# Strict Truthmaking Logic

## Mark Jago

### University of Nottingham

The notion of strict truthmaking is central to the logic of truthmaking and to the project of giving semantics in terms of truthmakers. A strict truthmaker for A is a state α in virtue of which A is true, so that states with irrelevant parts do not count as strict truthmakers for A. The notion of strict truthmaking is therefore non-monotonic. This semantics produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the logic highly unusual and worth investigating on purely logical grounds. But the investigation of strict truthmaker logic also has interesting applications in metaphysics.

Strict truthmaking logic has received very little attention in the technical literature. Fine notes in passing that ‘the notion of exact [i.e., strict] consequence is of great interest in its own right’ (Fine 2013, 21), but says nothing further about the notion. In this talk, I’ll set out systems of formal semantics for strict truthmaking, which have parallels with Fine’s (2013) truthmaking semantics for intuitionistic logic. I’ll spend some time investigating the resulting notions of entailment, building up to some representation theorems. I’ll then give sequent-style proof systems, establish a number of results about them, and prove soundness and completeness results.

I’ll finish by discussing applications of these semantic systems to various metaphysical debates about truthmaking. One application concerns the status of Rodriguez-Pereyra’s conjunction and disjunction theses; another concerns Armstrong’s entailment thesis. I’ll argue that truthmaking semantics (including the strict semantics presented here) help us to systematise philosophical intuitions about these important metaphysical concepts.

Mark Jago (Ph.D. 2006, Nottingham University) is a philosopher in Nottingham, UK, interested in philosophical and formal logic, language, metaphysics and the philosophy of mind.