Date: Mar 21, 2013 2:39 PM
Author: fom
Subject: Re: Matheology § 224

On 3/21/2013 6:32 AM, WM wrote:
>
> Note: For every finite set of natural numbers, we can look at all
> elements, at least in principle.


Would you care to prove this for your readers?

You have rejected Markov's careful development of
constructively interpreted quantifiers. So, you
need to explain how what is meant by "every" is
not an implied presumption of completed infinity.

You once invoked Abraham Robinson's views on
infinity in defense of yourself. Your readers
should know that Robinson actually developed an
outline for the formation of models in a finitary
framework.

This is what respectful mathematicians do. They
explain how their views might actually be implemented
in mathematical terms.

Your readers deserve no less from you.

Since you probably are assuming a completed infinity,
the next question is simple. Why may one not develop an
arithmetic for completed infinities if such arithmetic
does not lead to any absurdity in established deductive
calculi?

Notice the phrase "established deductive calculi". It
is relevant to responsible, appropriate answers.