FOM: terminological foolishness

Martin Davis martind at
Mon Aug 24 14:28:28 EDT 1998

"A word means what I say it does" -Humpty Dumpty

Quite a few have shared with me off-line their frustration with the
interminable disputes in which Steve engages on fom over the precise meaning
of terms that, in the nature of informal discourse, are used in somewhat
different ways by different people and in different contexts. In each case,
Steve has apparently determined a unique correct useage with which to pound
those quilty of wrong-think into submission.


It isn't that terminological issues are unimportant. It's just that after
everyone has had their say, the discussion becomes pointless. 

It's perfectly plain that Steve (and I as well) are excited by the
statements Harvey has proved independent because their flavor brings them
close to the kind of question that mathematicians who speak of themselves as
combinatorists consider in their normal work. It's also plain that
consistency of a formal system is in some abstract sense combinatorial in
nature, but is not the sort of question those people concern themselves
with. The underlying foundational question is what I like to call: G\"odel's
Legacy: will the incompleteness theorems extend their reach into ordinary
mathematical practice?

Now after that is said, what point is their in endless ruminations over
whether con(ZFC) is or is not truly combinatorial?


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