> On Jan 7, 2017, at 6:52 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> wrote: > With reference to individuals, I shall only remark that there are certain > general terms whose objects can only be in one place at one time, and these > are called individuals. They are generals that is, not singulars, because > these latter occupy neither time nor space, but can only be at one point and > can only be at one date. (W2:180-181; 1868) > > Peirce noted here that "the character of singularity" is itself a general, > which seems to render nominalism--the view that everything real is singular, > so nothing real is general--effectively self-refuting. He defined an > individual as a collection of singulars joined across places and times, which > is thus general when taken as a whole. Furthermore, absolute singulars are > "mere ideals," such that (ironically) an individual is really a continuum as > Peirce came to understand that concept decades later. Consequently, anything > that we cognize about individuals is necessarily general, rather than > singular.
I agree that this definitely tends to make nominalism self-refuting which I see as a problem rather than a strength. While I’m not quite sure how to deal with this issue, I suspect that this arises out of Peirce’s conception of infinity as opposed to say Cantor’s. Peirce thinks through it by division while Cantor tends to think through it in terms of sets of individuals. Since for Peirce any ‘individual’ is formed from two cuts, that implies a line that can itself be further cut. It’s really not set theory. I’m not sure how Peirce viewed number theory or even how much he knew of it given how much is from the 20th century. Certainly his father Benjamin Peirce had worked on the roots of number theory. If we think of number theory to arithmetic of integers in terms of sets that would appear to lead to thinking of individuals not as a collection of singulars. I did some Googling, since this is an area of Peirce’s thought I’m ignorant on. He did write on number theory in the paper “Logical Studies of the Theory of Numbers” around 1890. That paper seems to be somewhat similar to what Hilbert later did (his 10th problem). That is he was looking for an algorithm that would tell us if there are proofs. He thought we should do this by reducing equations to boolean algebra but that appears to merely be a hypothesis of what one might be able to do. I couldn’t find an online copy of that paper. The closest was this discussion of the paper by Irving Anellis. http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ANELLIS/csp&hilbert.pdf <http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ANELLIS/csp&hilbert.pdf> I’ll confess right up that I just am not at all sure how Peirce viewed mathematics. Given my own background in mathematics this is pretty embarrassing as you’d think I’d know something about this. I assume he’s somewhat platonic about mathematical objects. That is more akin to Godel than the logicists or the constructivists. Yet honestly if someone told me he was a logicist or a constructivist I’d not be at all shocked either. Those seem just as likely a way to conceive of in his philosophy, although he’d probably then argue that the structures of constructure or logic are themselves real independent of human thought as possibilities. Going back to infinity along with Cantor and Dedekind, Peirce asserted that Dedekind’s cut actually came from Peirce. Apparently before publishing on that Peirce had sent Dedekind a paper on such approaches. In contrast to their approaches Peirce saw a problem that needed to be solved. (Relating to the other thread, this suggests that he was thinking along metaphysical lines in what we’d today call modal realism) That is Peirce saw the issue tied to the logic of possibility. Peirce saw their approach as “inchoate” which brings to mind that quote on metaphysics we’ve been discussing in the other thread. Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing. (“What Pragmatism Is,” CP 5.431 1905) The continuum is a General. It is a General of a relation. Every General is a continuum vaguely defined. (“Letter to E. H. Moore,” NEM 3.925 1902) Continuity, as generality, is inherent in potentiality, which is essentially general. (...) The original potentiality is essentially continuous, or general. (“Detached Ideas on Vitally Important Topics,” CP 6.204-5 1908) The possible is general, and continuity and generality are two names for the same absence of distinction of individuals. (“Multitude and Number,” CP 4.172 1897) A perfect continuum belongs to the genus, of a whole all whose parts without any exception whatsoever conform to one general law to which same law conform likewise all the parts of each single part. Continuity is thus a special kind of generality, or conformity to one Idea. More specifically, it is a homogeneity, or generality among all of a certain kind of parts of one whole. Still more specifically, the characters which are he same in all the parts are a certain kind of relationship of each part to all the coordinate parts; that is, it is a regularity. (“Some Amazing Mazes,” CP 7.535 note 6 1908) The key to Peirce’s metaphysics which seems wrapped up in these investigation of continuity and the metaphysics of individualism is the idea that to be requires a repetition which demands that it not be singular in a strong sense.
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