Re: Cantorian pseudomathematics


cbrown@xxxxxxxxxxxxxxxxx wrote:
> david petry wrote:

> > The problem with
> > the actual infinite is that it is not observable.
>
> This is a reasonable philosophical stance; although not one I share. It
> depends on what one considers "observable"; and that is a
> philosophical, not a mathematical question. De gustibus non
> disputandum!


A statement has observable content if it makes predictions about the
results of a computational experiment. That's not merely a
philosophical notion.


> > That is, we have no
> > way to test (falsify) statements about the actual infinite.
>
> This justification is the illogical part of your argument to me.
>
> Is it possible to "observe" that there is no largest prime number? And
> yet, it's easy to prove, using a finite process; thus we have falsified
> the statement "the (actual) infinite set of naturals contains a largest
> prime". Euclid did it; why can't we?

In fact, an easy extension of Euclid's argument gives a bound on how
far we have to look for the next prime, given any prime. That extension
is falsifiable.

.

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