Kit Fine

This chapter considers a number of different ways to develop a semantics in which statements are evaluated at partial possibilities rather than possible worlds. These include the exact version of truth-maker semantics in which truth-makers are wholly relevant to the statements they make true, the inexact version in which they are relevant, but not necessarily wholly relevant, to the statements they make true, and the loose version, in which they need only necessitate the statements they make true, regardless of relevance. The chapter explores the question of how these different semantical schemes are related; and it argues for the surprising conclusion that classical logic can only be properly accommodated within the ‘relevantist’ version of these approaches by allowing possible worlds to be among the partial possibilities. Thus, whatever reasons there might be for adopting such a semantics, they should not include a distaste for possible worlds.

Please keep the original abstract. A number of philosophers have flirted with the idea of impossible worlds and some have even become enamored of it. But it has not met with the same degree of acceptance as the more familiar idea of a possible world. Whereas possible worlds have played a broad role in specifying the semantics for natural language and for a wide range of formal languages, impossible worlds have had a much more limited role; and there has not even been general agreement as to how a reasonable theory of impossible worlds is to be developed or applied. This chapter provides a natural way of introducing impossible states into the framework of truthmaker semantics and shows how their introduction permits a number of useful applications.

Bolzano takes the notion of grounding to be _factive_, so that grounds and their consequences are always _true_ propositions. But he also acknowledges that we sometimes invoke a non-factive notion of grounding. This paper discusses the two ways in which Bolzano attempts to explain the non-factive notion of grounding in terms of the factive notion and critically assesses these proposals from the standpoint of recent debates about grounding and its logic. It is argued that what he has to say, especially in regard to the question of complexity, is still very relevant to issues concerning the intelligibility and unity of ground.

Logicians and philosophers generally suppose that we now possess a perfectly good understanding of how variables work in the symbolism of logic and mathematics. Given Frege's account of their syntactic role and Tarski's account of their semantic role, it would appear that nothing more of any significance need be said. However, this common view is mistaken. There are deep problems concerning the role of variables that have never been properly recognized, let alone solved, and once we attempt to solve them, we see that they have profound implications not only for our understanding of variables but also for our understanding of other forms of expression and for the general nature of semantics. This chapter explains what these problems are and how they are to be solved, and indicates the implications for the rest of semantics.