Jeff and Gary, JBD
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
GF
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.
I agree with Gary. CSP is trying to break the circular definition by taking one concept as the standard and defining the others in terms of it. Note the term in italics: CSP
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.
For more discussion about Peirce's notion of continuity, see the introduction to RLT by Ketner & Putnam. Cantor, like Zeno, assumed that a continuous time interval is identical to a set of time points. That assumption led to Zeno's paradox. Aristotle's solution to Zeno's paradox is to assume that the proper parts of a continuous line are shorter line segments. Points are not parts of a line, but markers on a line. Peirce adopted Aristotle's solution. But then he took a further step by saying that you could have infinitesimal markers on a line. But all those markers are purely imaginary, since you could never observe them or draw them in actuality. Once you add infinitesimal markers, there is no stopping point, since you can keep imagining (or postulating) infinitely many orders of imaginary infinitesimals. John
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
