Higher-Order Logic & Modality
In this paper we explore the logic of broad necessity. Definitions of what it means for one modality to be broader than another are formulated, and we prove, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. We show, moreover, that it is possible to give a reductive analysis of this necessity in extensional language (using truth functional connectives and quantifiers). This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. We formulate this conjecture precisely in higher-order logic, and examine concrete cases in which it fails. We end by investigating the logic of broad necessity. It is shown that consistently with higher-order logic, the logic of broad necessity can be anywhere between S4 and Ver; we give some reasons to think that it is strictly weaker than S5.
Date: 9 March 2017, 18:00
Venue: Ertegun House, 37a St Giles OX1 3LH
Speaker: Dr Andrew Bacon (University of Oxford)
Organising department: Faculty of Philosophy
Organiser: Benjamin Brast-McKie (University of Oxford)
Part of: The MLE Seminar
Topics:
Booking required?: Not required
Audience: Members of the University only
Editor: Andy Davies