Newsgroups: alt.philosophy.jarf,alt.philosophy.objectivism,alt.philosophy.zen,comp.ai.philosophy,sci.philosophy.meta,sci.philosophy.tech,talk.philosophy.humanism,talk.philosophy.misc
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!gatech!howland.reston.ans.net!news.nic.surfnet.nl!sun4nl!cwi.nl!olaf
From: olaf@cwi.nl (Olaf Weber)
Subject: Re: The Search For Truth
Message-ID: <D8o9CG.HC8@cwi.nl>
Followup-To: alt.philosophy.objectivism,sci.philosophy.meta,sci.philosophy.tech,talk.philosophy.misc
Sender: news@cwi.nl (The Daily Dross)
Nntp-Posting-Host: havik.cwi.nl
Organization: CWI, Amsterdam
References: <mike.799620809@mik.uky.edu> <3oguiv$4ke@spool.cs.wisc.edu>
	<3on3j3$a69@usenet.ucs.indiana.edu> <D8B1q2.Cp5@cwi.nl>
	<3p1qsj$bj9@usenet.ucs.indiana.edu> <D8MBM0.2pu@cwi.nl>
	<3p9aqe$mml@degas.ICSI.Net>
Date: Tue, 16 May 1995 12:57:53 GMT
Lines: 67
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:28121 sci.philosophy.meta:18141 sci.philosophy.tech:18048

[ Followups trimmed. ]

In article <3p9aqe$mml@degas.ICSI.Net>, jalway@icsi.net (John Alway) writes:
> olaf@cwi.nl (Olaf Weber) wrote:

>> As you can see, these "obscure" logics are motivated by the desire to
>> formulate good rules concerning how we should reason about reality,
>> given that we work in a context of knowledge with uncertainties and
>> contradictions.  Simple binary logic is too simple a system to be a
>> model for this,

>     Oh no! Not again! Not that smeggin phrase "simple binary logic"
> again...

What's in a name?  But note that I'm using "logic" as in "the science
of correct argumentation", not as in "the art of non-contradictory
identification".  What I was arguing for is that, if you try to
formalize the latter (give rules on how to go about it), you need a
logic that handles underdetermined and overdetermined propositions.

Thus I talked about binary logic to contrast it with multivalued
logics, and simple binary logic to contrast it with fuzzy two-valued
logics, or variants in which proposition do not need to have a truth
value.

The term was not meant derogatory, but rather as an accurate
identification.

>     The phrase is rather a bit of nonsense, really.  I'm telling
> you... there is no other logic... everything builds on Aristotle's
> foundation (every logic that is valid, that is).

"Builds on" is the operative phrase here.  As soon as you've extended
the system you have left Aristotle's original behind.  And even within
simple two-valued logic we have progressed beyond Aristotle's work.
All his syllogisms fall naturally out of propositional calculus.

And the "self-evidence" of the law of the excluded middle isn't very
persuasive either.  A statement like

	This sentence is false

is a propostion to which no definite truth value can be ascribed.
What Gdel showed is that you have to cripple the system regarding the
things it can talk about if you want to exclude such self-referential
statements.  But such a paradox is only a problem if you insist that
every proposition has to have a definite truth value.

You can comapre the situation with rows in mathematics.  Some rows
converge, and thus have a definite value as their limit.  Others
diverge, and do not have such a limit value at all.  This is not
considered to be a problem.  Crippling mathematics to the point where
only rows with a definite limit can be describe would be a "cure" that
is far worse than the "disease".

In a similar spirit, I am quite comfortable with dropping the law of
the excluded middle _in general_.  Of course there are a number of
domains where I use it because it does hold for them.

>     Anyway... you are fooling yourself if you don't think that a
> "simple" inductive, deductive process can solve such a problem given
> enough data.  If you don't have enough data then, of course, it
> ain't soluable.

In which case you give it the truth value `underdetermined'.  ;-)

-- Olaf Weber
