Mike, list
A few further comments on your chapter - which I liked very much -
and your table.
I was about to comment on 'my' terms for time [present, perfect,
progressive] vs your terms [present, past, future] but see that
you've already done that in your notes. My terms come rom the
exceptional analysis of time by Koichiro Matsuno. The point is, that
3ns is not simply functioning in 'the future' but, as laden with
habits, is also bringing with it information from the past. But, as
its information is always general, then, the distinction between past
and future is irrelevant, and time becomes adaptive or progressive.
My quibble about the spatial definition of 3ns as a 'triangle' is
that I reject the whole image - such a very common image - of the
Peircean triad [O-R-I] as a triangle. Such a form nullifies the
actual nature of the triad as one where the Interpretant is not a
mimetic copy of the Object but is an action of growth of information.
I also have a problem with defining 1st as a 'form'. Since it has no
existentiality 'in itself', then I don't see how it can have a form,
which to me, at least, involves a 'cell wall' so to speak, a specific
image. And of course, I reject the notion that 1ns involves ideas
since an idea involves Mind. I prefer to consider Ideas as an
abductive property and define abduction as functioning within the
categorical mode of 3-2... Thirdness operating within physical
connections; that is, Mind connectinn to multiple local informational
data - and - coming up thereby, with a hypothesis to explain/organize
this data.
All in all - a great chapter. Thanks for letting us read it.
Edwina
On Mon 08/03/21 4:35 PM , Edwina Taborsky [email protected] sent:
Mike, list
Yes - I'm a strong supporter of the open dynamism of Peirce - cf
also Philip Rose's 'emergent evolution' and the notion of the growth
of information within the triadic process, where the interpretant is
in an asymmetrical relationship to the object. This process can
account for the growth of complexity and diversity within the
universe - a growth which is never random but adaptive and thus, a
process of Mind.
Edwina
On Mon 08/03/21 3:39 PM , Mike Bergman [email protected] sent:
Hi Bruce, Mauro,
As promised, I have split some of the earlier hierarchy paper
commentary with this one focusing on your ideas to date.
First, Mauro, Bruce was the author of the comment that prompted
your response, so thanks, Bruce, for responding. And, Bruce,
thanks for spending considerable time putting forth your ideas
around a mandela-strip twisted into a closed loop. I am interested
in learning more and I will try to keep some of these concepts in
mind. I see the regularity and continuity in your thinking.
However, I think there are some Peircean viewpoints (and my own!)
where, if I understand your ideas correctly, I may see or
interpret things a bit differently.
First, I very much like the dynamism of Peirce's semeiosis.
Basically, he postulates a continuous process of sign-making and
-representing: signs building upon signs and leading to more signs
and more representation. In this dynamic process, subsequent
iterations approach a bit more closely the 'truth' of the dynamic
object of the sign, with the modes and acceptances of the evolving
representations ultimately a social process of sign and
terminology consensus. In this manner, then, rather than seeing
the integral, closed mandela circle, I see something as evolving
dynamically over time. I also believe knowledge needs to be
treated in an open-world manner [1]. In line with Peirce's
strong beliefs in phenomenology, I would envision something
more akin to this representation of an electromagnetic wave:
It kind of approaches the look of the mandela if one looks down
the trajectory (propagation) of the wave, like looking down the
barrel of a gun. 😉 This is probably way off from what you where
thinking, but does capture my sense for the need of dynamism.
Second, Peirce's acceptance and then advocacy for 'absolute
chance' prevents absolute regularity or complete reductionism.
Variablity is the bogey in this scenario, and is the driver for
evolution, one source of the dynamism noted above. At the
miniscule scale, we encounter quanta, but not apparently at larger
scales of space or time. It is not clear to me how chance fits in
to your 'strip' concept.
Third, from a visualization standpoint, I have seen these figures
of spinning triangles around a centroid (the classic three-body
problem), as the triangle sides are varied in length. It is
mesmerizing, and there are patterns (such as reflected in fractals
or cellular automata) where one can see self-organization emerge
or perhaps new structures that represent new hierarchical levels.
I know it is pretty abstract, but this figure is something I refer
to on occasion when I want a more dynamic feel of how a Peircean
basis to 'seeing' the world may work out:
As I suggest in the hierarchy paper [2], new levels in natural
hierarchies may arise because new organizations of growing
numbers of current structures may better dissipate available
free energy than continuing to do "more of the same". Chance in
1ns is what supplies this variation.
Mauro's thoughts on 'line and continuum' I think might also be
productively related to Peirce's writing on infinitesimals. Peirce
thought deeply about Zeno and the basis for lines and continuity.
I've dabbled a bit, but am by no means a mathematician. An OK
starting place is Google Scholar:
https://scholar.google.com/scholar?q=peirce+infinitesimals
and then look for the listings with PDFs that you may read.
Hope this is helpful, Bruce. I'm glad you have found some
stimulation to share your work.
Best, Mike
On 3/7/2021 8:02 PM, [email protected] wrote:
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Mauro – I like this model you suggest, and the links you
point to.
I want to find a single closed algebraic form from which I
can derive all semantic structure – and my guess is, that
process will probably look like the kind of graph you drew.
Or include those kinds of elements.
I want to derive all the basic kinds of mathematical and
semantic analysis from a common “code base” – a
common underlying/fundamental partition from which/though
which all coded distinctions and compositional structures can
be derived, or from which they can be constructed – and on the
basis of which, all mathematical computation can flow.
Speaking of lexicographical order, an important theme is
that it is about ”total order” – not “partial
order”.
So – an instinctive guiding principles is
Create a generalized extremely simple master form that is
in “absolute order” – everything “100% linear in
every dimension” – and show how this form contains
everything in general terms – and then show how it also
contains along the way all conceivable “partially ordered”
structures.
I’m not sure if something like this is what Mike is
talking about when he says
Hierarchies in knowledge systems express subsumption
relations that have many flexible variants, which we can
represent algorithmically, and thus computationally.
“Subsumption relations with many flexible variants”
So this seems exciting: nest all partial orders within
absolute order.
We need to understand “the whole” in a 100% ordered
way – an example of “the whole” perhaps being
something like “the human body” (Leonardo’s “Vitruvian
Man”) or maybe the global ecology/economy.
Define “absolute order” over something that complex,
maybe around the concept of “homeostasis” – the
governing principle that keeps the interdependent moving parts
in balance.
So, in this case “absolute order” does not mean
“top-down fascist authoritarianism” or ramrod
do-it-my-way dictatorship. It means “Governance OF the Whole
BY the Whole.” Idealized global democracy in balance,
replicated at all levels of scale.
Mauro, I need to give your interesting idea more thought.
- Bruce
Hierarchical Cantor set in absolute linear order
Bruce Schuman
Santa Barbara CA USA
[email protected] [3] / 805-705-9174
www.origin.org [4] / www.integralontology.net [5]
From: [email protected] On
Behalf Of Mauro Bertani
Sent: Sunday, March 7, 2021 6:38 AM
To: [email protected]
Cc: [email protected]
Subject: Re: [ontolog-forum] Hierarchy, a la Peirce -
reply to Mike
Hi Mike,
about what you wrote
On Sat, 6 Mar 2021 at 00:30, 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
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 [7] aand
https://en.m.wikipedia.org/wiki/Reeb_graph [8] .
I hope this can help you.
Mauro
From: [email protected] [9]
On Behalf Of Mike Bergman
Sent: Thursday, March 4, 2021 8:23 PM
To: [email protected] [11];
[email protected] [12];
[email protected] [13]
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] [14]
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
[15]
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 [16]
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 [17] knowledge structure, and its
top-level KBpedia Knowledge Ontology [18] (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] [19] / 805-705-9174
www.origin.org [20] / www.integralontology.net [21]
-----Original Message-----
From: [email protected] [22]
[23] On Behalf Of Mike Bergman
Sent: Wednesday, March 3, 2021 7:57 PM
To: [email protected] [24];
[email protected] [25]
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 [26]. I
hope you enjoy!
Thanks, Mike
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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
[33]
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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
__________________________________________
Links:
------
[1]
https://www.mkbergman.com/wp-content/themes/ai3v2/files/2009Posts/the-open-world-assumption-elephant-in-the-room.pdf
[2] https://www.isko.org/cyclo/hierarchy
[3] http://webmail.primus.ca/javascript:top.opencompose(
[4] http://www.origin.org/
[5] http://www.integralontology.net
[6]
http://webmail.primus.ca/javascript:top.opencompose(\'[email protected]\',\'\',\'\',\'\')
[7] https://en.m.wikipedia.org/wiki/Level_set
[8] https://en.m.wikipedia.org/wiki/Reeb_graph
[9]
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[10]
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[11]
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[12]
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[13]
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[14]
http://webmail.primus.ca/javascript:top.opencompose(\'[email protected]\',\'\',\'\',\'\')
[15] http://originresearch.com
[16] http://originresearch.com/sd/sd4.cfm
[17] https://kbpedia.org/
[18] https://kbpedia.org/docs/kko-upper-structure/
[19]
http://webmail.primus.ca/javascript:top.opencompose(\'[email protected]\',\'\',\'\',\'\')
[20] http://www.origin.org
[21] http://www.integralontology.net
[22]
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[23]
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[24]
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[25]
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[26] https://www.isko.org/cyclo/hierarchy
[27] http://ontologforum.org/info/
[28]
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[30] http://ontologforum.org/info/
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[32]
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[33]
http://www.theparisreview.org/interviews/4331/the-art-of-fiction-no-39-jorge-luis-borges
[34] http://ontologforum.org/info/
[35] http://webmail.primus.ca/javascript:top.opencompose(
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