David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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||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.
Howard Wettstein (1990). Frege‐Russell Semantics? Dialectica 44 (1‐2):113-135.
Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
Sanford Shieh (2008). Frege on Definitions. Philosophy Compass 3 (5):992-1012.
Jamie Tappenden (2000). Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments? Notre Dame Journal of Formal Logic 41 (3):271-315.
Jamie Tappenden (1997). Metatheory and Mathematical Practice in Frege. Philosophical Topics 25 (2):213-264.
Kai F. Wehmeier (1997). Aspekte der frege–hilbert-korrespondenz. History and Philosophy of Logic 18 (4):201-209.
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
G. Aldo Antonelli & Robert C. May (2000). Frege's New Science. Notre Dame Journal of Formal Logic 41 (3):242-270.
Added to index2009-01-28
Total downloads23 ( #78,735 of 1,100,089 )
Recent downloads (6 months)1 ( #304,128 of 1,100,089 )
How can I increase my downloads?