[peirce-l] Re: NEW ELEMENTS: So what is it all about?

[Benjamin Udell]

Thomas, list   Sorry it took me a few days to respond. I've been busied with various practical matters.   > [Thomas] this thread on "The New Elements of Mathematics" started with Charles Peirce writing: > "None of them approved of my book, because it put perspective before metrical geometry, and topical geometry before either." > Even today if one would consider to engage in the project of writing such a book, one should really think twice. Nobody has a really good idea how to write it and if it were written, nobody would understand it, and if one would understand it, one would have to unlearn lots of things one already knows and that only for a curiosity. > One criterion for scientific progress is, that a new theory should explain everything that the preceding ones explained and something else besides (ha!). > Charles was, together with his father Benjamin Peirce, part of a movement in 19th Century mathematics called "Universal Algebra". Others were e.g. William Rowan Hamilton and Hermann Grassmann. All of them or their followers erected a "philosophy" on their mathematical ideas, by the way. > What Felix Klein has written about Hermann Grassman's Ausdehnungslehre ("Theory of Extension") in his "Lectures on the Development of Mathematics in 19th Century" (1926) applies to Charles Peirce too and is still considered relevant today. The main point is on page 178 in my Springer Reprint of Klein's book (I believe there exists an English translation too). > It is this: > The grand project in mathematics for much more than a century now has been "arithmetization, i.e. to reduce mathematical structures to the abstract structure of the natural numbers. If you put the continuous before the discrete, then you are not alone in history, but nobody has as yet really succeeded with such a project. The problem is, simplistically speaking, that, starting with a continuum, you will have great difficulties to introduce discrete entities, except by way of an arbitrary addition. So the relevant book today is David Hilbert's "Grundlagen der Geometrie (Foundations of Geometry). There are today followers of the other approach, especially in Grassmann's footsteps, e.g. David Hestenes with his "Geometric Calculus and "Geometric Algebra, but their success, despite some very striking simplifications and insights, till today is quite limited. It is more or less regarded as a curiosity, some "flashes of brilliant light relieved against Cimmerian darkness ... > On the other hand there is in Sir Roger Penrose's "Road to Reality (now we come to the noble celebrities) an introductory chapter on "The roots of science and especially "Three worlds and three deep mysteries (chap 1.5) with the usual Popperian sermon preached (sorry, Sir Karl Raimund). But one "deep puzzle for Sir Roger is "why mathematical laws should apply to the world with such phenomenal precision. Moreover, it is not just the precision but also the subtle sophistication and mathematical beauty of the successful theories that is profoundly mysterious(p.21). > Finally Roger Penrose writes in this context: "There is, finally, a further mystery concerning figure 1.3, which I have left to the last. I have deliberately drawn the figure so as to illustrate a paradox. How can it be that, in accordance with my own prejudices, each world appears to encompass the next one in its entirety? I do not regard this issue as a reason for abandoning my prejudices, but merely for demonstrating the presence of an even deeper mystery that transcends those that I have been pointing to above. There may be a sense in which the three worlds are not separate at all, but merely reflect, individually, aspects of a deeper truth about the world as a whole of which we have little conception at the present time. We have a long way to go before such matters can be properly illuminated.(pp. 22/23) > Noble words to be considered well! But don't tell Sir Roger about the sign and it's interpretants. That will not do for him. There are a lot of philosophical soap shops out there. You had better understand fully what his problems are in the next 980 or so pages of mathematics and physics that come then, before you tell him about "The New Elements of Mathematics.   I read about his Three Worlds picture in an earlier book of his, one which I understood only middlingly well. I once read a whole book explaining Goedel's incompleteness proof, but I just don't feel sure-footed on the subject, so I won't be the one to convince Penrose of anything if that's what it takes!. Penrose's Three Worlds strike me as possibly Peircean in ancestry, but it's not clear to me how best to align it with Peircean conceptions. Its structure, a cycle though the Worlds that gives you A, B, C, A, B, C... etc., doesn't seem a typically Peircean kind of determinational structure.   For instance 1st? Penrose's World of maths |> 3rd? Penrose's World of culture 2nd? Penrose's World of physical experience   Peirce divides the discovery sciences into (1) mathematics, (2) cenoscopy (=philosophy), and (3) idioscopy (=the special sciences). Joe Ransdell has associated those, respectively with 1stness, 2ndness, 3rdness, though I don't know his argument for it or maybe he has a citation from Peirce.   Peirce did have a "three worlds of experience":   1. Ideas. |>3. Habit-taking. 2. Brute facts.   Incidentally, the above manner of representing a triad or trichotomy was devised by Gary Richmond as part of his _trikonic_. A trikon is the trikon symbol |> with the terms arranged around it, the whole structure.   I disagree with both Penrose and Peirce on "Three Worlds", but I think Peirce's view is better thought out. Tegmark's four "Levels," though more physics-oriented, and philosophically less explicit (unless I'm discerning too much into it), make more sense to me, which is not to say that I think that Tegmark's Multiverse theory or his views of what comprises math are true.   > [Thomas] So what we do with Peirce's work appears to the outside world either as a more or less philatelistic pastime with historical curiosities. It's all good and fine and edifying and very logical except for a few paradoxes here and there, perhaps. Or else you start getting your hands really dirty and do whatever it takes to find out what is going on behind the scenes.  We had better find out and make our mistakes as quickly as possible in order not to flog a dead horse, I believe.   Well, peirce-l isn't really a "project."  It's just people interested in Peirce, for various reasons, and, accordingly, with various senses of time constraints, and with various views on what needs or doesn't need doing to his ideas. In particular, I have no career in this sort of thing, it's more like a hobby that got out of hand. I'm not sure that anybody here understands what I'm doing, though Gary Richmond seems to understand aspects of it somewhat though he utterly disagrees with it. You're the first person since I joined peirce-l who has suggested that I might be on the right track with structures even though they're noticeably fourfold rather than Peirceanly threefold. If you hadn't really noticed their fourfoldness, you may wish now to reconsider! I was already interested in fourfold structures by the time I read Peirce. I'm here because Peirce is the only modern philosopher who seeks & finds recurrent logical and categorial structure surfacing with varying degrees of clarity like a theme in every subject of interest, at least at a sufficiently general level.   > [Thomas] Enough name dropping for now. > Ben, you write:   <begin citation>   1. The idealized system of motions & forces -- classical Newtonian or pure-quantum-system -- is time-symmetric, completely deterministic in the given relevant sense, unmuddled, pure OBJECT to us, information about which object we can only approach indefinitely, as to a limit. 2. The material system is time-nonsymmetric, stochastic-processual, in which the system at a given stage is only ALMOST the system at another given stage, i.e., a SIGN to us of the system at other stage. 3. The vegetable-level biological system is time-nonsymmetric but LOCALLY pointed thermodynamically in the opposite direction from that of its material world, from which it filters order and is an INTERPRETANT to us. 4. The intelligent living system is time-nonsymmetric but INDIVIDUALLY pointed variously in both directions thermodynamically -- as living thing, it filters for order -- as intelligent, it is a sink, retaining sign-rich disorder as recorded -- I don't know how it pulls double-direction "trick" off -- anyway it is a RECOGNITION which we are.   The sign defined by its relationship to recogition is a proxy.   <end citation>   > [Thomas] Peirce distinguishes equiparants and disquiparants ("Classification of Simple Relatives; CP 3.136): > "Classification of Simple Relatives (cont.) > "Third, relatives are divisible into those for which every element of the form (A:B) have another of the form (B:A), and those which want this symmetry.  This is the old division into 'equiparants' and 'disquiparants', or in Professor De Morgan's language, convertible and inconvertible relatives.  Equiparants are their own correlatives. All copulatives are equiparant. > That was in 1870 ("Description of a notation for the logic of relatives). > In MS 293 (1906) under the title: "The Logical Form of Identity, he says (I have to retranslate things into English, since I only have Helmut Pape's German translation here before me), considering the question whether it is disquiparancy or equiparancy that is the more fundamental, important, elementary, simple: > "I hold that it is disquiparancy or, rather, it is the opposition or the relation, of which disquiparancy can be a specialization. > Sounds ugly, but maybe someone out there can give us the original English text. (My command of English is limited.) > We need something fundamentally asymmetric in physics as you implicitly remark. > We need a fundamental asymmetry in logic, since there are such things as memory, history, time.   I don't take a view on whether asymmetry or symmetry is more basic. If I see an equivalence in place A, and a strict implication in place B, and a strict reverse implication in place C, then I try to figure out a place D & figure out what take the form of the mutual non-implication there. I like to trace out, extend, & complete patterns, usually by finding a pair of mutually independent yet logically "twinned" bivaluate parameters.   > [Thomas] I guess we should discuss this "how it pulls double-direction "trick" off" further. No mercy!-) This is very important and something that seems to me to have been neglected as yet!   I've wondered about it. I've been toying with the idea of intelligence as a kind of localized or individualized sink for a while now, involving both the "running uphill" and "running downhill" of the system, somehow. Toying is about all that I can do with it. I don't know whether it's original. I mean, obviously things like "the soul is memory" have been said since as long as anybody can remember. Yet to try to take that retention idea seriously in terms of entropy, order, etc., that's something such that I wonder whether anybody has done it. (Less work for me down the road.) A sink of what, exactly?--a sink of something sufficiently general in conception to relate it to biological, material, & dynamic systems. And again, obviously it's been taken seriously in some sense, because of computers retaining memory (and, among other things, overheating). But I don't know what the "big picture" is between (a) memory, attachment, skill, adherence, and (b) things like entropy, order, energy, and thermodynamics.   > [Thomas] You write: "anyway it is a RECOGNITION which we are" > This "RECOGNITION effect, this is tremendously important. You've got it! That's it! We'll get that! We'll get that damned thing out. Be sure.   I'm glad that you think that it's important, and I'd be interested to know why you think so.  I know more or less why I think so. In using it in a series that begins with "object, sign, interpretant," what I'm doing is saying that semiosis is tetradic, not triadic.  You may not want to go along with this!  The short (okay, maybe not so short) version is this: Object, sign, & interpretant do not convey familiarity-dependent understanding of the object to the mind. The object does not convey familiarity-dependent understanding of itself to the mind because, otherwise, signs & interpretants would be unneeded.  The sign is not the object and thus familiarity with the sign is not familiarity with the object.  In this sense the sign is JUST a sign, and the interpretant is JUST a construal.  The sign is not the object itself, it's just a representation, amounting to no more than a claim.  As Peirce says, the sign & interpretant don't contain conveyable familiarity-dependent understanding of the object to the mind.  Even the mathematician must _observe_ and _experiment with_ the mathamatical diagram in order to check claims or signs about the diagram and, really, about the object for which the diagram stands proxy.  Thus the question of collateral experience, collateral observation, etc.  Peirce's idea was that by collateral experience you learned the denotations of signs, like learning the meanings of words in a foreign language. I see more ramifications in this than Peirce saw.  To the extent that sign & interpretant convey new info to the mind, the mind has to check its experience of the object, check it collaterally to the sign & interpretant, verify or disconfirm. To the extent that conditions change, the mind needs to at least spot-check signs & interpretants against object-observations.  The sign must be checked not only as to denoting that which it seems to denote, but also as to any other sign power -- does a certain symbol connote that which it seems to connote? etc.  If the mind does not have adequate collateral experience stored up and recallable to accomplish the task, then it must acquire such experience in order to confirm / disconfirm sign & interpretant. Verification, disconfirmation, etc., involve observation of the object, and not mere claims & construals regarding the object. Ergo, if semiotics is to be a study of logic, then it needs to regard verification and disconfirmation as part of semiosis, which it cannot do as long as it tries to view everything as object, sign, interpretant, which do not convey familiarity, observation, experience as such to the mind. Evolution is another subject which falls outside the province of semiotics as long as testing & checking are not part of semiosis. One can't adequately conceive of evolution as semiosis, since testing, trial, & error are things that happen, from outside, to triadic semiosis, not things that semiosis does. Without a stage of checking, confirming, etc., semiosis has no way to check its hopeful monsters (its interpretants), and cannot learn the difference between sense & nonsense. The object-observation which confirms sign & interpretant is what I call "collaterally based recognition," or "recognition" for short.  E.g., when I see somebody wearing a hat as I expected that s/he would. I regard the recognition as on a par with object, sign, & interpretant because, like object, sign, & interpretant, it has info about the object, and it is defined in semiotic terms: Object, sign, & interpretant have non-familiarity-based object info for the mind; the recognition has familiarity-based object info for the mind.  Ergo, again, it is semiotic. An interpretant is an understanding. A recognition is a knowing or coming-to-know, where "knowledge" isn't regarded as divinely infallible but as cognition based on confirmation sufficiently firm that it is reasonable to regard none more as being much needed. I _know_ that I live in Queens. Okay, maybe I'm just a simulation in a "computer" or something like that created by a majestic alien intelligence.  But for all practical intents & purposes, I _know_ that I live in Queens. I see no deep categorial divide between an understanding and a recognition, such that one is semiotic & the other is not. I regard the recognition as irreducible to object, sign, & interpretant, because, unlike them, it does contain & convey familiarity-dependent understanding of the object to & across the mind, commind, quasimind, etc. Ergo, again, it is not object, sign, or interpretant.  It may be an object, sign, or interpretant in other relations, in another semiotic frame of reference. But that's in exactly the same sense as the sense in which the sign may be a object in another frame, and so on. There's no "reducing" the recognition to interpretant, sign, or object, in that manner, without reducing away the classic semiotic triad itself. Object, sign, & interpretant, without recognition, are like source, encoding, & decoding, without recipient.   Since for each semiotic element there is a kind of sign defined in relation to it (index : object : : icon : sign : : symbol : interpretant), there must be such a sign defined in relation to the recognition, and that's what I called the "proxy," which is defined by the legitimacy and recognition-worthiness with which it can "act" & "make decisions" as the object in some respect, the recognition which it would receive from the recognizant that has collateral experience of its object. In fact it may receive that recognition on the basis of experience with other proxies. Somewhere along the line there usually needs to be a basis in direct experience of the object. Anyway, this turns out to slacken the direct-collateral-experience constraint which would otherwise become hopelessly strict.  At the same time, one can answer the question of just how it is that experience is enriched by semiosis:  one can conceive of experience as semiotically empowered, enriched, clarified, solidified, by being formed AS collateral to sign and interpretant in respect of the object.   > [Thomas] Ben, you write:   "ERGO: As sign, man is most of all a proxy. At intelligent life's best, only indefinitely approached, intelligent life is a genuine, legitimate proxy acting & deciding on behalf of the ideal, in being determined _by_ the ideal. Intelligent life shouldn't let it go to his/her head, though. Hard it is to be good; harder still to confirm & solidify it by entelechy = by staying good => continual renovation and occasional rearchitecting (entelechy is not necessarily a freeze) amid changing  & evolvable conditions.   > [Thomas] I fully agree.   Thank you. And, if you still agree after this post, you'll be the first peirce-lister to do so!   Best, Ben --- Message from peirce-l forum to subscriber archive@mail-archive.com