Closed structure

Journal article


Fritz, Peter, Lederman, Harvey and Uzquiano, Gabriel. (2021). Closed structure. Journal of Philosophical Logic. https://doi.org/10.1007/s10992-021-09598-5
AuthorsFritz, Peter, Lederman, Harvey and Uzquiano, Gabriel
Abstract

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle CLOSED STRUCTURE, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of CLOSED STRUCTURE is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, CLOSED STRUCTURE is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

Keywordsstructured propositions; Russell-Myhill; higher-order logic; plural quantification
Year2021
JournalJournal of Philosophical Logic
PublisherSpringer Netherlands
ISSN0022-3611
Digital Object Identifier (DOI)https://doi.org/10.1007/s10992-021-09598-5
Scopus EID2-s2.0-85105473183
Open accessPublished as ‘gold’ (paid) open access
Research or scholarlyResearch
Page range1-43
Publisher's version
License
File Access Level
Open
Output statusIn press
Publication dates
Online08 May 2021
Publication process dates
Accepted04 Mar 2021
Deposited13 Oct 2021
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