>Ingvar,
>
>That's an important point:
>
>>As it happens, I think the answer to my question is of practical
>>philosophical-pedagogical interest. I believe that the way
>>introductory courses in logic are usually taught - with their
>>problems of how to formalize ordinary English in propositional
>>logic and FOL - they give many students the impression that there
>>is a hidden formal-logical essence in ordinary language. If Pat is
>>right, efforts should be made in order to take such possible
>>impressions away.
>
>I agree with Pat that it's important to recognize that formal
>languages are not natural languages, but anything expressed in
>any formal language can always be paraphrased in a natural language (01)
Well, yes: but there are grave dangers. It is very very hard to do
this paraphrase without also introducing some non-logical nuance of
meaning, which often leads into a rat-hole (as witness this thread
itself). There is no way to avoid this kind of NL rendering when
teaching logic, but it is also important to guard against
complacency, so to speak. One of my favorite examples is to formalize
"Everybody loves my baby, but my baby don't love nobody but me",
which if done literally has the consequence that I am my baby. To get
the intended meaning one has to exclude self-love, a nuance of
meaning simply assumed when one hears the English rendering but not
by the logic. About half of a typical UG class can understand this
example when one spends an hour on it, which is a better rate than I
have found with anything else. (02)
>(but the converse is definitely not true).
>
>But the extreme emphasis on mathematical logic in the 20th
>century destroyed a valuable tradition of teaching logic and
>conceptual analysis using an Aristotelian approach.
>
>As an example, I often cite the following textbook as a useful
>introduction to conceptual analysis for knowledge engineers:
>
> Joseph, Sister Miriam (1937) _The Trivium: The Liberal Arts of
> Logic, Grammar, and Rhetoric_, Third edition 1948, reprinted
> by Paul Dry Books, 2002. (03)
Yay!! A fabulous book, I agree. (04)
Pat (05)
>
>John (06)
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