Hierarchy, a la Peirce
Mike Bergman
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. I hope you enjoy!
Thanks, Mike
bruces...@cox.net
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
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”?
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
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Mike Bergman
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:
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
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 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
knowledge structure, and its top-level KBpedia
Knowledge Ontology (KKO).
Best, Mike
bruces...@cox.net
Good morning from Santa Barbara. Thanks Mike and Daniel and Edwina. It’s exciting to see these comments. Thanks for taking a look at this previous work on hierarchy and concepts and dimensionality. I want to comment on your project and design, Mike, from the point of view that emerges for me. In your article, you sketch out a project design that feels very significant, and I want to comment on why I see it that way.
Yes, for me this work goes back a lot of years, and today is flirting around the edges of a very ambitious general theory intended to support a very broad kind of integration. For me, it actually began in the late 1960’s when I moved from the Haight-Ashbury in San Francisco to Santa Cruz, where I enrolled in the brand-new and awesome University of California (UCSC) as a junior psychology and philosophy major. In the very first semester in the fall of 1966 I took a course in pre-Socratic philosophy, and under the influence of “mandala” imagery – which was in those days appearing everywhere, and on hundreds of book covers – in my term paper, I proposed a visionary thesis on “the opposites” which more or less discussed the many properties of a diagrammatic/topological form that looked about like this:
Graphic resolution makes this image a little blurry, so I attach larger version of this image that better-preserves detail.
The important point here is that this image is a “hierarchy” drawn in a circle. It’s interesting that for many years I had to draw this image by hand, and it wasn’t until the last year or so that I found this form in an internet image search, apparently created by some computer algorithm preserving the precision I could never create by hand.
I became fascinated by this general form, defining its “levels” and facets in epistemological terms. I was inspired by Husserl’s call that “philosophy must be made scientific”, and this diagram seemed to me to be an opening into this important and transformative agenda.
***
Mike, I want to follow the agenda you outline in the abstract to your article, and see if I can introduce the “closed loop” concept in terms that make sense to you.
Hierarchies — real or artificial — abound to help us organize our world.
Yes, so true. I would say that hierarchy might be the most powerful and “natural” way that human beings organize their understanding of reality. And in your very first sentence, you introduce the challenging question of whether “hierarchies exist” in some form other than human cognition. For me, Herbert Simon’s 1969 book on “The Sciences of the Artificial” was a revelation on this subject. A few years later (1984), John Sowa’s Conceptual Structures book made additional important distinctions on this point that I personally see as foundational.
A hierarchy places items into a general order, where more "general" is also more "abstract".
This sentence might be why I instantly got so excited about your article, Mike. You are defining what I see as a (the) critical axis of human cognition. Generality is abstraction. I see this as a core and universal principle of cognitive structure. From my point of view, this might be the most important idea in cognitive theory. Everything can be defined relative to this primary axis or dimension – “levels of generality, levels of abstraction”. This is the essential spectrum that we are talking about when we use the term “upper ontology” and how an upper ontology contains and relates to its elements and nested categories/distinctions.
In 1991, I wrote an ambitious article on this subject, entitled “The Universal Hierarchy of Abstraction”, starting out by quoting Richard Feynman, and getting into details about the “levels of hierarchy” that structure human cognition across a spectrum. I describe how this spectrum has become fragmented, tending to separate human understanding into the broad general areas we think of as “quantitative” and “qualitative”, or “scientific” and “humanistic”. http://originresearch.com/sd/sd1.cfm This was/is the core idea in my “Bridge Across Consciousness” thesis, intended to bridge these levels across a common hierarchical model, with quantitative disciplines at one end of the spectrum and qualitative disciplines at the other.
On my circular diagram above, the center of the diagram is “the top” – the highest level of generality, the highest level of abstraction – and the cascading levels that radiate from that center descend like a taxonomy to the “instances” or “actual concrete real objects” that we are categorizing at the outer level or circumference (or “bottom”) of the diagram. For me, this distinction and spectrum of levels clearly indicates the relation between abstraction and empiricism.
The etymology of the word hierarchy is grounded in notions of religious and social rank.
Yes. The Wikipedia article on hierarchy begins by saying this, and it’s an important theme in the historical discussion of the idea. The “Great Chain of Being” idea is hierarchical.
https://en.wikipedia.org/wiki/Hierarchy
In my original 1966 article on this theme, I was influenced by diagrams and imagery from Theosophy (somebody had donated a large collection of metaphysical books to the UCSC library, which apparently the librarians did not find suitable, so they were for sale in the courtyard cheap), and thus began my romance with Uroboros, the snake swallowing its tail, which I tend to see as a metaphor for a closed/bounded universe or cosmology). https://www.theosociety.org/pasadena/gdpmanu/hierarch/herarc-2.htm. This idea helped shape the “closed loop” concept that I now find so intriguing and potent.
This article, after a broad historical review, focuses on knowledge systems, an interloper of the term hierarchy since at least the 1800s.
This “broad historical review” seems important to me. There is a very rich and broad array of influences that have come together to shape the idea we describe as “hierarchy”, in all its multitude of forms. There is actually a vast flood of imagery available on the internet that points towards the evolution of the hierarchy concept, as it emerged from mysticism and theology and began taking the form of engineering mathematics. This evolution is important, because it shows the original derivation of hierarchical ideas from “deep intuition”, sometimes taking a form that is commonly rejected by science or engineering, yet seems to reflect something deep and universal in human cognition – even if intuitive, fallible and metaphorical.
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.
This is an important list. These elements you cite, Mike, and probably many more, should be carefully itemized and examined for their exact hierarchical characteristics – and how they might confirm to some broad generalities that we might be able to say “are true of all hierarchical structures” – and perhaps of all conceptual structures that involve levels of abstraction. Is hierarchy the “master spectrum of human cognition”? I am inclined to say yes – and suppose that this can be illustrated in floods of detail. But this is a big project. I am inclined to suppose this review will eventually happen, as the centrality and generality of hierarchical structure becomes more widely recognized in not only in science and engineering, but across the full spectrum of human experience.
Hierarchies are the logical underpinning of inference and reasoning in these systems, as well as the scaffolding for classification and inheritance.
Yes. This statement must be looked at in detail. This is an important observation. Hierarchy is the logical underpinning – or underlying general form – of inference and reasoning and the structure of classification and inheritance. This is a very broad, powerful and integrating observation, that should be studied and illustrated with precision. This is a fundamental general principle, that governs hundreds of specific implications.
In my original 1966 article I began to define terms such as “top-down” and “bottom-up” or “general” and “specific” – and from there, terms in logic such as “induction” (reasoning from particular/specific/concrete to universal/general/abstract) and “deduction” as the opposite, (reasoning from general principles to specifics). I am still exploring this idea, more or less in these same terms.
Now, Mike, you make another important point, that I would argue suggests a major revolution in our collective understanding.
Hierarchies in knowledge systems express subsumption relations that have many flexible variants, which we can represent algorithmically, and thus computationally.
Yes. This is key. Maybe this statement helps explain why the evolution of philosophy and science tends to be stuck, unable to come to common agreement on the ubiquitous underlying presence of hierarchical form. There are indeed an endless number of “flexible variants” – and when viewed from a “local” or “empirical” or “immediately practical” point of view, the underlying common broad general hierarchical structure is not visible. The argument for hierarchy as a general form has to be very clear, and not become shattered or discredited because there are indeed endless flexible variants and “special cases”. So, I am grateful that you have made this point, which I think can help illustrate the generality of the “closed loop” thesis, which I hope to clarify in this comment.
This article dissects the dimensions of that variability, leading to a proposed typology of hierarchies useful to knowledge systems.
Yes. Great. We need a clear strong statement of these dimensions – showing, I think, how “the general form” appears in slightly different ways in hundreds of specific instances. And we need this typology. It could be a tremendous integrating and healing force across the spectrum not only of science and engineering, but of human knowledge in general, particularly when knowledge is seen as teeming and unmanageable diversity in our global environment.
This general form, as it becomes clear, can lead to a sweeping integration of “millions of instances” which today are seen as independent fragments with no common model or interpretation. This fragmentation partially accounts for the wide-spread understanding that “academics and scientists do not agree” on these definitions – that there are an endless number of alternatives ways that these logical elements can be defined, and no feasible common framework.
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.
This argument that “natural hierarchies are real” has a long history. I have recently been studying articles by Barry Smith, looking to broaden my understanding of abstraction and hierarchy in real-world practical applications. So, I am emerging from a point of view that was somewhat rigidly dogmatic about the character of abstract symbols, towards a “spectrum based” approach intended to reconcile these historically contrary perspectives within a common framework that recognizes multiple levels of legitimacy, rather than insisting that one point of view is correct and all other others wrong or misleading. Accommodating real-world practical applications is essential. I think a general theory of hierarchical spectrum can support and enable this approach.
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.
I need to learn more about this, as indeed I need to learn more about Peirce.
Here’s a review of Hierarchy Theory, as put together by Timothy Allen. In my early studies, I was familiar with most of these books and doctrines, and did my best to systematically incorporate these perspectives. I think they are highly applicable today. We need to know and include everything cited here. http://isss.org/hierarchy.htm
To conclude, I want to briefly mention the “strip” model of hierarchy, which I want to argue contains most or all of the points and agenda raised in your article abstract, Mike. I want to argue that this framework is a general form of hierarchy with a vast array of integrating implications. This object is hierarchical in the vertical dimension, and maps perfectly to the circle model cited above. I’ll go over this theme in a following posting. This simple form is obviously hierarchical in the vertical dimension. I want to explore multiple implications, particularly considering Mike’s thesis that
Hierarchies in knowledge systems express subsumption relations that have many flexible variants, which we can represent algorithmically, and thus computationally.
I want to argue that by recognizing simple linear hierarchy in this above form, we can integrate endless numbers of special case instances that do not conform to this simple linearity. Also note that this linear form is topologically isomorphic to the circular form. This above “strip” when twisted so as to connect point A to point D forms the “closed loop” that I see as a natural transcendent approach to integrating the full spectrum of ontology and semantics into one general form.
Bruce Schuman
Santa Barbara CA USA
bruces...@cox.net / 805-705-9174
www.origin.org / www.integralontology.net
Mike Bergman <mi...@mkbergman.com>; ontolo...@googlegroups.com; peir...@list.iupui.edu
João Oliveira Lima
I learned a lot, especially in the presentation of the historical facts about the evolution of the concept of hierarchical relationships.
In your "Typology of Hierarchical Types" (Table 1), the "part-of" relation is presented as a specific case of "Intensional Subsumption".
According to the Wikipedia entry "Hierarchy", in the Containment Hierarchy section:
Why does the "part-of" relation appear as a specialization of the subsumption relation in your hierarchy of hierarchical types?
Mike Bergman
Hi João Lima,
Thanks for reading the article and your comments. Yes, I
specifically addressed the Wikipedia entry on 'Hierarchy' in
Section 5 of my paper. There is no overall citation or author for
the Wikipedia schema and, as far as I know, it is not used by
anyone. The terms used of 'nested' and 'containment' are synonyms
or near-synonyms as best as I can tell for the word 'subsumption'.
In the Oxford English Dictionary, definitions of 'subsume' refer
to 'include', 'under', 'take up' and 'absorb', among others. The
typology I proposed asserts the primacy of the subsumption concept
and places mereological relationships as a sub-type under
intensional subsumptions. My reason for placing the 'part-of'
relationship where I did is that the relationship is firstly
subsumptive, but also intensional in that it is internal or
intrinsic to the item at hand. My view was that the typology
proposed does not invoke slightly different nuances of the
'subsumption' concept under multiple names (as does the Wikipedia
or other schema), but provides meaningful sub-type splits.
The paper also mentions Salthe's 'compositional' and
'subsumption' ('specification') designations, which are useful
IMO, but not adequate to cover the full scope of subsumption
relations and provide a false distinction and equivalence of
composition with subsumption. If you have not already done so, I
encourage you to find and review the specific definitional
citations provided in Section 5 (especially in the Table 1 notes)
to see the diversity of opinions expressed on how to classify
hierarchical relations.
Given the lack of consensus on definitions or typology, my hope was to provide a rational basis for deriving a 'hierarchy' of hierarchical types. Whether what I provided is helpful or not will be determined by its use and uptake by others. As of today, I remain comfortable with the typology I proposed. But, if one wanted to retain the idea of 'composition', I would organize it according to my proposed typology as follows:
SubsumptionIntensional subsumption
Compositional (in which case it becomes a synonym for 'part-of')
I hope that was helpful (even if you do not agree 😉 ).
Best, Mike
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-- __________________________________________ Michael K. Bergman Cognonto Corporation 319.621.5225 skype:michaelkbergman http://cognonto.com http://mkbergman.com http://www.linkedin.com/in/mkbergman __________________________________________
te...@earthlink.net
Mike, your response below is great, and in my mind inclusive of hierarchies, thank you!
It seems to me that this is partially also true of modeling holons/holonic systems, but it seems inconclusive to me. Is there an additional step one needs to model holonically, and also to reflect the different contextual ‘decompositions’ for holons? And how does one holonically model ontologies?
[Please excuse the inept expression of this, but I hope you get what I’m pointing at…].
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Mike Bergman
Hi Bobbin,
Thanks for the kudos. Always good to hear from you.
I have to say, however, that I don't buy and have never bought
the holon conjecture, which is one reason it is not mentioned in
my hierarchy paper. To me it is an artifice of how to describe
discretely transitions between organizational states. I don't
think it is necessary to employ it to describe Simon's
watchmakers. It is simply a new organizational level that emerges
by chance to maximize dissipation for a given (new) configuration.
I think our language and thinking is replete with these false
cartesian dichotomies that arise because we limit our
conceptualizations to a binary world. There is no wave-particle
duality. Both are integral aspects of photons. At that level, we
are getting close to the root of the root, so it should not be
surprising that we find physical evidence for both phenomena.
There is only conflict in the duality if your world is binary. It
is sort of the same way I feel about excluded middle aside from
its use in strict logic.
We do not need a 'holon', then, as a bridge between two
dichotomous structures. Further, these part-whole distinctions
that were the genesis of 'holons' are current as of a given
snapshot in time. As we see (and have evidence) for endosymbionts,
what begins as a mostly separate and mutualistic relationship
evolves to losses of function and greater incorporation and
symbiosis over time.
The power of evolution occurs at scales of time and degrees of
freedom that are greater than astronomical. There are alot of
throws of the dice that go into evolving an eye, for example, but
convergent evolution gives us dozens of examples. In my view,
holons are superfluous in a world of evolution and Peircean
triadic universal categories. I believe one can be holistic
without buying into holons.
If I'm missing something in what it is to be or like a holon, let
me know. One of the things I get from Peirce is a crankiness about
accepting physical realities for which there is absolutely no
phenomenological evidence. But we'll leave the discussion of dark
matter or memes
until another day. I've been clogging up the airwaves too much
lately anyway.
Best, Mike
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