Mathematical structuralism (数学的構造主義) has become the dominant view in the philosophy of mathematics. According to this view, the subject matter of mathematics consists first and foremost of mathematical structures. This raises the question: what are mathematical structures? (数学的構造)
In the first part of the session, Professor Horsten will review the standard positions on the question what mathematical structures are. The distinction between eliminative structuralism (消去主義的構造主義) and non-eliminative structuralism (非消去主義的構造主義) is discussed. Special attention is given to set theoretic structuralism. (集合論的構造主義)
In the second part of the session he will introduce his own research on the subject. He will argue that mathematical structures should be seen as generic systems (汎システム), and He will explain what the latter are.
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リンク
[1] http://www.h.kobe-u.ac.jp/sites/default/files/general_event/scishop_20180607_0.pdf
[2] https://www.jasso.go.jp/en/kyoten/hiec/access.html
[3] http://www.h.kobe-u.ac.jp/ja/node/3834