lanning@lll-crg.ARPA (09/20/84)
From: Stanley Lanning <lanning@lll-crg.ARPA>
"... induction is limited to statements on a countably infinite set."
Well, that depends how you define induction. If you define it in
the right way, all you need in a well-ordered set. Cardinality
doesn't enter into it.
Concerning the argument "All A are B, x is an A, therefore x is a B".
It is not true that the conclusion is true only if the two assumptions
are true. It is not even true that the argument is valid only if the
assumptions are true. What is true is that we are guarenteed that
the conclusion is true only if the assumptions are true.
Thanks for your indulgence.
-smL