On the role of triadic categories in Peirce’s philosophy and hierarchy, you might (if you haven’t already) want to check out some of the commentaries on Aristotle by the Conimbricenses, the Portuguese Jesuits of the 16th century (followed decades later by the important work of another Portuguese, Joao Poinsot). So far as I know it was here in their work (which Peirce knew well) that the first triadic basis of semiotics is explicitly mentioned (there is an excellent translation of some of this work by John Doyle, which I am sure most of this list will be familar with).
In the 20th century, Kenneth Pike (https://en.wikipedia.org/wiki/Kenneth_Lee_Pike) developed a pre-Chomskyan theory of linguistics, Tagmemics (https://www.degruyter.com/document/doi/10.1515/9783111657158/html <https://www.degruyter.com/document/doi/10.1515/9783111657158/html>), that also had a foundational triadic structure. In PIke’s work hierarchy was also crucial and he developed theories of various linguistic hierarchies (the basic three were referential, phonological, grammatical). Pike’s work predates Simon’s considerably. In his own work, mathematician-theologian Vern Poythress (https://en.wikipedia.org/wiki/Vern_Poythress <https://en.wikipedia.org/wiki/Vern_Poythress>) argued that the basis of the triadic organization of Tagmemics and elsewhere was the trinity (https://www.amazon.com/Knowing-Trinity-Perspectives-Knowledge-Imitate/dp/1629953199/ref=sr_1_3?dchild=1&keywords=trinity+by+vern+poythress&qid=1615232590&sr=8-3 <https://www.amazon.com/Knowing-Trinity-Perspectives-Knowledge-Imitate/dp/1629953199/ref=sr_1_3?dchild=1&keywords=trinity+by+vern+poythress&qid=1615232590&sr=8-3>) Poythress is a serious mathematician as well as a theologian and a solid linguist. I am inclined to believe that the doctrine of trinity was important in the thinking of the Portuguese Jesuits and also for Peirce (though I currently have no textual support to make a serious claim wrt the latter suggestion). Simon did win the Nobel Prize in Economics, but when I knew him at CMU (in conjunction with my role on the computational linguistics faculty of the Pitt-CMU program going at that time), he defined his long-term research program as human problem-solving, leading to computer science, psychology, and other fields, beyond economics. His work on the hierarchy can also be related to (though it is rarely, if ever, credited) the conception of all linguistics structure as endocentric and recursive that Chomsky has urged (and which I have long argued against). In any case, I highly recommend the Jesuit Aristotelian commentaries and the work of Poinsot (Deely has recently published a beautiful version of his Tractatus). Dan > On Mar 8, 2021, at 1:39 PM, Mike Bergman <[email protected]> wrote: > > Hi All, > > Given the number of questions regarding Peirce's universal categories in > relation to my hierarchy paper, I have split out my response to them > separately and have renamed the thread. I will follow up this thread with a > separate thread on Bruce's 'twisted, closed loop' idea. > > It is clear that Peirce's research and method of inquiry were based on what > he proudly classed as an 'architectonic' [1]. For me, it is one of the most > appealing aspects of Peirce since it reflects his commitment to applying > consistent logic and methods in all intellectual endeavors. Pragmatism has > perhaps survived as the most often-cited basis of Peirce's architectonic. I > agree with this in the context of praxis, but I have suspected for many years > that the root fount of Peirce's approach is in his triadism, what he himself > jocularly called his 'triadomany' [2]. > > His universal categories are the root of the root. When last published [3], I > had assembled up more than sixty instances where Peirce applied triadic > splits; I have perhaps two dozen more needing a published update. All > representations across these examples have a context to derive their meaning. > Yet, still, there is a character across the categories of Firstness (1ns), > Secondness (2ns) and Thirdness (3ns) that bring a unique feel and sense for > each, generalizations emerging from the vague. > > An author's release of my book chapter on Peirce's universal categories is > available for free from my Web site [3]. Table 6-2 and its table notes, in > particular, provide a flavor for how Perice's triadic categories were > expressed by him in scores of examples. For example, in the case of > 'reality', I would surmise Peirce to describe it as 'chance' (1ns), actuality > (2ns), and 'continuity' (3ns). More than 60 other examples and variants are > provided in the table. > > In the case for the KBpedia Knowledge Ontology > <https://kbpedia.org/knowledge-graph/> (KKO), the context is 'knowledge > representation'. That scope is close to being the same as 'everything there > is', but the expression and organization need to be geared to logical > constructs that are consistently used so as to be able to be reasoned over. > > In the KKO context, the triadic structure is 'monads' (1ns), 'particulars' > (2ns) and 'generals' (3ns). 'Monads' are the possible ideas or attributes > about things, but they are unexpressed. I have also called monads 'unrealized > building blocks'. They are pregnant with potential, but as monads are the > pure qualities, not yet embodied. Of course, once you try to represent or > capture the idea of something like 'redness', you have given it expression so > that it is no longer 1ns. Monads in the KKO context are best scoped as the > unconnected relations between things and the unembodied attributes of things. > > 'Particulars' (2ns) are the events and entities relevant to the scope of the > current domain. Every particular is individuated. How to categorize > 'attributes' into 'particulars', 'particulars' into 'generals', and > 'generals' into more abstract 'generals' is the motivator for my paper on > hierarchy. > > 'Generals' (3ns) are the types, classes, generalizations, abstractions, > rules, laws and processes relating to the nature of reality and interactions. > Thinking and continuity are 'generals'. Particulars are a predominant focus > of generalizations. Because KBpedia is an interacting amalgam of typologies, > aside from the 200 or so concepts in KKO, 58,000 of the remaining concepts > are all organized under the KKO 'generals' branch. However, specific > individuals in the knowledge graph may reference the KKO concepts under the > 'particulars' branch, and reasoning may occur across attributes and > predicates using the 'monads' branch. These latter two options are > nascent in KBpedia, but have not yet been tested and demonstrated. Now that > our first task to create a Peircean knowledge representation with KBpedia is > usable, I hope (and welcome others!) to begin applying such tests. > > I do not associate 1ns with 'matter, life and ideas' as Ravi may be implying. > Rather, the associates I see are matter (2ns), life (2ns) and ideas (3ns). > Monads do not have a position or representation in space. They are > unexpressed, unembodied attributes or relations. Absolute chance and > possibilities are 'monads'. > > While perhaps it has been useful for me to be the primary editor of KBpedia > and interpreter of Peirce in relation to knowledge representation, I think > more Peirce and knowledge representation afficiandos need to contribute. It > would be fantastic to see knowledge graphs suitable for testing and refining > computer programs in Peircean triadic logic and abductive logic, as examples. > > At any rate, I hope this note or the paper reference [3] may help you > understand my take on Peirce's universal categories. > > Best, Mike > > [1] http://www.commens.org/dictionary/term/triadomany > <http://www.commens.org/dictionary/term/triadomany> > [2] Peirce, Charles Sanders. 1891. “The Architecture of Theories”. The Monist > 1, no. 2: 161–76. See https://www.jstor.org/stable/pdf/27896847.pdf > <https://www.jstor.org/stable/pdf/27896847.pdf> > [3] https://www.mkbergman.com/publications/akrp/chapter-6.pdf > <https://www.mkbergman.com/publications/akrp/chapter-6.pdf> > > On 3/7/2021 1:34 PM, Ravi Sharma wrote: >> Mike and Bruce >> >> While coming from eastern (indian) philosophy and metaphysics based >> preliminary background, I would like to understand one of the three items >> above: >> (I have to fully read Mike's ISKO paper which is modern, and also understand >> in this context Aristotle, Pierce and Sowa, category theory!) >> Monads >> Particulars >> Generals >> and for example >> I. Firstness [1ns] — these are possibilities or potentials, the basic forces >> or qualities that combine together or interact in various ways to enable the >> real things we perceive in the world, such as matter, life and ideas. These >> are the unrealized building blocks, or elements, the essences or attributes >> or possible juxtapositions. They are not divisible, what Peirce called >> indecomposables, since they are integral qualities or ideas in themselves >> >> Regarding - 1ns - matter, life and ideas. >> These appear to me to be complex multi level hierarchies. While matter >> without life can not have ideas, life and ideas are somewhat acceptable as >> cognitive life (most of it is at the life's level to carry-on life's >> cycle.), but there are precursors to matter and life, namely some seed of >> becoming (desire) or consciousness before matter and life originate! >> >> II. Also what is the role of Monad, is it like origin in a multidimensional >> space, is it affine, Euclidean, Hilbert space, or a space later defined in >> terms of sets and groups? >> >> >> Thanks. >> Ravi >> (Dr. Ravi Sharma) >> MagicJack US 3133935264 >> India mobile 011 91 96366 58888 >> >> >> >> >> >> On Sun, Mar 7, 2021 at 6:38 AM Mauro Bertani <[email protected] >> <mailto:[email protected]>> wrote: >> Hi Mike, >> about what you wrote >> >> On Sat, 6 Mar 2021 at 00:30, <[email protected] >> <mailto:[email protected]>> wrote: >> Then this strip – now defined as containing in general form everything we >> know about epistemology and semantics and hierarchy and abstraction and >> taxonomy and conceptual structure – goes through this mysterious “twist” >> which “closes the space” and forms this amazing “closed loop” which seems to >> contain all of cognitive science within its single boundary. All elements >> within that boundary are defined as “intervals” – bounded ranges with lowest >> and highest values in some dimension. By virtue of “the twist”, the entire >> loop becomes a single boundary – a single “edge” -- which contains nested it >> (bounded within it) within all possible taxonomic distinctions in their >> general form. As a single boundary, the entire structure takes the same >> form as “the real number line” – it IS “the continuum” in a closed loop >> form. When seen in the flat plane, the “upper ontology” is the unbounded >> infinite and the ultimate meaning of “unit”, and the lowest level >> approaching infinitesimal differentiation, and the taxonomic categories we >> want to position at the bottom of our taxonomic hierarchy. When we close >> the loop, the infinite and the infinitesimal are mapped straight into each >> other as one continuous edge – where their differences are only apparent >> when viewed in the flat two dimensional perspective. Rotated through the >> twist, all the differences disappear and all that remains is unity. I think >> this is analogous to the Buddhist cosmology of “the beginningless universe” >> – maybe it’s the same idea. There are books out there on the subject “A >> universe from nothing”. I think these are all related. >> >> I made a theory that partly reflects your vision. Very briefly it is >> represented by this diagram >> >> <structure.png> >> >> there is the concept of line and continuum. Let's assume we have a >> hierarchical tree with simple concepts and a hierarchical tree with >> propositions. We combine these two trees according to the phrases Subject - >> Predicate - Object. We get a number. This number can be related in new >> subject-predicted-object phrases.. We thus obtain increasingly complex >> concepts, represented by increasingly large numbers, which are arranged on >> the line according to their complexity. similar a >> https://en.m.wikipedia.org/wiki/Level_set >> <https://en.m.wikipedia.org/wiki/Level_set> aand >> https://en.m.wikipedia.org/wiki/Reeb_graph >> <https://en.m.wikipedia.org/wiki/Reeb_graph> . >> I hope this can help you. >> Mauro >> >> >> >> >> From: [email protected] <mailto:[email protected]> >> <[email protected] <mailto:[email protected]>> On >> Behalf Of Mike Bergman >> Sent: Thursday, March 4, 2021 8:23 PM >> To: [email protected] <mailto:[email protected]>; >> [email protected] <mailto:[email protected]>; [email protected] >> <mailto:[email protected]> >> Subject: Re: [ontolog-forum] Hierarchy, a la Peirce >> >> >> Hi Bruce, >> >> I am glad this is a line of discourse you want to pursue (and have pursued >> since at least 1994 as your link indicates). I'm happy to engage on any >> questions or topics; there are many other Peirce afficiandos on these lists >> that also have helpful insights. For now, I only comment on one of your >> points below: >> >> On 3/4/2021 9:31 AM, [email protected] <mailto:[email protected]> >> wrote: >> >> Wow. I love this. I've been writing on this subject forever -- saying more >> or less the same things and citing the same authors -- e.g., Herbert Simon. >> I'm going to print your article, Mike, and take a close look at it. Back >> in the early days, I bought every book there was on Hierarchy. You make >> basic points in your opening that I’d say pave the way towards a very >> powerful general theory of epistemology. >> >> >> The basic themes you outline in this article are at the essence of my notion >> of “Closed Loop Interval Ontology” – which is hierarchical exactly as you >> describe, with the addition that the framework is defined as a closed loop >> interconnecting these “levels” into a single closed mathematical structure. >> >> >> My early stuff on this subject is here: http://originresearch.com >> <http://originresearch.com/> >> >> The trick here seems to be – that this thesis is so powerful, it becomes >> combinatorically explosive – heading towards the fabled “theory of >> everything” – maybe in explicit epistemological detail. >> >> >> Interesting that you say that “natural hierarchies are real” – which opens >> the way to some additional complexity or levels of inclusion. Maybe there >> is a “hierarchical relationship” across levels of reality, such that the >> kind of practical-real-world “reality” defined by Barry Smith can be mapped >> directly into an absolutely abstract model which I would say is a “science >> of the artificial”, as Herbert Simon might have described it. “Does >> absolute abstraction exist in nature”? >> >> My own view is that Peirce's universal categories of Firstness, Secondness, >> and Thirdness provide this level of "absolute abstraction [that] exists in >> nature". I don't know if you realize that some of your earlier references to >> Ogden and Richards <http://originresearch.com/sd/sd4.cfm> were actually a >> paraphrase of Peirce's insights. My own research focus has been on trying to >> understand the 'mindset' of Peirce's universal categories, expressed in >> perhaps a 100 different ways in his writings, that sets a frame of reference >> for tackling knowledge representation (epistemological) questions at >> virtually any level. Ogden and Richards picked up on one with respect to >> meaning, but there are other examples galore across Peirce's writings. >> >> What Peirce really offers, IMO, is a way to break away from either-or >> Cartesian mindsets that always pit issues as win-lose propositions, and >> ignore the "fact" that one can both be a realist and an idealist. By >> accepting the reality of absolute chance we are also removing false >> dichotomies between determinism and evolution. As with wave-particle duality >> or quantum v classic physics, Cartesian thinking is a cultural and >> intellectual posture that leaves us stymied and frustrated. I much prefer >> the trichotomous view of actuality bracketed by chance and continuity, the >> essence of Peirce's universal categories. >> >> BTW, there is no reason why this viewpoint can not inform the structure and >> basis of a top-level (upper) ontology. (One that I humbly feels offers an >> integrative framework for ANY knowledge graph or ontology.) That is exactly >> the approach we have taken with our KBpedia <https://kbpedia.org/> knowledge >> structure, and its top-level KBpedia Knowledge Ontology >> <https://kbpedia.org/docs/kko-upper-structure/> (KKO). >> >> Best, Mike >> >> >> Fascinating article and project, Mike. A lot to talk about. >> >> >> Thanks! >> >> >> - Bruce >> >> >> >> >> >> >> Hierarchies — real or artificial — abound to help us organize our world. A >> hierarchy places items into a general order, where more ‘general’ is also >> more ‘abstract’. The etymology of the word hierarchy is grounded in notions >> of religious and social rank. This article, after a broad historical review, >> focuses on knowledge systems, an interloper of the term hierarchy since at >> least the 1800s. Hierarchies in knowledge systems include taxonomies, >> classification systems, or thesauri in library and information science, and >> systems for representing information and knowledge to computers, notably >> ontologies, knowledge graphs, and knowledge representation languages. >> Hierarchies are the logical underpinning of inference and reasoning in these >> systems, as well as the scaffolding for classification and inheritance. >> Hierarchies in knowledge systems express subsumption relations that have >> many flexible variants, which we can represent algorithmically, and thus >> computationally. This article dissects the dimensions of that variability, >> leading to a proposed typology of hierarchies useful to knowledge systems. >> The article argues through a perspective informed by Charles Sanders Peirce >> that natural hierarchies are real, can be logically determined, and are the >> appropriate basis for knowledge systems. Description logics and semantic >> language standards such as RDF or OWL reflect this perspective, importantly >> through their open-world logic and vocabularies for generalized subsumption >> hierarchies. Recent research suggests possible mechanisms for the emergence >> of natural hierarchies involving the nexus of chance, evolution, entropy, >> free energy, and information theory. >> >> >> >> >> >> Bruce Schuman >> >> Santa Barbara CA USA >> >> [email protected] <mailto:[email protected]> / 805-705-9174 >> >> www.origin.org <http://www.origin.org/> / www.integralontology.net >> <http://www.integralontology.net/> >> >> >> >> -----Original Message----- >> From: [email protected] <mailto:[email protected]> >> <[email protected]> <mailto:[email protected]> On >> Behalf Of Mike Bergman >> Sent: Wednesday, March 3, 2021 7:57 PM >> To: [email protected] <mailto:[email protected]>; >> [email protected] <mailto:[email protected]> >> Subject: [ontolog-forum] Hierarchy, a la Peirce >> >> >> Hi All, >> >> >> I am pleased my open-access paper on hierarchy in knowledge systems, as >> informed by my understanding of CS Peirce, has been published by IEKO: >> >> https://www.isko.org/cyclo/hierarchy <https://www.isko.org/cyclo/hierarchy>. >> I hope you enjoy! >> >> >> Thanks, Mike >> >> >> >> -- >> All contributions to this forum are covered by an open-source license. >> For information about the wiki, the license, and how to subscribe or >> unsubscribe to the forum, see http://ontologforum.org/info/ >> <http://ontologforum.org/info/> >> --- >> You received this message because you are subscribed to the Google Groups >> "ontolog-forum" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/ontolog-forum/71e3a755-a102-6c0b-50a8-6fbcc6de2821%40mkbergman.com >> >> <https://groups.google.com/d/msgid/ontolog-forum/71e3a755-a102-6c0b-50a8-6fbcc6de2821%40mkbergman.com?utm_medium=email&utm_source=footer>. >> >> -- >> All contributions to this forum are covered by an open-source license. >> For information about the wiki, the license, and how to subscribe or >> unsubscribe to the forum, see http://ontologforum.org/info/ >> <http://ontologforum.org/info/> >> --- >> You received this message because you are subscribed to the Google Groups >> "ontolog-forum" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/ontolog-forum/007701d71217%2472829ff0%245787dfd0%24%40cox.net >> >> <https://groups.google.com/d/msgid/ontolog-forum/007701d71217%2472829ff0%245787dfd0%24%40cox.net?utm_medium=email&utm_source=footer>. >> >> >> -- >> "[..] events are primarily linguistic or cognitive in nature. That is, the >> world does not really contain events. Rather, events are the way by which >> agents classify certain useful and relevant patterns of change." >> Allen and Fergusson >> >> "No, no. History of Eternity. At first I wanted to find every single one of >> the buyers to apologize because of the book and also to thank them for what >> they had done. There is an explanation for that. If you think of >> thirty-seven people—those people are real, I mean every one of them has a >> face of his own, a family, he lives on his own particular street. Why, if >> you sell, say two thousand copies, it is the same thing as if you had sold >> nothing at all because two thousand is too vast—I mean, for the imagination >> to grasp. While thirty-seven people—perhaps thirty-seven are too many, >> perhaps seventeen would have been better or even seven—but still >> thirty-seven are still within the scope of one's imagination." >> http://www.theparisreview.org/interviews/4331/the-art-of-fiction-no-39-jorge-luis-borges >> >> <http://www.theparisreview.org/interviews/4331/the-art-of-fiction-no-39-jorge-luis-borges>-- >> >> All contributions to this forum are covered by an open-source license. >> For information about the wiki, the license, and how to subscribe or >> unsubscribe to the forum, see http://ontologforum.org/info/ >> <http://ontologforum.org/info/> >> --- >> You received this message because you are subscribed to the Google Groups >> "ontolog-forum" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/ontolog-forum/CAAhN2n4ri4HDOeXz1s782B851_vj34ybbxsC8tpC5iqdmb97iA%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/ontolog-forum/CAAhN2n4ri4HDOeXz1s782B851_vj34ybbxsC8tpC5iqdmb97iA%40mail.gmail.com?utm_medium=email&utm_source=footer>. >> -- >> All contributions to this forum are covered by an open-source license. >> For information about the wiki, the license, and how to subscribe or >> unsubscribe to the forum, see http://ontologforum.org/info/ >> <http://ontologforum.org/info/> >> --- >> You received this message because you are subscribed to the Google Groups >> "ontolog-forum" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/ontolog-forum/CAAN3-5em2xpNwW_Q45_nS2AwSoUMLGBdsa%2BN0gi07J7n1uk5kA%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/ontolog-forum/CAAN3-5em2xpNwW_Q45_nS2AwSoUMLGBdsa%2BN0gi07J7n1uk5kA%40mail.gmail.com?utm_medium=email&utm_source=footer>. > -- > __________________________________________ > > Michael K. Bergman > Cognonto Corporation > 319.621.5225 > skype:michaelkbergman <skype:michaelkbergman> > http://cognonto.com <http://cognonto.com/> > http://mkbergman.com <http://mkbergman.com/> > http://www.linkedin.com/in/mkbergman <http://www.linkedin.com/in/mkbergman> > __________________________________________ > _ _ _ _ _ _ _ _ _ _ > ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of > the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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