What is a primitive?
Bruce Schuman
Hi. Thanks for the discussion. I am continuing to explore approaches to sharper or more explicit definition in a "fully grounded" sort of context, and have worked through several articles on Wikipedia that deal with the concept of "primitive".
This concept seems to have a variety of meanings, depending on particular context, and for me, these articles have helped clarify these differences.
WHAT IS A PRIMITIVE?
Wikipedia offers a review page, that explores the meaning of “primitive” in several professional areas.
https://en.wikipedia.org/wiki/Primitive
It seems to me that the definition that comes closest to the meaning generally suggested here on Ontolog is “Primitive notion” – as per axiomatic systems, or particular domains, as listed in the Wikipedia section on primitives in mathematics. The concept of “primitive notion” makes sense in a particular professional or semantic or social domain.
My own instinct tends to the group of meanings associated with the Wikipedia section on primitives in computer science, including “Language primitive” (the smallest unit of comprehensible code in a computer program):
In computing, language primitives are the simplest elements available in a programming language. A primitive is the smallest 'unit of processing' available to a programmer of a given machine, or can be an atomic element of an expression in a language.
Primitives are units with a meaning, i.e., a semantic value in the language. Thus they are different from tokens in a parser, which are the minimal elements of syntax.
It looks to me like the concept of “primitive notion” as is apparently widely common in mathematics could quickly become problematic. The concept of “primitive notion” seems akin to the psychological concept of “gestalt” – a complex structure that is perceived as a whole – though a deeper and more precise analysis might clarify the detailed facts of its actual construction in terms of “parts”.
https://en.wikipedia.org/wiki/Primitive_notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or other formal system, the role of a primitive notion is analogous to that of axiom. In axiomatic theories, the primitive notions are sometimes said to be "defined" by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress.
Alfred Tarski explained the role of primitive notions as follows:[1]
When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expressions of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION...
The necessity for primitive notions is illustrated in several axiomatic foundations in mathematics:
· Set theory, the concept of the set is an example of a primitive notion. As Mary Tiles writes:[3] [The] 'definition' of 'set' is less a definition than an attempt at explication of something which is being given the status of a primitive, undefined, term. As evidence, she quotes Felix Hausdorff: "A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit."
· Naive set theory, the empty set is a primitive notion. To assert that it exists would be an implicit axiom.
· Peano arithmetic, the successor function and the number zero are primitive notions. Since Peano arithmetic is useful in regards to properties of the numbers, the objects that the primitive notions represent may not strictly matter.
· Axiomatic systems, the primitive notions will depend upon the set of axioms chosen for the system. Alessandro Padoa discussed this selection at the International Congress of Philosophy in Paris in 1900.[4] The notions themselves may not necessarily need to be stated; Susan Haack (1978) writes, "A set of axioms is sometimes said to give an implicit definition of its primitive terms."[5
I personally feel that this problematic issue will eventually be resolved by a dawning recognition that an increasingly explicit science of language and mathematics can and should be based on the fundamentals of computer science and the explicit construction of a “drawing canvas” for all common discussion based on simple and basic and “obvious” conventions.
In computer science, everything is explicitly constructed. No “floating variables” allowed. Fundamental mathematical objects like “sets” are given explicit definitions that can be “hard mapped” through a computing logic. It seems to me that we can and should do the same thing with an explicit theory of semantics and conceptual structure. Start at the bottom, with the simplest possible element of symbolic representation, and consciously and explicitly build every definition from that basis. Do it this way, and 1) unconscious/implicit/confusing assumptions can be stripped out of logical structure, and 2) a highly transparent methodology can be defined, in ways that might help encourage a wider acceptance.
>Verbing wierds language.
(laugh – yes, how true)
But then -- so do the unconscious assumptions inherent in “non-primitive primitives….”
Bruce Schuman, Santa Barbara CA USA
http://networknation.net/matrix.cfm
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-----Original Message-----
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John F Sowa
Sent: Tuesday, January 19, 2016 10:00 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] More about the lattice of all possible theories
Dear Matthew and Pat C,
PC
>> The number of primitives may be finite, if for no other reason than
>> that the number of concepts that people learn over a lifetime is finite.
>
> [MW] I agree it is likely the number is finite, but I would argue that
> you can never be certain you have found all of them. To say that you
> would have to be able to show that there was no other perspective or
> nothing new that could possibly be discovered or invented.
When talking about infinity, think of the integers. No brain, computer, or even the universe can store all of them. But when anyone sets an upper limit, someone else finds an application that needs a larger one.
Do you remember when Bill Gates said that no personal computer would ever need more than 640K bytes?
From
http://www.oxforddictionaries.com/words/how-many-words-are-there-in-the-english-language
> The Second Edition of the 20-volume Oxford English Dictionary contains
> full entries for 171,476 words in current use, and 47,156 obsolete
> words. To this may be added around 9,500 derivative words included as
> subentries. Over half of these words are nouns, about a quarter
> adjectives, and about a seventh verbs; the rest is made up of
> exclamations, conjunctions, prepositions, suffixes, etc. And these
> figures don't take account of entries with senses for different word
> classes (such as noun and adjective).
>
> This suggests that there are, at the very least, a quarter of a
> million distinct English words, excluding inflections, and words from
> technical and regional vocabulary not covered...
The last line is significant: there is an overwhelming amount of technical vocabulary for every branch of science, engineering, finance, law, business... and every department of every enterprise in any of those fields has many local senses.
In fact, nearly every family has local words and word senses that are rare or unknown outside the family. For example, 'heliotrope'
for "a cat that tries to stay warm in a moving shaft of sunshine."
For another example, see the dictionary of IBM Jargon, http://www.comlay.net/ibmjarg.pdf
It grew informally for many years without official IBM approval.
See for example, the terms 'strategic' and 'counter-strategic'.
For 'strategic', I contributed the word sense "supported by managers who had reached their level of incompetence." And for 'counter- strategic', I contributed the sense "embarrassingly superior to what is strategic." Although the dictionary itself was not official, those definitions were officially purged, or at least weakened.
Note that the kinds of jargon can be highly cryptic. For example,
SVC13 means "to generate a large amount of waste." It's derived from SuperVisor Call 13 for generating a memory dump in MVS.
These words are defined in terms of others. But any word can acquire new "microsenses" at any occurrence. For examples, 'SVC13' or the comic strip Calvin and Hobbs, which included
Any word in the English language can be verbed.
Verbing wierds language.
John
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Dear Pat C,
Matthew,
Thanks for the reference:
That paper on IIDEAS is a good summary of the general tactic of integration via a foundation ontology ("integration model"). Is there a citation I can use (other than the URL link) to its published version?
[MW>] This is the reference to the paper:
West, Matthew; Fowler, Julian The "IIDEAS" architecture and integration methodology for integrating enterprises PDT Days 2001 (2001)
The conclusion that the number of primitives is unlimited, however, does not follow from the experience of integrating a few domains and then noticing that new primitives are needed for another new domain. The number of primitives may be finite, if for no other reason than that the number of concepts that people learn over a lifetime is finite. It remains to be determined how large the number is.
[MW>] I agree it is likely the number is finite, but I would argue that you can never be certain you have found all of them. To say that you would have to be able to show that there was no other perspective or nothing new that could possibly be discovered or invented.
Even assuming that adding new domains to be integrated will inevitably lead to a requirement for *some* new primitives, there are practical reasons to try to identify some inventory of primitives that will handle a very large number of domains. Minimizing the need for supplementation of the foundation ontology, allows elements in domains linked to the foundation ontology to be specified in sufficient logical detail to be unambiguous and more easily related to other applications elements.
[MW>] Yes, our experience with ISO 15926 is that there is a substantial body that once established is reused by most domains. However, each domain brings something distinctive.
But having a complete set of primitives isn't necessary for the approach to be useful, since new primitives added for new applications will in general be irrelevant to pre-existing linked applications, which can continue to interoperate without the new primitives,, as they did before the addition.
[MW>] If only that were true. One of the problems of integration is that many domains overlap to a large extent with other neighbouring domains. However, far from having the same concepts, they take a rather different perspective on what are essentially the same underlying things. This requires identifying an underlying view that supports each. This is what the picture of successive integrations in the paper illustrates.
As to specific primitives, I gather from reading that paper that ISO 15926-2 should contain a good sample of primitives. Is there an easy way to distinguish the primitives from the derived concepts?
[MW>] Nearly everything in ISO 15926 is a primitive. Only things that are specifically identified as an the intersection of other entity types or classes would be non-primitive.
Regards
Matthew West
Information Junction
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Patrick Cassidy
As used in computational ontology, a “primitive” is an ontology element (type, relation) whose intended meaning cannot be logically specified as a combination of other elements in the ontology. Some concepts have co-primitive elements, such that the whole set of co-primitives can only be specified in terms of each other and possibly other primitive elements. A primitive on one ontology may be decomposable into more primitive elements, which can be added to the ontology and may make the original “primitive” a derived concept (non-primitive).
What one may use as a “primitive” in a given ontology may vary from what is used in other ontologies. If one wants to find (as I do) a set of primitives that can specify the intended meanings of all of the factual descriptive data that one may want to add to or get from the internet, that set should include, or be combinable to derive, all of the primitives in any other ontology.
PatC
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Alex Shkotin
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John Bottoms
[see below on "floating variables"]
I don't know the definition of "floating variables". The only references I found were to floating point [typed] variables. In terms of concepts, there are elements defined in DTD's that allow an element to be referenced from anywhere within a grammar These are referred to as abstract elements. An example is "figure" [drawing or image] which can be placed anywhere and does not have to be tied directly to a document structure. In effect you could put a picture in the table of contents or the index. Is this what you meant by floating variables?
Bruce Schuman
Yes, good point. The term “floating variable” is probably confusing. I tend to see a lot of things as “variables”.
By “floating” – I meant it’s “not grounded” – it’s “floating above the empirical ground”, so to speak – and thereby inherently ambiguous or non-scientific.
This issue was a major point of concern for the Vienna Circle. They wanted to regard all “metaphysics” as meaningless – because, I would say, they saw metaphysical concepts as ungrounded.
As regards the question about using a “picture” – this seems like a reference to the concept of “gestalt” – something like a “right brain” holistic perceptual unit that is understood by some people to be “concrete” – a complex thing seen as a whole.
There’s a lot that can be said on this subject – but this article on “empiricism” seems like a pretty good review of this issue: https://en.wikipedia.org/wiki/Empiricism
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https://en.wikipedia.org/wiki/Vienna_Circle
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From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John Bottoms
Sent: Wednesday, January 20, 2016 5:09 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is a primitive?
In computer science, everything is explicitly constructed. No “floating variables” allowed. Fundamental mathematical objects like “sets” are given explicit definitions that can be “hard mapped” through a computing logic. It seems to me that we can and should do the same thing with an explicit theory of semantics and conceptual structure. Start at the bottom, with the simplest possible element of symbolic representation, and consciously and explicitly build every definition from that basis. Do it this way, and 1) unconscious/implicit/confusing assumptions can be stripped out of logical structure, and 2) a highly transparent methodology can be defined, in ways that might help encourage a wider acceptance.
Alex:
Christopher Menzel
This issue was a major point of concern for the Vienna Circle. They wanted to regard all “metaphysics” as meaningless – because, I would say, they saw metaphysical concepts as ungrounded.
John Bottoms
Yes, good point. The term “floating variable” is probably confusing. I tend to see a lot of things as “variables”.
By “floating” – I meant it’s “not grounded” – it’s “floating above the empirical ground”, so to speak – and thereby inherently ambiguous or non-scientific.
This issue was a major point of concern for the Vienna Circle. They wanted to regard all “metaphysics” as meaningless – because, I would say, they saw metaphysical concepts as ungrounded.
As regards the question about using a “picture” – this seems like a reference to the concept of “gestalt” – something like a “right brain” holistic perceptual unit that is understood by some people to be “concrete” – a complex thing seen as a whole.
There’s a lot that can be said on this subject – but this article on “empiricism” seems like a pretty good review of this issue: https://en.wikipedia.org/wiki/Empiricism
*********
https://en.wikipedia.org/wiki/Vienna_Circle
********
Bruce Schuman, Santa Barbara CA USA
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John Bottoms
Sent: Wednesday, January 20, 2016 5:09 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is a primitive?
In computer science, everything is explicitly constructed. No “floating variables” allowed. Fundamental mathematical objects like “sets” are given explicit definitions that can be “hard mapped” through a computing logic. It seems to me that we can and should do the same thing with an explicit theory of semantics and conceptual structure. Start at the bottom, with the simplest possible element of symbolic representation, and consciously and explicitly build every definition from that basis. Do it this way, and 1) unconscious/implicit/confusing assumptions can be stripped out of logical structure, and 2) a highly transparent methodology can be defined, in ways that might help encourage a wider acceptance.
Alex:
I don't know the definition of "floating variables". The only references I found were to floating point [typed] variables. In terms of concepts, there are elements defined in DTD's that allow an element to be referenced from anywhere within a grammar These are referred to as abstract elements. An example is "figure" [drawing or image] which can be placed anywhere and does not have to be tied directly to a document structure. In effect you could put a picture in the table of contents or the index. Is this what you meant by floating variables?
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Bruce Schuman
I would define the term “grounded” by suggesting that the meaning of an abstraction like “dog” can be “empirically grounded” by defining the general abstract type based on discernible and measureable attributes of the instances (specific actual dogs).
So, if the question is “what is a dog?” – we might list a series of attributes – all of which would be true of all the instances – and the definition would be “grounded” by empirical measurement of the instances.
In this way, the definition of “dog” becomes an n-dimensional envelope – and if some dimensional characterization of “the instance” does not fall within the boundaries of that envelope, then the instance is not an instance of that type.
The Wikipedia article on “concept” illustrates this issue by connecting the abstraction “tree” with instances of trees.
At what point would one of these objects shown as “trees” become an instance of the general type “bush”?
Our definition of tree would be “grounded” in the properties of the instances.
https://en.wikipedia.org/wiki/Concept
Bruce Schuman, Santa Barbara CA USA
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John Bottoms
Sent: Wednesday, January 20, 2016 10:24 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is a primitive?
On 1/20/2016 11:36 AM, Bruce Schuman wrote:
Yes, good point. The term “floating variable” is probably confusing. I tend to see a lot of things as “variables”.
By “floating” – I meant it’s “not grounded” – it’s “floating above the empirical ground”, so to speak – and thereby inherently ambiguous or non-scientific.
This issue was a major point of concern for the Vienna Circle. They wanted to regard all “metaphysics” as meaningless – because, I would say, they saw metaphysical concepts as ungrounded.
I don't understand. My image of this is that all types are "floating" and all instances are grounded. We signal (tag) those in English with the determinate such as "There is a dog." vs "There is the dog.". Am I missing something. Did the VC not recognize the distinction between types and instances? Are all types "metaphysical"?
As regards the question about using a “picture” – this seems like a reference to the concept of “gestalt” – something like a “right brain” holistic perceptual unit that is understood by some people to be “concrete” – a complex thing seen as a whole.
There’s a lot that can be said on this subject – but this article on “empiricism” seems like a pretty good review of this issue: https://en.wikipedia.org/wiki/Empiricism
*********
https://en.wikipedia.org/wiki/Vienna_Circle
********
Bruce Schuman, Santa Barbara CA USA
From: ontolo...@googlegroups.com [mailto:ontolo...@googlegroups.com] On Behalf Of John Bottoms
Sent: Wednesday, January 20, 2016 5:09 AM
To: ontolo...@googlegroups.com
Subject: Re: [ontolog-forum] What is a primitive?
In computer science, everything is explicitly constructed. No “floating variables” allowed. Fundamental mathematical objects like “sets” are given explicit definitions that can be “hard mapped” through a computing logic. It seems to me that we can and should do the same thing with an explicit theory of semantics and conceptual structure. Start at the bottom, with the simplest possible element of symbolic representation, and consciously and explicitly build every definition from that basis. Do it this way, and 1) unconscious/implicit/confusing assumptions can be stripped out of logical structure, and 2) a highly transparent methodology can be defined, in ways that might help encourage a wider acceptance.
Alex:
I don't know the definition of "floating variables". The only references I found were to floating point [typed] variables. In terms of concepts, there are elements defined in DTD's that allow an element to be referenced from anywhere within a grammar These are referred to as abstract elements. An example is "figure" [drawing or image] which can be placed anywhere and does not have to be tied directly to a document structure. In effect you could put a picture in the table of contents or the index. Is this what you meant by floating variables?
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