Aristotelian realist philosophy of mathematics holds that mathematics studies properties such as symmetry, quantity, continuity and order that can be realized in the physical world (or in any other world there might be). It contrasts with Platonist realism 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 the most philosophically central parts of mathematics. The category also includes Aristotle's own philosophy of mathematics and its Thomist developments.
|Key works||Franklin 2014 is a recent version of Aristotelian realism, arguing that mathematics is the science of quantity and structure. While Aristotelianism was rare in 20th-century philosophy of mathematics, versions of it were revived in Bigelow 1988 and Maddy 1990. The main Aristotelian view of numbers, as relations between heaps and unit-making universals, is due to Kessler 1980, while Armstrong 1991 gives an Aristotelian account of sets. Frege's influential argument that numbers cannot be properties of physical reality is addressed from an Aristotelian perspective by Irvine 2010 and Katz 2023 .|
|Introductions||Franklin 2022 introduces and surveys the range of Aristotelian options in the philosophy of mathematics. Bostock 2012 introduces Aristotle's philosophy of mathematics. Maurer 1993 introduces Thomist views of mathematics.|
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