The Humpty-Dumpty Principle in Definitions

In dealing with empty concepts, we came across the issue that if somebody uses a term that potentially has an unintelligible definition, they are likely to defend themselves by quickly making up some kind of definition.   I strongly suspect that in such cases, the usage of the term will be inconsistent with the definition.  Which brings us to Humpty-Dumpty.

Lewis Carroll (Rev. Charles Lutwidge Dodgson) is best known for his children's' books Alice's Adventures in Wonderland and Through the Looking Glass.  It is in the latter that Humpty Dumpty - an argumentative egg perched on a wall has the following exchange with Alice:

'And only one for birthday presents, you know. There's glory for you!'
`I don't know what you mean by "glory",' Alice said.
Humpty Dumpty smiled contemptuously. `Of course you don't -- till I tell you. I meant "there's a nice knock-down argument for you!"'
`But "glory" doesn't mean "a nice knock-down argument",' Alice objected.
`When I use a word,' Humpty Dumpty said, in rather a scornful tone, `it means just what I choose it to mean -- neither more nor less.'
`The question is,' said Alice, `whether you can make words mean so many different things.'
`The question is,' said Humpty Dumpty, `which is to be master -- that's all.'

What Humpty-Dumpty is saying is that he can stipulate what the definition of a term is.  Lewis Carroll was a processor of logic and mathematics at Oxford University (Christ Church College), and wrote extensively on logic.  He elaborated on the theme in Humpty Dumpty in Chapter 2 of Book 10 of his work Symbolic Logic, where he says:

"...I maintain that any writer of a book is fully authorized in attaching any meaning he likes to any word he intends to use.  If I find an author saying at the beginning of his book, 'Let it be understood that by the word white I shall always mean black' I meekly accept his ruling, however injudicious I may think it. " 

[I quote from Lewis Carroll's Symbolic Logic by William Warren Bartley III,  ISBN 0-517-52383-3 - a book I had great difficulty in obtaining].   

Carroll implies that an author must use such a term consistently - that is, without varying the underlying definition.  This appears to be the principle that Humpty Dumpty was getting at.  Varying the definition of a term within an argument is the fallacy of equivocation, but Carroll is going beyond that and demanding consistent usage throughout a universe of discourse.

A second point here is that if a term is to be used in a nonconventional way, then the definition should be explained up front.  Again, Carroll implies this in his example of white.  This is one place where I would agree with the maxim of "starting with definitions".  However, this maxim is often misused.  For instance, in analysis we nearly always aim to arrive at definitions, as we do not understand concepts at the outset.

Thus, I think we now have a reasonable framework for dealing with individuals who use terms that they cannot supply adequate definitions for, particularly in the context of empty concepts.

One quick Lewis Carroll story.  Carroll found it necessary to deny that he had ever presented Queen Victoria with a book.  The story circulated that the Queen has been so charmed by reading Alice in Wonderland that she expressed her desire to receive the author's next work - whereupon he sent her The Condensation of Determinants. 

What is an Empty Concept?

In the last post, univocal, equivocal, and analogous terms were discussed.  It occurred to me afterwards that all of these classes of term presuppose terms that signify concepts.  But what about a term that does not signify any concept?  

At first this sounds a bit stupid.  Surely we would not waste our time on terms that do not signify a concept.  However, I have listened to several decades of marketing hype in Information Technology and I think that I have heard terms that do not signify anything - but which have some kind of emotive power.

I have tried to look for philosophical sources about terms that signify empty concepts, but have not been able to find any - probably due to the short time I have been able to invest in the search.  This makes me cautious, so I will confine the discussion of empty concepts mostly to data management.

First, if a term signifies a concept that can supposit for actual materially existing instances, then the concept is non-empty.  E.g. "Computer".  Unfortunately, in information management, we are mostly dealing with concepts who instances are immaterial, such as "Mortgage Backed Securities" (MBS's).  These exist, but not materially.  They are essentially contracts between human beings and/or institutions.   This way of thinking about empty concepts is now at a point where my metaphysics runs out.  

Let's try another approach.  If a concept can be empty, that implies it can possibly have content.  What "content" has traditionally been taken to mean by logicians (in the context of concepts) is a definition.  Thus, I would suggest that an empty concept is one with either (a) no definition; or (b) an unintelligible definition.

And it gets more complex.   Someone who uses a term can generally attempt to provide a definition for it.  They are very unlikely to admit there is no definition.   The definition provided is likely either a definition for a concept signified by another term or terms; or the definition supplied is unintelligible.  

Perhaps an unintelligible definition is more interesting.  Such a definition must fail significant quality checks,  Such checks may be those we formally use to assess all definitions, or may be checks based in the subject matter of what is being defined.  For instance, I suppose that "Platonic Forms" (which proposed real existence of concepts such as "table" or "chair") is a concept ultimately found to be unintelligible by philosophers.  More mundanely, I think "data owner" has an unintelligible definition insofar as it contains anything about "ownership".

This is yet another topic I will have to follow up. 

Univocal, Equivocal, and Analogous Terms

This is a topic which we will probably have to return to in the future, but a start has to be made.  Definitions are inextricably bound up with terms, and one classification of terms  divides them up into Univocal, Equivocal, and Analogous.  Let us briefly review these three classes.  

• Univocal Term: A terms that has only one meaning.  That is, it signifies only one concept, and thus corresponds to only one definition.  Such a term always has the same intension wherever it is used.   E.g. the term "entomology" signifies the study of insects. 
• Equivocal Term: A term that has more than one meaning.  That is, it signifies more than one concept, and thus corresponds to more than one definition.  An equivocal term has different intensions when it is used.  E.g. the term "chihuahua" can signify (a) a breed of dog; (b) a state of Mexico. 
• Analogous Term:  A term that is intended to convey one or more similar characteristics that exist between two concepts.  E.g. the term "data owner" is applied to individuals who have no legal title to the data they manage, but are expected to exercise responsibilities like those owners would typically exercise.  Sometimes an analogous term can be no different to an equivocal term. 

It is not always easy to know if a univocal term really is univocal.  For instance, I am not aware of any equivocal use of "entomology".  There might be, but I am unaware of it if it exists.  Also, a univocal term might become equivocal in the future.  

With respect to equivocal terms, a big problem is that there are far more concepts than there are terms to describe them.  This is a reason why equivocal terms come into being, and there seems to be no way to avoid it happening.  From a practical point of view the problems with equivocal terms arise when a term is being used equivocally in communication.  For instance, if I use "backup" within a group managing databases, everybody knows what I mean - even if " backup " has other meanings, such as in police operations. 

One way round this is to maintain specialized vocabularies for "subject fields" (as the terminologists call them).  Roughly speaking this means that an equivocal term can be taken to be univocal in a specific context.  We will need to come back to this.

Analogous terms are more difficult.    Problems include: (a) only one of the related objects is identified; (b) the characteristics supposedly in common between the two objects are never identified.  This means that an analogous term may not actually signify a concept - it may be unintelligible and just used for emotive effect.  It certainly implies that there is a more complex relationship between analogous terms and definitions.  This too we will have to return to.

Is a Definition Just a List of Attributes?

If we look at a data model, is a definition of an entity type automatically produced by listing the attributes of the entity type?  If this were true then a data modeler would not need to produce entity definitions - he or she would simply need to identify and list a sufficient number of attributes.  I have actually heard data modelers being criticized by terminologists for doing just this.  The extent to which such criticism is fair or not is a separate discussion, but the question remains as to whether a list of attributes can suffice as a definition.

I do not think that a list of attributes is sufficient based on the recent discussions about concept systems in this blog.  No concept exists in isolation.  Every concept exists in some kind of concept system where it has relationships to other concepts.  At least some of these relationships and/or related concepts have to enter into a definition so that the concept being defined can be located properly in a concept system, which appears to be necessary for knowledge.

A list of attributes usually will not distinguish between those that are determining for the concept under consideration, and those which are not - some of which may be shared with other concepts.  Thus, just reviewing a list of attributes becomes a test of figuring out which ones are pertinent to a definition.  This surely defeats the practical aspects of definition.

It would seem therefore that something more than a list of attributes is required to produce a quality definition.  While many data modelers do produce quality definitions, it can be seen that the practice of data modeling may present the temptation to just assume that the definition of an entity type is provided by the attributes captured for it.  Of course, relationships and other concepts are present in a data model, but it will need another blog to answer the question of whether a data model has enough information to produce a definition based on entity types, attributes, and relationships alone.

Generic vs. Partitive Concept Systems

For the past couple of blogs I have been exploring different types on concept systems.  I have found these discussed, oddly enough, not in the literature on data modeling, but in the literature on terminology work.  At this point, I want to look at the two major concept systems.  These are very abundant in the raw material of information management, and require special attention.

Generic:  This is the familiar supertype-subtype concept system, where a more generic concept encompasses a range of more specific concepts.  E.g. Animal - Chordate - Vertebrate - Mammal - Primate - Homo sapiens.  There are a couple of interesting properties of this concept system:

• Any instance found in a specific concept is also covered by a more general concept.  The more general concepts possess fewer attributes than the more specific ones, but every specific concept possesses the attributes of each "parent" generic concept.  
•  Intention is inversely related to extension.   That is, the greater the number of specifying characteristics (intension), the more restricted the population of instances that is covered by the concept (extension).

Partitive: This is the part-whole concept system.  The study of part-whole relationships is called mereology.  It seems a bit odd to have a named discipline for this type of concept system, but not for others.  Perhaps it is an artifact of the evolution of philosophy.  Anyway, an example of a part whole system would be the organs of the human body, such as brain, liver, pancreas, kidney, and so on.  To have a complete view of the human body we would have to include tissues, such as epithelium, blood, muscle, nerves, etc.  This concept system is totally unlike the generic one as the parts have quite different identities that do not share characteristics.  We also run into interesting problems such as denial that the whole is anything more than the sum of its parts.  To summarize its properties:

• Each concept in a partitive concept system covers a range of instances that are not found in any other concept in the system.  There is no overlap of instances among the concepts in the system, unlike the generic type of concept system.  
• There is no relation between extension and intension of the concepts in the system.  Each concept has characteristics, none of which apply to the system as a whole.

I think that understanding different types of concept system has been overlooked by data modelers. Presumably this is because the arrangement of boxes and lines in a data model does not look very different for a generic or a partitive concept system.

On Types of Concept System

In my previous blog I discussed the existence of different types of concept systems.  I have found these discussed, oddly enough, not in the literature on data modeling, but in the literature on terminology work.  I have not found discussion of concept systems in philosophy, but that might merely reflect my lack of education, reading in, and general knowledge of philosophy.

Before going further into types of concept systems, we need to establish what a concept system is.  Nordterm 8 Guide to Terminology by Heidi Suonuuti (ISBN 952-9794-14-2) states the following:

Concepts are not independent phenomena.  They are always related to other concepts in one way or another, and form concept systems which can vary from fairly simple to extremely complicated.  In terminology work, an analysis of the relations among concepts and an arrangement of them into concept systems, is a prerequisite for the successful drafting of definitions.

This is not a great definition of "concept system" but it is a good start.  The ISO 704 standard from ISO/TC 37/SC 1 tells us the following:

Concepts do not exist as isolated units of knowledge but always in relation to each other. Our thought processes constantly create and refine the relations between concepts, whether these relations are formally acknowledged or not. A set of concepts structured according to the relations among them is said to form a concept system. 

In organizing concepts into a concept system, it is necessary to bear in mind the subject field that gave rise to the concept and to consider the expectations and objectives of the target users. The subject field shall act as the framework within which the concept field, the set of thematically related but unstructured concepts, is established.

ISO 704 also states:

The terminology of a subject field is not an arbitrary collection of terms. The relevant concepts constitute a coherent concept system based on the relations existing between concepts. The unique position of each concept within a system is determined by the intension and the extension.

This is not the place to get into what is meant by a "subject field".  However, it does seem apparent that a concept system is a number of concepts and the relations between them.  This corresponds to what data modelers call a "conceptual data model", but which they should call a "conceptual model".  A conceptual model describes a set of business information as such, without any thought of how it might be stored as data.

A concept system also differs from a single relationship between two or more terms.   Baldwin's Dictionary of Philosophy defines "relation" in logic as follows:

The mutual dependence of two or more subjects upon a common principle, fact, or truth, of such a kind that any assertion regarding one modifies the meaning of the other.  Accordingly, the predicate is true or false of one taken not independently or in isolation, but only in reference, regard, or respect to the other.  

The way in which a concept system differs from a relationship is that a concept system contains many relationships.

So we have some idea of what a concept system is.   What is interesting is that concept systems are not all of different kinds, but are distributed in types.  This idea is found in terminology work, but does not seem to be found in data modeling.  Perhaps this is because data models are oriented to building databases for data storage, and not for describing business information.    

If there are types of concept system, then each type should have its own properties.  Understanding these properties might help us work with concept systems and hence with definitions.   Data modelers do not seem to have contributed much if any thought about types of concept systems.  It is true that there are many books on data model patterns, but these are oriented to data modeling goals such as not needing to change a database structure unless it is unavoidable.

A challenge will therefore be to catalog the different types of concept system, and their special properties, and find ways to apply them in the practical work of definition management.

The Idea of Concept Systems

An involuntary hiatus has prevented me from the pleasure of blogging on definitions for about a month.  I am now gradually getting back to normal, and am able to blog again.

Today I want to look at concept systems, and types of concept system.

In data modeling, only one type of concept system commonly appears - the generic concept system, containing Supertypes and Subtypes.  Very occasionally, the part-whole type of concept system can also be found.  The latter be seen in "bill of material" structures.  Strangely, the visual representation of a generic concept system and a part-whole concept system can look very similar in a data model.   I think that this leads data modelers to play down the idea of concept systems, and indeed the term "concept system" is not really met with in data modeling.

However, if we turn to the discipline of terminology, the idea of concept system is very prominent, and different types of concept systems are called out.  Let me quote from the Nordterm Guide to Terminology by Heidi Suonuuti (ISBN 952-9794-14-2):

"Concepts are not independent phenomena.  They are always related to other concepts in one way or another, and form concept systems which can vary from fairly simple to extremely complicated.  In terminology work, an analysis of the relations among concepts and an arrangement of them into concept systems, is a prerequisite for the successful drafting of definitions."

It is interesting that from the data modeler's perspective, concept systems are viewed only with respect to designing data storage solutions.  A terminologist, by contrast, is more interested in business information and how concepts are related within it - irrespective of how such information might be stored as data.

This makes me wonder about semantic modelers.  We hear a lot about semantics these days, and there is no doubt that semantics involves identifying concepts and providing definitions for them.  But finding the relationships between the concepts must be done prior to forming the definitions.  This is because a definition, in part, describes a concept's relations to other concepts in the concept system in which it is found.  So what good methodologies, notations, and techniques exist for describing or visualizing concept systems?  I am not sure we have yet got any good ones.   The danger is that we then fall back on the data modeling methodologies, notations, and techniques, which fail to capture significant semantic details.

But perhaps more important is that the terminologists have the idea of types of concept systems.  The generic and partitive types of concept system are the major ones, but there are others.  We will deal with the different types in a future post.