[EM] Richard's frontrunners example

[MIKE OSSIPOFF]

>If A then B, is commonly understood to mean that A causes B.  In mathmatics
>this isn't the case.  An if...then statement is a truth functional
>statement, saying that whenever A is true, B is true.  If we have
>established the truth of 'if A then B' (or we are positing the truth of 
>that
>statement), the following is true;
>- if A is true, B is true
>- if B is false, A is false

So far so good, I didn't doubt those things.

>
>Because it is a truth functional statement, if A is false, the statement A
>then B will be true (irrespective of the truth of B).

That's the part I didn't understand.


>This is the tricky
>bit - if A is false, it is an impossible contradiction for A to be true.  
>As
>a result; if A is true then anything is true.  The statement 'if A then...'
>will always hold. eg. if water can talk then I'm a banana - a true &
>logically valid statement.

I understand what you're saying, but, supposing that water actually
can talk, and, because that's impossible then we can suppose everything
that's impossible--that sounds a bit weak, doesn't it? Wouldn't it
make much more sense to just say that, since water can't talk, then
the statement that you're a banana if water can talk isn't saying
you're a banana? Can it be true or false to not say that you're a
banana? The statement would be true if it said that you aren't a banana.
But it doesn't. It merely doesn't say that you are one.

Now we're talking about conventions of logicians & mathematicians.
But conventions aren't the same as facts.

Mike Ossipoff

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