Jeff, list,
I was struck by that passage too, but I don’t think Peirce’s claim is “that the
continuity of our experience of time can serve as a kind of standard for
measure.” Rather I think the claim is that our experience of time is the
prototype for all conceptions of a perfect continuum. The analogy with atomic
weight is misleading if we think of time as a metrical space. Rather time is a
continuum because there are no points in real time (as opposed to
representations of ‘distance’ between events), and that pointlessness is the
‘essence’ of continuity, so to speak.
This however is a point (if you’ll pardon the expression) that Peirce has made
before, so it wouldn’t explain Peirce’s suggestion that he is saying something
new here — if that’s what he is suggesting in the addendum.
Gary f.
} The perfect knot needs neither rope nor twine, yet cannot be untied. [Tao Te
Ching 27] {
http://gnusystems.ca/wp/ }{ Turning Signs gateway
From: Jeffrey Brian Downard [mailto:[email protected]]
Sent: 22-Feb-17 00:07
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
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