Concept

Aristotelian realist philosophy of mathematics

Overview

In the philosophy of mathematics, Aristotelian realism holds that mathematics studies properties such as symmetry, continuity and order that can be immanently realized in the physical world (or in any other world there might be). It contrasts with Platonism in holding that the objects of mathematics, such as numbers, do not exist in an "abstract" world but can be physically realized. It contrasts with nominalism, fictionalism, and logicism in holding that mathematics is not about mere names or methods of inference or calculation but about certain real aspects of the world.

Aristotelian realists emphasize applied mathematics, especially mathematical modeling, rather than pure mathematics as philosophically most important. Marc Lange argues that "Aristotelian realism allows mathematical facts to be explainers in distinctively mathematical explanations" in science as mathematical facts are themselves about the physical world. Paul Thagard describes Aristotelian realism as "the current philosophy of mathematics that fits best with what is known about minds and science."

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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Quantities have no contraries. In the case of definite quantities this is obvious; thus, there is nothing that is the contrary of 'two cubits long' or of 'three cubits long', or of a surface, or of any such quantities. A man might, indeed, argue that 'much' was the contrary of 'little', and 'great' of 'small'. But these are not quantitative, but relative; things are not great or small absolutely, they are so called…
Aristotle, The Categories
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And the Greek name of this faculty is derived from the use of the term συνιέναι in learning: μανθάνειν and συνιέναι being often used as synonymous. The faculty called γνώμη,[40] in right of which we call men εὐγνώμονες, or say they have γνώμη, is “the right judgment of the equitable man.” A proof of which is that we most commonly say that the equitable man has a tendency to make allowance, and the making allowance…
Aristotle, The Nicomachean ethics of Aristotle
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(2) The _Realism_ of the purposiveness of nature is also either physical or hyperphysical. The _former_ bases the purposes in nature, by the analogy of a faculty acting with design, on the _life of matter_ (either its own or the life of an inner principle in it, a world-soul) and is called _Hylozoism_. The _latter_ derives them from the original ground of the universe, as from an intelligent Being (originally…
Immanuel Kant, Kant's Critique of Judgement
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Philosophers who discussed Aristotelian realist philosophy of mathematics

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Place in the tradition

Part of Analytic philosophy.

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