Metaphilosophy 44 (1-2):145-156 (2013)

This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object-place but also predicate-place variables in higher-order logic in a criticism of a recent effort to define the concept of heterologicality in a strengthened derivation of Grelling's paradox within type theory requirements. If the objections were correct, they would offer a more general moral for the proper formal definition of terms in philosophical logic. The criticism nevertheless seems mistaken both in the substance and specific application with respect to legitimate synctactical constraints on definitions of key concepts in the case of Grelling's paradox. As such, the critique provides no justification for overturning previous conclusions concerning the possibility of resurrecting a type-observant version of Grelling's heterologicality paradox
Keywords Alfred Tarski  syntactical constraints  Jeffrey Ketland  logical and semantic paradoxes  Kurt Grelling  definitions  Dale Jacquette  concepts  syntax
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DOI 10.1111/meta.12017
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The Semantic Conception of Truth and the Foundations of Semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
Philosophy of Logics.Susan Haack - 1978 - Cambridge University Press.
The Calculi of Lambda-Conversion.Alonzo Church - 1941 - Princeton University Press.
Grelling's Revenge.D. Jacquette - 2004 - Analysis 64 (3):251-256.

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