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The role of syntactic representations in set theory

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
Creators:
CreatorsEmailORCID
Weber, Keithkeith.weber@gse.rutgers.edu0000-0001-8877-1552
Keywords: Derivation; Proof; Mathematical practice; Set theory
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics
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
Date: 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15774

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