Re: circular relationships ok?

From: David Cressey <dcressey_at_verizon.net>
Date: Sat, 04 Mar 2006 18:18:58 GMT
Message-ID: <mSkOf.259$eJ1.121@trndny05>

"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.

> Received on Sat Mar 04 2006 - 12:18:58 CST