Re: Review of Mueckenheims book.

On Feb 21, 3:43 am, mueck...@xxxxxxxxxxxxxxxxx wrote:
Of course the natural numbers are a sequence. In Cantor's case, the
sequential construction leads to contradictions. Some advocates of set
theory have recognized this and, therefore, postulated that everything
happens at once, but that does not mean that this position is correct
or sensible.

It would be better to understand that IF the mathematics is described
with a temporal ANALOGY, then the best fit is that "it all happens at
once". But we are NOT obligated to regarding mathematics as being
describable with a temproral analogy. Any state of affairs that is a
model of set theory is an ABSTRACT state of affairs in which time is
not even expressed as a feature. So surely we do NOT have to describe
the state of affairs as a chronology, not even as a singular
"happening all at once". Set theory does axiomatize the mathematics
that is used for theories in which time is a feature, but that does
not entail that a model of set theory is itself or must be itself a
state of affairs in which time is a feature.

One cannot do infinitely many transactions at once.

And set theory is not a theory about what transactions a finite
intelligence can perform. However, set theory does axiomatize the
theorems about computability which can be taken as about what
transactions a finite intelligence and/or also a computing machine can
perform. And meanwhile, you are welcome to advance a mathematical
theory that limits itself to such computability.

The question for you is: Are you interested in understanding that or
are you vastly more interested in continuing to harrump that set
theory is "wrong"?

MoeBlee

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