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!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!Germany.EU.net!EU.net!sun4nl!cwi.nl!olaf
From: olaf@cwi.nl (Olaf Weber)
Subject: Re: The Search For Truth
Message-ID: <D8MBM0.2pu@cwi.nl>
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>
Distribution: inet
Date: Mon, 15 May 1995 11:51:48 GMT
Lines: 82
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:28083 sci.philosophy.meta:18114 sci.philosophy.tech:18034

In article <3p1qsj$bj9@usenet.ucs.indiana.edu>, sgoehrin@copper.ucs.indiana.edu (scott goehring) writes:
> In article <D8B1q2.Cp5@cwi.nl>, Olaf Weber <olaf@cwi.nl> wrote:

>> The statement that "anything can be derived in an inconsistent
>> system" indicates that you are wedded to a particular system of
>> logic for which this happens to be the case.  In paraconsistent
>> logics this "rule" has been dropped, and it can be specified what
>> can and cannot be derived from an 'overdetermined' statement.

> i admit to no experience at all with tri-valued or fuzzy logic
> systems.  i have yet to find a use for them.

You wrote in article <3on3j3$a69@usenet.ucs.indiana.edu> that

> [If the system is inconsistent] you extend the system by accepting
> either the statement's truth or falsity as a new axiom.

Consider the following statement:

(1)	Napoleon ate an egg on the day before the battle of Waterloo.

True or false?  Presumably there _is_ a "fact of the matter" in this
case, but the information we'd need to establish that fact is no
longer available.

Does this mean that we can simply add either (1), or its denial to our
historical knowledge, depending on our whims?  It is precisely the
assumption that there is a fact of the matter that gives a reason not
to do so: only one choice is correct, and we lack the information to
decide which is which.  So within the context of our knowledge, it
should be accepted that (1) has the truth value `underdetermined'.

Now consider the following argument:

(2)	Quakers are pacifists.
(3)	Pacifists do not conduct wars.
(4)	Nixon was a Quaker.
(5)	Nixon conducted a war.
(6)	Columbus landed in America in 1492.
.: (7)	Columbus didn't land in America in 1492.

According to the "contradiction implies anything" school of logic,
this is a correct conclusion, given the validity of the premises.
Most people find that an exteremely counterintuitive result.

"Check your premises," is sometimes offered as a solution, but which
premises should be checked?  Once you accept that contradictions may
occur in a system because information can be unreliable, it is
tempting to extend the system to cope with that.  One way to do this
is to make inference rules that tell you which premises should be
considered for dropping, in this case (2), (3), (4), and (5), but not
(6).

Quite often we think of some premises as being more certain than
others.  In this case, (5) would be an established fact, and (2)
follows from the definition of "pacifist".  Which leaves room for
a conclusion like

(8)	Nixon was an a-typical Quaker.

if one considers (3) to be a useful "default rule" that can be
invalidated in particular cases, or

(9)	Nixon wasn't a real Quaker.

if one considers (4) to be something that can only be considerd to be
established if the person in question actually lived to all the Quaker
ideals.

The important thing to note is that we are suddenly using both the
`underdetermined' and `overdetermined' truth values, and are arguing
about the relative certainties of truth values.  In other words, we
are working in a fuzzy four-valued logic.

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, which is shown by the fact that you cannot "check your
premises" without stepping outside the system.

-- Olaf Weber
