🚀 go-pugleaf

In article <Bx5DIB.8qF@cck.coventry.ac.uk> esz001@cck.coventry.ac.uk (Will Overington) writes:
>I missed the start of this thread, but wonder if the the problem
>that people are having with
>
>All crows are not black
>
>is along the lines of
>
>All that glitters is not gold
>
>where the "All" is, in fact, a peculiar idiom of the English language
>that means "Some", but with an emphasis of a kind.

This is an ambiguity of English (and many other languages), and
concerns the scope of adverbs.  The question here is whether the adverb
"not" governs the whole sentence: "Not(all that glisters is gold)" or
just the predicate: "All that glisters (not(is gold))".  More
precisely, "Not(for all x[glister(x) -> gold(x)])" vs. "For all
x[glister(x) -> not(gold(x))]".  (For some reason "For all
x[not(glister(x) -> gold(x))]" is not among the permitted readings, any
linguists out there care to explain this?)

>The book from which I have been learning logic, namely Teach Yourself
>Logic, warns that All ... not ... of this kind needs to be expressed as
>
>No ... ...
>
>in order to avoid this idiom.

Absolutely, to avoid the ambiguity.

>I have found the study of Logic fascinating, but still have a long way
>to go. I note that it was a compulsary subject in the Medieval Universities.
>I believe that it should become a compulsary subject again, starting in
>schools and continuing in everyday usage, much as other basic skills such
>as reading, writing, spelling and mathematics.

I have very mixed feelings about this.  Freshman math at Gunn High
(where my 14 year old goes) started out this year with a couple of
weeks of propositional logic before getting into geometry etc.  My
intuitive feeling was that she got much less useful math out of the
logic than out of the geometry.  On the other hand logic is fundamental
to thought, and even if humans don't reason propositionally it is good
to at least be aware of a logical system that they could plausibly
reason in, albeit clumsily.

Based on what I've observed in people's thought processes I'm pretty
convinced that human propositional logic is considerably weaker than
intuitionistic logic.  I think it would be more useful to teach these
weaker logics in high school, both because they entail fewer axioms and
because they are more representative of human thought.  However even
grad school curricula today barely touch on these "minimal logics", and
when they do they don't make the connections with human reasoning that
I am pretty certain are there to be made.
-- 
Vaughan Pratt				There's no truth in logic, son.