Magal, Oran (2013) On the mathematical nature of logic, featuring P. Bernays and K. Gödel. In: UNSPECIFIED.

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Abstract

The paper examines the interrelationship between mathematics and logic, arguing that a central characteristic of each has an essential role within the other. The first part is a reconstruction of and elaboration on Paul Bernays’ argument, that mathematics and logic are based on different directions of abstraction from content, and that mathematics, at its core it is a study of formal structures. The notion of a study of structure is clarified by the examples of Hilbert’s work on the axiomatization of geometry and Hilbert et al.’s formalist proof theory. It is further argued that the structural aspect of logic puts it under the purview of the mathematical, analogously to how the deductive nature of mathematics puts it under the purview of logic. This is then linked, in the second part, to certain aspects of Gödel’s critique of Carnap’s conventionalism, that ‘mere syntax’ cannot capture the full content of mathematics, which is revealed to be closely related to the characteristic of mathematics argued for by Bernays. Finally, this is connected with Gödel’s latter-day views about two kinds of formality, intensional and extensional (corresponding to logic and mathematics), and the relationship between them.

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Item Type:	Conference or Workshop Item (UNSPECIFIED)
Creators:	Creators Email ORCID Magal, Oran oran.magal@gmail.com
Keywords:	Bernays, Goedel, Gödel, Philosophy of Logic, Philosophy of Mathematics
Subjects:	General Issues > History of Philosophy of Science General Issues > Logical Positivism/Logical Empiricism Specific Sciences > Mathematics General Issues > Philosophers of Science
Depositing User:	Oran Magal
Date Deposited:	26 Mar 2013 12:07
Last Modified:	26 Mar 2013 12:07
Item ID:	9643
Subjects:	General Issues > History of Philosophy of Science General Issues > Logical Positivism/Logical Empiricism Specific Sciences > Mathematics General Issues > Philosophers of Science
Date:	March 2013
URI:	https://philsci-archive.pitt.edu/id/eprint/9643

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