From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Jun 14 2002 - 21:22:03 MDT
Scerir pointed out some potentially useful links for
my query
> [Lee writes]
> > I don't know of any rigorous guidelines to suggest to
> > one that an apparently completely rational argument
> > may have a hole in it. But one is that if the conclusion
> > of an argument goes against long deeply held beliefs that
> > you have, then it's wise to reserve judgment for an
> > extended period.
>
> These might be relevant?
> http://logica.rug.ac.be/WoPaLo/
Well ;-) sorry, but my statement was really a claim
that there *aren't* any "rigorous guidelines to suggest
to one that an apparently completely rational argument
may have a whole in it". Now in mathematics in theory
every demonstration can be reduced to axiomatics, and
can hence be checked for utter rigor. However, perhaps
it isn't well known that this is almost never done in
practice. For example, proving the Fundamental Theorem
of Algebra has never (to my knowledge) been reduced to
a symbolic formulation together with a set of appropriate
axioms; it would be a gigantic mess, and no one would
really learn anything from it.
But I wasn't even talking about mathematics! Mathematics
is **easy** so ***easy*** compared to the sheer impossibility
of reducing, say, the Israeli-Palestinian dispute to rigorous
analysis. So please read the above remarks in light of the
following example: the Israeli Prime Minister on vacation discusses
the Middle East question with a historian from Lima, Peru, for
whom he has a great deal of respect. The historian lays out
a very detailed logical argument for why the Palestinians should
be granted a homeland next to Israel. Every concern that the
Prime Minister raises is dealt with in the historian's presentation,
and the Prime Minister can find no serious flaw in his arguments.
Is he to then return to Tel Aviv the following week and say, "Guess
what?". Certainly not. Let's say that this Prime Minister has
believed certain things for 40 years, and must deeply suspect some
flaw in the argument he heard. He has every right to say, "Well,
I don't see where you've gone wrong right now---everything you
say seems quite rigorous---but I'm probably missing something."
Anyway, Scerir provided two interesting links. The first is
"On Paraconsistency
Paraconsistency developed in the second half of the XX Century as the study of non-trivial
inconsistent logics.
The use of such logics has since then proved useful in several contexts, ranging from the
formulation of set theories with
stronger abstraction principles, and the handling of inconsistent databases, to the
formulation and understanding
of problems related to the formalization of argumentation and in the development of a
formal philosophy of science, with applications to epistemology. This workshop aims to be
representative of the main directions of current research
on paraconsistency."
> http://logica.rug.ac.be/WoPaLo
The second was
"This workshop deals with paraconsistency and its relationship to computational logic. The
"ex falso quodlibet" rule of classical logic predicts that everything (i.e., nothing
useful at all) would follow from the least bit of inconsistency. Although logical data
consistency is a requirement of high priority in all of computing, 100% consistency is
almost never given in practice. Taking logic seriously, this means nothing less than a
complete mismatch of theory and practice, which in fact profoundly challenges the
legitimacy of logical foundations of computing in general. Paraconsistent logic offers a
way out of this dilemma. Unlike classical logic, paraconsistency is compatible with the
fact that, despite ubiquitous inconsistencies, most computing systems in practice usually
are able to provide meaningful information.
It seems that this mismatch has never been bothering the community of computational logic
to any significant degree. However, this phenomenon has been more attentively observed in
the field of mathematical and philosophical logic. Around the middle of last century,
Stanislaw Jaskowski and Newton da Costa have shown that inconsistency needs not be
identified with ex falso quodlibet. They devised paraconsistent logics to cater for
inconsistent yet useful theories. While the potential of paraconsistency to study, explain
and improve the behavior of inconsistent systems has been widely recognized in
philosophical circles, it has not (yet) enjoyed a broad-scale uptake in computational
logic.
"The workshop aims to raise the awareness of paraconsistency as a matter of fact in
everyday computing. It also is meant to build a bridge between paraconsistent logic(s), on
one side, and theoreticians and practitioners of computing, on the other. The workshop
will provide a forum for presenting and discussing existing and novel work on coping with
inconsistency in all fields of computational logic. Thus, it intends to further encourage,
fertilize and improve such work, and to lead paraconsistent logic out of its current
parochial status. Topics (in alphabetic order) related to paraconsistency and
computational logic include, but are not limited to... "
Well, I found the sentences "Although logical data consistency is a requirement of high
priority in all of computing, 100% consistency is almost never given in practice. Taking
logic seriously, this means nothing less than a complete mismatch of theory and practice,
which in fact profoundly challenges the legitimacy of logical foundations of computing in
general."
Gee, that just doesn't seem surprising for anything outside
of mathematics! What have we here? Have a lot of people
(neither scerir nor the authors above) been experiencing
"math envy"? ;-)
Lee
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