Re: Cantorian pseudomathematics

"david petry" <david_lawrence_petry@xxxxxxxxx> writes:

> cbrown@xxxxxxxxxxxxxxxxx wrote:
>> david petry wrote:
>
>> > "Falsifiable" means that it is possible to search for counterexamples
>> > that, if found, would prove the assertion to be false.
>>
>> When you say "it is possible", do you mean "we can observe it as the
>> result of a computation performed in the real world"? Or do you mean
>> "in principle, such a search could be performed by an idealized
>> computer, given arbitrarily large but still finite resources"?
>
> I suppose you could distinguish "strong" falsifiability from "weak"
> falsifiability with the distinctions you make. Weak falsifiability is
> sufficient for my arguments here.

But existential claims are not falsifiable, so we should banish the
existential quantifier.

Suppose I prove: There exists n, P(n).

What will your computer do to refute this? It has to check *every*
number and see that P fails. If he has checked 10^1000 numbers and it
fails for each of those, he's still not done.

Of course, if your computer could prove directly: For all n,
P(n).... but we can't guarantee that.

--
"Your knowledge is the power that promote good thought, how then can you have
good thought without powerful knowledge or how can you have powerful knowledge
without learning or how can you learn without a teacher and how can a teacher
teach if he or she has not learned the subject." --CA Alternative High School
.

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