The philosophy of Charles S. Peirce is chock-full of triples, but especially present are his three universal categories of experience. Threes aren’t really my specialty, but while reading a chapter of Richard Bernstein’s book on the “pragmatic turn”, I was reminded of Peirce’s relational ontology: Firstness, Secondness, and Thirdness. Wondering how these could be extended to a Fourthness, I immediately found a fair amount of work on the subject.
Of course, Peirce argued that such a Fourthness was redundant, unnecessary to the structure of his systematic philosophy. He used various reasons for his conclusions, including mathematical, logical, and semiological. There is also a wealth of subsequent work by later researchers on defending this claim, but what is interesting is that others have investigated extending his three into a four.
So, what might be Fourthness? Some of the aspects of fourfolds collected here have commonalities with some of the attributes of Firstness, Secondness, and Thirdness. For Firstness: feeling, quality, possibility; For Secondness: will, fact, existence; For Thirdness: knowledge, law, representation. I really don’t have anything to add at the present time and I have merely gathered these notions together for my future consideration.
References:
http://en.wikipedia.org/wiki/Categories_%28Peirce%29
http://en.wikipedia.org/wiki/Hypostatic_abstraction
http://www.paulburgess.org/triadic.html
http://tetrast.blogspot.com/2006/09/compare-to-aristotle-aquinas-peirce.html
Carl G. Vaught / Semiotics and the Problem of Analogy: a critique of Peirce’s theory of categories. Trans. of the Charles S. Peirce Society, Vol. 22, No. 3 (1986) 311-326
http://www.jstor.org/stable/40320143
Carl R. Hausman / Fourthness: Carl Vaught on Peirce’s categories. Trans. of the Charles S. Peirce Society, Vol. 24, No. 2 (1988) 265-278
http://www.jstor.org/stable/40320211
Donald W. Mertz / Peirce: logic, categories, and triads. Trans. of the Charles S. Peirce Society, Vol. 15, No. 2 (1979) 158-175
Richard J. Bernstein / The Pragmatic Turn. Polity (2010)
Also:
Ben Goertzel / The Hidden Pattern: a patternist philosophy of mind
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Equivalent eXchange 
Wow, I ought to say something here. I’ll try to come up with something in the next week or so.
Paul Burgess is a swell guy, I’ve been in contact with him over the years and exchanged a bunch of messages with him just recently.
Ben, I look forward to your comments! You appear to be a major contributor for the main Wikipedia entry.
I thought Paul’s article was very informative. And after looking at more of his web site, I must say that I enjoyed his appreciation of Neon Genesis Evangelion!
I’m working on a few more notes to the above post, so check back.
Okay, now I’ll try to say something not too beside the point.
I think you already understand quite a bit about Peirce’s threes.
Peirce discussed medads (i.e., zero-ads) a few times. People have sometimes discussed the possibility of a category of “zerothness” or “pure zero”. Unfortunately I have trouble finding any of the richer discussions that I seem to recall as having occurred at peirce-l.
Peirce’s categories involve a division of all phenomena into three kinds or modes. Adding a fourth category is usually regarded by Peirceans, at least initially, in terms of attributing an extra slice to a pie, leaving Peirce’s original three categories pretty much the same, rather than as re-dividing a pie into four instead of three. (I had my own fours going when I began to read Peirce, and most of my fours did not originate as modifications or augmentations of Peirce’s threes; an exception is my idea of a semiotic tetrad). Peirce regards both vagueness and arbitrariness as firstness but to me they seem mutually opposite and complementary, like probabilism and novelty. Anyway, if one _accepts_ Peirce’s three categories, then the problem of finding a fourth category becomes the big challenge of how to _expand_ the pie as a whole in order to make room for a fourth category.
Among other things, Peirce’s categories involve his doctrine of monadic, dyadic, and triadic predicates or relations. I haven’t read and don’t begin to understand the more abstract proofs (Robert Burch 1991; Correia & Pöschel, 2006) that have been offered that all relations are essentially monadic, dyadic, or triadic. Years ago I put a list of those and related texts with links in what is currently Footnote 6 at https://en.wikipedia.org/wiki/Categories_%28Peirce%29 . (Note, the long Peirce quote near the article’s start is confusing and many think it’s not about Peirce’s categories but about some other division.) I look at these things so differently that it’s hardly worth discussing my own views here; I generally don’t look for things like irreducible dyads, irreducible triads, etc.
Still, I’ve ventured claims of an irreducible tetrad in something like Peircean terms. Now, in his later years, Peirce said that sign and interpretant do not convey acquaintance, observation, or experience of their object (their subject or subject matter). The observation, etc., of the object is _collateral_ to signs and interpretants in respect of their object. (The interpretant is generally a further and interpretive sign.) You can look up Peirce’s discussions under “collateral experience”, “collateral acquaintance”, and “collateral observation”, all of which he discussed in pretty much the same terms. The basic idea is that the map is not the territory. So what _does_ convey acquaintance, observation, or experience of the object? Until some time in 2007, I argued a number of times at peirce-l that there is an irreducibly fourth semiotic “stage” or correlate, that of the collaterally based recognition (the “recognizant”) of interpretant and sign as corresponding to their object. I stopped arguing about it because I convinced hardly anybody of anything, and the argument was starting to dominate peirce-l in a way that I thought was bad for peirce-l, where I’ve become co-manager and don’t plan to restart the argument unless I have something new or more powerful to say.
Thanks for the comment. I don’t know if I really understand very much about Peirce’s three categories, but I think I do understand a bit more now. And I’m not sure if I think Thirdness should be split into two, or that a new Fourthness should be added to the usual interpretations. But, you know, Fours!
Several ideas discussed in the papers and links above for what Fourthness might be are value, importance, and even analogy. These are good, but one of my favorites is synergy and emergence, discussed in “The Hidden Pattern” by computer scientist Ben Goertzen. Check out Ch. 6 “Four Levels of Mind” in the pdf below.
Also, here’s a nice new article on Peirce’s Triad from the standpoint of another computer scientist, Mike Bergman (link below). No Fourthness, though.
You mention collaterality as a possible Fourthness, the object as interpretant. What about the simple reflexiveness of triad recognition? That doesn’t seem to be implicit in the usual meanings.
I like emergence because of my notion that Fourthness should be temporal Function, as the source of dynamic combinatorial creativity, as opposed to Thirdness as static spacial Structure. I guess I have in mind the rule of Linear Logic’s Tensor…
Ben Goertzel / The Hidden Pattern: a patterns philosophy of mind (2006)
Click to access HiddenPattern_march_4_06.pdf
http://wp.goertzel.org/
http://www.mkbergman.com/1932/a-foundational-mindset-firstness-secondness-thirdness/
Thanks for continuing, Martin, and for pointing me toward those writers.
Mike Bergman recently joined peirce-l and asked for comment on an essay of his, and some people comment. He says many things in it and gets Peirce partly right and partly wrong. I didn’t follow the discussion closely because I’ve been so busy with practical matters.
Goertzel’s 2006 book is not currently available at that link, and a robots.txt file prevents access through the Wayback Machine, but I found it via Google Books, in particular Chapter 6 “Four Levels of Mind”:
https://books.google.com/books?id=juj30GyFzOUC&pg=PA69&lpg=PA69&dq=%22four+levels%22+%22goertzel%22
Likewise Goertzel’s chapter “A Fourfold Model of Information Space” (from his _Wild Computing_, 1999) is no longer available except in Google cache:
http://webcache.googleusercontent.com/search?q=cache:o4lnSqThLbsJ:www.goertzel.org/books/wild/chap4fold.html
The latter seemed familiar and it turned out that he was basing his ideas on those of Kent Palmer, who emailed me in 2006 to say that he liked some of my ideas (the ‘recognizant’) and suggested that I read some of his texts, which texts, however, just made me dizzy. Computer programming, AI, etc., are leagues above anything that I understand, and the philosophical insights based on experience with them are quite difficult for me to read critically, I usually don’t really understand them. All I ever was was a Word & PowerPoint guru for a while, and handy with html & css since then. I’m kind of stuck in the baby section of the philosophers’ sandbox of 1st-order logic with identity.
As for Goertzel’s “Four Levels of Mind,” I’ve read through it once, and will try again. Peirce is not as similar to Nietzsche on the question of reality as Goertzel seems to think. For Peirce the whole cognitive point of semiosis is for oneself to be determined or influenced by the real to the truth, not to invent beautiful lies. Anyway, I’m trying to get a handle on Goertzel’s conception of emergent structure, which in that chapter is his fourth and does seem sort of like mine too.
The recognizant is not the object as interpretant. It’s more like the alternate picture that you offer, the recognition of the object-sign-interpretant triad. If the interpretant is a kind of ‘second’ sign, the recognizant is a kind of ‘second’ object, sort of, kind of, like the Kantian subject (I’ll probably regret saying that), at least as much of that subject (a ‘subjection’ if you will) as is involved in a given semiosis and determines/influences the semiosis going forward. Another analogy extends the famous object-sign-interpretant analogy with source-encoding-decoding. It’s been said that each interpretant is another sign just as each decoding is another encoding. So I say, the recognizant is like the destination in the (more complete) source-encoding-decoding-destination series. The destination (as I’ve gleaned the idea) is what does or would collaterally check or spot-check, directly or indirectly, the source and indeed the whole communication system in order to corroborate what the destination is being told and in order potentially to correct the system, even redesign it, if possible and needed.
I’ve been told that my fourth category involves splitting secondness in two, since I think of my fourth as structure, and structure as a more or less stable balance of forces or motions. But it’s worse than that since my first is more like Peirce’s second, and since my categories don’t generally involve various irreducible arities, even if I do tend to order them 1st, 2nd, 3rd, 4th. Relations of inverseness between 1st & 4th and between 2nd & 3rd result sometimes a 1-2-3-4 seeming to align one-to-one with a 4-3-2-1. (Why not either of the other two Klein-groupish permutations? Well, I looked for them but found only one seeming example of one of them.)
Well, it’s apples to oranges, but if I had to give a series that might be compared to Peirce’s three categories, I’d offer, roughly:
1. primary substance (“this man, this horse,” to quote Aristotle)
— causation/connection, reaction/resistance (CSP’s 2ndness).
2. quality (CSP’s 1stness), characteristic, property
— correlation, likeness.
3. ‘situation’, involvement of an alternative, optima/probabilities/information/givens (modes of attribution)
— meaning (CSP’s 3rdness).
4. mathematical relation
— legitimacy, counting-as, establishing (about), lessonfulness.
By tomorrow I should have read Goertzel some more.
Thanks again for continuing this so thoughtfully.
Peirce-l looks pretty lively! I don’t know if I’m ready to sign up or dig through it yet, though. Of course I could just start lurking. Interesting that Bergman recently joined.
Goertzel’s web site must be having some issues because I just accessed it recently, both for the book and for the “Fourfold Model” page. (Now I see that it’s back.) I had run into Goertzel before with my very short mention of Palmer’s fourfold of being:
https://equivalentexchange.wordpress.com/2013/03/12/kent-palmers-levels-of-being/
I’ve also not devoted sufficient time to Palmer’s large body of work for understanding. I’m generally in the “computationalist” camp, too, although I don’t agree with too much that other computationalists have offered.
The fourfold source-encoding-decoding-target was called the modeling relation by biologist Robert Rosen. I mention him briefly below (but nothing about fourfold above) and planned to return to him but got sidetracked.
https://equivalentexchange.wordpress.com/2012/09/21/antisynthesis/
Thanks for correcting my notion of the recognizant! Your last explanation makes more sense and I’m happier with it. And I’ll have to think some more about your Tetrastic-Peircean amalgam.
Which brings me to another point. Why do you think that those fascinated by fours can’t even agree on a basic conceptual core? When I started my blog, I thought I could discover or invent such a beast. Oh, the folly of youth!
I suspect that the reason that Goertzel’s site has some newly unavailable pages is that he’s closing access to them. On his books page, he mentions
– I interrupt myself to say that I just went to find the URL for his books page and found that his book _Hidden Patterns_ is available at his site again
Click to access HiddenPattern_march_4_06.pdf
I’ve read Chapter 6 “Four Levels of Mind” again but I still have little to say about it as yet, just a few notes about Peirce’s ideas.
1. Peirce in earlier years included cheerfulness, pain, etc., as feelings, but in later years he regarded pleasure and pain as volition or reaction, and as secondary feelings at most. He found no common feeling-element to all pain or to all pleasure. At least once he associated pleasure with generalization (and pain with volition/reaction). His typical example of feeling is a feeling of redness. He distinguishes feeling from sensation insofar as a sensation occurs at a given time and place, while a feeling can occur in imagination.
2. As regards mind and reality, Peirce called himself an “objective idealist.” (The Wikipedia article seems to get it wrong in saying that it involves the belief that there is only one perceiver). Peirce: “…matter is effete mind, inveterate habits becoming physical laws.” Peirce also held, as a principle of investigators’ self-regulation (prior to any specifically metaphysical considerations), that the real is only that which inevitably _would be_ found by _sufficient_ investigation and is independent of what any actual investigators think. So for him the real is independent of particular minds but dependent on mind, representational relation, etc., in general.
“Why do you think that those fascinated by fours can’t even agree on a basic conceptual core?”
Four is more than three, two, or one, so I guess there are more numerous conceivable ways to make it a principle of sets of ideas. Mine are all interrelated, or have affinities to one another, although I don’t always quite understand why the affinities appear (as when the light cone gets involved). Some people are more eclectic than others, for example Hyatt Carter (who is also interested in threefolds), see his “Meta-Fours”: http://www.hycadventures.com/page30.php
Hyatt is a punster, who has said:
“May the Fours be with you.”
“A mighty Fourtress is our Quad.”
“You can’t see the fourist for the threes” (regarding my involvement with Peirceans).
Your mention of Robert Rosen led me to reading some online things about him again. In the past I thought that his ideas about models resemble Peirce’s ideas about diagrams. I notice that pages and illustrations at the http://www.panmere.com/ site are disappearing and it’s best explored through http://www.archive.org/ .
I see that encoding and decoding are aspects of Rosen’s idea of the model, but I couldn’t find anything online about Rosen and _target_ or _destination_ (as in source-encoding-decoding-destination/target). Can you point me in a direction?
I believe I spoke too quickly and loosely. Rosen’s modeling relation usually fixes a “natural” system as the source and a “formal” system as the target. Look at images found by “modeling relation rosen”:
https://www.google.com/search?q=modeling+relation+rosen&noj=1&site=webhp&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwi5ofaQmv3LAhVH5iYKHT2XBMsQsAQINw&biw=1896&bih=888#imgrc=_
I don’t really have a favorite reference except I do remember this one from a while back (found by adding “life itself” to 3 terms above):
http://www.people.vcu.edu/~mikuleck/PPRISS3.html