

"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)

"If one, with the scientist, studies the works of nature, which are made up of elements or matter and form, his reasoning is dependent on the data provided by sense-experience. And if one, with the mathematician, abstracts figures or calculates numerically, he must, in order to gain assent, accurately adduce many examples of both differentiated plurality and quantitative extension. The like holds true of the philosopher, whose domain is [abstract] reasoning, and who is the client of both the scientist and the mathematician. For the philosopher, too, begins with those things which are based on the evidence of the senses and contribute to the knowledge of immaterial intelligibles." (John of Salisbury, "Metalogicon", 1159)

"It is true that mathematics, which deals theoretically with abstractions, and in its subtle analysis separates things that are united in nature, treats matter and form apart from one another, so that the nature of what is composite may be more accurately and definitely understood. Still, the one cannot exist apart from the other, as [in this case] either matter would be without form, or form would lack a subject and hence be ineffective." (John of Salisbury, "Metalogicon", 1159)

"Nor is it enough to say that the intelligible notions formed by the active intellect subsist somehow in the phantasmata (mental image), which are certainly intrinsic to us; for as we have already observed in treating the passive intellect, objects only become actually intelligible when abstracted from phantasmata; so that merely by way of the phantasmata, we cannot attribute the work of the active intellect to ourselves" (St. Thomas Aquinas, "De Anima" III, cca. 1268) [On Aristotle's phantasmata]

"Abstraction involves perceiving something, relating it to other things, grasping some common trait of those things, and conceiv­ing of the common trait as to it can be related not only to those things but also to other similar things."  (John Locke, "An Essay Concerning Human Understanding", 1689)