1.You're right, I was focusing on [A-->B, B, ...?] rather than the much
simpler [ A-->B, A, ...? ].
2. I mischaracterized the students as high schoolers when your
acquaintance actually teaches college students.
3. The 19thC Central Asian tribesmen were asked questions tougher than the
simple [A-->B, A, ...?]. (I saw the NYT article before, and the Soviet
Uzbeki experiments were different than the ones I'm referring to.)
All of which leads me to share your astonishment that the college students
couldn't get [A-->B, A, ...?]. It seems you would have to have a very
poor understanding of the word "if" to not get it. I'd be interested to
hear a classroom transcript.
On Fri, 4 May 2001, John Hall wrote:
> Obviously, definitions would be included in any discussion before you asked
> them to answer a question, but in the context of 'us bitheads' I hardly
> figured that the definitions were necessary.
> Also note that A --> B, B is something I've seen people have trouble
> understanding. Including, apparently, on FoRK. I can understand teaching
> that one, and how to do it, and why it might be necessary.
> But I only introduced it in comparison to A --> B, A. That is the one that
> flips my circuits.
> -----Original Message-----
> From: Matt Jensen [mailto:email@example.com]
> Sent: Friday, May 04, 2001 5:17 AM
> To: FoRK
> Subject: Re: How do you teach fundamental logic to someone that
> doesn'tgrok it?
> I took Tony's post as "here's how an average high schooler, without any
> logic training, might understand the question." That was the original
> context. Monotonic logic versus information theory is just the FoRK
> discussion context.
> For a typical high schooler, I suspect Tony's description *is*
> the simplest framework; it describes the commonsense ways in which people
> casually think. In contrast, it's the imposition of rules of prepositional
> logic which seems unnatural and arbitrary (and thus, you need a teacher
> for it).
> We bitheads are so used to our logical forms, and so enamored of the
> benefits it has brought us through millions of silicon logic gates, that
> we come to see it as the natural way to view things. But it's not
> natural; everyone who knows such logic had to learn it at some point. In
> contrast, induction is natural. If you eat an onion and don't like it,
> you have a high confidence that you won't like other onions. You don't
> have to inventory the space of "all onions". So it shouldn't be
> surprising that a high schooler given [ A-->B, B ] concludes "A,
> -Matt Jensen
> On Thu, 3 May 2001, Jeff Bone wrote:
> > Tony Berkman wrote:
> > > I have to disagree. Where does it say they are statements??? I am
> > > considering
> > Ahem, *assuming.*
> > > them Binary Random Variables over some unknown distribution
> > Assuming.
> > > in
> > > which case if B is a discreet Random Variable, even without knowing it's
> > > mass, you know a little bit more about A once you know that B is True.
> > >
> > > At 10:44 PM 5/3/01, John Hall wrote:
> > > >Similarly, if A => B and you know that B is true you have no idea
> whether A
> > > >is true or false. No information. None.
> > > >Zero. Zilch. Nada.
> > > >
> > I have to agree with John, Tony. Given the discussion, it was entirely
> > that A => B meant "A implies B," with A and B being simple truth values.
> No need
> > to make it more complex; always choose the smallest possible context for
> > interpretation of mathematical assertions. "Principle of Least
> Assumption" and
> > all that. No reason to assume that the logic of the system is
> nonmonotonic or
> > contextual unless we're told otherwise.
> > In straightforward (i.e., introductory) monotonic / symbolic logic, A =>
> B, B
> > tells you nothing about A's truth value.
> > Tony does suggest a point, however, in that introducing statistical or
> > relationships or facts about the quantities involved or other state makes
> > problem more interesting. But then, that's moving towards information
> theory ---
> > very interesting indeed, but not something John has to figure out how to
> teach to
> > HS kids. (Unless he's very lucky.:-)
> > jb
> > PS - though in ASCII I would've said A --> B. ;-)
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