LUW Fev 09 2022 An Intuitionist Reasoning Upon Formal Intuitionist Logic: Logical Analysis of Kolmogorov’s 1932 Paper

[jean-yves beziau]

After the session of January 14, celebrating the World Logic Day
https://www.logica-universalis.org/wld4
we are now starting for the 2nd year regular sessions of the Logica
Universalis Webinar two times a month.
The next session will be Wednesday February 9, 2022 at 4pm
with a talk by Antonino Drago (University “Federico II” of Naples, Italy)
"An Intuitionist Reasoning Upon Formal Intuitionist Logic: Logical Analysis
of Kolmogorov’s 1932 Paper"
Abstract: Two dichotomies are considered as the foundations of a scientific
theory: the kind of infinity—either potential or actual-, and the kind of
organization of the theory—axiomatic or problem-based. The original
intuitionist program relied on the choices of potential infinity and the
problem-based organization. I show that the logical theory of Kolmogorov’s
1932 paper relied on the same choices. A comparison of all other theories
sharing the same foundational choices allows us to characterize their
common theoretical development through a few logical steps. The theory
illustrated by Kolmogorov’s paper is then rationally re-constructed
according to the steps of this kind of development. One obtains a new
foundation of intuitionist logic, which is of a structural kind since it is
based on and developed according to the structure of the above mentioned
two fundamental choices. In addition, Kolmogorov’s illustration of his
theory of intuitionist logic is an instance of rigorous reasoning of the
intuitionist kind.
Full paper:
https://link.springer.com/article/10.1007/s11787-021-00292-3
Everybody is welcome to attend, register here:
https://www.springer.com/journal/11787/updates/20065848
Jean-Yves Beziau
Organizer of the  Logica Universalis Webinar
https://www.jyb-logic.org/
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