Journal of Philosophical Logic 50 (6):1249-1291 (2021)

Authors
Peter Fritz
Australian Catholic University
Harvey Lederman
Princeton University
Gabriel Uzquiano
University of Southern California
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.
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DOI 10.1007/s10992-021-09598-5
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References found in this work BETA

Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and Other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 481-563.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
To Be F Is To Be G.Cian Dorr - 2016 - Philosophical Perspectives 30 (1):39-134.
Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.

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Citations of this work BETA

Classicism.Andrew Bacon & Cian Dorr - forthcoming - In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics. Oxford University Press.
Essence and Necessity.Andreas Ditter - 2022 - Journal of Philosophical Logic 51 (3):653-690.
Reply to Speaks.Juhani Yli-Vakkuri & John Hawthorne - 2020 - Philosophical Studies 178 (9):3061-3065.
Ramified structure.Gabriel Uzquiano - forthcoming - Philosophical Studies:1-24.

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