Australian Realists are fond of talking about truth-makers. Here are three examples from the recent literature

It is twelve years since the publication of “Truth-makers, entailment and necessity”, and some of my views on the topics discussed have changed in that time. More recent work on truth-making (in particular, Lewis's “Truth-making and difference-making”, this vol., Ch. 6) has convinced me that the idea that truth depends on ontology can be captured in a number of different ways. Which ways we take to be most appealing will depend on a whole host of views or commitments, not the least being those concerning what different kinds of things there are.

Elsewhere I have shown that the robust picture of truth-making in “Truthmakers, entailment and necessity” can apply in a very simple “world” in which the truth-makers are regions in which atoms are either present or not (Restall 2000). No strange “negative” or “universal” facts need to be added to that picture; regions together with their inhabitants can suffice, so worries about the queerness of “negative” or “universal” facts need not worry the friend of robust truthmaking if the metaphysics is kind enough to supply everyday objects that do the job.

However, some of my views have changed more significantly, since 1996. I am now convinced by an argument of Stephen Read, in “Truthmakers and the Disjunction Thesis” (2000) that the “or and shmor” argument in §3 of “Truthmakers, Entailment and Necessity” is too swift. In the rest of this note, I will give an account of Read's concern, and then chart four possible responses to it from the perspective of one who wishes to maintain the broad outline of the position of “Truth-makers, entailment and necessity”.

Abstract. In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic [9, 15], or multipleconclusion calculi for classical logic [22, 23, 24]).

The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free (the proof of cut-elimination is a simple generalisation of the systematic cut-elimination proof in Belnap's Display Logic [5, 21, 26]) and the circuit proofs are normalising.