Is there a neutral metalanguage?

Synthese 198 (Suppl 20):4831-4858 (2019)

Abstract

Logical pluralists are committed to the idea of a neutral metalanguage, which serves as a framework for debates in logic. Two versions of this neutrality can be found in the literature: an agreed upon collection of inferences, and a metalanguage that is neutral as such. I discuss both versions and show that they are not immune to Quinean criticism, which builds on the notion of meaning. In particular, I show that the first version of neutrality is sub-optimal, and hard to reconcile with the theories of meaning for logical constants, and the second version collapses mathematically, if rival logics, as object languages, are treated with charity in the metalanguage. I substantiate by proving a collapse theorem that generalizes familiar results. Thus, the existence of a neutral metalanguage cannot be taken for granted, and meaning-invariant logical pluralism might turn out to be dubious.

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Rea Golan
Freie Universität Berlin

References found in this work

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Philosophy of Logic.W. V. Quine - 1970 - Harvard University Press.
Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford, England: Oxford University Press.
On the Very Idea of a Conceptual Scheme.Donald Davidson - 1973 - Proceedings and Addresses of the American Philosophical Association 47:5-20.
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.

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