Properties, Propositions and Conditionals

• Published in: Australasian philosophical review Vol. 4; no. 2; pp. 112 - 146
• Main Author: Field, Hartry
• Format: Journal Article
• Language: English
• Published: Routledge 02.04.2020
• Subjects: conditionals; paradoxes; Philosophical logic
• ISSN: 2474-0500; 2474-0519
• DOI: 10.1080/24740500.2021.1886687

Section 1 discusses properties and propositions, and some of the motivation for an account in which property instantiation and propositional truth behave 'naively'. Section 2 generalizes a standard Kripke construction for naive properties and propositions, in a language with modal operators but no conditionals. Whereas Kripke uses a 3-valued value space, the generalized account allows for a broad array of value spaces, including the unit interval [0,1]. This is put to use in Section 3, where I add to the language a conditional suitable for restricting quantification. The shift from a value space based on the 'mini-space' {0, , 1} to one based on the 'mini-space' [0,1] leads to more satisfactory results than I was able to achieve in previous work: a vast variety of paradoxical sentences can now be treated very simply. In Section 4 I make a further addition to the language, a conditional modeled on the ordinary English conditional, paying particular attention to how it interacts with the restricted quantifier conditional. This is all done in the [0,1] framework, and two alternatives are considered for how the ordinary conditional is to be handled; one of them results from adding a tweak to a construction by Ross Brady. Section 5 discusses a further alternative, a standard relevance conditional (for the ordinary conditional, perhaps for use with a different quantifier-restricting conditional), but argues that it is not promising. Section 6 discusses the identity conditions of properties and propositions (again in the setting of a value space based on [0,1]); the issue of achieving naivety for coarse-grained properties is seen to be more complicated than some brief remarks in Field [ 2010 ] suggested, but a way to get a fair degree of coarse-grainedness is shown.