🚀 go-pugleaf

In article <1192@epimass.EPI.COM> jbuck@epimass.EPI.COM (Joe Buck) writes:
>In article <8135@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) 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. 
>
>Godel's first incompleteness theorem states that you WILL, not MIGHT,
>come up with unproveable statements if your axiom system is powerful
>enough.  

The upshot of Goedel's incompleteness theorem is the unprovability of
necessarily true statements, i.e., statements true in every model, for
sufficiently powerful systems.  That there are *some* statements your
system can't prove is a good thing: but this is the requirement of
consistency, not completeness.  First order predicate calculus is both
consistent and complete.
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--Paul.