Modal logic is actually quite useful. If modal realism turns you off you can just accept it as a language game (which any sort of formal logic is going to be.)
The non-sequitur in Plantinga’s argument, as presented by cousin it, is P3. (Plantinga’s own argument is a bit more subtle, and its ultimate error is in eliding between different meanings of the term “possible.” He successfully shows that under formal logic if possibly necessarily x then necessarily x, and then ascribes possible necessity to God because God is one of the most few things that often is argued to be necessary, and that God seems like the sort of sufficiently abstract thing that it might be necessary. But this isn’t the sort of possibility that’s germane to formal logic.)
Eh. He didn’t really show they’re not valuable, just that they haven’t reduced the notions they work with to something other than black boxes. Modal operators can mean all sorts of things, aside from “possibility” and “necessity”, and black boxes are fine as long as they work properly—if you need to know what their internals look like, that’s just a project for some other formalism.
Modal logic is actually quite useful. If modal realism turns you off you can just accept it as a language game (which any sort of formal logic is going to be.)
The non-sequitur in Plantinga’s argument, as presented by cousin it, is P3. (Plantinga’s own argument is a bit more subtle, and its ultimate error is in eliding between different meanings of the term “possible.” He successfully shows that under formal logic if possibly necessarily x then necessarily x, and then ascribes possible necessity to God because God is one of the most few things that often is argued to be necessary, and that God seems like the sort of sufficiently abstract thing that it might be necessary. But this isn’t the sort of possibility that’s germane to formal logic.)
Haven’t read Plantinga and not going to, but ‘possibly necessarily P’ does not imply ‘necessarily P’ in all modal logics.
I agree with Eliezer’s critique of the value of modal logics: 1, 2.
Eh. He didn’t really show they’re not valuable, just that they haven’t reduced the notions they work with to something other than black boxes. Modal operators can mean all sorts of things, aside from “possibility” and “necessity”, and black boxes are fine as long as they work properly—if you need to know what their internals look like, that’s just a project for some other formalism.