The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)

The correspondence theory of truth has experienced something of a revival recently in the form of the Truthmaker Axiom: whatever is true, something makes it true. We consider various postulates which have been proposed to characterize truthmaking, in particular, the Disjunction Thesis (DT), that whatever makes a disjunction true must make one or other disjunct true. In conjunction with certain other assumptions, DT leads to triviality. We show that there are elaborations of truthmaking on which DT holds (which must therefore (...) take steps to avoid the triviality); but that there are more plausible accounts of truthmaking on which DT fails. (shrink)

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Argues that a set is the mereological whole of the singleton sets of its members (following Lewis's Parts of Classes), and that the singleton set of X is the state of affairs of X's having some unit-making property.

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. (shrink)

A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now. ” I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.

According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and their co-workers (...) [1, 2, 8, 11]. Furthermore, I proposed a number of theses about truthmaking as necessitation. The most controversial of these is the disjunction thesis: x makes a disjunction A v B true if and only if it makes one of the disjuncts (A or B) true. That paper left one important task unfinished. I did not explain how the theses about truthmaking could be true together. In this paper I give a consistency proof, by providing a model for the theses of truthmaking in my earlier paper. This result does two things. First, it shows that the theses of truthmaking are jointly consistent. Second, it provides an independently philosophically motivated formal model for relevant logics in the 'possible worlds' tradition of Routley and Meyer [8, 16, 17]. (shrink)