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Re: [ontolog-forum] new logic

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Thu, 19 Nov 2009 12:27:38 -0600
Message-id: <A8537BF3-E17B-4188-813B-F7527669CA6A@xxxxxxxx>
On Nov 19, 2009, at 11:38 AM, Schiffel, Jeffrey A wrote:

Christopher Menzel  replied 
On Nov 18, 2009, at 4:48 PM, Schiffel, Jeffrey A wrote:
In our discussions of "new logic," we should probably recall some other categorizations of logic before we wander into the desert. There are three that have been around a very long time. Their present definition is mostly from Pierce. They are:
-- Deduction, which is reasoning where necessary conclusions are made from statements - FOL,
-- Induction, which are arguments by inference, i.e., by likelihood, usually from experience, and
-- Abduction, which forms hypotheses from observed patterns.

I'm afraid I couldn't recommend this description.  For excellent, expert accounts of the many different aspects and kinds of logic, I recommend the entries found under "Logic" in the online Stanford Encyclopedia of Philosophy.  There are, in particular, very fine, informative entries on classical first-order logicsecond- and higher-order logic, modal logic, and intensional logic.

JS:  Although the words are my own, the definitions I stated are drawn in part from the expert account in the Standford Encyclopedia of Philosophy.

I had no issue with the tripartite division above, which is fairly standard (albeit both overly broad and not exhaustive), although the blurbs that follow them are problematic.  However, you deleted the gloss you provided on the above, which is what I was actually referring to:

Notice that induction and abduction are particularly phenomenological. Deductive logic is the most worked out, with first order varieties arising from reducing the number of the usual base axioms, or restricting the definition of the usual axioms; and higher order varieties gotten by expanding the number of axioms, as in adding possibility to get modal logics.

This brief summary is off the mark at several points so I felt it was important, solely for the sake of accuracy, to direct interested readers on this public forum to more reliable accounts.  No disrespect was intended.

Chris Menzel

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