Note on Absolute Provability and Cantorian Comprehension

Abstract

We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.

Categories

Keywords

Reprint years

Other Versions

No versions found

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

My notes

Similar books and articles

Cantorian Set Theory and Limitation of Size.Michael Hallett - 1984 - Oxford, England: Clarendon Press.
Sets and Plural Comprehension.Keith Hossack - 2014 - Journal of Philosophical Logic 43 (2-3):517-539.
Provability and Interpretability Logics with Restricted Realizations.Thomas F. Icard & Joost J. Joosten - 2012 - Notre Dame Journal of Formal Logic 53 (2):133-154.
On the syntax of logic and set theory.Lucius T. Schoenbaum - 2010 - Review of Symbolic Logic 3 (4):568-599.
On The Syntax Of Logic And Set Theory.Lucius Schoenbauma1 - 2010 - Review of Symbolic Logic 3 (4):568-599.
Distinguishing non-standard natural numbers in a set theory within Łukasiewicz logic.Shunsuke Yatabe - 2007 - Archive for Mathematical Logic 46 (3-4):281-287.
The negative theology of absolute infinity: Cantor, mathematics, and humility.Rico Gutschmidt & Merlin Carl - 2024 - International Journal for Philosophy of Religion 95 (3):233-256.
Descriptions and unknowability.Jan Heylen - 2010 - Analysis 70 (1):50-52.
Natural deduction based set theories: a new resolution of the old paradoxes.Paul C. Gilmore - 1986 - Journal of Symbolic Logic 51 (2):393-411.
On arithmetic in the Cantor- Łukasiewicz fuzzy set theory.Petr Hájek - 2005 - Archive for Mathematical Logic 44 (6):763-782.

Analytics

Added to PP
2015-01-13

Downloads
425 (#67,401)

6 months
70 (#85,954)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Holger Leuz
Universität Regensburg

Citations of this work

No citations found.

Add more citations

References found in this work

A Logical Journey. From Gödel to Philosophy.Hao Wang - 1998 - Philosophy 73 (285):495-504.
On formal and informal provability.Hannes Leitgeb - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan. pp. 263--299.
E pluribus unum: Plural logic and set theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
New waves in philosophy of mathematics.Otávio Bueno & Øystein Linnebo (eds.) - 2009 - New York: Palgrave-Macmillan.

View all 6 references / Add more references