Prof. Giovanni Sambin (University of Padua)

"From constructive topology to dynamics in foundations, and back"

オープンラボ（三田キャンパス東館4階）
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◆17:00-18:30
Speaker: Prof. Giovanni Sambin
Title: "From constructive topology to dynamics in foundations, and back"

◆18:30-19:00
Discussion

logic@abelatd.flet.keio.ac.jp

Risako Ando, Koji Mineshima, Mitsuhiro Okada (Keio University), Kentaro Ozeki (University of Tokyo)

"From constructive topology to dynamics in foundations, and back"

We show that topology, understood as a mathematical discipline, is the basis of a dynamic vision of mathematics in which the main criterion is a genuine interaction with reality and not just the mere absence of contradictions.

The distinction between real mathematics, expressed by pointfree topology, and ideal mathematics, expressed by the notions of ideal point and ideal space, allows the development of an abstract mathematics, such as that which began at the end of the 19th century with set theory, but which does not suffer from the abstrusities of the usual axiomatic set theory and, in particular, maintains the priority of the effective and computational aspects of mathematics.

This could be the beginning of a new paradigm in mathematics in the sense of Thomas Kuhn, or rather the completion of the revolution initiated by Frege and Cantor, in which however mathematics is seen not as a given absolute truth, but rather as a cultural product constructed by humanity.