Impossible world

Abstract: Publisher Summary This chapter discusses the semantics of entailment. Earlier, modal logics had no semantics. Bearing a real world G, a set of worlds K, and a relation R of relative possibility between worlds, Saul Kripke beheld this situation and saw that it was formally explicable and made model structures. It came to pass that soon everyone was making model structures, and some were deontic, some were temporal, and some were epistemic, according to the conditions on the binary relation R. The models made by Kripke, Hintikka, and Thomason were, however, not relevant. Central to the semantics being developed is a ternary relation R that takes the place for the relevant logics of the Kripke binary relation for standard modal and intuitionistic logics.

Abstract: It has often been claimed that the by now familiar possible-two rids analysis of propositional attitudes like knowledge and belief which I have advocated since 1962 is unrealistic,1 if not downright mistaken, because it apparently commits us to the assumption of logical omniscience, that is, to the assumption that everyone knows all the logical consequences of what he knows, and analogously for all the other propositional attitudes. Since the assumption of such logical omniscience is obviously mistaken, this commitment seems to constitute a grave objection to the whole possible-worlds treatment of propositional attitudes.

Abstract: In the last dozen years or so, our understanding of modality has been much improved by means of possible-world semantics: the project of analyzing modal language by systematically specifying the conditions under which a modal sentence is true at a possible world. I hope to do the same for counterfactual conditionals. I write A□→C for the counterfactual conditional with antecedent A and consequent C. It may be read as ‘If it were the case that A, then it would be the case that C’ or some more idiomatic paraphrase thereof.

Abstract: In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve more finely than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics.