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From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: On the discovery of formal systems (Was: On the possibility of enumerating all
Message-ID: <1995Aug9.232702.1506@media.mit.edu>
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Date: Wed, 9 Aug 1995 23:27:02 GMT
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Xref: glinda.oz.cs.cmu.edu sci.logic:13837 comp.ai.philosophy:31507

In article <40b48s$1f0@nntp5.u.washington.edu> forbis@cac.washington.edu (Gary Forbis ) writes:
>OK, I'm willing to cheat.  Now how do I cheat in specifing A1, A2, etc. in
>a way that I'm guaranteed to reach my desired formal system in some finite
>number of steps while hiding my cheat well enough that it won't be obvious
>I cheated?

No need to cheat.  All you need to do is enumerate the integers in
binary notation.  Then, for example, the 10th axiom set will be
represented by 1010 -- and you interpret this as 
  
  Axiom 4 = Yes
  Axiom 3 = No
  Axiom 2 = Yes
  Axiom 1 = No

This will enumerate all the finite sets of axioms in a nice order, and
no set will be covered twice (which would not matter anyway).

I can't imagine why your friend thinks that any cheating is necessary.
Maybe you should replace hesh by a mathematics or logic grad student.

--

