David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 11 (2):185-192 (1990)
Serious difficulties attend the reading of David Hilbert's 1925 classic paper ?On the infinite?. I claim that the peculiarities of presentation plaguing certain parts of that paper, as well as of the earlier ?On the Foundations of Logic and Arithmetic? (1904), are due to a tension between two incompatible semantical approaches to numerical statements of elementary arithmetic, and accordingly two incompatible metaphysical conceptions of the natural numbers. One of these approaches is the referential, or model-theoretical one; the other is the iterativist's approach. I draw out the two tendencies in these works, with more attention paid to Hilbert's iterativistic tendency because of the unfamiliarity of iterativism generally. I begin with an exposition of this view
|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
Yvon Gauthier (1994). Hilbert and the Internal Logic of Mathematics. Synthese 101 (1):1 - 14.
Kai F. Wehmeier (1997). Aspekte der frege–hilbert-korrespondenz. History and Philosophy of Logic 18 (4):201-209.
Yaroslav Sergeyev (2010). Counting Systems and the First Hilbert Problem. Nonlinear Analysis Series A 72 (3-4):1701-1708.
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
Ansten Klev (2011). Dedekind and Hilbert on the Foundations of the Deductive Sciences. Review of Symbolic Logic 4 (4):645-681.
Paolo Mancosu (1999). Between Russell and Hilbert: Behmann on the Foundations of Mathematics. Bulletin of Symbolic Logic 5 (3):303-330.
José Ferreirós (2009). Hilbert, Logicism, and Mathematical Existence. Synthese 170 (1):33 - 70.
G. Kreisel (1953). A Variant to Hilbert's Theory of the Foundations of Arithmetic. British Journal for the Philosophy of Science 4 (14):107-129.
Richard Zach (2004). Hilbert's 'Verunglückter Beweis', the First Epsilon Theorem, and Consistency Proofs. History and Philosophy of Logic 25 (2):79-94.
Philip Kitcher (1976). Hilbert's Epistemology. Philosophy of Science 43 (1):99-115.
Added to index2010-08-10
Total downloads5 ( #259,745 of 1,679,386 )
Recent downloads (6 months)1 ( #182,933 of 1,679,386 )
How can I increase my downloads?