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From: olaf@cwi.nl (Olaf Weber)
Subject: Re: The Search For Truth
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Date: Tue, 9 May 1995 09:44:38 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:27831 sci.philosophy.meta:17923 sci.philosophy.tech:17928

In article <3on3j3$a69@usenet.ucs.indiana.edu>, sgoehrin@copper.ucs.indiana.edu (scott goehring) writes:
> In article <3oguiv$4ke@spool.cs.wisc.edu>,
> Ron Peterson <ronp@sun5.cs.wisc.edu> wrote:

>> Statements can be of four types:

>> True
>> False
>> Inconsistent (i.e. cannot be interpreted as true or false)

> only if your system is inconsistent (that is, it allows statements
> which cannot be either true or false without engendering a
> contradiction).  no useful system of logical reasoning is
> inconsistent, because anything can be derived in an inconsistent
> system.

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.

>> Undecidable (i.e. can be either true or false and be consistent
>> with our axioms)

> in which case you extend the system by accepting either the
> statement's truth or falsity as a new axiom.

In which case you end up with a different system.  You might have good
reasons not to do that.

Again, this is something that you do if you are wedded to the notion
that a statement must be either true or false.  If you do not start
from that point, there is no compelling reason to accept it.

> in fact, a statement is either true or false.  it may be that it can
> be either, but in that case we _choose_ it to be either true or false.

Not if the system is supposed to describe reality.  Then you can come
to the conclusion that a statement is 'underdetermined' in the
context of our knowledge, even if you have good reasons to believe it
to be either true of false.  In those cases it is often better (IMHO)
not to assume one or the other, but just accept that the fact of the
matter remains undecidable.

By the way: "a statement is either true or false" also leaves little
room for fuzzy logic.

-- Olaf Weber
