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Which mathematical objects do Platonists consider abstract besides numbers?
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philosophy of mathematics
German philosopher of mathematics, logic, and language Gottlob Frege.
In the philosophy of mathematics, Platonists maintain that mathematical objects are abstract, meaning they are nonphysical, nonmental, and nonspatiotemporal entities that exist independently of human thought. Beyond numbers, Platonists consider a wide variety of mathematical entities to be abstract objects, including:12
- Functions12
- Sets12
- Vectors12
- Circles12
- Mathematical structures and patterns, such as infinite series, geometric spaces, and set-theoretic hierarchies1
For Platonists, mathematics is the study of these various structures, which are considered real and objective. While some nontraditional views, such as structuralism, argue that individual mathematical objects are merely positions within these patterns rather than objects in the ordinary sense, the overarching Platonic doctrine holds that these structures themselves are abstract in nature.12