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rhys44503@xxxxxxxxx wrote:
> I have a problem. If you take two true but completely unrelated
> premises and pop them into a modus ponens, how can you call the result
> valid--i.e. If the moon orbits the earth, then I am wearing white
> carpenter's pants. The moon orbits the earth. Hence, I am wearing
> white carpenter's pants--and take my word for it, I am.
This has puzzled logicians since the origins of symbolic logic. Here
is my take on the subject.
First of all, you may take any true proposition, call it Q, and
make a conditional out of it. For any proposition P at all, "if P then
Q" is likewise true. So, what? It's true, but it's totally useless. You
can't use that fact to deduce anything else you don't already know.
If you already knew that some statement P were false, you could also
assert for any proposition Q, true or false, "If P then Q". But again,
so what? You can't use that to prove anything you don't already know,
either.
By asserting "if P then Q" you have claimed that some kind of
relation exists between the two statements, namely, that Q is at least
as true as P, or that you may not have P true and Q false. This may be
trivially the case, as when you already know that P is false, or you
already know that Q is true. But the question of whether or not there
is some deep cause-and-effect connection between the statements is
beyond the scope of propositional logic. The concern of logic is more
more narrowly with whether arguments are consistent and whether you are
deducing false conclusions from true premises.
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