Re: Cantorian pseudomathematics

In article <7759c$43d48fe3$82a1e2b0$9045@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

> cbrown@xxxxxxxxxxxxxxxxx wrote:
>
> > You are falling prey to exactly what Jaynes is warning about - you are
> > mixing up properties from "after" the limit is taken with properties
> > from "before" the limit is taken.
>
> No. It's the other way around: _you_ are making this mistake.
>
> > The fact that each P_n is a uniform distribution is not relevant to
> > whether or not P is a uniform distribution.
>
> Limits come from physical experience that, in the real world, everything
> is just finite. Hence the fact that _each_ P_n is a uniform distribution
> already _proves_ that P is a uniform distribution as well, with P(x) = 0
> infinitesimally small (instead of absolutely zero, speaking in TO terms)
> and this explains why it still sums up to unity. There is no point where
> all of a sudden finitary properties would cease to exist, because all of
> infinity should be approached through the finite, by limits.

Since the finite naturals have no more reality outside of the mind than
do infinities, there is no difference in the nature of their existence,
it is all in the mind.
.

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