[FOM] Re: Truth value algorithm for tokens
Sandy Hodges
SandyHodges at attbi.com
Sat Nov 9 19:45:55 EST 2002
CV- There exists a Boolean Solution and no paradox. Running a SAT
program against the entire set of clauses (I wrote my own for the sake
of this discussion) yields 4 Boolean Solutions, with the following
values for variables 1-8:
T F F T T T T T
T F F T F T T T
F F T T T F T T
F F T T F F T T
SH- But the existence of more than one solution is itself a paradox:
that is why this is not simply a SAT problem. The simplest case is
the Truth-Teller:
Token t: Token t is true.
This has two boolean solutions, that token t is true, and that token t
is false. But if we were to claim that token t is in fact true (and
not false), we would have no grounds for saying that our claim is the
right answer, while someone else who says that token t is false is
mistaken. So the Truth-Teller, like the Liar, is paradoxical and
GAP. But this is not the result of GAP being the only solution of any
set of conditions.
There are those (not many) who think the Truth-Teller is true. But
whatever the arguments in support of this position may be, the fact that
it makes the problem into a SAT problem is not one of them.
------- -- ---- - --- -- --------- -----
Sandy Hodges / Alameda, California, USA
mail to SandyHodges at attbi.com will reach me.
More information about the FOM
mailing list