Re: How about Self-Inconsistency
Rich,
The traditional notion of infinity is a limit
that is approached, but never completed. Cantor
switched to the view that an infinite set could
be considered as a single entity. But you can do
most of mathematics (except, of course, Cantor's
set theory) without that concept.
> A good mathematician I once knew well told me he
> likes the concept of sets without infinities. Other
> than induction, most infinities are very messy.
> Is there any way to use WordNet's meronymy relations
> to properly form a basis of your 'mereology plus integer'
> foundations?
I wouldn't start with WordNet's definitions, but with
any decent set of axioms for mereology. You can see
examples in Ch. 2 of my KR book, where I discuss that
point in further detail. And there are lots of books
and papers about mereology. Try Google.
John