🚀 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:
>
>> I just thought of something: a consistent logician cannot believe
>> in its own consistency IF IT HAS READ GOEDEL.  
>
>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.

   Paraphrasing Godel on incompleteness: "A formal system is either incomplete
or inconsistent". Taking the example of the predicate calculus, there are
statements that can neither be proven or disproven, but you cannot tell me
how many of them there are, and you cannot prove to me that there are no more
such statements. Thus the system MAY be consistent, but you cannot know that
it is for sure. You may end up with an infinite number of axioms.....
Someone should have shot Godel at birth.


Ian "Motorcycle Maaaaan"  Gunn         UK JANET : ian@uk.ac.rl.vd
Rutherford Appleton Laboratory             UUCP : ..!mcvax!ukc!rlvd!ian 
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