Adaptive Fregean Set Theory

Studia Logica 108 (5):903-939 (2020)
  Copy   BIBTEX


This paper defines provably non-trivial theories that characterize Frege’s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.



    Upload a copy of this work     Papers currently archived: 94,659

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

It might have been Classical Logic.Diderik Batens - 2012 - Logique Et Analyse 55 (218):241.
La contrastación de teorías inconsistentes no triviales.Luis Felipe Bartolo Alegre - 2020 - Dissertation, Universidad Nacional Mayor de San Marcos
Consistency and Decidability in Some Paraconsistent Arithmetics.Andrew Tedder - 2021 - Australasian Journal of Logic 18 (5):473-502.
Two Consistency Results on Set Mappings.Peter Komjath & Saharon Shelah - 2000 - Journal of Symbolic Logic 65 (1):333-338.
Two consistency results on set mappings.Péter Komjáth & Saharon Shelah - 2000 - Journal of Symbolic Logic 65 (1):333-338.
Contradiction and contrariety. Priest on negation.Heinrich Wansing - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):81-93.


Added to PP

50 (#315,169)

6 months
30 (#127,624)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Diderik Batens
University of Ghent

Citations of this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

Add more citations

References found in this work

Transfinite numbers in paraconsistent set theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
A universal logic approach to adaptive logics.Diderik Batens - 2007 - Logica Universalis 1 (1):221-242.
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
Minimally inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.
A semantical Analysis of the Calculi C n.Newton C. A. Da Costa & E. H. Alves - 1977 - Notre Dame Journal Fo Formal Logic 18 (4):621-630.

View all 18 references / Add more references