Logica Universalis 15 (4):537-552 (2021)

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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11787-021-00292-3
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,114
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Interpretations of Intuitionist Logic in Non-Normal Modal Logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
Relating Intuitionist Negation and Triviality.Wagner de Campos Sanz - 2004 - Logic Journal of the IGPL 12 (6):581-599.
On Analysing Relevance Constructively.Garrel Pottinger - 1979 - Studia Logica 38 (2):171 - 185.
Brouwerian Intuitionism.Michael Detlefsen - 1990 - Mind 99 (396):501-534.
First-Order da Costa Logic.Graham Priest - 2011 - Studia Logica 97 (1):183 - 198.
Intuitionist Type Theory and Foundations.J. Lambek & P. J. Scott - 1981 - Journal of Philosophical Logic 10 (1):101 - 115.


Added to PP index

Total views
6 ( #1,129,525 of 2,499,228 )

Recent downloads (6 months)
6 ( #118,136 of 2,499,228 )

How can I increase my downloads?


My notes