Talk:Arithmetization of analysis

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
???	This article has not yet received a rating on the project's priority scale.

Philosophy: Logic Low‑importance

This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles

Low

This article has been rated as Low-importance on the project's importance scale.

Associated task forces:
/
	Logic

History of Science

	History of science portal This article is part of the History of Science WikiProject, an attempt to improve and organize the history of science content on Wikipedia. If you would like to participate, you can edit the article attached to this page, or visit the project page, where you can join the project and/or contribute to the discussion. You can also help with the History of Science Collaboration of the Month.History of ScienceWikipedia:WikiProject History of ScienceTemplate:WikiProject History of Sciencehistory of science articles
???	This article has not yet received a rating on the project's importance scale.

problematic article[edit]

This article apparently treats an important idea in the history of math-foundational thought; see for example Simpson, who asserts:

Another important development was the "arithmetization of analysis" (Weierstrass, Dedekind). Thus it was no longer necessary to regard real numbers and continuous functions as basic, unanalyzed concepts; instead they could be reduced to the natural numbers. This made possible the axiomatization of analysis in terms of second order arithmetic (carried out systematically by Hilbert and Bernays).

From a modern perspective, though, the treatment is kind of misleading, because the real numbers are not in fact reduced to natural numbers, but rather to sets of natural numbers, a fundamentally richer and more complicated notion. A related problem is the discussion of

the more extreme philosophical position that all of mathematics should be derivable from logic and set theory, ultimately leading to Hilbert's program, Gödel's theorems and non-standard analysis.

where "logic" and "set theory" seem to be more or less conflated, suggesting, say, that the reals should be a purely logical, analytic notion, because sets are supposed to be. But in fact sets have, if anything, less claim to analyticity than do the reals. This, of course, is clear only in retrospect and there's no warrant to hold Weierstrass or Dedekind accountable for it, so from a historical perspective the treatment is probably correct. That doesn't save it from being potentially confusing to a contemporary reader. --Trovatore 18:11, 1 April 2006 (UTC)[reply]

WikiProject class rating[edit]

This article was automatically assessed because at least one WikiProject had rated the article as stub, and the rating on other projects was brought up to Stub class. BetacommandBot 03:47, 10 November 2007 (UTC)[reply]

What to do?[edit]

Yes, this is an important concept in the history of math & phil of math -- lots of work has been done. However, the text of this article (at this date) appears to have been lifted from the following web location:

http://tensegrity.wikispaces.com/Arithmetization

... or is it the other way round, viz., that this is the source for that article? HH. In any case, it would be possible to deal with the problems noted by others above by incrementally building up the history of the arithmetization process/program/project, were there a need for it. But is there? Whayes43 (talk) 20:31, 26 May 2014 (UTC)[reply]