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&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 <[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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