Re: Constructive Math query.

david petry says...

>Daryl McCullough wrote:

>> No, it doesn't. "If A then B" *implies* "If we can prove A, then B",
>> but the other way around is dubious.
>>
>> Take an example in which A is neither provable nor refutable.
>> The interpretation "If we can prove A, then B" becomes vaccuously
>> true, in that case, but "If A then B" isn't vaccuously true.
>
>You are mixing up constructive and classical notions of implication.

No, they are the same in this one regard: Anything follows from a
falsehood. So if the statement "we can prove A" is false, then anything
follows from it.

Lacking a proof is *not* synonymous with being false, constructively
or classically. Which means that "If A then B" is not synonymous with
"If we can prove A, then B".

--
Daryl McCullough
Ithaca, NY

.

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