Friday, November 29, 2013

Who's Afraid of Veridical Wool?

Do we need non-classical logic to resolve the Liar paradox? Or do we need to see that the natural context of classical logic – natural language – has a slight but ubiquitous vagueness? When something is as much the case as not, it is a borderline case; and similarly, self-descriptions like ‘this is false’ are about as true as not. And when there is no sharp division between something being the case and it not being the case, then the precision of any mathematical logic is inapposite.
......The modern literature on the Liar paradox is very formal, but following Russell there has been a related effort to resolve Cantor’s mathematical paradoxes, which may well explain that. My analysis of the Liar paradox has 4 sections: Vagueness (1,300 words), Liar Paradox (1,300), Set-Theoretic Paradox (1,200), Semantic Paradox (900), plus notes (700)...

......Who's Afraid of Veridical Wool?


Monday, November 18, 2013

I think, so I'm iffy

"I deliberate, so the future is open," is, if you think about it, a pretty good description of a rational argument with one premise (a premise of which one can be certain). My making the effort to deliberate well (because I would blame myself if I did not) presupposes that there is, as yet, no fact of the matter of what I will be thinking.
......To make such an effort is to force the future away from a state that it would otherwise be in, of course. And for me to think of that state as already unreal would undermine my motivation to make such an effort. And of course, for me to make no such effort would be for me to care little for the quality of my thoughts, which would be irrational.
......That was a précis of my comments on a Prussian post, themselves inspired by Nicholas Denyer's 1981 defence of arguments like "I deliberate, so my will is free."

Wednesday, November 13, 2013

The Use of Brackets... squirrel away, via RSPB blogs on 21 Oct and 8 Nov :)