David Cressey wrote:
> "JOG" <jog_at_cs.nott.ac.uk> wrote in message
> news:1141494992.645738.283070_at_z34g2000cwc.googlegroups.com...
> > David Cressey wrote:
> > > "JOG" <jog_at_cs.nott.ac.uk> wrote in message
> > > news:1141480471.362482.59010_at_e56g2000cwe.googlegroups.com...
> > > > David Cressey wrote:
> > > > [snip]
> > > > >
> > > > > I think "A implies B" is the same as "B or not A".
> > > > >
> > > >
> > > > ? By "A implies B", he surely just means "if A then B". Or using
> > > > standard predicate logic notation "A -> B."
> > >
> > > I don't get it. How is "A -> B" different from "B^~A" ?
> > >
> >
> > Hi David. Bit confused by your response. Originally you were talking
> > about "B or not A" but then talk about "B^~A" which is "B and not A".
> > (I'll take the second as a typo). The distinction is:
> >
>
> You are right. It was a typo. Thanks for correcting it.
>
>
> > A -> B is a proposition
> > B v ~A is a boolean expression
> >
> > The first is a declared fact, the second just a boolean statement that
> > resolves to true or false, obviously a very different kettle of fish.
>
> It may be obvious to you, but it ain't obvious to me. It seems to me that
> the assertion
> that A -> B is always true in a given univers of discourse, and the
> assertion that
> B is true or A is false in the same universe of discourse boil down to the
> same thing.
>
>
>
> > So I thought that you might perhaps have meant "B v ~A = True", but
> > substituting a couple of values in for A and B highlights there still
> > exists a difference:
> >
> > A -> B
> > IF it is raining THEN I wear a coat
> >
> > B OR ~A = True
> > EITHER I wear a coat OR it is NOT raining
> >
> > These are clearly very different things. For example, in the second
> > statement I have declared that I will not be wearing a coat if it is
> > dry but very cold outside, however this would be a perfectly acceptable
> > state of affairs according to the first statement.
> >
>
> I don't think the above analysis is correct. Your analysis requires OR to
> mean "exclusive or".
> It doesn't. It means inclusive or, doesn't it?
>
> In the case where B = I will wear a coat and A= it is raining
> Then if I wear a coat and it's not raining we get:
>
> B v ~A becomes True v not false becomes True v true becomes
> true. Right?
>
>
> > All best, Jim.
> >
*cough* David, you (and vc) are of course completely correct. A -> B is
(just obviously) identical to A v ~B. Rereading my post, I'm left
scratching my head as to what on earth I was wittering on about. Well,
quite frankly I appear to be having a nonsense day in general,
mistaking trivial mathematics being the least of it. Note to self: Must
cut down the booze on friday nights.
Received on Sat Mar 04 2006 - 17:59:28 CST
