David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Ivan Welty (2011). Frege on Indirect Proof. History and Philosophy of Logic 32 (3):283-290.
Richard G. Heck Jr (1997). Finitude and Hume's Principle. Journal of Philosophical Logic 26 (6):589 - 617.
Edward N. Zalta, Frege's Logic, Theorem, and Foundations for Arithmetic. Stanford Encyclopedia of Philosophy.
Kai F. Wehmeier (1999). Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects. Synthese 121 (3):309-328.
G. Aldo Antonelli & Robert C. May (2005). Frege's Other Program. Notre Dame Journal of Formal Logic 46 (1):1-17.
Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
Richard Heck (1999). Frege's Theorem: An Introduction. The Harvard Review of Philosophy 7 (1):56-73.
Fernando Ferreira & Kai F. Wehmeier (2002). On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze. Journal of Philosophical Logic 31 (4):301-311.
Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
Added to index2009-01-28
Total downloads334 ( #3,408 of 1,781,168 )
Recent downloads (6 months)207 ( #2,564 of 1,781,168 )
How can I increase my downloads?