[FOM] A question about dialetheism and sorites

[Axiomize@aol.com]

On 14 Nov 2002, Sandy Hodges wrote:

> Allen Hazen suggested I look at Graham Priest's Logic of Paradox.   The
> primary claim made by this paper is:

> Claim (1): Some sentences are both true and false.

> But in his "Concluding self-referential postscript" he says (the
> equivalent of):

> It is not the case that some sentences are both true and false.

Any system that concludes that a particular sentence is both true and false 
is inconsistent, so that everything is provable and there is no significance 
to the system.  It proves false statements.  It is not sound.

The Liar paradox is simply the semantics of a program that gets into an 
infinite loop, expressed in English.  The first thing that "This is false." 
does is to perform a GOTO to itself.  Thus it gets into an infinite loop, it 
never halts, and is neither true nor false.  A Turing Machine can halt yes, 
halt no, or loop.  These semantics expressed in English produce sentences 
that are true, false and neither, respectively.  No Turing Machine can both 
halt yes and halt no, and no English sentence is both true and false.

Both "This is true." and "This is false." (as well as my own, " 'It is false 
of itself.' is true of itself.") express the semantics of programs that get 
into infinite loops.  The difference is, if "This is false." had a truth 
value (i.e., its program halted), then we would have an inconsistency, and 
English would be inconsistent, whereas there is no inconsistency in "This is 
true." having a truth value.  However, since neither does halt, this fact is 
of no consequence, there is no inconsistency demonstrated in English, and 
neither has a truth value.

Charlie Volkstorf
Cambridge, MA