## Sunday, December 23, 2007

I got the preliminary reading list for my qualifying exams today. Here it is.

#

Jon Barwise and John Etchemendy, The Liar.

JC Beall (ed.), Liars and Heaps.

George Boolos, Logic, Logic and Logic.

Vann McGee, Truth, Vagueness, and Paradox.

Michael Hallett, Cantorian Set Theory and Limitation of Size.

Colin McGinn, Logical Properties.

Robert Martin (ed.), Recent Essays on Truth and the Liar Paradox.

Graham Priest, In Contradiction (2nd edition).

Graham Priest, Doubt Truth to Be a Liar.

Graham Priest, Beyond the Limits of Thought (2nd edition).

Graham Priest, Towards Non-Being.

Graham Priest, JC Beall and Brad Armour-Garb (eds.), The Law of Non-Contradiction.

#### 1 comment:

J said...

Intersting list. I am not a professional logician (thankfully) but I think the somewhat "constructivist" approaches to the liar paradox (or apparent paradox) might offer some solutions. Which is to say, if the liar paradox doesn't really manifest itself in reality (say in computing), who cares, except some type of platonist who dreams of some perfect logical system? Kripke (or was it Tars-kee) said something along those lines, didn't he: if the supposed paradox does not concern some matter of fact, it's sort of meaningless (a real barber in a village with some rule that he must shave all who don't shave themselves??? ok, I think that DOES show a paradox but rather un-f-n-likely scenario).

By carefully constructing domains and then making statements (or applying functions, logical operators, what have you) instead of just going from assumed infinite sets (sets of what?) the problem is attenuated: indeed the problem might be "infinity" itself.

There are perhaps some problems with paradoxes and computability (or at least some say there): the Halting Problem or something. That seems more a matter of some proof procedure that will always produce a answer: i.e some arguments cannot be proven to be T v F (a reductio a absurdum will not suffice).

However, most of those types of recursive issues--incompleteness or something--seem fairly negligible from a pragmatist perspective (ie what real, practical significance--say for computing--- does the Liar, or even Goedel's incompleteness theorem entail? Put in those terms the paradoxes seem rather petty if not a type of philosophical escapism).......