the boundaries of language

For the uninitiated, go here.

1. Chuck Norris knows what it is like to be a bat

2. Chuck Norris grabs logic by the throat

3. Chuck Norris knows everything except fear

4. Chuck Norris is independent of ZFC

5. Chuck Norris' roundhouse kicks refute the skeptic thus

6. Chuck Norris' Godel number is 1

7. Chuck Norris secretly reads Brian Leiter

8. Chuck Norris can make zombies feel pain

9. Chuck Norris convinced the Tortoise of 'q'

10. God cannot create a stone so heavy that Chuck Norris cannot lift it

Labels: Misc

Some homework for the logically inclined amongst you:

I've been reading Chris Kelp and Duncan Pritchard's draft for the forthcoming OUP collection on the Knowability Paradox. The Church-Fitch proof I mentioned in a recent post starts out by assuming that knowledge is factive ((FAC): Kp -> p) and that it distributes over conjunction ((CON): K(p&q) -> (Kp & Kq)). Fine assumptions one might think, but Chris and Duncan argue that the anti-realist has good reason to reject factivity, and that (CON) is only plausible given a prior committment to (FAC). The Church-Fitch proof is thus exposed as relying entirely on thoroughly classical/realist assumptions.

I've found myself in pretty intense disagreement with almost every point in the paper, which doesn't happen very often. I have some stuff written about why I don't think the anti-realist should be too thrilled by their proposal, but here I just want to concentrate on the claim that the plausibility of (CON) rests on an assumption of (FAC). In the body of the paper (p8) they give a extremely puzzling argument to this effect. Then in an endnote (p17n6) they write:

'A related reason to be suspicious about (CON) given prior doubts about (FAC) is that (CON) can be shown to be a theorem of (FAC) plus the closure principle for knowledge (which states, roughly, that if one knows one proposition, and one knows that this proposition entails a second proposition, then one knows the second proposition).'

Now for the homework. Where does one require an appeal to (FAC) in the derivation of (CON) from closure? This is meant to be a proposal on behalf of the anti-realist, so make sure all moves are intuitionisitically acceptable.

Now, I would have thought we could just do the following. Assume the antecendent of (CON):

1. K(p&q)

Presumably we also know basic logical truths, so:

2. K((p&q) -> p)
3. K((p&q) -> q)

The following are instances of the closure principle:

4. [K(p&q) & K((p&q) -> p)] -> Kp
5. [K(p&q) & K((p&q) -> q)] -> Kq

It looks like the consequent of (CON) should now follow by propositional logic (conjuction introduction and modus ponens, both of which are intuitionistically kosher). I just don't see the play with factivity at all, but then I'm pretty fallible on such matters.

Labels: Epistemology

Like Andreas, I've discovered that the topics I've wanted to blog about have been much broader than I thought they were going to be. Originally this blog was going to be predominantly philosophy of language, and this was reflected in the name and the description. Much to my surprise, most of my posts have been about epistemology, with occasional forays into vagueness, philosophy of maths and logic, and complete nonsense (of the sort that even the early Wittgenstein wouldn't have approved).

Now, I don't have any inclination whatsoever to change the name of this blog, which comes from the Frege's Puzzle inspired Death Cab for Cutie song 'Different Names for the Same Thing':

'Alone on a train aimless in wonder
An outdated map crumpled in my pocket
But I didn't care where I was going
'Cause they're all different names for the same place.

The coast disappeared when the sea drowned the sun
And I knew no words to share with anyone
The boundaries of language I quietly cursed
And all the different names for the same thing'

But it has struck me that the description I've had up of the blog - 'language-oriented philosophy from the lone star state' - has to go. So for the moment I'm going to go with a wonderful quote from Davidson which reflects the move away from a focus on language. It's an exciting time here at 'the boundaries of language'.

While I'm pointlessly navel-gazing, another change you may have noticed is I've added one of those little maps that charts where in the world hits to this blog come from. It's been pretty surprising so far; I thought it would just be Texas, St Andrews and California, but even in the few days it's been running there's been hits from various places in Europe and beyond, and the east coast of America. So on the tendentious assumption that these haven't been people mistakenly directed here when they googled unusual phrases, let me say welcome, and offer a promise to resume posting proper philosophy soon.

Pack it up, pack it in, let me begin..............

Labels: Metablogging

I broached at the end of my last post the difficulties surrounding questions about the relationship between pre-axiomatic theories and their axiomatic counterparts. I still don't have anything useful to say on the matter, but two of my former professors - Stewart Shapiro and Graham Priest - do, and they're saying it right now over at the Online Philosophy Conference.

There's some really interesting stuff in their papers about the status of logic and of axioms in mathematics, the nature and history of mathematical reasoning, and about diatheism and the possibilities it opens up regarding the study of the mathematical universe. Go check it out.

Labels: Links, Philosophy of Mathematics