On Levels of Definitions and the Semantic Web

Stijn made a couple of sharp points in a comment on the post How is a Definition Different from an Explanation? (Part 1) (http://definitionsinsemantics.blogspot.com/2011/11/how-is-definition-different-from.html). 

He notes that there is a need for definitions to be short in certain circumstances, as when a user is scanning through a list.  I think this is a good point.  Users may be more in search mode when they are doing something like this.  They want to know if the definition is close to some target they have in mind.  Obviously, a full definition is not fit for such a purpose.

So we might have three levels of definition: (a) a one-liner, suitable for lists; (b) a one-paragraph, suitable for a quick read with some detail - and display on a screen with scarce real estate; and (c) the full definition, as an authoritative reference.  I have no problem with the last one being very long and including pictures - certainly more than half a page.   

The second point Stijn makes is about the Semantic Web, where there is a need for a "general purpose" description.  I agree with Stijn that there is a problem here.  The definition of a concept must include something about the concept system the concept is located in - such as relationships to proximate concepts. So if one concept can be placed in different concept systems, then the definition will change.  A mortgage loan in a servicing system is not the same as in a loan origination system, and is not the same as in a securitization system.  The Semantic Web may have an unspoken assumption of a single model of reality.  This will cause problems if, as I maintain, one concept can be placed in many concept systems.  It will lead to the frustration Stijn describes.  

Where I disagree with Stijn is his equating explanation with description.  These are quite distinct.  There can certainly be descriptive definitions, and these are very common in natural science.  But explanations are different.

How is a Definition Different from an Explanation? (Part 2)

In Part I of this series (http://definitionsinsemantics.blogspot.com/2011/11/how-is-definition-different-from.html), we explored explanation defined as "bringing a mind to an understanding of a topic".  

There is, however, another form of explanation, of which Aristotle said "We believe ourselves to know a thing when we are acquainted with its cause" (Posterior Analytics, II C. II para 1).

One way to provide this kind of explanation is by arguing from the cause to the effect.  Traditionally this involved using syllogisms where the cause was in the major premiss and the effect was in the conclusion.  E.g. All ellipses show a pattern of positions X; the orbit of Mars shows a pattern of positions X; therefore the orbit of Mars is an ellipse.

This form of explanation is very satifying, and it might seem natural to try to incorporate it into definitions.  However, there are reasons not to do so.  First, the above form requires putting the concept to be defined into propositions, and then putting the propositions into a syllogism (an argument).  And then putting all of that into the definition.  But if all this is part of the definition, and the definition is supposed to substitute for the term being defined, we would seem to end up with an infinite regression.  Of course, this is always a danger when the term to be defined is in the definition, but having an argument in the definition seems to assure this as the term has to be included in the argument.  At least it seems that way to me - although I cannot find any description of my opinion in the literature, and I will willingly defer to others who can prove me wrong.

Secondly, putting argument into a definition exposes the definition to much greater chance of error.  The propositions may be false, and the argumentation may be invalid.  And why would we put the concept into propositions and arguments before we have a completed definition - surely that is jumping the gun.

My provisional conclusion, therefore, is that causal explanations should not be placed in definitions.  

BUT, there is another consideration.  In modern enterprises, definitions are containers as well as content.  If an explanation has to be provided, and there is nowhere else to put it, then it should be put into the definition (as container, not content).  The distinction between container and content is not found (at least by me) in traditional logic.  Yet it is a most important consideration.  I suppose we need another blog on definition as container vs. content.

If we are forced to put a causal explanation in the definition (container) then at least get the concept defined fully (content) before any explanation is provided, so the explanation is not part of the true definition (content).

How is a Definition Different from an Explanation? (Part 1)

This topic will require more than one post, because there is more than one definition of "Explanation".  That is, the term "Explanation" signifies more that one concept.

The first kind of explanation we will deal with can be defined as:

"Bringing a mind to an understanding of a topic".

This means that an explanation must be relative to the mind which is to be brought to the intended understanding.  For instance, the way we explain the solar system to an 8-year old child will likely be different to the way we explain the solar system to a college undergraduate.  The explanation offered will depend on prior knowledge, experience, developed intelligence, and probably many other factors.  Differences between defintion and explanation can be summarized as follows:

• A definition is not intended to be proportional to any mind.  It has to be the best description of a concept that is available. This is is quite unlike explanation, where there will be many explanations proportionate to the types of minds which are to be provided with a given explanation.  
• There can be many explanations for a concept, but there should be only one definition.  
• An explanation may exclude difficult points (say to convey an initial understanding), but a definition must be as complete as possible.  
• An explanation may avoid technical language.  A definition should aim to exclude technical language, but it may sometimes need to include technical language.

There is always a danger that an analyst creating a definition will treat it as an explanation.  This will likely make the definition unusable as an authoritative reference.  The analyst will probably only be guessing at the type of mind any explanation is aimed at.  It is one reason careful governance of definitions is needed (so analysts do not go in the wrong direction).  

It can be argued that there is an environment in which the definition is to be used, and that the definition should be the best for that environment - but might be vary across such environments.  For instance, the insurance concept of "Incurred But Not Reported" can be defined within the environment of Insurance Company X, without any intent to be used in any other insurance company.

An issue here is that if a definiton is the best for a particular environment, how can this satisfy the vision of the Semantic Web which would seem to have common definitions of concepts across the entire web?  However, this is an issue beyond comparing definition to explanation.