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)
http://www.jfsowa.com/peirce/remark.pdf
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)
http://www.jfsowa.com/peirce/ms514.htm
Existential Graphs (014)
John (015)
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