[EM] "If" meanings--they're the same.

[MIKE OSSIPOFF]

>MIKE OSSIPOFF wrote:
>
> > I still haven't heard anyone actually say what the mathematical
> > definiton of "if" is. Will it be in a definition of mathematics?
> > Won't someone tell me what it is?
>
>I don't know about the word "if" being defined in math except that it's
>usage is the same as in logic. But I think logic actually just defines
>implication (or inference).  "If A then B" is understood as an equivalent
>way of saying "A implies B".
>
>Implication is defined as a logical expression which is true if the
>consequent (B) is true for all cases in which the antecedent (A)
>is true. That definition doesn't come from a textbook but I think
>it's fairly close.

That sounds the same as the definition that I posted. Martin appears
to have been mistaken in his claim that my meaning for "if" is different
from that of mathematicians.

Maybe it's better to say that (If A then B) is true if B is true in
all cases in which A is true, rather than saying that (If A then B)
means that A being true means that B is certain to be true.

But the meaning is the same. You were wrong about my using a different
meaning for "if", Martin.

p.s. My probability definition might need a little touch-up modification.
I wrote it hurriedly late at night.

Mike



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