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Re: [ontolog-forum] txtbk on logic

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 22 Jul 2007 15:23:14 -0400
Message-id: <46A3AEA2.3030005@xxxxxxxxxxx>
Chris and Wacek,    (01)

I agree with Chris:    (02)

CM> ... the natural deduction system they [Copi & Cohen] use
 > is an inelegant hash of primitive rules, derivable rules,
 > and substitution patterns.    (03)

But I would qualify the following statements:    (04)

CM> In my view, the best general intro to deductive logic for both
 > average students and good/excellent students is Bergmann, Moor,
 > and Nelson's _The Logic Book_.  This text first builds natural
 > deduction systems The Right Way :-) using primitive introduction
 > and elimination rules only, and only thereafter extends the
 > systems by introducing derived rules, showing in each case *that*
 > the new rule is derivable from the primitive rules.    (05)

vQ> The one you propose has some nasty comments on amazon, perhaps
 > from less-than-average students.    (06)

I haven't read that book, but from looking through the front matter,
I would agree (1) their approach is better than Copi & Cohen's, but
(2) the reviewers who made nasty comments had very good reasons for
hating it (and most other available logic books).    (07)

Unfortunately, most logicians, including B. M. & N., have never
seen the far more elegant and vastly more teachable system of
natural deduction by Peirce, which makes every other version
seem kludgy and ill-motivated by comparison.    (08)

I used to teach logic using traditional textbooks, but in 1978,
I discovered Peirce's rules and began to discuss them in my
courses as an interesting alternative.  When I did that, the
students themselves complained: "Why didn't you start with that
method?"  And they were right.  Students really understand logic
when you teach Peirce's method *first* -- after that, they can
see the fundamental principles behind any method of proof.    (09)

Students who were previously exposed to logic by the *wrong* way
(i.e., any method other than Peirce's) really become excited when
I show how full FOL plus proofs can be taught in *one hour* in
a way that people can actually understand.    (010)

Following are the slides of a 45-minute talk that I presented at
a conference in June (too bad I didn't have the extra 15 min):    (011)

    Peirce's Remarkable Rules of Inference    (012)

Page 7 has a table that summarizes Gentzen's rules of 1935, and
the next few pages compare them to Peirce's rules of 1897.
For a more complete intro, see Peirce's tutorial of 1909:    (013)

    Existential Graphs    (014)

John    (015)

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