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 obvious
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 other
relationships or facts about the quantities involved or other state makes the
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. ;-)
This archive was generated by hypermail 2b29 : Sun May 06 2001 - 08:04:38 PDT