Jim Choate wrote:
>
> With regard to completeness, I have Godel's paper ("On Formally
> Undecidable Propositions of Principia Mathematica and Related Systems", K.
> Godel, ISBN 0-486-66980-7 (Dover), $7 US) and if somebody happens to know
> the section where he defines completeness I'll be happy to share it.
That's* the wrong paper. You want "The completeness of the axioms of the
functional calculus of logic" which is a 1930 rewrite of his doctoral
dissertation. This is known as Godel's completeness theorem.
Godel didn't invent the term though, and may not have said "this is the/my
definition of completeness". I haven't read them for some time, and can't
remember. He may well have assumed his readers would already know it.
Or try "Some metamathematical results on completeness and consistency" or
"On completeness and consistency" from 1931. Reports of his 1930 lecture
would also be useful.
Afaik they aren't available on the 'net. Some or all of these are in: From
Frege to Gödel, Jean van Heijenoort, Harvard University Press. ISBN
0-674-32450-1 , (recently ?reissued? as ISBN 0-674-32449-8 at around $25,
but I haven't seen the new version) which should also give you the history
of the term.
--
Peter Fairbrother
* The one mentioned is available at
http://www.ddc.net/ygg/etext/godel/godel3.htm
if anyone wants to have a look. It's commonly called his incompleteness
theorem paper, but the paper doesn't talk directly about completeness,
rather about the existence of undecidable propositions - however the
"incompleteness" name is a bit of a giveaway... if an undecideable
proposition exists within a system then the system is incomplete.
