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From: eisinger@uklirb.UUCP (Norbert Eisinger)
Newsgroups: comp.ai
Subject: Re: abduction vs. induction
Message-ID: <5196@uklirb.UUCP>
Date: 29 May 89 08:09:00 GMT
References: <1480@crin.crin.fr <14820@paris.ics.uci.edu> <6144@cognos.UUCP>
Reply-To: eisinger@uklirb.UUCP (Norbert Eisinger)
Organization: University of Kaiserslautern, W-Germany
Lines: 12

Induction means to derive generalizations from facts, that is, statements of
which the facts are instances. Of course such a generalization is not in general
a logical consequence of the facts.
The proof principle used in mathematics is really called COMPLETE induction.
There is an indispensable axiom of the natural numbers (and similar structures)
saying that a property P for which P(0) holds and also the implication
forall n P(n) ==> P(n+1) holds, is a property of all natural numbers.
This induction axiom cannot be expressed in first-order predicate logic.
Thus, for natural numbers complete induction works because it is part of their
very definition that it does.

Norbert Eisinger