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.