Article View: comp.ai
Article #8363Re: abduction vs. induction
From: Norbert Eisinger
Date: Mon, 29 May 1989 08:09
Date: Mon, 29 May 1989 08:09
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1174 bytes
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
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Path: arc1-ca.pugleaf.net!utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!cs.utexas.edu!uunet!mcvax!unido!uklirb!eisinger 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