Weber, Keith (2019) The role of syntactic representations in set theory. [Preprint]
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Abstract
In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the Derivation Indicator position that asserts that the ordinary proofs given in mathematical discourse indicate syntactic derivations in a formal logical system. In particular, we note that several of the arguments against the Derivation Indicator position would seem to imply that set theorists could gain no benefits from the syntactic representations of concepts indicated by their definitions, yet set theorists clearly do.
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Item Type: | Preprint | ||||||
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Keywords: | Derivation; Proof; Mathematical practice; Set theory | ||||||
Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics |
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Depositing User: | Dr. Keith Weber | ||||||
Date Deposited: | 01 Mar 2019 18:54 | ||||||
Last Modified: | 01 Mar 2019 18:54 | ||||||
Item ID: | 15774 | ||||||
Subjects: | Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics |
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Date: | 2019 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/15774 |
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