

Logical Literacy - plinkplonk
http://matt.might.net/articles/logical-literacy/

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gacba
It's unfortunate that this kind of logic isn't emphasized more in mathematics
or science in a pure form. I'm pretty sure in high school I had one semester
of this kind of logic associated with geometry. That was it until I hit
discrete structures in college.

Failure to understand this logic might be part of the reason there's so much
magical thinking about things relating to pseudoscience (e.g. paranormal
activity, UFOs, conspiracy theories, New Age anything). A stronger base in
logic would help people understand exactly why these things are impossible,
stupid, or plain crazy with simple deductive and inductive reasoning
techniques taught in logic courses.

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Jach
I think a stronger base in real probability theory (as opposed to simply
frequency analysis) would be more beneficial, especially if you follow Jaynes'
route and treat it as an extension to logic. As a commenter noted above,
"implication" is easy to grasp, except it's not, because logical implication
is not necessarily causal or does not even have to make real-world sense,
whereas one of the goals of Bayesian Probability Theory is that it should have
a qualitative correspondence with common sense.

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astrofinch
This is a great example of how awesome teaching yourself using the Internet
can be. If you read and understood that in 30 minutes then you learned it in
about one quarter of the time we spent covering this stuff in my discrete math
class--and I'm supposedly going to a really good college.

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omaranto
I don't see why you mention your college is good seemingly surprised it took
longer than 30 minutes to cover this: wouldn't you expect a good college to
have good teachers and wouldn't you expect a good teacher to go slowly enough
that all or most students understand?

~~~
nitrogen
I suspect there is an optimum speed at which the greatest number of students
are able to understand, and I suspect that it isn't the slowest speed
possible.

In late elementary and junior high school I recall getting in trouble for
being ahead of the class, particularly in computer-related classes and
assignments. A faster pace would've allowed students like me to benefit from
the class, but may have left slower students behind.

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cristoperb
Upvoted especially for his list of suggested reading at the end of the
article.

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ESchmidtSeesYou
Wonderfully straightforward resource for the basics.

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sid0
Good article overall, but I think I should make a comment:

> Many understand implication intuitively, yet find its symbolic formulation
> puzzling.

Yes, and for a reason: material implication (the kind of implication discussed
in the article) _cannot_ always explain our intuitive sense of implication. My
favourite example, from Priest's _Introduction to Non-Classical Logic_ : (A ⇒
B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid when ⇒ is material, yet the
statement:

"If John is in Paris he is in France, and if John is in London he is in
England. Hence, it is the case either that if John is in Paris he is in
England, or that if he is in London he is in France."

makes no intuitive sense. It is very important to discard intuition when
dealing with implication in mathematics -- this is why although I'm a big fan
of using English connectives instead of symbolic ones, I try to not use the
English "if" and "then" in proofs.

~~~
Someone
I also think it is unfortunate that his first theorem is incorrect (n=1 cannot
be written as the product of two distinct integers)

That may cost the author some of the readers for whom this text is the most
educational, i.e. the ones that have trouble grasping the logic.

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nene
Even if it's not meant to be true, I find it even more disturbing that the
symbolic and English formulations doesn't seem to quite match up. (IMHO the
symbolic formulation doesn't state that n must be integer.)

It's like the source code and comments being out of sync - you don't know
which one is wrong.

~~~
mattmight
Another great point.

I fixed the broken theorem, and I added a blurb on the "universe of
discourse."

