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

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

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10.2478/slgr-2021-0042

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References found in this work

Model-Theoretic Logics.Jon Barwise & Solomon Feferman - 2017 - Cambridge University Press.
What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Annalen der Philosophie Und Philosophischen Kritik 2 (1):73-75.

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