Abstraction 101
Bruce Schuman
Over the years, I've been periodically saving the Wikipedia article on "Abstraction" -- considering it an excellent introduction to this central theme in cognitive science and philosophy.
https://en.wikipedia.org/wiki/Abstraction
Perhaps because the subject is complex or controversial, that page continues to be edited and changed, and I have saved 6 versions of the page since 2013. The recent Ontolog discussion on this theme has struck me as a bit scattered or fragmented, so this morning I looked at the article again, and was surprised to see that it had been edited today (July 26, 2017). I was more surprised to see an article I had written years ago cited at the bottom.
There are a lot of reasons for the chronic controversies or fragmentation of this subject. Philosophy and cognitive science do not have a large "orienting framework" of generally accepted definitions and concepts. We don't have a definition of "abstraction" we accept. We don't have a definition of "concept". Instead, there is a tendency for anyone weighing in to the subject to present their own point of view and system of definitions based on that perspective. The socialization of this discussion is essential to any significant general progress on this broad subject, so it seems that this collective enterprise is chronically stuck at the beginner's level.
For me, the Wikipedia article begins to be a landmark or paradigm or "orienting framework" for a large-scale and powerful discussion on this subject -- and for any significant integrating scientific or philosophical breakthrough that might be possible. The article expresses a refined and intuitive discussion of many important facets of this subject, that when seen as a whole -- and not viewed as fragments to be considered independently -- points towards a broad historical and scientific tendency that could emerge with a sound and clarified universal foundation for the collective enterprise.
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The first paragraph of the Wikipedia article is a powerful and succinct general definition:
Abstraction in its main sense is a conceptual process by which general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the product of this process—a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.
The second paragraph explains how it works:
Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only the aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball. In a type–token distinction, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').
The third paragraph confirms the definition:
"An abstraction" is the product of this process—a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.
When studied closely, there are hundreds of moving parts within this general framework, and to understand them, they must be considered as a whole. Though a helpful exercise along the way, mulling through the fragments independently (as we tend to do here in Ontolog and in most other philosophical contexts), as if these elements had some arguable stand-alone meaning, in the end is a lost cause and something of a “bottomless pit”.
This general Wikipedia definition can be confirmed in hundreds of ways, and appears as a recurring pattern in philosophy and science everywhere. World-class programmer and author Grady Booch presents something like these definitions in his book Object-Oriented Analysis and Design with Applications. https://goo.gl/DRxXmW
I was surprised when I read that book to see his reference to libertarian philosopher Ayn Rand’s Introduction to Objectivist Epistemology, but when I read her book, I saw she had a powerful point of view on abstraction in her concept of “measurement omission”. https://goo.gl/W5S85Q That’s a precise way of describing how abstractions are formed (“abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball”), and goes to an important principle clarified by John Sowa – that such choices are driven by purpose-oriented human selection in some specific context.
The process of abstraction occurs across levels of generality. Its general form is hierarchical. “More abstract concepts contain less abstract concepts”. This theme is discussed in various ways in the Wikipedia article, and is well illustrated by the example from Douglas Hofstadter:
Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):
(1) a publication
(2) a newspaper
(3) The San Francisco Chronicle
(4) the May 18 edition of The San Francisco Chronicle
(5) my copy of the May 18 edition of The San Francisco Chronicle
(6) my copy of the May 18 edition of The San Francisco Chronicle as it was when I first picked it up (as contrasted with my copy as it was a few days later: in my fireplace, burning)
An abstraction can thus encapsulate each of these levels of detail with no loss of generality.
This “progression from abstract to concrete” (and conversely, from concrete to abstract) is a universal principle inherent in all cognition and in all logic. This general framework provides clear definitions for many logical and epistemological processes.
Abstraction involves induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of specification, which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated with Francis Bacon's Novum Organum (1620), a book of modern scientific philosophy written in the late Elizabethan era of England to encourage modern thinkers to collect specific facts before making any generalizations.
Bacon used and promoted induction as an abstraction tool, and it countered the ancient deductive-thinking approach that had dominated the intellectual world since the times of Greek philosophers like Thales, Anaximander, and Aristotle. Thales (c. 624–546 BCE) believed that everything in the universe comes from one main substance, water. He deduced or specified from a general idea, "everything is water", to the specific forms of water such as ice, snow, fog, and rivers.
Modern scientists can also use the opposite approach of abstraction, or going from particular facts collected into one general idea, such as the motion of the planets (Newton (1642–1727)). When determining that the sun is the center of our solar system (Copernicus (1473–1543)), scientists had to utilize thousands of measurements to finally conclude that Mars moves in an elliptical orbit about the sun (Kepler (1571–1630)), or to assemble multiple specific facts into the law of falling bodies (Galileo (1564–1642)).
This image of trees – taken from an earlier Wikipedia article on abstraction and removed from recent ones – illustrates the process of generalization, abstraction and measurement omission. From diverse concrete particular examples, by selecting common features and “omitting some measurements”, an accurate abstract generalization can be defined.
Most or all of the fundamental macro-concepts of interest to semantic ontologists are particular examples of this general “many-to-one” principle, and include
1. taxonomy: https://en.wikipedia.org/wiki/Taxonomy_(general)
classification of specific concrete objects into increasingly abstract and generalized categories
2. mereology: https://en.wikipedia.org/wiki/Mereology
the study of parts and the wholes they form
3. ontology: https://en.wikipedia.org/wiki/Ontology_(information_science)
a formal naming and definition of the types, properties, and interrelationships of the entities within a domain
The Wikipedia article on mereology begins by saying “In philosophy and mathematical logic, mereology is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation between a set and its elements, mereology emphasizes the meronomic relation between entities, which—from a set-theoretic perspective—is closer to the concept of inclusion between sets.”
On this basis, we might also include set theory as a hierarchical expression of the relationship of a set and its members. https://en.wikipedia.org/wiki/Set_theory
And we might consider the notion of upper ontology in the same terms – a framework defined in levels of inclusion or generality with a “top level” that contains everything, in a form that is “ultimately abstract”.
Something like this cascade of definitions ought to be foundational to applied ontology – and could help steer the ontology community around the sharp rocks of many useless controversies. Why endlessly debate all these themes? Set up a clear simple classical universal paradigm and create definitions within its framework. This is a potent and intuitive way to avoid the endless problems arising from incommensurate “siloed” models and theories. The fragmented approach is endlessly myopic and endlessly controversial, and the pieces never fit together. All the major concepts of semantic ontology involve the same underlying principles, and basic texts, like Barry Smith’s Applied Ontology should be reviewed as foundational sources for must-include concepts and brought together into a common framework. https://goo.gl/meRoxT
What is “real”? The Smith book emphasizes this question, and it’s a subject that comes up all the time here on Ontolog. A shared cascade of common foundational definitions could help avoid useless or fragmenting approaches.
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John recently sent us a graphic on “Logos” as an ancient and classical expression of absolute ontological inclusion.
I chose the term 'abstract' because Alonzo Church, who made important contributions to logic and ontology, adopted it. For historical reasons, we could use the terms Logos and Physis by Heraclitus, who had a strong influence on ancient Greek and later philosophy. The attached file, logos.jpg, is the definition of Logos, as written by C. S. Peirce for the _Century Dictionary_.
By any name, the basic distinction is that all categories on the physical or physis branch are empirical (about observable things, processes, or stuff) and all categories on the abstract or logos branch are about forms or patterns that are logical, mathematical, linguistic, or semiotic.
All of semiotics, of which Pat gave a summary, is part of the Abstract or Logos category. And every theory, formal or informal, is also part of it.
So what is the connection between the physical and the abstract? The Wikipedia article generalizes this issue, and defines a universal abstract spectrum that takes a hierarchical multi-level form, with the physical (or empirical or concrete or “real”) as the absolute bottom limit of the abstraction cascade. All abstractions (logical, mathematical, linguistic, semiotic) are built from symbols as maps of this territory. Science is the correlation of these maps with their territory.
In classical intuitive terms, Logos is an expression of “The One” – in all its multiplicity of meanings. It is the ultimate container, the “top” of the universal conceptual ontology, the organizing framework and implicit law of all logic and reasoning, the ultimate “set of all sets.” Because Logos is the law of ontology, the law of being, all reality conforms to its logic and obeys its law. All cognition occurs within its framework and boundaries, and its principles constrain the difference between correct and incorrect logic – and between good and bad science, safety and danger, wisdom and foolishness. All across society today, we struggle with the issues of Babel (of fragmented Logos), looking for a safe guiding map for society, some principle of guidance that can rescue the world from myopia and fragmentation and indulgence.
Bruce Schuman
Santa Barbara California 93101
-----Original Message-----
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John F Sowa
Sent: Tuesday, July 25, 2017 7:10 PM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is applied ontology? (was The 4 fundamental... and deception-collaboration)
James,
I wouldn't call it a minor question.
> A minor question: Do you see different levels of abstraction?
That is like asking the question whether there are different levels of physicality:
Is a hydrogen atom more or less physical than an oxygen atom?
A water molecule? A photon of blue light? A bacterium?
An elephant? The sun? A black hole? The Andromeda galaxy?
They're all physical. Just different kinds.
Everything abstract is a type of sign.
> Might the concept of the desk where you work be less abstract than the
> concept of humanity?
They're just as abstract as the concept of God or the concept of 0.
All sign types are abstract. All sign marks are physical.
Every sign token is a mark that has been classified by a type.
The text of _War and Peace_ is a sign type. Every printed book of that type is a token.
John
Bruce Schuman
> A minor question: Do you see different levels of abstraction?
Biological taxonomy is a posterchild for "levels of abstraction" -- taking a general form that is repeated in many other ontological constructions. Computer operating systems are organized in terms of "levels of abstraction" (think of the nesting of folders – “higher levels contain lower levels”). In programming, this is often called “drill-down”.
When I was a child, I regularly played “twenty questions” with my sister, starting off with the famous question “Is it plant, animal or mineral?” and descending in levels of abstraction until the specific item was identified by its particular dimensions (attributes).
This taxonomic form from biology is defined in terms of “descending levels”, where the top level (“the upper ontology”) contains everything within it, in decreasing levels of abstraction and generality and increasing levels of specificity and detail. The notion of “measurement omission” applies precisely, as specific details are factored out as levels of generality increase.
https://en.wikipedia.org/wiki/Taxonomy_(biology)
Bruce Schuman
Santa Barbara California 93101
-----Original Message-----
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John F Sowa
Sent: Tuesday, July 25, 2017 7:10 PM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is applied ontology? (was The 4 fundamental... and deception-collaboration)
James,
I wouldn't call it a minor question.
> A minor question: Do you see different levels of abstraction?
That is like asking the question whether there are different levels of physicality:
Is a hydrogen atom more or less physical than an oxygen atom?
A water molecule? A photon of blue light? A bacterium?
An elephant? The sun? A black hole? The Andromeda galaxy?
They're all physical. Just different kinds.
Everything abstract is a type of sign.
> Might the concept of the desk where you work be less abstract than the
> concept of humanity?
They're just as abstract as the concept of God or the concept of 0.
All sign types are abstract. All sign marks are physical.
Every sign token is a mark that has been classified by a type.
The text of _War and Peace_ is a sign type. Every printed book of that type is a token.
John
--
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