Path: utzoo!attcan!uunet!ogicse!ucsd!swrinde!zaphod.mps.ohio-state.edu!mips!apple!amdahl!kp From: kp@uts.amdahl.com (Ken Presting) Newsgroups: comp.ai Subject: Re: A definition of *INTELLIGENCE* Summary: Axiomatic definitions (as of sets) are still definitions Message-ID: Date: 16 Mar 90 18:31:41 GMT References: <2752@castle.ed.ac.uk> <1407@oravax.UUCP> <5177.25fa2fb6@mva.cs.liv.ac.uk> <8533@mentor.cc.purdue.edu> Reply-To: kp@amdahl.uts.amdahl.com (Ken Presting) Organization: Amdahl Corporation, Sunnyvale CA Lines: 26 In article <8533@mentor.cc.purdue.edu> g2g@mentor.cc.purdue.edu (Ranjan Muttiah) writes: > >If mathematics be the most precise of sciences and its desiderata of >numbers and sets are left undefined, then how in a more imprecise >field such as AI can we define intelligence ? > >Answer: You don't ! The axioms of a set theory or a number theory can serve as *either* a a definition of the entities under discussion, or as assumptions regarding the properties and relations of those entities. If the axioms are treated as definitions, then it is uncertain whether any entities actually exist which satisfy the definitions. It is impossible for an axiomatic definition to distinguish between isomorphic models, so the "proper" reference of "set" is indeterminate. If the axioms are treated as assumptions, then the truth of the axioms is (of course) unprovable. Consistency, utility, representational power, et. al. may be investigated, but such work bears at best indirectly on truth. We can't have both certainty of reference and certainty of truth, but by no means does mathematics provide an excuse for vagueness. Ken Presting