Joe, Thank you for offering Schneider's paper to my attention. I haven't read it, but I've read about it in "Why Triadic" http://www.paulburgess.org/triadic.html by Paul Burgess. Satisfaction through "scratching an itch" apart from any summum bonum doesn't seem like verification to me, though Schneider's conception does seem to involve instantiation. But the most general and basic relationship of truth/validity/legitimacy etc. to the good seems to be that when one seems to achieve an end, one often needs to check, often by side effects, after-effects, stabilized and legacy conditions, etc., that one has in fact achieved it and that it really is good, etc.
Burgess writes: 66~~~~~~ A more detailed proposal for Fourthness comes from Herbert Schneider. Schneider concedes three categories to be adequate for dealing with cognitive processes, but argues for "importance" as a category of Fourthness. He notes that, for Peirce, any purpose or good has meaning only in relation to a completely general _summum bonum_. "No Kantian idealist could have stated this conception of moral science more formally." Schneider observes this scheme does not accommodate norms which might apply "even in the absence of a _summum bonum_," itches that call to be scratched for their own sake. Such norms he proposes as a phenomenological aspect of Fourthness: logical import is Thirdness, vital importance Fourthness. Satisfaction may comprise either the Thirdness of achievement or the Fourthness of satiety or contentment. The moral self-control of Thirdness in pursuit of an abstract _summum bonum_ is only an abstract "intellectual framework" until it is taken up into the "concrete universal" of the moral self-criticism of Fourthness. Fourthness supplies what depth psychology, but not the Kantian "moral law within," acknowledges. In logical terms, Fourthness would constitute a temporal sequence, though one which is an absolutely discontinuous string of points superimposed on the triadic continuum. Triadic semiosis is "prospective and cumulative"; tetradic semiosis adds a fourth factor which is non-cumulative, but "retrospective" along the hierarchy of categories, giving "meaningful individuality" to instances of Firstness. Since Firstness and Secondness "look 'forward'" to Thirdness while Fourthness "looks back" to Firstness, Thirdness in a sense "governs" Fourthness while Fourthness provides the steam to "drive" Thirdness. ~~~~~~99 After I read Burgess's accounts of various attempts at fourthness, I felt unmotivated to read the original papers. None of the attempts reminded me of my own, and all of the attempts seemed motivated by certain internal Peircean issues, and not by a broader "fourfold" vision. (It's natural for me to look at it that way, since I was a four-ist well before I read Peirce). Peirce himself, on the other hand, put forth broad and bold inductively expanded threefold themes reaching across and not only _over_, but deeply _through_, philosophy, research, and experience. My 'fourthness' corresponds to form as structure, a balancement and stability of forces. It's more spatial than temporal, at least on some elementary level, though, on the other hand, its continual renovation and occasional redesign is evolution. In terms of mechanics, you could think of it as distance untraveled by the system due to potential and/or actual motion being balanced, "tied up," (statically or kinetically) within the system. I don't know whether Kant talks about a _summum verum_ but that, or something like it, would seem to be the verificational counterpart to a _summum bonum_. Where the Scholastics spoke of "one, true, good" I would put (along with the revision of the causal principles which was my first fourfold, long ago): 1. agent, strong ~ ~ ~ ~ 3. act, good 2. bearer, apt ~ ~ ~ ~ ~4. borne, true which I would relate, for instance, to: 1. will, character, ethics ~ ~ ~ ~ ~ ~ ~ 3. affectivity, sensibility, "aesthematics" 2. ability, competence, "hicanotetics" ~ 4. cognition, intelligence, logic This is one of the structures that gives me hope of adding two more orders to the "order of being" (appeal to explanatory principles), and the "order of knowledge" (appeal to knowledge principles). In the order of "what's important," what one cares about, etc., life and ends come first. In terms of the above, "3." would come first. So of course I'm sympathetic to Gary Richmond's vectors. They're what I would be doing if I were a triadist, even if there weren't a thorny occasioning issue such as that of the difference between the order of semiotic determination and the order of the categories. Now, since the permutations represented by Klein four-group have looked "right" to me (I spelt them out before learning that they made a "group"), I'd expect an "order of importance" of 3, 4, 1, 2. But I don't see a clear reason in terms of the contents of the above examples to order them in that sequence when 3 comes first. Yet, if I pull this off, then any sufficiently major division of research will be able to be at least roughly considered as "foundational" for the rest; it will be a matter of specifying the sense of foundationality and the _kind_ of principles which it makes available to the rest. Likewise I'm kind of dithering about discreteness, continuity, infinity, etc. The discrete finite character of definite instantiation doesn't prevent a general logic from holding. The corresponding character of an actualization (as culmination, not as establishment or settlement into an entelechy) seems not continuity but perhaps discrete infinity, as the interpretant selects, so to speak, from a continuous universe represented, "measured," by the sign, and (the interpretant) narrows that universe down to a range of conceivable experiences. This also doesn't prevent there being a quite general good, a highest good, etc., as far as I know, even if it's never achieved in any finite amount of time. But I'm dithering about continuity, partly because of the odd historical fact that the field of study of continuous local groups (local Lie groups) has been quiet for quite a long time, or so I've read; are they not really important? Yet each such group amounts to a continuous function of a finite number of variables -- this includes the functions about which one learns in high school calculus. A mathematician told me a few years ago that algebra was busily encroaching on analysis and maybe he was talking about new activity in local Lie groups, but I don't know. Ideas about continuity get complicated and I'm not sure that what seem parallel distinctions are really equatable. I'm trying to think of (1) a kind of "local" continuity, or metric continuity, etc. which I think of as the durable and rhythmic bearer's continuity, and (2) a "global" continuity, non-metric continuity, which I think of as the continuity of potency and agency. In the latter I would put all "higher" continuities (hyperreals, surreals, etc.). The two divisions would correspond roughly to (1) the kind of continuity which Peirce regarded as being farthest from true continuity and (2) kinds of continuity with at least some of the topological relevance which Peirce thought was to be reached via absolute continuity "beyond all multitudes" and beyond all Cantor's alephs. (All this is notwithstanding newly achieved conceptions of continuity based on category theory, about which I know even less than I know about "traditional" continuity). INCIDENTALLY, I just noticed that Burgess in "Why Triadic?" says something relevant to the left-right issue and triadicity. 66~~~~~ On the phenomenological front, I note that mathematicians define the "orientation" or handedness of a space by dyadic and triadic arguments alone. The proof is rather technical, but it enables one to speak of left- or right-handedness in space (of three dimensions, or even more) without resort to any tetradic combinations and without any prior invocation of right or left.(36) (36) The argument requires in rigorous form some knowledge of vector spaces, mathematical induction, and finite group theory. But the basic argument runs as follows. On a line, we can arbitrarily select one of the two possible directions and call it "positive"; the other, "negative." We can then extend this definition one dimension at a time by selecting one of the two directions along the nth coordinate axis as "positive" and joining it to the "positive" (n -1)-dimensional structure already established. ~~~~~99 Best, Ben ----- Original Message ----- From: "Joseph Ransdell" <[EMAIL PROTECTED]> To: "Peirce Discussion Forum" <peirce-l@lyris.ttu.edu> Sent: Saturday, July 29, 2006 8:11 AM Subject: [peirce-l] Re: MS 399.663f On the sign as surrogate Sorry, Ben, for the garbled message. I sent it off accidentally before rereading it to pick up on rewordings without corresponding correction of the syntax. The first sentence should read: I'm wondering if you are acquainted with the paper "Fourthness," by Herbert Schneider in the 1952 collection of essays _Studies in the Philosophy of Charles Sanders Peirce_, ed. Wiener & Young (Harvard U Press)? Joe ----- Original Message ----- From: "Joseph Ransdell" <[EMAIL PROTECTED]> To: "Peirce Discussion Forum" <peirce-l@lyris.ttu.edu> Sent: Saturday, July 29, 2006 6:55 AM Subject: [peirce-l] Re: MS 399.663f On the sign as surrogate Ben, It is sometimes referred to retrospectively as the "First Series" since a volume subsequently appeared which is also called "Studies in the Philosophy of CSP", but differentiated from the first by being called the Second Series of this collection. It was published, however, by the University of Massachusetts Press in 1964 and edited by Moore and Robin. Schneider calls the supposed fourth factor "importance" (which he distinguishes from "import") and explicates it in terms of "satisfaction", which seems to have much the same logical function as what you discuss in terms of "verification". I am not saying that I see your view in his exactly but rather that I seem to see some similarity with your view in his explication of it as being required in order to account for the universal as "concrete" rather than merely an abstraction. (Peirce does talk somewhere of "concrete reasonableness" as being a fourthness while denying at the same time that this introduces something not formally resolvable in terms of the other three factors. That is, I seem to recall this, but I can find nothing in my notes that says where that passage is. Does anyone else recall this, I wonder, or have I merely hallucinated it?) Joe Ransdell ----- Original Message ----- From: "Benjamin Udell" <[EMAIL PROTECTED]> To: "Peirce Discussion Forum" <peirce-l@lyris.ttu.edu> Sent: Friday, July 28, 2006 4:10 PM Subject: [peirce-l] Re: MS 399.663f On the sign as surrogate --- Message from peirce-l forum to subscriber archive@mail-archive.com
