Jeff, List: JD: 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?
Kelly Parker discusses the same passage on pages 116-117 of *The Continuity of Peirce's Thought*. The continuum of time is a species of generality, and is present in any event whatever. Moreover, time is the most perfect continuum in experience. Accordingly, when Peirce defined a continuum as that which, first, has no ultimate parts, and second, exhibits immediate connection among sufficiently small neighboring parts, he appealed to the experience of time to illustrate the notion of immediate connection. Time serves as the experienced standard of continuity, through which we envisage all other continua (CP 6.86). There is an apparent circularity in using time to define continuity. The definition of continuity involves the idea of immediate connection, immediate connection is clarified by an appeal to the concept of time, and time is conceived as continuous (CP 4.642). In chapter 4, I sought to clarify the notion of immediate connection *without* an appeal to time, so as to break this circle. With the mathematical account of immediate connection in hand, though, we can see that Peirce's appeal to time identifies it as the experiential standard of continuity. Peirce asserts that to say time is continouos is "just like saying the atomic weight of oxygen is 16, meaning 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" (CP 4.642). Time, the standard of continuity, is the "most perfect" continuum in experience, but should not be taken as an absolutely perfect continuum. The perfect *true continuum* is only described hypothetically in mathematics. Peirce observed that time is in all likelihood not "quite perfectly continuous and uniform in its flow (CP 1.412). Phenomenological time does exhibit the properties of infinite divisibility and immediate connection, but is probably *not* best conceived as an unbroken and absolutely regular thread. The only constant we have noted in time is the regularity of development or change, but change is not smooth. Changes differ from one another. The "regular" phenomenon of change consists, on closer examination, of numerous (perhaps infinite) parallel courses of development with different patterns and histories that interweave and diverge. Here is what Parker says in chapter 4, page 89, about "immediate connection." Immediate connection is a kind of relation, but a rather peculiar kind. That the connection is *immediate* suggests that there is no need of a third, C, which mediates the relation of A to B. Not only does this exclude the possibility that there is anything located between A and B, it also excludes the possibility that A and B are related only in virtue of belonging to some class of objects. In the case where A and B are connected *only* in co-being, for example, the third is that which brings the two independent things together in a collection. My dog and my hat are "connected" in the sense that both are elements of the set of things in the house as I write this sentence. Suppose that two things, A and B, have some part in common. If that part is the *region of intersection* of A and B, then the region acts as a third and the relation is mediated by that third. Now suppose that A and B have *everything* in common. This means that A and B are *the same*. In fact, the relation of immediate connection appears to be tied up with the relation of identity. Roughly speaking, the "mode of immediate connection" between sufficiently small neighboring parts of a continuum is that such parts are in some sense identical. If I read Peirce correctly, he is here flirting with what would appear to be a disastrous contradiction: *neighboring parts of a continuum may be the same in every respect, including location*. But if all neighboring parts of a continuum are thus identical, there seems to be no way to explain how they make up a continuum rather than collapsing into a single point. How is it that we get from the identity of neighboring points to a line with a left hand and a right hand region? Peirce escapes the paradox by denying that the relations of identity and otherness strictly hold in respect to sufficiently small neighboring parts of a continuum (NEM 3:747). This assertion demands some elaboration. Parker goes on to cite "a loophole in Leibniz's Law," since "difference is equated with discernable difference, that is, a difference that *in principle* could become apparent to a mind." If "A and B are neighboring parts of a continuous line" that "are sufficiently small to be immediately connected," they must be "shorter than any specifiable positive length"; i.e., infinitesimal. "The only difference between A and B must be in their location on the continuous line of which they are parts. Because they are neighboring parts and are connected, they have parts in common; because they are immediately connected, they have *all* their parts in common." Parker then invokes Peirce's illustration from the third RLT lecture of cutting a line at a point, such that it becomes two points. "It is clear that if the original 'point' thus admits of being divided, it must be divisible into parts of the kind we have been discussing. This example illustrates that the immediately connected neighboring parts A and B (which are at the same 'point' before the cut) must be ordered." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
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