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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 11:32:29 -0600
Message-id: <8AF6391F-D432-4976-AE4F-684E751575DF@xxxxxxxx>
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.
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.

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.

the other two forms are not as mathematized, and mainly show up informally or in rhetoric.

Both are in fact often informally presented, but there are also highly mathematical treatments of them.  See in particular the SEP entry on inductive logic.

For example, in the scientific method, all three occur to some extent.

Certainly true.

Chris Menzel

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