[extropy-chat] Non-classic logics

[Technotranscendence]

On Monday, March 21, 2005 1:02 AM Ian Goddard iamgoddard at yahoo.com
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.

I think so too.:)

> Thanks for the text-pointers. Could you cite
> some of the better online intros?

Wikipedia is a good place to start:

http://en.wikipedia.org/wiki/Main_Page

For modal logic, there's:

http://plato.stanford.edu/entries/logic-modal/

Which also happens to be at the top of the google search on that topic.

This paper also has a section on different logics:

http://www-formal.stanford.edu/jmc/mcchay69/mcchay69.html

and it covers them in the context of AI.

> Last semester I took a course in metalogic
> (Phil 470) covering the semantics of classic
> logic (propositional and first-order predicate).

I found Raymond M. Smullyan's _First-Order Logic_ -- available in an
inexpensive Dover reprint -- to be a great introduction to first-order
logic.  It was especially helpful with the tableaux method that Priest,
Beall, and Bas C. van Fraassen rely heavily on.  (In fact, it's not too
inaccurate to say a lot of Priest's exposition is relating how different
logics have different tableaux rules.  At least, that's one device he
uses throughout his book to relate the differences.)

> 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.

The Beall and van Fraassen book focus to a large extent on modal
logic -- as the title reveals.  If you're interested in one
philosopher's view of modality, you might want to read Alvin Plantinga's
_Essays in the Metaphysics of Modality_.  If you want to learn more
about second- and higher-order logic in the context of metamathematics,
there's Stewart Shapiro's _Foundations without Foundationalism: A Case
for Second-Order Logic_.

> 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. [*]

Haven't heard of that one and thanks for the reference.

Cheers!

Dan
    See "Free Market Anarchism: A Justification" at:
http://uweb.superlink.net/~neptune/AnarchismJustified.html