[FOM] Theories of truth

[JC Beall]

On Friday, September 6, 2002, at 12:02 AM, Harvey Friedman wrote:

> I am at least aware of an enormous literature on the liar's paradox by 
> philosophers, before, but particularly after Saul Kripke's "theory of 
> truth". The idea is to make interesting/natural definitions by 
> transfinite induction that determine the truth and falsity of many 
> self referential assertions, but leave some undecided as to truth 
> value. For instance, "this sentence is true" would be decided as true, 
> but "this sentence is false" would have an undetermined truth value. 
> This is normally done in for the language L of Peano arithmetic with a 
> unary predicate symbol T(n) added. Syntactically, there are no issues 
> with regard to L. The question is: which sentences of L are to be 
> true, which are to be false, and which undetermined? The 
> interpretation of T(n) is to be "n is the Godel number of a sentence 
> of L that is true".
>
> Many people on this list know this literature better than I do and 
> could provide a nice set of references.
>

I'm working on a book which, in part, surveys contemporary theories of 
truth.  The book is under contract but won't be out until early 2004.  
(I will send an announcement when chapters are ready for circulation.)  
For now, here are a few (a very few) places to start---assuming one has 
already read Kripke's "Outline".

Albert Visser.  Four valued semantics and the Liar.  JPL 13:181--212.

Albert Visser.  Semantics and the Liar Paradox.  In volume 4 of Gabbay 
and Guenthner, Handbook of Philosophical Logic, 1983--1989.  [There may 
be a revised copy of this, since a second, revised and expanded edition 
of the given handbook is slowly coming out.]

J. Barwise and J. Etchemendy.  The Liar.  OUP 1987.

Vann McGee.  Truth, Vagueness, and Paradox.  Hackett.  1991.

Anil Gupta and Nuel Belnap.  The Revision Theory of Truth.  MIT.  1993.

Keith Simmons.  Universality and the Liar.  Cambridge. 1993.

Start with Visser, and then any of the three books above will give you 
a good idea of the three standard approaches (fixed point, 
contextualist, revision).  There are also two collections by Robert L 
Martin:

* The Liar Paradox.  Yale.  1970 (?)

* Recent Essays on Truth and the Liar.   OUPO 1984.

Hope that helps.

JC Beall
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