Being Necessary: Themes of Ontology and Modality from the Work of Bob HaleIvette Fred-Rivera, Jessica Leech What is the relationship between ontology and modality - between what there is, and what there could be, must be, or might have been? Bob Hale interwove these two strands of metaphysics throughout his long and distinguished career, putting forward his theses in his book, Necessary Beings: An Essay on Ontology, Modality, and the Relations Between Them (OUP 2013). Hale addressed questions of ontology and modality on a number of fronts: through the development of a Fregean approach to ontology, an essentialist theory of modality, and in his work on neo-logicism in the philosophy of mathematics. The essays in this volume engage with these themes in Hale's work in order to progress our understanding of ontology, modality, and the relations between them. Some directly address questions in modal metaphysics, drawing on ontological concerns, while others raise questions in modal epistemology and of its links to matters of ontology, such as the challenge to give an epistemology of essence. Several essays also engage with questions of what might be called 'modal ontology': the study of whether and what things exist necessarily or contingently. Such issues have an important bearing on the kinds of semantic commitments engendered in logic and mathematics (to the existence of sets, or numbers, or properties, and so on) and the extent to which one's ontology of necessary beings interacts with other plausible assumptions and commitments. |
Contents
| 1 | |
On Some Arguments for the Necessity and Irreducibility of Necessity | 15 |
The World of TruthMaking | 36 |
Essentialism and Logical Consequence | 60 |
Radical Contingentism or Why Not Even Numbers Exist Necessarily | 77 |
Properties and Predicates Objects and Names Impredicativity and the Axiom of Choice | 92 |
Predication Possibility and Choice | 111 |
Logicism Ontology and the Epistemology of SecondOrder Logic | 140 |
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abstract accept actual allow approach argues argument arithmetic assume assumption axiom choice claim classical commitment compatible comprehension conceiving conception concerned condition consequence consider corresponding definable definition deflationary depend determinate discussion distinct domain entities epistemology essence essential essentialist example existence explain expressions fact first-order formula Frege functions given Hale Hale's holds impredicative individuals infinite instances intuitionistic logic kind knowledge language least mathematics matter means metaphysical modal names natural natural numbers necessary necessity notion objects ontology ordinals Oxford particular Philosophy plural position possible predicate present principle proof properties proposition quantifiers question range reason reference relation requires restriction result rules second-order logic semantics sense singular skepticism space specified suggests Suppose Theorem theory things thought true truth truth-maker understanding University Press variables worlds Wright