🚀 go-pugleaf

In article <8135@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) writes:
>In article <3977@sdcc3.ucsd.EDU>, ma188saa@sdcc3.ucsd.EDU (Steve Bloch) writes:
>Godel's *incompleteness* theorems simply say that your
>hypothetical logician, if consistent, might come across
>unprovable statements. In the first order predicate calculus, for
>example, there are fully quantified statements that can neither
>be proven or disproven. Such a statement, or its denial, can be
>as an axiom to the system, which remains consistent thereby.

>Godel is second only to Einstein in having pseudophilosophical
>claptrap "based" on his work. Poor Godel.

How ironic that your name is Russell!  Too bad it's not your last
name :-).  Actually Einstein isn't even in the running; the other
big scientific discovery with philosophical implications is quantum
theory; by contrast relativity is only a slight adjustment of Newton.

Godel's first incompleteness theorem states that you WILL, not MIGHT,
come up with unproveable statements if your axiom system is powerful
enough.  But his second theorem is more interesting, in that it
asserts that a sufficiently powerful system (one that includes Peano
arithmetic, for example) can never prove its own consistency.  This
has far more philosophical consequences than the first.

Some people still seem to want to hold on to 19th century
clockwork-universe objective (or should I say Objectivist?  Better
not :-)) viewpoints despite the fact that Heisenburg and Godel
blasted these notions quite effectively in the 20s and 30s.
You can't know that you're right.  You can't observe something
without changing it.  There is no such thing as an objective
observer.  C'est la vie.
-- 
- Joe Buck    jbuck@epimass.EPI.COM  (in the brave new world of domains!)
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