Against Second-Order Primitivism

In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press (2024)
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Abstract

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion.

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2023-05-22

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Bryan Pickel
University of Glasgow

Citations of this work

Two conceptions of absolute generality.Salvatore Florio & Nicholas K. Jones - 2023 - Philosophical Studies 180 (5-6):1601-1621.

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References found in this work

Semantics in generative grammar.Irene Heim & Angelika Kratzer - 1998 - Malden, MA: Blackwell. Edited by Angelika Kratzer.
The logical syntax of language.Rudolf Carnap - 1937 - London,: K. Paul, Trench, Trubner & co.. Edited by Amethe Smeaton.
Objects of thought.Arthur Norman Prior - 1971 - Oxford,: Clarendon Press. Edited by P. T. Geach & Anthony Kenny.
The logical form of action sentences.Donald Davidson - 1967 - In Nicholas Rescher (ed.), The Logic of Decision and Action. University of Pittsburgh Press. pp. 81--95.

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