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Mathematical validity

You reversed my edit at non-standard analysis with the justification that the content of the section is contained in the last sentence of the previous paragraph. The sentence you are referring to mentions vaguely that there is no argument about the mathematical validity of non-standard analysis. I don't think this is sufficiently precise. Namely, even a system containing additional axioms could also be mathematically valid, so long as nobody has found an internal contradiction in such a system. The specific point that non-standard analysis is "conservative" in the sense that it does not go beyond ZFC deserves to be mentioned explicitly. If you disagree please raise the issue at WP math rather than using deletions. For the time being I will revert my edits. Katzmik (talk) 08:11, 31 August 2008 (UTC)

Please respond to my comments at the talk page of non-standard analysis. Katzmik (talk) 13:24, 31 August 2008 (UTC)

non-standard calculus

There is a dispute regarding the proof of the intermediate value theorem, please comment. Katzmik (talk) 12:27, 2 September 2008 (UTC)

Please respond to my comment at talk:transfer principle. Katzmik (talk) 12:43, 10 September 2008 (UTC) and again Katzmik (talk) 14:19, 11 September 2008 (UTC)

Thanks for your comment at talk:transfer principle. I added a couple of paragraphs to the lead at transfer principle. Please give it a professional edit. I still feel that the thrust of this material goes contrary to the remarks in the first section, as I tried to explain at the talk page. Katzmik (talk) 12:23, 14 September 2008 (UTC)

your comment

Hi, You made the following comment at talk:transfer principle:

Reply to comment of User talk:Katzmik) posted 14:14, 9 September 2008 (UTC). Sorry to take so long to respond. You are correct that quantification over sets is required, but this doesn't make it a higher order theory. For example, there are no type distinctions between sets of integers and integers. In ZFC all variables range over the entire set-theoretic universe. If one had a weaker no-standarad analysis, with limits on the range of quantification, the resulting theory would be less interesting. In fact, you can make the transcendental extension 'R into an ordered field in which the indeterminate t is infinite and 1/t is a non-zero infinitesimal. But this is pretty much useless for a development of calculus. I don't know if I've addressed any of your concerns.--CSTAR (talk) 14:48, 11 September 2008 (UTC)

I have thought about your comment for a while and I do not understand it fully, surely this is due to my lack of training in logic. At any rate, I am not sure what you mean when you say "there are no type distinctions between sets of integers and integers"; why aren't there? Also, I understand the assertion "In ZFC all variables range over the entire set-theoretic universe" but I am not sure I understand what you are driving at when you say this. Certainly in NAS one needs to interpret statements as referring to internal sets only; I see this not as a weakness of the theory but rather the main tool in the realisation of Robinson's goal. When you say "you can make the transcendental extension 'R into an ordered field in which the indeterminate t is infinite and 1/t is a non-zero infinitesimal. But this is pretty much useless for a development of calculus", are you referring to the absence of a transfer principle in such a naive approach to NAS? Katzmik (talk) 09:05, 15 September 2008 (UTC)

AfD nomination of Abstract nonsense

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Intelligent design

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Interpretations of quantum mechanics

Up till now I have restricted my dealings with this subject on Misplaced Pages to small edits, although I certainly have quite a bit of experience on this matter, having worked professionally on it for over 30 years by now (see my web site to which a link is provided at User:WMdeMuynck). However, as you can see there, my views on this subject are not shared by everyone, to say the least. Because there is a Misplaced Pages policy not to engage in scientific controversies I have up till now not tried to deal with this subject on Wikidepia. I am still updating my own web site, and it does not seem fruitful to me to duplicate this in Misplaced Pages since my web site is open to everyone interested.WMdeMuynck (talk) 14:50, 23 October 2008 (UTC)

No I certainly didn't want to suggest you insert your views into the article. Basically I am unhappy with the introductory paragraph which is supposed to explain what an interpretation of quantum mechanics is. I am aware of your interest in this area and I thought that you could thinks of a suitable formulation based on some independent source. This should be less controversial than adopting one or another interpretation as the "right one".--CSTAR (talk) 15:49, 23 October 2008 (UTC)

My first problem is that in physical discourse the notion of `interpretation' is different from the one used in philosophical discourse. In physics most of the time by an `interpretation' is meant a `mapping from the mathematical formalism of quantum mechanics' into reality. In philosophy, if I remember well, the mapping is often thought to be from reality into the theoretical terms of the theory (like the term `electron'). I restrict myself to the physical notion.

Disregarding the instrumentalist interpretation (because it is too vague and, moreover, is confusing) I distinguish two possibilities: either the mapping is into the reality of microscopic objects, or it is into the macroscopic reality of phenomena (the first is the interpretation which has become fashionable after logical positivism has become obsolete, the last one might be in agreement with logical positivism although the situation is actually more involved). I refer to these interpretations as realist and empiricst, respectively.

In the empiricist interpretation a measurement result refers to a property of the macroscopic measuring instrument (a pointer position), rather than to a property of the microscopic object. Bohr and Heisenberg (the Copenhagen interpretation) did not entertain an empiricist interpretation (notwithstanding Heisenberg's empiricist utterings), since they assumed a (measurement) phenomenon to be a property of the microscopic object (e.g. a particle `being within the confines of the detector' when position is measured). What is essential to the Copenhagen interpretation, is that the measurement is a fundamental issue, the measurement arrangement playing an essential role (this is often seen as a weakness, but I consider it its strenght).

The Copenhagen interpretation can best be viewed upon as a contextualistic-realist interpretation, as opposed to Einstein's objectivistic-realist one.

There is still another dichotomy, viz. in the interpretation the wave function may refer to an individual object (the Copenhagen interpretation) or to an ensemble (Einstein). Although the first one is most popular both among physicists as well as philosophers, I think nowadays we have experimental evidence that the wave function does not describe an individual object but an ensemble. The emiricist interpretation allows only an `ensemble' version, the realist interpretations allow both versions.

Personally I prefer the empiricist interpretation because i) it is in agreement with what physicists do experimentally, ii) since it is the weaker interpretation (although stronger than the instrumentalist one) it can evade all paradoxes of the realist interpretations (although a realist ensemble interpretation also solves most of these, but not all!), iii) it gives rise to a generalization of standard quantum mechanics which is necessary to encompass all experiments which nowadays are performed in the quantum domain.

My problem is that I do not see how this can be cast in a brief and simple formulation that is illuminating rather than confusing.

Please let me know what you think.WMdeMuynck (talk) 12:48, 24 October 2008 (UTC)

limits

Hi, Please comment at the talk page of limit of a function if you get a chance. Katzmik (talk) 09:06, 24 October 2008 (UTC)