Article/Publication Details

Mathematical Objects: Discovered or Invented?

(Original title: Matematické objekty: nálezy, alebo vynálezy?)
Filozofia, 2015, vol. 70, No 7, pp. 518-530.
Language: Slovak
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Abstract

The question whether mathematical objects are things to be discovered or rather invented belonged for a long time among the most discussed issues in philosophy of mathematics. The answers range from strictly Platonist approaches to radical constructivism and even fictionalism. The paper is an attempt to bring this philosophical question down to earth before we set out to search for highly sophisticated but controversial explanations. The methods we employ are inspired by those implemented in philosophical remarks of the later Wittgenstein. The main goal of the paper is to strip the question of its reputed philosophical depth by means of paying closer attention to what its meaning could intelligibly be in the first place.

Keywords

Antirealism, Discovery, Invention, Mathematical objects, Philosophy of mathematics, Platonism, Wittgenstein

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