Formalization, syntax and the standard model of arithmetic

Synthese 154 (2):199 - 229 (2007)
  I make an attempt at the description of the delicate role of the standard model of arithmetic for the syntax of formal systems. I try to assess whether the possible instability in the notion of finiteness deriving from the nonstandard interpretability of arithmetic affects the very notions of syntactic metatheory and of formal system. I maintain that the crucial point of the whole question lies in the evaluation of the phenomenon of formalization. The ideas of Skolem, Zermelo, Beth and Carnap (among others) on the problem are discussed. ‘A tries to explain to B the meaning of negation. Finally A gives up, saying: “You don’t understand what I mean, and I am not going to explain any longer,” to which B replies: “Yes, I see what you mean, and I am glad you are willing to continue your explanations”’. G. Mannoury, reported by E. W. Beth (Beth, 1963, 489)
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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References found in this work BETA
Rudolf Carnap (1937). The Logical Syntax of Language. London, K. Paul, Trench, Trubner & Co., Ltd..
Akihiro Kanamori (2000). The Higher Infinite. Studia Logica 65 (3):443-446.
Paul Benacerraf (1985). Skolem and the Skeptic. Proceedings of the Aristotelian Society 59:85-115.

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