Editing Charles Sanders Peirce (section)

==== Continua ====
Continuity and [[synechism]] are central in Peirce's philosophy: "I did not at first suppose that it was, as I gradually came to find it, the master-Key of philosophy".<ref>Peirce (1893–1894, MS 949, p. 1)</ref>

From a mathematical point of view, he embraced [[Infinitesimal|infinitesimals]] and worked long on the mathematics of continua. He long held that the real numbers constitute a pseudo-continuum;<ref>Peirce (1903 MS), ''Collected Papers of Charles Sanders Peirce'', 6.176: "But I now define a ''pseudo-continuum'' as that which modern writers on the theory of functions call a ''continuum''. But this is fully represented by [...] the totality of real values, rational and irrational [...]."</ref> that a true continuum is the real subject matter of ''analysis situs'' ([[topology]]); and that a true continuum of instants exceeds—and within any lapse of time has room for—any [[Aleph number]] (any infinite ''multitude'' as he called it) of instants.<ref>Peirce (1902 MS) and [[Joseph Morton Ransdell|Ransdell, Joseph]], ed. (1998), "Analysis of the Methods of Mathematical Demonstration", [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm#m4 Memoir 4] {{Webarchive|url=https://web.archive.org/web/20131103160621/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-02.htm#m4 |date=2013-11-03  }}, Draft C, MS L75.90–102, see 99–100. (Once there, scroll down).</ref>

In 1908 Peirce wrote that he found that a true continuum might have or lack such room. Jérôme Havenel (2008): "It is on 26&nbsp;May 1908, that Peirce finally gave up his idea that in every continuum there is room for whatever collection of any multitude. From now on, there are different kinds of continua, which have different properties."<ref>See:

* Peirce (1908), "Some Amazing Mazes (Conclusion), Explanation of Curiosity the First", ''The Monist'', v. 18, n. 3, pp. 416–444, see [[iarchive:bub_gb_CqsLAAAAIAAJ_2/page/n544|463–464]]. Reprinted ''Collected Papers of Charles Sanders Peirce'', 4.594–642, see 642.
* Havenel, Jérôme (2008), "Peirce's Clarifications on Continuity", ''Transactions'' Winter 2008 pp. 68–133, see 119. [https://www.jstor.org/pss/40321237 Abstract].</ref>