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From: afo@s.cc.purdue.edu (Neil Rhodes)
Newsgroups: comp.ai
Subject: Re: The Ignorant assumption
Message-ID: <3546@s.cc.purdue.edu>
Date: 9 Sep 88 03:40:56 GMT
References: <1383@garth.UUCP> <2362@uhccux.uhcc.hawaii.edu>
Reply-To: afo@s.cc.purdue.edu.UUCP (Neil Rhodes)
Organization: Purdue University
Lines: 30

In article <2362@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes:
>From article <1383@garth.UUCP>, by smryan@garth.UUCP (Steven Ryan):
>" That's it. Any formal system requires such assumptions.
>
>Well, I would say that some natural deduction systems of logic have
>no assumptions -- only rules of derivation.  But you can probably
>find a definition of 'assumption' that makes what you say true.
>

I have a problem with Mr. Lee's reasoning in the above statement, and it
seems to be the foundation of most of his recent arguments.

If a formal system were to contain "only rules of derivation," what would
these rules act upon to form statements (theorems) about the system?
Rules alone in a formal system give you nothing.  For this reason, you
need a given set of statements (axioms) from which these rules can derive
other statements (theorems).  Since these axioms are not derived and are
necessary to the formal system, then you must "believe" them to be true
while working within the system.

Since many scientific statements are derived within formal systems, to
believe these statements you must also believe other statements which
cannot be proved.

If Mr. Lee still believes that science asks us to take nothing on
"faith," then I am curious to know what flaws he finds in *my*
reasoning.

--
Neil Rhodes
afo@s.cc.purdue.edu