Michael, Jeff D., Jerry, list, Michael wrote: I part with this very late gem [ca. 1908], where I think the continuity-continuum seamlessness is quite evident - continuous, if you will.
I quite agree, and *if* one could say of a quotation offered to prove a point that it did, one might say of this one: Q.E.D. Jeff asked: What might we do to arrive at greater clarity about what the distinction between the conceptions of a perfect and an imperfect continuum consists in and what the basis of the distinction rests on? As Michael noted earlier, this is a *very* different question than the one he was arguing with Jerry. I don't see that it offers any particular difficulties in answering (Peirce is quite explicit), and Michael in passing did offer a remark clearly articulating this distinction (I didn't quickly find it). Best, Gary R [image: Gary Richmond] *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690 <718%20482-5690>* On Mon, Nov 17, 2014 at 11:53 PM, Michael DeLaurentis < [email protected]> wrote: > Lest you lost sight of my sample citations -- and for your further > musement -- I part with this very late gem [ca. 1908], where I think the > continuity-continuum seamlessness is quite evident - continuous, if you > will. > > > > In going over the proofs of this paper, written nearly a year ago [1907], > I can announce that I have, in the interval, 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... . If in an otherwise unoccupied continuum a figure of lower > dimensionality be constructed __ such as an oval line on a spheroidal or > anchor ring surface __ either that figure is a part of the continuum or it > is not. If it is, it is a topical singularity, and according to my concept > of continuity, is a breach of continuity. If it is not, it constitutes no > objection to my view that all the parts of a perfect continuum have the > same dimensionality as the whole. (Strictly, all the material, or actual > parts, but I cannot now take the space that minute accuracy would require, > which would be many pages.) That being the case, my notion of the essential > character of a perfect continuum is the absolute generality with which two > rules hold good, first, that every part has parts; and second, that every > sufficiently small part has the same mode of immediate connection with > others as every other has. (CP 4.642) > > > > With that, I will rest my case. > > > > *From:* Michael DeLaurentis [mailto:[email protected] > <[email protected]>] > *Sent:* Monday, November 17, 2014 7:56 PM > *To:* 'Jerry LR Chandler'; 'Peirce List' > *Subject:* RE: [PEIRCE-L] Continuity, Generality, Infinity, Law, > Synechism, etc. > > > > Jerry - A lot of words, but no explication whatsoever of any distinction > CSP makes between continuity and its instantiation in continua. After some > irrelevancy re the Continuum Hypothesis, you make some statements about > continuity and the philosophy of the natural sciences, continuity and > chemistry, and "continuity in term of units, individuals and collections" > -- three sets of comments about continuity, none involving the continuum. > Where's the purported distinction between continuity and the continuum - > i.e., between the continuity exhibited in continua and any other alleged > continuity? Where are CSP's words that indicate such a distinction? What > has this claim - "One notion of continuity was constructed by CSP from > units, individuals and collections" -- contrasted with this claim - "A > second notion of usage of continuity emerges from Cantor's view of the > number line as a closed interval that could be separated into two notions > of distance" - got to do with a purported distinction PEIRCE makes between > continuity and the continuum, other than that the former is exhibited in, > and only in, continua? And how do these meandering musings confirm that > "Kirsti's intuition was spot on"? Nothing you say even begins to addresses > this. > > > > I cited the late articles and passages where, to the contrary, CPS, as > even Kirsti has now acknowledged, moves seamlessly between the two, in just > the manner I have described. You have splashed a bunch of disconnected > comments around, but have cited nothing in Peirce to the contrary. > > > > I don't see the point of continuing this thread if you're just going to > toss a hodge-podge of unrelated statements around. And with this post, I > will therefore close end my responses to these aimless meanderings. > > > > > > *From:* Jerry LR Chandler [mailto:[email protected] > <[email protected]>] > *Sent:* Monday, November 17, 2014 7:26 PM > *To:* Peirce List > *Cc:* Michael DeLaurentis > *Subject:* Re: [PEIRCE-L] Continuity, Generality, Infinity, Law, > Synechism, etc. > > > > List, Michael, John, Kirsti: > > > > On Nov 14, 2014, at 11:41 AM, Michael DeLaurentis wrote: > > > > Jerry - All due respect, but my post concerned the distinction Kirsti > claimed to find, not anything in your post. So I don't see the relevance.. > > > > The immediate relevance of my post is that this is a listserve for CSP > writings and the recent correspondence relate to his writings, although I > do not think that is what was of concern to you. > > > > Your post leave me puzzled about your penultimate post which in turn was > puzzling, so I reviewed the tread from its beginning and read more widely. > > > > The immediate motivations for my contributions and, as I understand it, > yours also, was the issue raised by Kirsti with respect to the possible > distinction the continuum and continuity in philosophy, mathematics and > CSP's writings. > > > > Your post (Nov 12) expresses this perspective: > > Continuity is simply the unique quality which continua, and only > continua, exhibit. > > > > Does this assertion close the philosophical issue that Kirsti raised? > > > > In response to John Deely's questions (post 18 in the listing) > > "Deely, John N." [[email protected]] kirjoitti: > > Kirsti, would you mind clarifying for me, if possible (but not > necessarily) with some specific ref. to a Peirce text(s), your remark re > the difference between "continuity" and "continuum": > > > > I believe that it is relevant to cite the specific texts 4.172-176 from > CSP in part of the answer to John's and Kristi's questions. > > These paragraphs brought to mind the Cantor's famous "Continuum > Hypothesis" . A couple of citation from the web place the concept of the > Continuum is a completely different context that that of mere continuity. > > > > [Introduction. Arguably the most famous formally unsolvable problem of > mathematics is Hilbert's first problem: Cantor's *Continuum Hypothesis*: > > {The proposal originally made by Georg Cantor that there is no infinite > set with a cardinal number > <http://mathworld.wolfram.com/CardinalNumber.html> between that of the > "small" infinite set of integers > <http://mathworld.wolfram.com/Integer.html> [image: aleph_0] and the > "large" infinite set of real numbers > <http://mathworld.wolfram.com/RealNumber.html> [image: c] (the "continuum > <http://mathworld.wolfram.com/Continuum.html>"). Symbolically, the > continuum hypothesis is that [image: aleph_1=c]. Problem 1a of Hilbert's > problems <http://mathworld.wolfram.com/HilbertsProblems.html> asks if the > continuum hypothesis is true.] > > > > Another aspect of this issue was how did CSP relate his views on > continuity to the philosophy of the natural sciences? > > And these to synechism? > > 4.584 (1906) It is that synthesis of tychism and of pragmatism for which > I long ago proposed the name, Synechism > > > > Yet, with respect to chemistry and continuity, he writes CP1.62 (1896?) > > Now it enters into every fundamental and exact law of physics or of > psychics that is known. The few laws of chemistry which do not involve > continuity seem for the most part to be very roughly true. It seems not > unlikely that if the veritable laws were known continuity would be found to > be involved in them... > > > > This is to be contrasted with his statements in 4. 173 where he justifies > the origin of continuity in term of units, individuals and collections, > strongly implies a consistency with the legisigns of chemistry with atoms > as units, individuals as proper names of elements and collections becoming > continuous. > > > > Thus, my conclusion from these readings is that Kristi's intuition was > spot on. > > One notion of continuity was constructed by CSP from units, individuals > and collections. > > A second notion of usage of continuity emerges from Cantor's view of the > number line as a closed interval that could be separated into two notions > of distance, as shown in his well know "removal of the middle third" > argument to construct infinite numbers of continuous closed intervals from > a line of UNIT length. The "Continuum Hypothesis" is a proposition about > Cantor's mathematical philosophy. It is not an extension of CSP's notion > of continuity. > > > > On another topic, I think it is important to support Stefan's quote of CP > 5.131: > > "Man makes the word, and the word means nothing which the man has not made > it mean, and that only to some man. But since man can think only by means > of words or other external symbols, these might turn round and say: "You > mean nothing which we have not taught you, and then only so far as you > address some word as the interpretant of your thought." In fact, therefore, > men and words reciprocally educate each other; each increase of a man's > information involves and is involved by, a corresponding increase of a > word's information." > > > > I was not aware of this quote, but have had a similar thought in mind for > decades from my sensory experiences in the world. The observation that > meaning is individualized is true for all individuals as a consequence of > their antecedent sensory experiences. It is also true of language usage > among disciplines. It is particularly important for those who love > knowledge. > > > > Cheers > > > > Jerry > > > > > > > > > > > > > > > > > > *From:* Jerry LR Chandler [mailto:[email protected] > <[email protected]>] > *Sent:* Friday, November 14, 2014 12:33 PM > *To:* Peirce List > *Cc:* Michael DeLaurentis; John N. Deely; Määttänen Kirsti > *Subject:* Re: [PEIRCE-L] Continuity, Generality, Infinity, Law, > Synechism, etc. > > > > List, Michael, Kirsti, John: > > On Nov 12, 2014, at 11:47 AM, Michael DeLaurentis wrote: > > I don't find any such distinction, implicit or explicit, in Peirce's late > writings. > > Motivated by your assertions, I re-read 4.172 and later paragraphs, > searching for distinctions between CSP logic and set theory logic. > > In contrast to your assertion, I certainly find numerous critical > philosophic distinctions between CSP logic and Cantorian/Russellian logic > with respect to inquiry into the mathematics/logic of the continuum. > > Although a large number of texts could be cited, availability of time > and energy restrict my rhetoric principally to 4.172 to 4.176. > > 1. 4.173 introduces with the notion of a collection. > > A collection is a consequence of "bring or gather together", parts of a > whole. > > CSP bases his notion of relation on collections as parts of a whole. It > requires activity to bring together a collection. > > Thus, CSP is grounding his argument, among other mathematical concepts, on > the theory of numbers, the collectability of numbers, and the antecedent > parts being brought together to construct a whole. > > This is clearly distinct from Cantor / Russell views which pre-supposes > a geometric line. > > 2. 4.174 (and 4.172) introduces the notion of a relative of a part > versus the relative of a whole, drawing on the statistical example in 4.172 > and the concept of a unit of a partition of a role of a pair of dice. Each > role of the pair of die generates a relative value among all possible roles > of the pair of six-sided die, exactly 36. > > This is clearly distinct from Cantor / Russell views. > > 3. 4.175 "But when the units lose there individual identity because > the collection exceeds every positive existence of the universe, the word > multitude ceases to be applicable. I will take the word multiplicity to > mean the greatness of any collection discrete or continuous." > > I infer from this, in light of 4.172-175, that individual identity is > related to parts of a whole such that parts, as units, can be collected > into whole, generating the NOUN, collection. The "bringing together" of a > collection is of the nature of a sublation. The quality of the collection, > is, presumable for CSP, a matter of sensory experience, as one perceives > from the usage of the term "because" in this sentence, inferring causality. > > (And qualities are an aspect of sensory experiences, are they not?) > > This is clearly distinct from Cantor / Russell views of memberships and > classes. > > Yes, set theory, as a dominant force in modern mathematics, has ignored > the logical basis of CSP notion of multitude and his terminology for > distinguishing between parts and wholes, points and lines, and sensory > experiences. > > But, CSP's philosophy expressed in 4.172-4.175 is consistent with many > aspects of chemical logic; modern mathematics is not consistent with > chemical logic for very specific reasons of the non-transitivity of the > mathematics of chemical sublations of individual identities. > Non-transitivity is illustrated, for example, by the handedness of chemical > isomers.) > > I conclude that although many many aspects of CSP logic and set theory > logic are consistent with one another, the distinction between them (modes > of constructions) at the rhetorical and semantic levels differ in > mathematically profound ways. > > The basic conundrum of the nature of distinction between discrete and > continuous mathematics remains alive and open. Indeed, a very active > subfield of mathematics is the Brouwer School of intuitionism. > > ( http://en.wikipedia.org/wiki/Intuitionistic_logic ) > > Parenthetically (or perhaps metaphorically) I conclude that studying CSP > texts without an in-depth knowledge of the state of the science in the 2nd > half of the 19 Th Century is like attempting to solve a crossword puzzle > with only the superficial "across" clues. The depth of his thought > corresponds with knowledge of mathematics and the natural sciences and the > natural propositions in his time, that is, the "down" clues. > > Extending the metaphor, the sensory experiences of the American cultural > milieu of the late 19 Th Century are interwoven into the very fabric of > CSP's text. > > Cheers, Jerry > > (BTW, Thanks to Gary F. for suggesting a puzzle analogy for > hermeneutics.) > > > > > > > > > > > > > > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2015.0.5577 / Virus Database: 4213/8570 - Release Date: 11/14/14 > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. 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