Alex,
As I said, we are in total agreement. Every dictionary definition, everything you cited in your previous note, and your most recent comment:
Alex> Diagrams are geometrical structures (special kind of pictures, figures, usually labeled) chosen by humans to help with representations, explanations and reasoning.
That is what Peirce said, I said, all the dictionaries said, and all the references you cited said. The only differences are in the amount of surrounding detail. And none of that detail denies the conclusion.
In summary. structures are or can be described by mathematical formulas that are independent of any plans, purposes, or uses that any human might intend. But diagrams are structures that people have selected or drawn for the purpose of representing, explaining, or reasoning about something.
That's my summary of the basic points in all the references any of us copied or cited. That includes everything you, I, or anybody else said in this thread. What else is there to say?
John
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
John,
Let's write down my dissenting opinion:
Diagrams are geometrical structures (special kind of pictures, figures, usually labeled) chosen by humans to help with representations, explanations and reasoning.
Let's just note this difference.
Alex
чт, 14 сент. 2023 г. в 23:13, John F Sowa <sowa(a)bestweb.net>:
Alex,
Both dictionaries I quoted (and others I did not bother to quote) make a very clear distinction between structures (as patterns that exist independently of what anybody may think or say about them) and diagrams (as patterns that people or animals or computers choose to represent for explaining or reasoning about structures).
And thank you for the definition from Wikipedia, which makes exactly the same distinction and emphasizes that it goes back to prehistoric times (over 10 thousand years ago). Euclid and other geometers (more than 2,000 years ago) adopted diagrams for the foundation of mathematics, especially geometry -- and those diagrams are also used for reasoning and for applications in science, engineering, and architecture.
And thank you for the three citations to the Stanford articles. The one on diagrams discusses the writings by C. S. Peirce, and it also cites two things by me: (1) My book on Knowledge Representation, published in 2000, and (2) an article I wrote in 2011, which was published in the journal Semiotica: https://jfsowa.com/pubs/egtut.pdf
The article about the structure of scientific theories admits that humans may have discovered and stated the theories. But it focuses on the patterns in the theory that are independent of the scientists who discovered or stated them. Their primary example is Newtonian mechanics, but it ignores anything that Newton himself thought or did. I discusses only the mathematical patterns.
Today, we know that the mathematical pattern of Newtonian mechanics is only approximately true about the universe. But the patterns implied by that theory exist (in a mathematical sense) independently of what we think about them. When considered as a mathematical formula and the collection of patterns implied by that formula, it is independent of what anyone may think about those patterns..
The article about structural realism admits that some people might consider structures as things that people built or imagined. But it also makes a case that the structures that are really real -- they exist independently of what anybody may think about them.
In summary, the American heritage definition of diagram is as good as any and better than most:
- A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole.
- A graphic representation of an algebraic or geometric relationship.
- A chart or graph.
This implies that diagrams are chosen by humans for explanations and reasoning. Structures are patterns considered as existing by themselves. The processes that create the structures (human or non-human) are not relevant to their existence as structures. Unless anybody can find any better terminology for any application of ontology, I believe that this distinction is the best we have.
John
----------------------------------------
From: "alex.shkotin" <alex.shkotin(a)gmail.com>
IN ADDITION
"A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment.[1] Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram."
https://en.wikipedia.org/wiki/Diagram
Alex,
Both dictionaries I quoted (and others I did not bother to quote) make a very clear distinction between structures (as patterns that exist independently of what anybody may think or say about them) and diagrams (as patterns that people or animals or computers choose to represent for explaining or reasoning about structures).
And thank you for the definition from Wikipedia, which makes exactly the same distinction and emphasizes that it goes back to prehistoric times (over 10 thousand years ago). Euclid and other geometers (more than 2,000 years ago) adopted diagrams for the foundation of mathematics, especially geometry -- and those diagrams are also used for reasoning and for applications in science, engineering, and architecture.
And thank you for the three citations to the Stanford articles. The one on diagrams discusses the writings by C. S. Peirce, and it also cites two things by me: (1) My book on Knowledge Representation, published in 2000, and (2) an article I wrote in 2011, which was published in the journal Semiotica: https://jfsowa.com/pubs/egtut.pdf
The article about the structure of scientific theories admits that humans may have discovered and stated the theories. But it focuses on the patterns in the theory that are independent of the scientists who discovered or stated them. Their primary example is Newtonian mechanics, but it ignores anything that Newton himself thought or did. I discusses only the mathematical patterns.
Today, we know that the mathematical pattern of Newtonian mechanics is only approximately true about the universe. But the patterns implied by that theory exist (in a mathematical sense) independently of what we think about them. When considered as a mathematical formula and the collection of patterns implied by that formula, it is independent of what anyone may think about those patterns..
The article about structural realism admits that some people might consider structures as things that people built or imagined. But it also makes a case that the structures that are really real -- they exist independently of what anybody may think about them.
In summary, the American heritage definition of diagram is as good as any and better than most:
- A plan, sketch, drawing, or outline designed to demonstrate or explain how something works or to clarify the relationship between the parts of a whole.
- A graphic representation of an algebraic or geometric relationship.
- A chart or graph.
This implies that diagrams are chosen by humans for explanations and reasoning. Structures are patterns considered as existing by themselves. The processes that create the structures (human or non-human) are not relevant to their existence as structures. Unless anybody can find any better terminology for any application of ontology, I believe that this distinction is the best we have.
John
----------------------------------------
From: "alex.shkotin" <alex.shkotin(a)gmail.com>
IN ADDITION
"A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment.[1] Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram."
https://en.wikipedia.org/wiki/Diagram
четверг, 14 сентября 2023 г. в 12:26:31 UTC+3, alex.shkotin:
John,
We can dive into a fascinating exploration of how the terms diagram and structure are used in everyday life.
Meanwhile I decided to look into the Stanford Encyclopedia of Philosophy. And I was glad to find an article [1] that explained your approach to me.
Unfortunately, the term structures does not have a separate article. But there is an article “The Structure of Scientific Theories” [2]. This is what I do to the best of my ability with an emphasis on formalization. After all, before formalizing a theory, it must be structured. However, there is an interesting article “Structural Realism” [3].
Alex
[1] https://plato.stanford.edu/entries/diagrams/
[2] https://plato.stanford.edu/entries/structure-scientific-theories/
[3] https://plato.stanford.edu/entries/structural-realism/
чт, 14 сент. 2023 г. в 01:27, John F Sowa <so...(a)bestweb.net>:
Since I suggested that anybody who is trying to define anything should check the definitions in a good dictionary, I decided to take my own advice. See the attached defs.htm for definitions of the words 'diagram' and 'structure' in the American Heritage Dictionary and the Merriam Webster Dictionary. In general, I have found the American Heritage definitions and etymologies very good. They are usually clearer and more precise than the definitions in other dictionaries. But it's always useful to get a second or third opinion.
An important distinction: A structure is a pattern in an entity of some kind. A diagram is a pattern that somebody draws or imagines as a representation or explanation of a pattern that somebody observed of found in some structure.
Therefore, a diagram would be more likely to be the kind of pattern that some human or animal or computer would be likely to use to support reasoning or computation about a pattern of any kind.
John
Signspiel • 1
• https://inquiryintoinquiry.com/2019/04/17/signspiel-1/
All sorts of players have given us all sorts of spiel about speech acts
over the years but Peirce stands out from the chorus in giving us models
of semiotic processes whose generation by triadic sign relations allows
them to maintain a constant relation among signs, their active interpretants
in conduct, and their ultimate pragmata, the objects and objectives of the
whole action. Shy of that, the speilerei of Austin and Wittgenstein simply
never gets off the ground.
Regards,
Jon
cc: https://www.academia.edu/community/Vvr3EV
cc: https://mathstodon.xyz/@Inquiry/11106389953288650
Since I suggested that anybody who is trying to define anything should check the definitions in a good dictionary, I decided to take my own advice. See the attached defs.htm for definitions of the words 'diagram' and 'structure' in the American Heritage Dictionary and the Merriam Webster Dictionary. In general, I have found the American Heritage definitions and etymologies very good. They are usually clearer and more precise than the definitions in other dictionaries. But it's always useful to get a second or third opinion.
An important distinction: A structure is a pattern in an entity of some kind. A diagram is a pattern that somebody draws or imagines as a representation or explanation of a pattern that somebody observed of found in some structure.
Therefore, a diagram would be more likely to be the kind of pattern that some human or animal or computer would be likely to use to support reasoning or computation about a pattern of any kind.
John
Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 6
http://inquiryintoinquiry.com/2022/03/01/sign-relations-triadic-relations-r…
Re: FB | Charles S. Peirce Society
https://www.facebook.com/groups/peircesociety/posts/2551077815028195/
::: Alain Létourneau
https://www.facebook.com/groups/peircesociety/posts/2551077815028195?commen…
All,
Alain Létourneau asks if I have any thoughts
on Peirce's Rhetoric. I venture the following.
Classically speaking, rhetoric (as distinguished from dialectic)
treats forms of argument which “consider the audience” — which
take the condition of the addressee into account. But that is
just what Peirce's semiotic does in extending our theories of
signs from dyadic to triadic sign relations.
We often begin our approach to Peirce's semiotics by saying he puts the
interpreter back into the relation of signs to their objects. But even
Aristotle had already done that much. Peirce's innovation was to apply
the pragmatic maxim, clarifying the characters of interpreters in terms
of their effects — their interpretants — in the flow of semiosis.
Some reading —
Awbrey, J.L., and Awbrey, S.M. (1995),
“Interpretation as Action • The Risk of Inquiry”,
Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inqu…
Regards,
Jon
Logical Graphs • First Impressions 1
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Introduction • Moving Pictures of Thought —
A “logical graph” is a graph-theoretic structure in one
of the systems of graphical syntax Charles Sanders Peirce
developed for logic.
In numerous papers on “qualitative logic”, “entitative graphs”,
and “existential graphs”, Peirce developed several versions of
a graphical formalism, or a graph-theoretic formal language,
designed to be interpreted for logic.
In the century since Peirce initiated this line of development,
a variety of formal systems have branched out from what is abstractly
the same formal base of graph-theoretic structures. This article
examines the common basis of these formal systems from a bird's eye
view, focusing on the aspects of form shared by the entire family of
algebras, calculi, or languages, however they happen to be viewed in
a given application.
Regards,
Jon
cc: https://independent.academia.edu/JonAwbrey
cc: https://mathstodon.xyz/@Inquiry/110945139629369891
Alex,
I very strongly agree with your comment below: The diagrams are fundamental, and the words are secondary. Whenever there is any dispute -- start with the diagrams. Formalisms, such as mathematical notations, always have a more direct mapping to diagrams than to words. Euclidean geometry is the best example. But any book that uses algebraic notations can always map the algebra more clearly and precisely to a diagram than to any words in any natural language.
Re engineering diagrams: Anybody who can't read the engineering diagram, can't understand a precise explanation written in their native language. Any simple explanation that they can understand is guaranteed to be an oversimplification. But if the engineering diagram is carefully explained to them then they can and do understand the subject.
I know that point very well -- because I've done it. I also know that people who claim they understand a simple explanation, but cannot understand the diagram don't know what they're talking about. If you ask them some simple questions about how the thing works, their answers are hopelessly confused. I know that because I've met such people.
If you doubt that point, try that exercise with people who claim that they understand the simple explanation.
The mapping to diagrams is especially important for robots. Every action by a robot has a direct mapping to and from some kind of diagram. But the explanation in a natural language is more complex, more unreadable, and more prone to misreading and misunderstandings.
John
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
John,
Very briefly about formal definitions. The formal definition should be compared with an engineering drawing.
Everyone uses various devices, but few people can and should be able to read engineering drawings.
The construction of formal definitions is important, for example, because they can be transferred to robots.
Alex
The subject line comes from an article in the New York Times (excerpts below). Data from the James Webb telescope is raising serious difficulties with long-held assumptions about the evolution of the universe and the things in it.
This raises yet another objection to the idea of a universal formal ontology of everything. But it adds further support for the idea of an open-ended collection of specialized ontologies for any particular topic or system that anybody may be working on or with.
The overall framework of everything may be more like a dictionary or encyclopedia written by humans for humans (and also computers). Wikipedia is a good example. The editors of Wikipedia post warning notes about articles that need more or better references. But the best articles are far more reliable than anything that can be derived from LLMs -- and they have reliable citations, not the phony citations that the LLMs generate (or hallucinate).
This is one more reason for abandoning the project of creating a universal ontology of everything. Science and engineering have made excellent progress without them. The task of determining what should replace them is a very important issue for Ontolog Forum.
John
_________________________
The Story of Our Universe May Be Starting to Unravel
Sept. 2, 2023
By Adam Frank and Marcelo Gleiser
www.nytimes.com/2023/09/02/opinion/cosmology-crisis-webb-telescope.html
Not long after the James Webb Space Telescope began beaming back from outer space its stunning images of planets and nebulae last year, astronomers, though dazzled, had to admit that something was amiss. Eight months later, based in part on what the telescope has revealed, it’s beginning to look as if we may need to rethink key features of the origin and development of the universe.
According to the standard model, which is the basis for essentially all research in the field, there is a fixed and precise sequence of events that followed the Big Bang: First, the force of gravity pulled together denser regions in the cooling cosmic gas, which grew to become stars and black holes; then, the force of gravity pulled together the stars into galaxies.
The Webb data, though, revealed that some very large galaxies formed really fast, in too short a time, at least according to the standard model. This was no minor discrepancy.
It was not, unfortunately, an isolated incident. There have been other recent occasions in which the evidence behind science’s basic understanding of the universe has been found to be alarmingly inconsistent.
Take the matter of how fast the universe is expanding. This is a foundational fact in cosmological science — the so-called Hubble constant — yet scientists have not been able to settle on a number. There are two main ways to calculate it: One involves measurements of the early universe (such as the sort that the Webb is providing); the other involves measurements of nearby stars in the modern universe. Despite decades of effort, these two methods continue to yield different answers.. . .
Physicists and astronomers are starting to get the sense that something may be really wrong. It’s not just that some of us believe we might have to rethink the standard model of cosmology; we might also have to change the way we think about some of the most basic features of our universe — a conceptual revolution.. . .
The standard model today holds that “normal” matter — the stuff that makes up people and planets and everything else we can see — constitutes only about 4 per.cent of the universe. The rest is invisible stuff called dark matter and dark energy (roughly 27 percent and 68 percent).
Cosmic inflation is an example of yet another exotic adjustment made to the standard model. Devised in 1981 to resolve paradoxes arising from an older version of the Big Bang, the theory holds that the early universe expanded exponentially fast for a fraction of a second after the Big Bang. This theory solves certain problems but creates others. Notably, according to most versions of the theory, rather than there being one universe, ours is just one universe in a multiverse — an infinite number of universes, the others of which may be forever unobservable to us not just in practice but also in principle.
Cosmology is not like other sciences. The universe is everything there is; there’s only one and we can’t look at it from the outside. You can’t put it in a box on a table and run controlled experiments on it. Because it is all-encompassing, cosmology forces scientists to tackle questions about the very environment in which science operates: the nature of time, the nature of space, the nature of lawlike regularity, the role of the observers doing the observations.
Alex, Gary, Dan B.
Before writing any detailed comments, I want to emphasize three points: (1) Major software systems survive in one form or another for 40 years or more. Few, if any precise definitions from the early days remain unchanged for more than a tiny fraction of that time. As an example, IBM developed the first Airline reservation system for American Airlines in the 1960s to run on the IBM 7094. An updated version of that became IBM's airline reservation system running on System/360. The ontology and terminology of that system became the industry-wide basis for all reservations for hotels, cars, and any kind of services that travelers might need. The ontology and choice of word definitions that IBM adopted in collaboration with American Airlines has become the universal world-wide standard. The formal definitions change with every update, but the choice of words and their translations from English to other languages do not change.
(2) The researchers and programmers working on the details of any system may understand the formal details, but the top-level managers, the great majority of the users, and the investors who have money will never see or understand the details of those definitions. They will interpret the terminology according to the way those words are used in everyday life. If the formal definitions diverge too far from common usage, the result will be confusion and repeated errors.
(3) Any attempt to edict an official, precise definition for all terms will guarantee that whatever system uses those terms exactly as defined will become obsolete within a few years. Please note that the manuals for every product -- from a refrigerator to a programming language -- will have a new manual with new definitions of key terms for every update.
IBM used the term 'functionally stabilized' for any hardware or software system whose terminology would never change. That term was a synonym for "obsolete". IBM would continue to sell those obsolete systems to customers who could not afford to update their systems to accommodate the new products. Microsoft, for example, just recently stopped producing and delivering updates for System/95 (wjocj was introduced in 1995)..
Alex> Is there a chance to have one world wide dictionary for every science and technology?
You can define it, if you like, but it is guaranteed to become obsolete with the first new discovery in science or new development in engineering. And even if you define it, 99.999% of the people in the world would never use more than a tiny percentage of the words as defined.
Alex> AI is first of all summa technologiae, each with its own glossary.
There is no universal glossary of AI. New terms are constantly being defined by people who never read or understood similar terms that had been defined and published before. AI terminology changes very rapidly because many AI people never read anything that is more than five years old.
Alex> Why is the theory of directed graphs with composition of arrows called category theory?
For historical reasons. Mathematicians, unlike Ai people, cite publications of any date and make updates compatible with the original definitions.
Alex> Why did the DBMS guys call their company Oracle?
Because it answered questions, like an oracle. There are many horror stories about compatibility in DB systems, but they developed in different ways than AI for different reasons -- mostly bad: preserving incompatibility. Preserving incompatibility was also one of the worst reasons for Windows 95. But that is another story.
Dan> In general, ML-AI terminology is a mess. Eg Labelled/unlabelled data, unsupervised/supervised learning, giving way (thankfully) to the otherwise wordy “self-supervised”. And the word “inference” is used in ways that might make some ontolog-forum readers splutter their coffee.
That's a good answer to Alex's questions.
Gary> One may leverage results from prior efforts with best practices but often we don't have the vision or time or temperament to do this.
That's a good explanation for the points by Alex and Dan.
In summary, most people who need to know something about Ai technology (users and funding agencies, for example) will not know or remember the detail of a formal definition, Even if they read the definition, it will be easier to understand and remember if the words are used in ways that are consistent with common usage -- as codified in common dictionaries.
An example of a bad choice is the term 'fundamental model'. Both words are commonly used, but that combination does not give any hint of what the term means. But the terms 'functional pattern' and 'structural pattern' use common words that give an approximate idea of the meaning. That makes them easier to learn, easier to remember and easier to use by everybody -- programmers, managers, funding agencies, and intelligent outsiders who want to know what is happening.
John
Alex.
I read that web page you cited. What Google calls "foundation models" I would call "mappings based on specialized ontologies". They include three kindds: (1) text to image, (2) text to code, and (3) speech to text.
I believe they are making a serious mistake by using English text in their foundation. The article I'm writing, which puts Peirce's diagrammatic reasoning at the center, is more general, flexible, and powerful. It also avoids a huge number of complex issues that differ from one natural language to another -- even worse, the words differ from one kind of application to another, even in the same language.
Thanks for citing that article. I am now finishing the final Section 7 of my article, and this method by Google gives me a clear target to shoot at. I'm actually glad to see that Google is making that mistake -- because it makes it easier to compete with them.
That diagram by Gartner puts foundation models at the top of the hype cycle. That means they are about to plunge into the trough of disillusionment. I would enjoy giving them a little push.
John
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
John,
I am talking about this part of Gartner's picture you gave in attachment.
[image.png]
It was unknown to me that guys from AI technology have their own ideas for the term "foundation models" [1] (just an example).
Alex
[1] https://ai.google/discover/foundation-models/
