DEFLATIONARY TRUTH: CONSERVATIVITY OR LOGICALITY?

Relativism, Assertion and Deflationary Truth∗

We provide a deflationarily acceptable account of assertion in truth-relativistic domains. First, we state what we take relativism and deflationism to be. Second, we clarify the problem of assertion in relativistic domains by singling out the features that make assertion within those domains problematic. Then, we tackle the problem directly by generalizing a standard deflationary account of the...

Conservativity for theories of compositional truth via cut elimination

We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a critical error in Halbach’s original presentation. Our methods show that the admission of these axioms determines a hyper-exponential reduction in the size of de...

Truth-bearers or Truth-makers?

Logicality and Invariance

This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski-Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized o...

Logicality of Conditional Rewrite Systems

A conditional term rewriting system is called logical if it has the same logical strength as the underlying conditional equational system. In this paper we summarize known logicality results and we present new sufficient conditions for logicality of the important class of oriented conditional term rewriting systems.