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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,

probably."

-Matt Jensen

NewsBlip.com

Seattle

On Thu, 3 May 2001, Jeff Bone wrote:

*>
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*> Tony Berkman wrote:
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*>
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*> > I have to disagree. Where does it say they are statements??? I am
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*> > considering
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*>
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*> Ahem, *assuming.*
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*>
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*> > them Binary Random Variables over some unknown distribution
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*>
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*> Assuming.
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*>
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*> > in
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*> > which case if B is a discreet Random Variable, even without knowing it's
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*> > mass, you know a little bit more about A once you know that B is True.
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*> >
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*> > At 10:44 PM 5/3/01, John Hall wrote:
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*> > >Similarly, if A => B and you know that B is true you have no idea whether A
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*> > >is true or false. No information. None.
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*> > >Zero. Zilch. Nada.
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*> > >
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*>
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*> I have to agree with John, Tony. Given the discussion, it was entirely obvious
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*> that A => B meant "A implies B," with A and B being simple truth values. No need
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*> to make it more complex; always choose the smallest possible context for
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*> interpretation of mathematical assertions. "Principle of Least Assumption" and
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*> all that. No reason to assume that the logic of the system is nonmonotonic or
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*> contextual unless we're told otherwise.
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*>
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*> In straightforward (i.e., introductory) monotonic / symbolic logic, A => B, B
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*> tells you nothing about A's truth value.
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*>
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*> Tony does suggest a point, however, in that introducing statistical or other
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*> relationships or facts about the quantities involved or other state makes the
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*> problem more interesting. But then, that's moving towards information theory ---
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*> very interesting indeed, but not something John has to figure out how to teach to
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*> HS kids. (Unless he's very lucky.:-)
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*>
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*> jb
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*>
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*> PS - though in ASCII I would've said A --> B. ;-)
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*>
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*>
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*>
*

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