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Article 4904 of comp.ai.philosophy:
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>From: silber@orfeo.Eng.Sun.COM (Eric Silber)
Newsgroups: comp.ai.philosophy
Subject: Re: ai
Keywords: ai,realism,Goedel,platonism
Message-ID: <ktp7d0INNgna@exodus.Eng.Sun.COM>
Date: 3 Apr 92 18:02:08 GMT
References: <atten.702298596@groucho.phil.ruu.nl>
Organization: Sun Microsystems, Mt. View, Ca.
Lines: 51
NNTP-Posting-Host: orfeo

In article <atten.702298596@groucho.phil.ruu.nl> atten@phil.ruu.nl (Mark van Atten) writes:
>There is an ongoing discussion right now on mathematical realism in the ai
>group. Some people question the relevance of this to ai. In this article,
>I want to discuss
>1 The objective existence of mathematical objects
>2 The significance of this for ai
>
>...
>
quoting Leibniz Re: Hobbes:
>I.1 'Hobbes saw that all truths can be demonstrated from definitions [we're
>not so sure anymore since Kant, but for the sake of argument, never mind], but
>he believed that all definitions are arbitrary and nominal, since the
>imposition of names on things is arbitrary. But it must be known that concepts
>cannot be combined in an arbitrary fashion, but a possible concept must be
>formed from them, so that one has a real definition. From this it is evident
>that every real definition contains some affirmation of at least possibility.
>Further, even if names are arbitrary, yet once they have been imposed their
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>consequences are necessary and certain truths arise which, though they depend
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>on the symbols imposed, are nevertheless real. For example, the rule of nine
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 This only establishes 'local-truth' insofar as the naming and inference
 apparatus are bound to the anatomy of an individual mind or class of minds.
 ( The genetically encoded base-layout of the human brain circumscribes how
 any instance of a human brain/mind can 'name' and 'infer' )
>depends on symbols imposed by the decimal system, and yet it contains a real
>truth. Again, to form a hypothesis, i.e. to explain a way of producing
>something, is simply to demonstrate the possibility of the thing; and this is
>useful, even though the thing in question has often not been generated in such
>a way.'
>( Leibniz, Of universal synthesis and analysis; or, of the art of discovery
>and of judgement, 1683)
>
>I.2 Goedel on objectivity
>'The same possibilities of thought are open to everyone, so the world of
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>possible forms is objective and absolute. Possibility, then, is not dependent
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>on an observer; it is therefore real because it is not subject to our will.'
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 These propositions suffer from the same error as Leibniz above, viz.
 they assume that because a certain class of minds is subject to the same
 constraints, ALL minds, and even the Universal Mind (if any) must admit
 the existence of the same 'fundamental forms'. 
 Well, I may be grossly wrong , if so, please show me how, but I think that
 all members of Goedel's class named 'everyone' are humans, and he cannot use
 the inherited common architecture of the class of human brains
 as a hook upon which to hang the existence of "absolute possible forms".
....


