Ben, you’re right, the addendum is Selection 27 in Matthew Moore’s collection, and his commentary on it goes in part like this:
Peirce rightly points out that even if there is an upper bound on the multitude titude of points that can be placed on a line, it does not follow that a line can be filled with a point set of the appropriate multitude; and he appeals once again to our consciousness of time (in particular, to memory) to argue the need for a "more perfect continuity than the so-called `continuity' of the theory ory of functions"; as in his supermultitudinous theory, "a line [with this more perfect continuity] does not consist of points." By the time he received the proofs of the article, Peirce thought he could do better, and wrote three versions of an addendum for the published essay. The latest of the three, written on 26 May 1908, is included in this selection; it is the one that was completed and published. Peirce announces a new theory ory of continuity, based in topical geometry rather than the theory of collections. tions. A true continuum obeys the (corrected) Kantian principle that every part has parts, and is such that all sufficiently small parts have the same mode of immediate connection to one another. Moreover, Peirce asserts, all the material parts (cf. selections 26 and 29) of a continuum have the same dimensionality. Rather than explaining the central idea of immediate connection, tion, he notes that the explanation involves time, and answers the objection that his definition is therefore circular. It is perhaps an ominous sign that Peirce devotes to much space to what appears to be a somewhat manufactured tured objection: since he does not explain what he means by `immediate connection,' nection,' it would hardly have occurred to the reader that time was bound up with such connection, had Peirce himself not brought it up. (In selection 29, the involvement of time in `contiguity' is made clearer.) The excessive attention tion to side issues, when the main ideas are still so underexplained, would be less worrisome if Peirce had explained himself more fully elsewhere; but so far as we know, he did not. * Charles S. Peirce. Philosophy of Mathematics: Selected Writings (Kindle Locations 3293-3304). Kindle Edition. Gary f. From: Benjamin Udell [mailto:[email protected]] Sent: 22-Feb-17 12:48 To: [email protected] Subject: Re: [PEIRCE-L] Cyclical Systems and Continuity Jeff D., list, I agree with John S. and Gary F. about Peirce's not very detailed analogy between time regarded as continuous and oxygen's atomic weight regarding as 16 in Peirce's addition (beginning "_Added_, 1908, May 26.") of "Some Amazing Mazes (Conclusion), Explanation of Curiosity the First". The addition is rather important, as it happens, because of what Peirce winds up saying in it. Jérôme Havenel (2008): "It is on May 26, 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." I don't remember whether Havenel gets into the analogy of continuity with atomic weight. Havenel, Jérôme (2008), "Peirce's Clarifications on Continuity", _Transactions_ Winter 2008 pp. 68–133, see 119. Abstract http://www.jstor.org/pss/40321237 I think Matthew Moore also discusses the addition in his Peirce collection _Philosophy of Mathematics: Selected Writings_ http://www.iupui.edu/~arisbe/newbooks.htm#peirce_moore <http://www.iupui.edu/%7Earisbe/newbooks.htm#peirce_moore> , but I don't have it handy at the moment. The addition itself is there. You might also look into the collection, edited by Moore, of essays on Peirce, _New Essays on Peirce's Mathematical Philosophy_ http://www.iupui.edu/~arisbe/newbooks.htm#moore <http://www.iupui.edu/%7Earisbe/newbooks.htm#moore> Other links for interested peirce-listers: Peirce (1908), "Some Amazing Mazes (Conclusion), Explanation of Curiosity the First", _The Monist_, v. 18, n. 3, pp. 416-64, see 463-4 for the addition. Google link to p. 463: https://books.google.com/books?id=CqsLAAAAIAAJ <https://books.google.com/books?id=CqsLAAAAIAAJ&pg=PA463> &pg=PA463 Oxford PDF of article: http://monist.oxfordjournals.org/content/monist/18/3/416.full.pdf Reprinted CP 4.594-642, see 642 for the addition. Best, Ben On 2/22/2017 12:06 AM, Jeffrey Brian Downard wrote: List, I've been trying to sort through the points Peirce is making about topology and the mathematical conception of continuity in the last lecture of RLT. In the attempts to trace the development of the ideas concerning the conceptions of continua, furcations and dimensions in his later works, I've been puzzled by some later remarks he makes about cyclical systems in "Some Amazing Mazes" (Monist, pp. 227-41, April 1908; CP 4.585-641). In a short addendum, Peirce indicates that he has, in the year since writing the paper, "taken a considerable stride toward the solution of the question of continuity, having at length clearly and minutely analyzed my own conception of a perfect continuum as well as that of an imperfect continuum, that is, a continuum having topical singularities, or places of lower dimensionality where it is interrupted or divides ." (CP, 4.642) Here is a passage that has caught my attention: Now if my definition of continuity involves the notion of immediate connection, and my definition of immediate connection involves the notion of time; and the notion of time involves that of continuity, I am falling into a circulus in definiendo . But on analyzing carefully the idea of Time, I find that to say it is continuous is just like saying that the atomic weight of oxygen is 16, meaning that that shall be the standard for all other atomic weights. The one asserts no more of Time than the other asserts concerning the atomic weight of oxygen; that is, just nothing at all. I'm wondering if anyone can explain in greater detail what Peirce is suggesting in this passage in making the comparison between the atomic weight of oxygen and the continuity of Time--or if anyone knows of clear reconstructions of what he is doing in the secondary literature? The claim that the continuity of our experience of time can serve as a kind of standard for measure is, I think, quite a remarkable suggestion. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Jon Awbrey <mailto:[email protected]> <[email protected]> Sent: Wednesday, February 8, 2017 1:26 PM To: Peirce List Cc: Arisbe List Subject: [PEIRCE-L] Re: The Difference That Makes A Difference That Peirce Makes
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