This chapter investigates the thesis that Invariance Under Isomorphisms is a criterion of logicality (logical operators) and the roots of this criterion in Tarski. It discusses the philosophical significance of this criterion, offers a philosophical justification for it, examines its ramifications for the relation between logic and mathematics, responds to Feferman's criticisms of this criterion, and critically examines Feferman's alternative criterion. The chapter also investigates methodological issues involved in a providing criterion of logicality (e.g. foundationalism vs. holism), logic's role in our system of knowledge, the relation between logicality and truth, and the idea of logicality as formality.
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