Dear all, The next meeting of the Moral Sciences Club will be held next Tuesday (17th November). We are delighted to welcome Hartry Field (NYU), who will be giving a talk entitled 'Naive Properties'. The abstract for the talk is as follows:
Naive property theory consists of (1) an Abstraction Principle, asserting the existence of each property definable (from parameters) in the property-theoretic language; (2) an Instantiation Principle, making the obvious generalization of the claim that (necessarily) the property of not being an electron is satisfied by just those things that aren’t electrons; and perhaps (3) an Identity Principle, which takes necessary coextensiveness as sufficing for identity of properties. (3) seems less obvious than the others, but in any case, (1) and (2) by themselves lead to contradiction in classical logic. A classical logician is likely to follow the lead of the standard resolution of the set-theoretic paradoxes, by weakening (1). This is highly problematic, and I tentatively suggest that weakening (2) is the better option for the proponent of classical logic. But I prefer keeping both (1) and (2), in a non-classical setting. This allows us to also come very close to keeping (3), if we want it. There’s much prior work allowing us to keep (1) and (2) in a non-classical setting, but until recently, only in logically weak languages. Gilmore and Kripke did it for a language without well-behaved conditionals, and without restricted quantifiers, in a logic with a 3-valued semantics. Skolem and Chang did it for a language that did include a well behaved conditional, but without any quantifiers at all, in a logic with a continuum-valued semantics. Both theories are very attractive in their limited domains, and they agree where they overlap, so it’s natural to try for a common generalization of both. In this talk I’ll show how to achieve that. (My previous published work generalized only Gilmore-Kripke, not Skolem-Chang, and gave a less tractable theory.) I’ll include some discussion of two different kinds of conditionals: ordinary indicative conditionals and quantifier-restricting conditionals. We ultimately need a theory of both, and of how they interact, in a framework suitable for the paradoxes. There won’t be time for the details, but I’ll try to hit some key points about how this goes. The meeting will be held from 2:30 until 4:15 on Zoom: https:/ <https://zoom.us/j/98343588455>/zoom.us/j/98343588455 <https://zoom.us/j/98343588455> (Meeting ID: 983 4358 8455). Best wishes, Christopher, Emma, Sofía and Wouter. -- Christopher Benzenberg, Emma Curran, Sofía Meléndez-Gutiérrez and Wouter Cohen Acting Secretaries of the Moral Sciences Club Faculty of Philosophy University of Cambridge msc...@hermes.cam.ac.uk <msc...@hermes.cam.ac.uk> http://www.phil.cam.ac.uk/seminars-phil/seminars-msc _____________________________________________________ To unsubscribe from the CamPhilEvents mailing list, or change your membership options, please visit the list information page: http://bit.ly/CamPhilEvents List archive: https://lists.cam.ac.uk/pipermail/phil-events/ Please note that CamPhilEvents doesn't accept email attachments. See the list information page for further details and suggested alternatives.
