Just a couple of references:

https://www.amazon.com/Conimbricenses-Questions-Mediaeval-Philosophical-Translation/dp/0874622417
 
<https://www.amazon.com/Conimbricenses-Questions-Mediaeval-Philosophical-Translation/dp/0874622417>

https://www.amazon.com/Tractatus-Signis-Semiotic-John-Poinsot/dp/1587318776/ref=sr_1_1?dchild=1&keywords=poinsot+tractatus&qid=1615234027&s=books&sr=1-1
 
<https://www.amazon.com/Tractatus-Signis-Semiotic-John-Poinsot/dp/1587318776/ref=sr_1_1?dchild=1&keywords=poinsot+tractatus&qid=1615234027&s=books&sr=1-1>

https://www.amazon.com/Inference-Signs-Ancient-Debates-Evidence/dp/0198250940/ref=sr_1_3?dchild=1&keywords=james+allen+inference+from+signs&qid=1615234053&s=books&sr=1-3
 
<https://www.amazon.com/Inference-Signs-Ancient-Debates-Evidence/dp/0198250940/ref=sr_1_3?dchild=1&keywords=james+allen+inference+from+signs&qid=1615234053&s=books&sr=1-3>

https://plato.stanford.edu/entries/semiotics-medieval/ 
<https://plato.stanford.edu/entries/semiotics-medieval/>

I realize most on this list will be aware of these works, including others 
such: Πυῤῥώνειοι ὑποτυπώσεις by S Empiricus

Etc. 



> On Mar 8, 2021, at 2:51 PM, Daniel L. Everett <[email protected]> 
> wrote:
> 
> 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 
> <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] 
>> <mailto:[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.
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>>>  
>>> <https://groups.google.com/d/msgid/ontolog-forum/71e3a755-a102-6c0b-50a8-6fbcc6de2821%40mkbergman.com?utm_medium=email&utm_source=footer>.
>>> 
>>> -- 
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>>> 
>>> 
>>> -- 
>>> "[..] 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.
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>> -- 
>> __________________________________________
>> 
>> 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>
>> __________________________________________ 
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