Kit Fine

An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results.

Che cos'e la realta, cosa definisce il reale? Hegel ci ha detto che tutto cio che e reale e razionale, ma non ci ha detto che cosa e reale. Una roccia e reale o sono reali solamente i suo elementi primari? Sembrano interrogativi piuttosto eccentrici e con scarsa valenza pratica giornaliera. Eppure filosofi, scienziati e studiosi di scienze sociali si vanno interrogando sui fondamenti della realta e sulle ragioni del realismo, il costrutto teorico del reale. Questo testo per la prima volta propone in sequenza i contributi di alcuni dei maggiori studiosi di questa materia, provenienti dalle tre aree del pensiero coinvolte nel dibattito sulla reality: la filosofia, la scienza e le scienze sociali. Si tratta di testi impegnativi da leggere, seppur spiegati e commentati dai loro giovani curatori. Eppure la loro lettura vi dara una ricompensa unica come quella di un paesaggio terrestre osservato da una vetta alpina dopo averla scalata."

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b).

In the early seventies, several logicians developed a semantics for propositional systems of relevance logic. The essential ingredients of this semantics were a privileged point o, an ‘accessibility’ relation R and a special operator * for evaluating negation. Under the truth- conditions of the semantics, each formula A(Pl,…,Pn) could be seen as expressing a first order condition A+(pl,…,pn, o, R,*) on sets p1,…,pn and o, R, *, while each formula-scheme could be regarded as expressing the second-order condition ∀p1,…,∀pn A+(p1,…,pn, o, R, *). It could then be shown that many standard systems of propositional relevance logic were complete in the sense that their theorems were just those formulas true in all models whose components o, R and * conformed to the second-order conditions expressed by the axioms of the system.

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal.

The book is about the problem of vagueness. It begins by discussing some of the existing views on vagueness and then explains why they have not been thought to be satisfactory. It then outlines a new account of vagueness, based on the general idea that vagueness is a global rather than a local phenomenon. In other words, the vagueness of an expression or object is not an intrinsic feature of the object or an expression but a matter of how it relates to other objects and expression. The development of this idea leads to a new semantics and logic for vagueness. The semantics and logic are then applied to a number of issues, including the sorites paradox, the transparency or luminosity of mental states, and personal identity. It is shown that the view allows one to hew to a much more intuitive position on these various issues.

This paper is an attempt to apply the truthmaker approach, recently developed by a number of authors, to the problem of providing an adequate formulation of the is–ought gap. I begin by setting up the problem and criticizing some other accounts of how the problem should be stated; I then introduce the basic apparatus of truth-making and show how it may be extended to include both descriptive and normative truth-makers; I next consider how the gap principle should be formulated, attempting to deal as systematically as possible with the ‘harmless’ counter-examples; I also consider the relationship between the gap principle and various other doctrines concerning the separation between the normative and descriptive realms; and I conclude this part of the paper with some general remarks in favor of adopting the truth-maker approach over some of the alternative approaches. The paper concludes with a formal appendix, which gives precise expression to some of claims made in the previous informal part of the paper.