Is there a neutral metalanguage?

Research output: Contribution to journalArticlepeer-review

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 (i) the first version of neutrality is sub-optimal, and hard to reconcile with the theories of meaning for logical constants, and (ii) the second version collapses mathematically, if rival logics, as object languages, are treated with charity in the metalanguage. I substantiate (ii) 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.

Original languageEnglish
Pages (from-to)4831-4858
Number of pages28
JournalSynthese
Volume198
DOIs
StatePublished - 1 Aug 2021
Externally publishedYes

Keywords

  • Collapse
  • Logical pluralism
  • Meaning
  • Quine

ASJC Scopus subject areas

  • Philosophy
  • General Social Sciences

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