Tuesday, January 30, 2007

My mind is blown

This is probably evidence of how little it takes to surprise me. Today I found out that the later Russell was committed to the view that one could quantify over truth-functional connectives. So, one could infer from p&q to (\exists C)pCq for the appropriate types of &. This probably shouldn't be surprising since he thought you could quantify over functions of the various types (ramified theory era) and he viewed the connectives as propositional functions. Since the connectives are just some propositional functions among others, they will be included in the various levels of the order (type? I'm getting mixed up) hierarchy. Russell's type theory is also committed to the connectives being stratified, since you can't have a lower order connective connecting higher order propositions.

Among other things that should have probably come to my attention before: Ruth Millikan has a book called "White Queen Psychology and Other Essays for Alice". I must say, that is a fantastic title. This is something that should've been apparent earlier since last semester I read an essay by McDowell in which he quoted large parts of a Millikan essay called "White Queen Psychology". I remember seeing that title and being distinctly puzzled, cause all that came to mind was the X-men villain, which really made no sense.


Nate Charlow said...

Kind of interestingly, you get the same (or a similar) kind of quantification in the literature on the epistemology of logic. Boghossian, for instance, thinks that '(\exists C)pCq' is a perfectly good sentence (and uses this to move a lot of dirt in giving his own epistemology). The domain of quantification is (I think) more or less the same as Russell's, too: roughly a domain of abstract propositional functions.

Shawn said...

Does Boghossian move a lot of dirt in a substantive way or does he move it around like a bump under a rug? I've never read anything by him. Nor have I read much about the epistemology of logic except insofar as it shows up in Russell, Wittgenstein, and criticisms of Tarskian ideas about logical consequence.

Having had the view pointed out to me, it makes a fair amount of sense. If you are treating the connectives simply as functions albeit somewhat special ones (maybe ones that wear red jackets), and your domain of already includes functions, then you should be committed to the idea of quantifying over connectives.

Does that make logic more epistemologically sound because we have no problem with the epistemology of (propositional?) functions? Or is it an ontological point? (I should sort this out with regard to Russell at the least...)

Nate Charlow said...

You're right to be suspicious. Boghossian's epistemology, and that of others who've tried to ground the epistemology of logic in a similar way (Peacocke, Hale & Wright), is completely inert. Basically the epistemology of logic reduces to the epistemology of the "extensions" of the connectives, which isn't any less problematic. There's a lot of complexity in the debate, and working through it is actually really rewarding, but that gets to the heart of it.