Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!mailrus!ames!zodiac!joyce!sri-unix!garth!smryan
From: smryan@garth.UUCP (Steven Ryan)
Newsgroups: comp.ai
Subject: Re: The Ignorant assumption
Message-ID: <1389@garth.UUCP>
Date: 11 Sep 88 00:07:50 GMT
References: <3546@s.cc.purdue.edu> <2365@uhccux.uhcc.hawaii.edu>
Reply-To: smryan@garth.UUCP (Steven Ryan)
Organization: INTERGRAPH (APD) -- Palo Alto, CA
Lines: 9

>There are formalizations of logic that require axioms, but not all
>do.  Gerhard Gentzen created systems that have no axioms.  For
>instance:
>	Suppose p (one can introduce provisional assumptions freely)
>	Conclude p (one can repeat an assumption as a conclusion)
>  So, p implies p (since p was concluded on the basis of the provisional
>	  assumption p, one can derive the implication)

Well, I see an assumption--it assumes the existence of a formal system.