[MD] Flying Spaghetti Monsters

[Gene M]

On 10/11/06, pholden at davtv.com <pholden at davtv.com> wrote:
>
> Quoting craigerb at comcast.net:
>
>
> > Actually, Godel proved that logic was complete:
> > Gödel's completeness theorem
> > >From Wikipedia, the free encyclopedia
> > Gödel's completeness theorem is an important theorem in mathematical
> logic which
> > was first proved by Kurt Gödel in 1929. It states, in its most familiar
> form, that
> > in first-order predicate calculus every logically valid formula is
> provable.
> > It was ARITHMETIC that Godel's Theorem states is INcomplete.  Logic is
> the method
> > of determining the CONSEQUENCES that follow from one's
> > assumptions/axioms/premisses.  It has nothing to say about the
> provability of
> > those assumptions/axioms/premisses.
>
> Disagree. From "History of Mathematics" by Carl B. Boyer:
>
> "Gödel showed that within a rigidly logical system such as Russell and
> Whitehead had
> developed for arithmetic, propositions can be formulated that are
> undecidable or
> undemonstrable within the axioms of the system. That is, within the
> system, there
> exist certain clear-cut statements that can neither be proved or
> disproved.
> Hence one cannot, using the usual methods, be certain that the axioms of
> arithmetic
> will not lead to contradictions ... It appears to foredoom hope of
> mathematical
> certitude through use of the obvious methods. Perhaps doomed also, as a
> result, is
> the ideal of science - to devise a set of axioms from which all phenomena
> of the
> external world can be deduced."


You pretty much wrote Exactly what Craig did, and disproved your Own
original point. Odd...

-Gene