A Logic for Frege's Theorem

In Frege's Theorem. Oxford University Press (2011)
It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic".
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 32,607
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
Logic in the Tractatus.Max Weiss - 2017 - Review of Symbolic Logic 10 (1):1-50.
Classes, Why and How.Thomas Schindler - forthcoming - Philosophical Studies:1-29.
Frege on Sense Identity, Basic Law V, and Analysis.Philip A. Ebert - 2016 - Philosophia Mathematica 24 (1):9-29.

View all 7 citations / Add more citations

Similar books and articles
Frege on Indirect Proof.Ivan Welty - 2011 - History and Philosophy of Logic 32 (3):283-290.
Finitude and Hume's Principle.Richard G. Heck Jr - 1997 - Journal of Philosophical Logic 26 (6):589 - 617.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Frege's Theorem: An Introduction.Richard Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
Completeness and Categoricity: Frege, Gödel and Model Theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
Added to PP index

Total downloads
467 ( #5,796 of 2,235,726 )

Recent downloads (6 months)
7 ( #82,381 of 2,235,726 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature