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.