Editing Charles Sanders Peirce (section)

=== Ontology ===
On the issue of universals, Peirce was a [[Scotistic realism|scholastic realist]], declaring the reality of [[Problem of universals|generals]] as early as 1868.<ref>Peirce (1868), "Nominalism versus Realism", ''Journal of Speculative Philosophy'' v. 2, n. 1, pp. [https://books.google.com/books?id=YHkqP2JHJ_IC&pg=RA1-PA57 57–61]. Reprinted (CP 6.619–624), ([http://www.iupui.edu/~peirce/writings/v2/w2/w2_14/v2_14.htm ''Writings of Charles S. Peirce'', 2:144–153] {{Webarchive|url=https://web.archive.org/web/20080531074944/http://www.iupui.edu/~peirce/writings/v2/w2/w2_14/v2_14.htm |date=2008-05-31  }}).</ref> According to Peirce, his category he called "thirdness", the more general facts about the world, are extra-mental realities. Regarding [[Modal logic|modalities]] (possibility, necessity, etc.), he came in later years to regard himself as having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote:

{{Quote|I formerly defined the possible as that which in a given state of information (real or feigned) we do not know not to be true. But this definition today seems to me only a twisted phrase which, by means of two negatives, conceals an anacoluthon. We know in advance of experience that certain things are not true, because we see they are impossible.}}

Peirce retained, as useful for some purposes, the definitions in terms of information states, but insisted that the pragmaticist is committed to a strong [[modal realism]] by conceiving of objects in terms of predictive general conditional propositions about how they ''would'' behave under certain circumstances.<ref>On developments in Peirce's realism, see:
* Peirce (1897), "The Logic of Relatives", ''The Monist'' v. VII, n. 2 pp. 161–217, see [https://books.google.com/books?id=pa0LAAAAIAAJ&pg=PA206 206] (via Google). Reprinted ''Collected Papers of Charles Sanders Peirce'', 3.456–552.
* Peirce (1905), "Issues of Pragmaticism", ''The Monist'' v. XV, n. 4, pp. 481–499, see [https://archive.org/details/monist18instgoog/page/n568 495–496] (via Google). Reprinted (CP 5.438–463, see 453–457).
* Peirce (c. 1905), Letter to Signor Calderoni, ''Collected Papers of Charles Sanders Peirce'', 8.205–213, see 208.
* Lane, Robert (2007), "Peirce's Modal Shift: From Set Theory to Pragmaticism", ''Journal of the History of Philosophy'', v. 45, n. 4.</ref>

==== 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>