“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic

Studies in Logic, Grammar and Rhetoric 66 (3):673-708 (2021)
  Copy   BIBTEX

Abstract

In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks concerning the development of infinitary logic. I also stress the fact that the second axiomatization of set theory provided by Zermelo in 1930 involved the use of extremal axioms of a very specific sort.1.

Categories

Add categories

Keywords

Reprint years

DOI

10.2478/slgr-2021-0042

Other Versions

No versions found

Links

PhilArchive

External links

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

Through your library

My notes

Similar books and articles

A Theory of Infinitary Relations Extending Zermelo’s Theory of Infinitary Propositions.R. Gregory Taylor - 2016 - Studia Logica 104 (2):277-304.
Zermelo's Cantorian theory of systems of infinitely long propositions.R. Gregory Taylor - 2002 - Bulletin of Symbolic Logic 8 (4):478-515.
Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory.Gregory H. Moore - 1980 - History and Philosophy of Logic 1 (1-2):95-137.
Review: Toshio Nishimura, Note on Axiomatic Set Theory I. The Independence of Zermelo's "Aussonderungsaxiom" from Other Axioms of Set Theory; Toshio Nishimura, Note on Axiomatic Set Theory II. A Construction of a Model Satisfying the Axioms of set Theory without Zermelo's Aussonderungsaxiom in a certain axiom system of ordinal numbers.Gert Heinz Muller - 1964 - Journal of Symbolic Logic 29 (2):107-107.
The origins of zermelo's axiomatization of set theory.Gregory H. Moore - 1978 - Journal of Philosophical Logic 7 (1):307 - 329.
Zermelo and set theory.Akihiro Kanamori - 2004 - Bulletin of Symbolic Logic 10 (4):487-553.
Note on Axiomatic Set Theory I. The Independence of Zermelo's "Aussonderungsaxiom" from Other Axioms of Set Theory.Toshio Nishimura - 1964 - Journal of Symbolic Logic 29 (2):107-107.
Infinitary S5‐Epistemic Logic.Aviad Heifetz - 1997 - Mathematical Logic Quarterly 43 (3):333-342.
On the Proof Theory of Infinitary Modal Logic.Matteo Tesi - 2022 - Studia Logica 110 (6):1349-1380.
Game logic and its applications I.Mamoru Kaneko & Takashi Nagashima - 1996 - Studia Logica 57 (2-3):325 - 354.

Analytics

Added to PP
2022-01-05

Downloads
70 (#846,009)

6 months
14 (#869,043)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Inconcistency of ℕ from a not-finitist point of view.Enrico Pier Giorgio Cadeddu - 2023 - International Journal of Modern Research in Engineering and Technology 8 (10):2.

Add more citations

References found in this work

What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Model-Theoretic Logics.Jon Barwise & Solomon Feferman - 2017 - Cambridge University Press.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Cantorian Set Theory and Limitation of Size.Michael Hallett - 1984 - Oxford, England: Clarendon Press.

View all 83 references / Add more references