🚀 go-pugleaf

In article <3977@sdcc3.ucsd.EDU> ma188saa@sdcc3.ucsd.edu.UUCP (Steve Bloch) writes:
>I just thought of something: a consistent logician cannot believe
>in its own consistency IF IT HAS READ GOEDEL.  But a person with a
>mental block against Goedel's proof is perfectly capable of
>consistently believing in its own consistency.  Anyone for banning
>all publication of Goedel's proof, or anything inspired by it, so
>that humans can be consistent again?
>Sorry; I'm falling into Russell-and-Whitehead, who avoided
>self-referential statements by making them inadmissible in the same
>way that I'm making Goedel inadmissible.  I suspect any procedure
>capable of RECOGNIZING Goedelese reasoning would necessarily believe
>it, and therefore not consistently believe in its own consistency.


	Er, well, no.  It's not that simple.  You have to explain what
you mean by "consistently believe".  (Hint -- don't try :-)).  If the
logician is consistent, then she may consistently believe in her consistency.
This remains true, even though she knows that she cannot demonstrate her
consistency.

	This is much the situation modern logic is actually in.  We believe
that arithmetic is consistent.  Yet we know that we cannot prove the
consistency of arithmetic without using methods less elementary than
arithmetic.  Whence the belief in the consistency of arithmetic is a
matter of faith.

	Incidentally, there is a school that believes that arithmetic
is, in fact, inconsistent, but that the smallest demonstration of this
inconsistency would take more time than the entire lifetime of the universe.
Members of this school consistently believe in the inconsistency of logic.
I am not quite up to determining whether they consistently believe in
their own inconsistency.
-- 

Richard Harter, SMDS Inc. [Disclaimers not permitted by company policy.]