RAZD responds to me:
quote:
I was not replying to you
(*chuckle*)
You say you weren't responding to me and yet the very first word in your post was my name. How very strange to mention my name when you're not referring to me.
How many times do I need to tell you my answer before you remember it?
(4) None of the above.
Until you define what {A} is, I can't say anything about it.
Not even that I don't know.
Let's follow your claim:
Absent proof that A exists or that A does not exist.
OK. We notice that A only if B. That doesn't tell us if A exists or not so we are still in the realm of your premise.
We then notice that ~B. This, too, in and of itself, is not proof of the existence or nonexistence of A.
But the two of them together, however, indicate that A does not exist:
A only if B.
~B.
Therefore, ~A.
Note, this doesn't quite follow the other way. That is, given (A only if B) and B does not necessarily mean that we have A. For example, an object can be a square only if it is a rectangle. That an object is a rectangle does not mean it is a square though if an object is not a rectangle, then it cannot be a square.
Instead, we use direct implication:
A if B.
B.
Therefore, A.
And again, even though we don't have any proof of the existence or nonexistence of A in the first two statements, the two of them combined tell us that A does exist.
There are other logical constructions we can create such that we arrive at an unknown state. I've already given an example:
A only if B.
B.
Well, we don't know about A at this point because the existence of B does not guarantee the existence of A.
But notice, this only works when we have some sort of definition of what A is. And that is my original claim:
Until you define what {A} is, I can't say anything about it.
Not even that I don't know.
Rrhain
WWJD? JWRTFM!
™ Version 4.2
