Frege's New Science

Notre Dame Journal of Formal Logic 41 (3):242-270 (2000)
Abstract
In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege's debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege's critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be other than true. Because of his adherence to this view, Frege was precluded from the sort of metatheoretical considerations that were available to Hilbert; but from this, we shall argue, it does not follow that Frege was blocked from metatheory in toto. Indeed, Frege suggests in Die Grundlagen der Geometrie a metatheoretical method for establishing independence proofs in the context of the New Science. Frege had reservations about the method, however, primarily because of the apparent need to stipulate the logical terms, those terms that must be held invariant to obtain such proofs. We argue that Frege's skepticism on this score is not warranted, by showing that within the New Science a characterization of logical truth and logical constant can be obtained by a suitable adaptation of the permutation argument Frege employs in indicating how to prove independence. This establishes a foundation for Frege's metatheoretical method of which he himself was unsure, and allows us to obtain a clearer understanding of Frege's conception of logic, especially in relation to contemporary conceptions
Keywords Frege   Hilbert   logicism   logical truth   logical constants   independence proofs
Categories (categorize this paper)
DOI 10.1305/ndjfl/1038336844
Options
 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: 30,370
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
The Composition of Thoughts.Richard Heck & Robert May - 2011 - Noûs 45 (1):126-166.

View all 10 citations / Add more citations

Similar books and articles
Added to PP index
2013-11-01

Total downloads
24 ( #216,351 of 2,193,771 )

Recent downloads (6 months)
1 ( #290,983 of 2,193,771 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature