Definition as Content and Container

We often use terms without fully thinking out how we are using them - particularly if abstraction is involved.  The other day I was looking at a data modeling tool, and asked a colleague "What did you put into the definition?".  It suddenly occurred to me that I was not talking about the content of the definition, but about the definition field into which I could type the content.

After thinking about it some more, I realized that the definition field is a container which we are free to use as we want (at least in the tool I was working with).  So an immediate question is, how do we want to structure what goes into this field (e.g. with section headings) and what metadata about the definition do we want to put in (e.g. what person last updated it)?  

Of course, the more sophisticated tools have these separate elements of the definition more explicitly segregated.  The "definition" is a set of smaller containers inside a bigger container. Perhaps this might mean that a different set of questions arises, such as the order in which we develop content in this set of smaller containers.  Or perhaps such questions depend on the actual set of containers that are exposed to use in each of these tools.  Either way, I think questions arise.

It is good to be concerned about how to develop good definitional content, quite apart from what this content is stored in.  However, the fact that some kind of container exists (whether simple or complex) means that we have to be concerned with the management of the container also.  Since both container and content are signified by the term "definition" there is ample scope for confusion here.  

I do not think this is being pedantic.  Information Knowledge Management is difficult because it is dealing with things that are inherently abstract and immaterial.  It means we really have to think our way through it, and it is easy to make mistakes.  Keeping in mind that there is a distinction between container and content may help us to avoid a few of these mistakes.

Why Do Definitions - Why Not Just Use Wikipedia?

Today I spoke to the New York ERwin Modeling User Group (NYEMUG) on "Creating Great Definitions".  One question came up, which was why bother crafting definitions at all - why not simply rely on Wikipedia for them?  I suppose it could be any external source, and not necessarily Wikipedia (e.g. the Enterprise Data Management's Semantics Repository).  The way it would work conceptually would be to associate a link to Wikipedia with any term.

It might be thought that Wikipedia only deals with common terms, and not specialized technical terms.  However, there are a good number of technical terms that are present in Wikipedia.

My first reaction was both "yes" and "no".  "Yes" because it is simply obvious there is considerable value in Wikipedia, but "no" because Wikipedia does not understand the enterprise I work in, which ultimately supplies an enormous amount of context that influences definitions.   

I will have to think about this topic some more before I can fully answer it.  But, I at least wanted to capture a few initial ideas.  I take it for granted that Wikipedia has value, so I need to think why this value might be so limited that we still need to do definitions.   

(a) Wikipedia cannot provide details of a concept which is defined by a common relation of the instances included in the concept to another concept (usually a special way of managing these instances) that is unique to the enterprise (or part of the enterprise).  So Wikipedia cannot tell us what a Financial Asset is for our enterprise, because what we include in "Financial Asset" depends on our business model.    

(b) Wikipedia cannot deal with definitions modified on a per-context basis.  Speech communities are contexts.  So, for instance, Wikipedia cannot tell us what our Marketing department considers a Customer to be, versus what our Accounts Receivables department considers a Customer to be.  Wikipedia does not know the speech communities in our enterprise.

(c) The structure of Wikipedia entries differs on a per page basis.  There is no consistent set of sections to a definition, nor metadata for a definition.  This might inhibit use in an enterprise.

(d) Concepts are arranged in concept systems.  A definition shows how a concept is placed in a concept system.  One concept can occur in many concept systems, and the definition is modified in each case.

(e) Wikipedia can be wrong.  I have found errors, but very few - so I am not sure how valid this objection is.

Some of the above points may or may not overlap.  They are also preliminary, so subject to revision. 

That is all for now - I will have to return to this one.  However, the question raised in the title is one that must be answered.

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).

Dodd-Frank "Swap" - A Definitional Disaster?

The Dodd-Frank Act is intended to reform the financial system in order to reduce the chance of any future systemic failure.  Obviously, it is very important, and one of the most important parts of Dodd-Frank revolves around swaps.  It may be recalled that lack of understanding about Credit Default Swaps (CDS) was a big part of the financial crisis that began in 2008 - and specifically caused AIG to fail.  CDS, however, are only one species of swap.  Prior to 2008 there had been little regulation of swaps.

Before we go further, there is one other piece of background for those unfamiliar with the sausage-making process of US financial regulation.  An Act of Congress is just the beginning.  Agencies of the US government must take the Act and turn it in to rules - usually many rules - and then enforce them.  This means that if there is a problem in the Act, there can be difficulties across many rules.

Back to swaps.  The Dodd-Frank definition of "swap" is given below.  It is a pretty mind-numbing read.  This definition clearly shows that there is no simple definition of a swap.  The definition has a long list of concepts that are included, and a long list of concepts that are excluded (Paragraph B).

What we have is a collection of "things" that the government wants to be regulated in an identical manner - as "swaps".  However, the only consistency is the way these "things" are to be regulated.  There is no consistency - no common attributes intrinsic to these things - that distinguishes them from other things.  If there was a set of common characteristics, then these would presumably have been listed.  Instead, we get enumeration of members of the class (a practice frowned upon by traditional logicians). This is seen especially in the items labelled "(I)" through "(XXII)".  These are part of the definition, not a list of illustrations.

The definition even abstracts from enumeration of members when it says:  "(iv) that is an agreement, contract, or transaction that is, or in the future becomes, commonly known to the trade as a swap".  

I was shocked when I first read this.  How can a definition simply point back to common usage of a term?  The government is throwing the burden of definition back on the speech community!  Even then, what is meant by "the trade" and "commonly known" is puzzling (I cannot find definitions for these terms in the Act).  Also, if some bright investment banker figures out a new product that he or she brands as something other than a swap, then they can presumably escape regulation.  However, there is an "escape hatch" - the Commodities Futures Trading Commission (CFTC) is delegated the authority to broaden the definition, which should prevent this kind of problem.  But suppose something gets called a "swap" that is nothing like a "real swap".  That sort of thing happens all the time in the evolution of language.  There is no way the definition can be modified to exclude it as the Act is written. 

There is a lot more to be said on the Dodd-Frank definition of "swap" and we will cover more topics in future posts.  This post is merely an appetizer to what promises to be a true feast of lessons that can be drawn about definitions.

Here is the defintion of "swap" - only subparagraphs (A) and (B) of the text - subparagraphs (C) through (F) are not part of the general definition.  The full text of the Act can be found at: www.sec.gov/about/laws/wallstreetreform-cpa.pdf - please refer to Section 721 and scroll down until you see "SWAPS".

‘‘(47) SWAP.—
‘‘(A) IN GENERAL.—Except as provided in subparagraph (B), the term ‘swap’ means any agreement, contract, or transaction—
‘‘(i) that is a put, call, cap, floor, collar, or similar option of any kind that is for the purchase or sale, or based on the value, of 1 or more interest or other rates, currencies, commodities, securities, instruments of indebtedness, indices, quantitative measures, or other financial or economic interests or property of any kind;
‘‘(ii) that provides for any purchase, sale, payment, or delivery (other than a dividend on an equity security) that is dependent on the occurrence, nonoccurrence, or the extent of the occurrence of an event or contingency associated with a potential financial, economic, or commercial consequence;
‘‘(iii) that provides on an executory basis for the exchange, on a fixed or contingent basis, of 1 or more payments based on the value or level of 1 or more interest or other rates, currencies, commodities, securities, instruments of indebtedness, indices, quantitative measures, or other financial or economic interests or property of any kind, or any interest therein or based on the value thereof, and that transfers, as between the parties to the transaction, in whole or in part, the financial risk associated with a future change in any such value or level without also conveying a current or future direct or indirect ownership interest in an asset (including any enterprise or investment pool) or liability that incorporates the financial risk so transferred, including any agreement, contract, or transaction commonly known as—
‘‘(I) an interest rate swap;
‘‘(II) a rate floor;
‘‘(III) a rate cap;
‘‘(IV) a rate collar;
‘‘(V) a cross-currency rate swap;
‘‘(VI) a basis swap;
‘‘(VII) a currency swap;
‘‘(VIII) a foreign exchange swap;
‘‘(IX) a total return swap;
‘‘(X) an equity index swap;
‘‘(XI) an equity swap;
‘‘(XII) a debt index swap;
‘‘(XIII) a debt swap;
‘‘(XIV) a credit spread;
‘‘(XV) a credit default swap;
‘‘(XVI) a credit swap;
‘‘(XVII) a weather swap;
‘‘(XVIII) an energy swap;
‘‘(XIX) a metal swap;
‘‘(XX) an agricultural swap;
‘‘(XXI) an emissions swap; and
‘‘(XXII) a commodity swap;
‘‘(iv) that is an agreement, contract, or transaction that is, or in the future becomes, commonly known to the trade as a swap; ‘‘(v) including any security-based swap agreement which meets the definition of ‘swap agreement’ as defined in section 206A of the Gramm-Leach-Bliley Act (15 U.S.C. 78c note) of which a material term is based on the price, yield, value, or volatility of any security or any group or index of securities, or any interest therein; or
‘‘(vi) that is any combination or permutation of, or option on, any agreement, contract, or transaction described in any of clauses (i) through (v).

‘‘(B) EXCLUSIONS.—The term ‘swap’ does not include—
‘‘(i) any contract of sale of a commodity for future delivery (or option on such a contract), leverage contract authorized under section 19, security futures product, or agreement, contract, or transaction described in section 2(c)(2)(C)(i) or section 2(c)(2)(D)(i);
‘‘(ii) any sale of a nonfinancial commodity or security for deferred shipment or delivery, so long as the transaction is intended to be physically settled;
‘‘(iii) any put, call, straddle, option, or privilege on any security, certificate of deposit, or group or index of securities, including any interest therein or based
on the value thereof, that is subject to—
‘‘(I) the Securities Act of 1933 (15 U.S.C. 77a et seq.); and
‘‘(II) the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.);
‘‘(iv) any put, call, straddle, option, or privilege relating to a foreign currency entered into on a national securities exchange registered pursuant to section 6(a) of the Securities Exchange Act of 1934 (15 U.S.C. 78f(a));
‘‘(v) any agreement, contract, or transaction providing for the purchase or sale of 1 or more securities on a fixed basis that is subject to—
‘‘(I) the Securities Act of 1933 (15 U.S.C. 77a et seq.); and
‘‘(II) the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.);
‘‘(vi) any agreement, contract, or transaction providing for the purchase or sale of 1 or more securities on a contingent basis that is subject to the Securities
Act of 1933 (15 U.S.C. 77a et seq.) and the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.), unless the agreement, contract, or transaction predicates the purchase or sale on the occurrence of a bona fide contingency that might reasonably be expected to affect or be affected by the  creditworthiness of a party other than a party to the agreement, contract, or transaction;
‘‘(vii) any note, bond, or evidence of indebtedness that is a security, as defined in section 2(a)(1) of the Securities Act of 1933 (15 U.S.C. 77b(a)(1));
‘‘(viii) any agreement, contract, or transaction that is—
‘‘(I) based on a security; and
‘‘(II) entered into directly or through an underwriter (as defined in section 2(a)(11) of the Securities Act of 1933 (15 U.S.C. 77b(a)(11)) by the issuer
of such security for the purposes of raising capital, unless the agreement, contract, or transaction is entered into to manage a risk associated with capital raising;
‘‘(ix) any agreement, contract, or transaction a counterparty of which is a Federal Reserve bank, the Federal Government, or a Federal agency that is
expressly backed by the full faith and credit of the United States; and
‘‘(x) any security-based swap, other than a securitybased swap as described in subparagraph (D). 
...
(b) AUTHORITY TO DEFINE TERMS.—The Commodity Futures Trading Commission may adopt a rule to define—
(1) the term ‘‘commercial risk’’; and
(2) any other term included in an amendment to the Commodity Exchange Act (7 U.S.C. 1 et seq.) made by this subtitle.
(c) MODIFICATION OF DEFINITIONS.—To include transactions and entities that have been structured to evade this subtitle (or an amendment made by this subtitle), the Commodity Futures Trading Commission shall adopt a rule to further define the terms ‘‘swap’’, ‘‘swap dealer’’, ‘‘major swap participant’’, and ‘‘eligible contract participant’’.

F.A. Hayek on Definitions - An Anti-Scientistic Stance

F.A. Hayek is well known for his battles against Socialism and Keynesianism.  Less well known is his critique of the misapplication of the techniques and language of natural science to the social sciences - an attack on Positivism made eloquently in his 1952 book "The Counter-Revolution of  Science - Studies on The Abuse of Reason" (ISBN 0-913966-66-5).  Hayek termed this misapplication of the natural sciences "Scientism".  In Chapter 3 of the book the Nobel laureate makes some interesting observations on definitions.  Hayek writes:
 

'Take the concept of a "tool" or "instrument", or of any particular tool such as a hammer or barometer.  It is easily seen that these concepts cannot be interpreted to refer to "objective facts", that is, to things irrespective of what people think about them.  Careful logical analysis of these concepts will show that they all express relationships between several (at least three) terms, of which one is the acting or thinking person, the second one the desired or imagined effect, and the third a thing in the ordinary sense.  If the reader will attempt a definition he will soon find that he cannot give one without using some term such as "suitable for" or "intended for" or some other expression referring to the use for which it is designed by somebody.  And a definition which is to comprise all instances of the class will not contain any reference to its substance, or shape, or other physical attribute.  An ordinary hammer and a steamhammer, or an aneroid barometer and a mercury barometer, have nothing in common except the purpose for which men think they can be used.

It must not be objected that these are merely instances of abstractions to arrive at generic terms just as those used in the physical sciences.  The point is that they are abstractions from all physical attributes of the things in question and that their definitions must run entirely in terms of mental attitudes of men toward these things.  The significant difference between the two views of the things stands out clearly if we think, for example, of the problem of the archaeologist trying to determine whether what looks like a stone implement is in truth an "artifact", made by man, or merely a chance product of nature.  There is no way of deciding this but by trying to understand the working of the mind of prehistoric man, of attempting to understand how he would have made such an implement.  If we are not more aware that this is what we actually do in such cases and that we necessarily rely on our own knowledge of a human mind, this is so mainly because of the impossibility of conceiving of an observer who does not possess a human mind and interprets what he sees in terms of the working of his own mind."

There is much in the above passage to think about.  For me, the critical point is "...they are abstractions from all physical attributes of the things in question and that their definitions must run entirely in terms of mental attitudes of men toward these things".  This implies that definitions cannot always be based on qualities, but sometimes need to be based on relationships involving a human mind.  We will return to the implications of Hayek's viewpoint in future posts.

One last thing.  Few writers have had the courage to criticize any aspect of natural science.  R.G. Collingwood was one, calling "pseudo-sciences" what Hayek calls "Scientism".  I do not think Hayek was aware of Collingwood, but the above passage very closely resembles ideas Collingwood expressed.

Is the IAU Definition of "Planet" A Quality Definition?

In this post we continue to learn lessons from the International Astronomical Union's definition of "planet" in 2006 (http://www.iau.org/public_press/news/detail/iau0603/).  The question tackled here is whether the IAU's definition of "planet" is a quality definition.  After close examination, it seems it is not.

Here is the definition:

'A "planet" [1] is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

[1] The eight planets are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.' 

And here is the analysis of the definition:

(a) The definition is not actually of "planet" but of "planets in our Solar System".  This can be mined out of the text of Resolution 5A, which states: 

"RESOLUTION 5A The IAU therefore resolves that planets and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way..." 

So the IAU did not define "planet" at all, but merely "planets in our Solar System".  We will need to explore this in a further post, but it is clearly a source of confusion, and hence the definition is of poor quality (definitions are not supposed to cause confusion).

(b) The superordinate genus identified in the definition is "celestial body".  If I look up "celestial body" in Wordnet (http://wordnet.princeton.edu) I get "natural objects visible in the sky".  So, celestial bodies must include planets, stars, comets, asteroids, nebulae, galaxies, and so on.  As such, the genus seems too remote for a quality definition - it is little better than "thing".  There seems to be a strong possibility that it could be divided into genera that are superordinate to "planet", but subordinate to "celestial body".  What are they?  That is not my job - I am not an astronomer.  But I can tell you that a more proximate superordinate genus is required for this to be a quality definition.

(c) The definition contains the phrase "is in orbit around the Sun".  This clearly shows that only our Solar System" is being considered, as we saw above.  Guess what - I could tell from the term "planets in our Solar System" (the definiendum) that the planets would be orbiting the Sun.  That is part of the definition (or description) of "our Solar System".  The term "Sun" should not have been used in the definition.  It is an essential characteristic of "our Solar System", not "planet".  Another point that shows we do not have a quality definition.

(d) If the IAU chooses to define "planet in our Solar System" it is obliged to define "extrasolar planet" (the coordinate species) and "planet" (the proximate superordinate genus).  At the very least these should have been referenced in Resolution 5A.  There is no such reference in 5A.  Again, an indication of a poor quality definition.

(e) What does "(c) has cleared the neighbourhood around its orbit" actually mean?  What is "neighbourhood" in the celestial context?  It is easily understood as a general (human, non-astronomical) term, but that cannot possibly apply here.  What is it?  Suppose I make the presumption that "cleared" means "to have removed matter".  I really do not have any right to do so, but suppose I do.  Well, the Earth has not absorbed the Moon or ejected the Moon from its proximity.  So is the Earth not a planet?  This is a big failure, because definitions are supposed to make things clear.  Again, we have a poor quality definition.

In defense of the IAU, it is quite difficult to produce definitions in natural science.  There is usually no alternative to them being other than descriptive (as opposed to essential or causal).  However, the IAU could have done better.

Thus, we see that we have a poor quality definition of "planet".  Sorry, I meant to say "planet in our Solar System".

The Problems of Pluto - 2: What is a Definition Authority?

In a previous post (http://definitionsinsemantics.blogspot.com/2011/11/evolution-of-definitions-problem-of.html) the topic of the IAU's 2006 redefinition of the term "planet" was discussed (see http://www.iau.org/public_press/news/detail/iau0603/). 

There are many topics relevant to definitions surrounding this event - one of them is the problem of authority.  The International Astronomical Union (IAU) is the organization that came up with the new definition of "planet".  Does this make it an authority?  It does if we define "authority" as "a source of a definition that publishes, and administers, and supports this definition". 

However, the term "authority" carries emotional content also.  "Authority" can imply (a) a role of active enforcement; (b) an obligation of obedience upon the body politic.  These implications exist because "authority" is a term that defines many concepts, and some of them have to do with enforcement and legislation. Now, some entities that produce definitions also have enforcement roles and legislative roles, but that is not as any direct consequence of producing definitions.  

Additionally, the IAU is presumably a collection of scientists, and scientists have an almost priestly aura in contemporary Western civilization.  To challenge any scientist is presumably to challenge science.  To challenge a scientific consensus is presumably an even worse sin.  Just having scientists as an authority seems to add to the intimidating implications when we use the term "authority" when speaking of definitions.

I think the basic stance on this issue must come from the logicians' warning about appeal to authority - the fallacy of argumentum ad verecundiam.  First, let us remember that we are only dealing with definitions here, not argumentation such as deduction or induction.  The idea is presented above that an authority is a special type of source of a definition.  To be an authority, I suggest, means that you are doing more than just creating a definition.  You are publishing it so it is available to some form of wider audience.  You are administering it, so e.g. there is an orderly way to change it.  And you support it - as an authority you stand ready to be consulted on it.

None of this means the definition is of high quality.  An authority can do all of the above and create poor quality definitions.  An authority can also cause terminological havoc outside of the narrow field of definitions.  That it probably why I cannot stop thinking of Pluto as a planet.

We must be very careful, therefore, to understand what an authority is for a definition, and what to expect of an authority. Above all we should not be intimidated.  Remember, just because a source of a definition claims to be an authority, or is styled as such, does not mean they automatically produce high quality definitions.