[extropy-chat] Non-classic logics

[Ian Goddard]

--- Technotranscendence <neptune at superlink.net> wrote:

> Anyone interested in them as a general topic for
> discussion?  For the last year or so, I've been 
> studying them in earnest, particularly using Graham 
> Priest's _An Introduction to Non-Classical Logic_ 
> and J.C. Beall's and Bas C. van Fraassen's 
> _Possibilities and Paradox: An Introduction to 
> Modal and Many-Valued Logic_ as my main tour guides.
> (There are a few other titles too and anyone 
> interested who's not familiar with these types of 
> logics can google them.  There're quite a few good 
> intros online.)


Sounds like an interesting topic. Thanks for the
text-pointers. Could you cite some of the better
online intros? Last semester I took a course in
metalogic (Phil 470) covering the semantics of classic
logic (propositional and first-order predicate).
During the last two weeks we skimmed the surface of
propositional modal, or intensional, logic, which is a
nonclassic logic. I want to study further than that.

It was the most enjoyable course I've ever taken due
in part to the text we used (when the professor wasn't
teaching off-text) which I highly recommend! It was
"Logic, Language, and Meaning" volumes 1 and 2 by
L.T.F. Gamut. [*] The author's name is a pseudonym for
five professors (van Bentham, Groenedijk, de Jongh,
Stokhof, and Verkuyl) in the fields of mathematics,
philosophy, and linguistics. Clearly that ideal
breadth of collective knowledge accounts for the
unparalleled quality and scope of this two-volume
text. The first fairly slim volume covers classic
logic and the second goes above. [*]

The first volume is remarkable for one thing in the
fact that it teaches classic logic simultaneously at
both at the beginner's level covering logical syntax
and at the metalogic level covering the semantics of
logic. And not only does it cover both levels, it does
so more clearly and in fewer pages than most
syntax-only texts, which is quite a feat! So even for
those already versed in classic-logic syntax (which is
what basic logic courses teach) this text can take you
a step above even as they recover the basics. 

Also unique is the focus on the relevance of logics to
matters of language per se and understanding natural
language as opposed to mathematics, and yet the text
is also logico-mathematically rigorous. It's certainly
an ideal logic text for anyone interested in computer
science and AI. Geez, enough already! ;)

~Ian

[*] "Logic, Language, and Meaning" Vol I
http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/7087.ctl
http://www.bestwebbuys.com/Logic_Language_and_Meaning-ISBN_0226280853.html
Vol II
http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/7088.ctl
http://bestwebbuys.com/Logic_Language_and_Meaning-ISBN_0226280888.html

http://IanGoddard.net

 

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