RETURN
edited 7/2/20

Contents:

Introduction

District's failure to write a measurable written language goal was not a fatal procedural error and did not constitute a denial of FAPE -- I.P. and Centennial, DP 00-115 [1a]

As the day-to-day practices of various public services become more heavily influenced by judicial decision as well as by legislation and bureaucratization, public service professionals are increasingly forced to define explicitly what were formerly casual, seldom questioned, traditional concepts that had vague, though generally understood, meanings.

If leadership in developing critical practical distinctions does not come from within the professional ranks of educators, social workers, health maintenance professionals, non-profit managers, librarians, and the like, then the governing norms that determine practice in public service fields are conceded to imposition from without.

Concerns for accountability and equity produce pressure for specific criteria to support public service decision-making and to open it up to general scrutiny. For public service professionals to sit back and allow the courts, the legislature or other special interests to specify criteria is to give up on the traditions and knowledge base of their own professions.

But the task of developing critical practical distinctions in consonance with the best traditions and knowledge bases that inform one's field of practice is made formidable by both the pluralism and dynamism of our society. Many different interests struggle for resources; change is an inescapable factor in public service. This article -- with its accompanying exercises -- aims at developing skills pertinent to the task of formulating a justifiable base of criteria for professional decision.

The Approach

The method developed below derives from a philosophical school of the late 20^th century known as linguistic analysis. (See, for example, Austin, 1965; Ryle, 1949) It has been adapted here from the methods of its early proponents to deal with problems of consensus in a pluralistic society. This adaptation helps avoid the major pitfall of developing criteria in a pluralistic context: the politicization of criteria selection.

The basic assumption of this method -- contrary to some prominent opinions (see Stone, 1997, or Susskind & Cruikshank, 1987) -- is that decisions need not always be political: neutrality with respect to specific interest group alignments is not only possible, but generally achievable. The words dispassionate, disinterested, fair, balanced, neutral, and equitable still have practical meaning.

Many of us have had the experience of committee meetings interminably lengthened by disputes over criteria. This can be expected in any pluralistic context, because politically astute participants look to negotiate criteria they perceive to support their interests.

But, not infrequently, the result of such early machinations is a set of criteria that violates or, at least, ignores established practice. In addition, broad understandings that support public confidence in the organization are undermined by neologistic usage. Political rhetoric -- which easily infects the deliberations of uncautious practitioners --gives us many examples of these: health care reform, school reform, accountability, ownership, no-tolerance, minority, mandatory sentencing, discrimination, inclusion, and the like. The implementation following from these specially defined words seldom conforms to the expectations the terms conjure up in their normal usage.

The method found herein helps ward off such politicization in the following way:

General Notes

We begin each section below by mentioning the strategy intended to keep the process as apolitical as possible, and the possible counter-strategy we believe an astute partisan might use to bias the technique in his or her favor. Then a description of the technique is given with examples. Finally exercises are provided to strengthen the skills proposed in the section.

I. Describing versus Defining
 

a. Suppose Harry is someone we all know. It is an everyday kind of question to ask, "Could you describe Harry?" It is somehow odd to ask them, "Could you define Harry?" This contrast between what it is not unusual and what it is strange to ask points out an important difference between the activities of describing and defining.

It is easier for people to describe things narratively, than to break the descriptions down into sets of conditions that make up a formal definition. It is feels more natural to say, "A cormorant is a kind of diving bird which is often domesticated in Japan to catch fish for its master,"  than, to say,

" A cormorant is

1. a bird;

2. that dives;

3. is often domesticated in Japan; and

4. catches fish for its master."

b. Describing and defining are, in some ways, similar activities but normally differ in three dimensions: focus, criteria used, and range.

1. Focus. The focus of a description is usually, though not always, an individual person, or object. The focus of a definition is a class or set of persons, or objects. (We will use the words, class and set, generally interchangeably throughout this essay.)

2. Criteria used. The characteristics used to describe a person tend to be readily recognizable ones. Often these characteristics are unique to that person. They are often accidental, in the sense of "random, a natural accident," rather than essential characteristics. But a definition uses essential (sometimes called necessary) characteristics, that all (normal) members of the class possess. These characteristics may be hard to recognize.

3. Range. A description is often context-bound, e.g. "the man in the hat next to the door." Definitions attempt to generalize over many, if not all, specific contexts.

The chart that follows sums up the differences between describing and defining:
 

c. Consider the difference between the following answers to the question "Who is the town coroner?"

The second answer is something more of a definition. It mentions different characteristics that could apply to people in many different places. Those characteristics are, being a doctor, being elected, conducting official medical inquiries, for a town.

Next you will find an exercise in distinguishing between descriptions and definitions that also has you identify the conditions or criteria specified in a definition.

Exercise: Description or Definition. If definition, list the conditions mentioned.
 

II. a. A condition (criterion) defines a class or a set.
 
 

a. For example, if the condition (criterion) is "is taller than six feet" then it defines a class of objects, which, when properly positioned, are taller than six feet.

b. A second example, if the condition (criterion) is "is a mammal" then it defines a class of objects, which are mammals.

a. For example, the class of green hats can be understood to specify a compound criterion, "is a green hat" which could be broken down into two criteria, "is green" and "is a hat."

b. This practice will follow our normal language usage, e.g. "big, red ball" yields three criteria, "is big," "is red," "is a ball."

Exercise: Change the following descriptions into sets of criteria for the variable X
 

III. a. Measure of Membership. (MM)
 

With respect to a class, A, any object, call it X for purposes of illustration, meets one of the following conditions:

IV. a. Using the Membership Measure in a Group
 
 

If members of an analysis group differ drastically on the status of an object (or event) as paradigm, say MM=5 or 4 and MM=1 or 2,

Exercise: Individually, then in a group evaluate each case as a possible paradigm of punishment.:

V. a. Paradigms.

NOTE: It is advisable to check out by survey among group members whether the "logical" conclusions we draw about paradigms are in fact what we take them to be.

V. c. Using Case Narrative to Identify Paradigms.

Narratives can be seen as expanded descriptions. They are sets of conditions arranged into a natural idiom. Constructing narratives to illustrate a concept is a common way to begin an analysis. The techniques we have discussed so far and those that follow below apply to them as well. A set of well-constructed narratives helps not only to sort out paradigms but can be used to investigate the relationship among concepts of interest. Consider the next exercise.

Rank each case of Jack's behavior toward Sam for each of the concepts indicated, violence, imposition, and/or wrongdoing.
Is any of the cases a paradigm of any of the concepts?

VI. Restricting Negative Paradigms.
 

a. Since anything that is definitely not-A is a negative paradigm (NP) of A, arbitrary NP's do not shed much light on the nature of A. For example, if A = President of the United States, then the moon is an NP of A. So, also, is the last person to talk to Julius Caesar. These and similar NP's do not help us understand A very much.

b. If, however, we restrict the NP's to within one of the conditions defining A, they help us to understand contrasts with paradigms of A. For example, A = President of the United States, then "being a U. S. Federal officer" is a condition that helps define A. So if we restrict our NP's to U.S. Federal Officers, we can more easily see how U.S. Federal officers in general are different from "President of the United States." Or, we could choose another condition, "being an elected official" to help specify our NP's .

Exercise: Give the paradigms indicated for each class.

Note: the inability of your group to agree upon a paradigm may be an important indicator --see 6 below -- of the adage, De gustibus non disputandum, i.e. "There is nothing to be disputed about taste."
 

VII. Definitions

A definition is constructed from a set of one or more conditions used to logically specify or isolate a desired group or individual. To reiterate somewhat, definitions can be more or less context-bound or context free.
 

a. Context-bound definitions depend upon prior restrictions on our attention to a particular circumstance or situation which may give special meaning to terms and usage. They are very much like descriptions when tightly context-bound. An example of this are the definitions in Special Education for "mentally retarded" and "learning disabled" which, when applied according to the criteria specified in many state statutes, are mutually exclusive. That is, no student who is classified mentally retarded can be classified learning disabled, and vice versa. But outside of public education, the language of even highly educated English speakers does not follow the practitioners definitions. Generally, non-educators would normally expect the mentally retarded to be learning disabled, whatever that means.

b. Context-free definitions do not depend upon prior restrictions on our attention to a particular circumstance or situation Such definitions attempt to be universal.

VIII. A Metaphor for Definition: a net.

Think of a definition as a net. If our net catches all of those particular things we are concerned to identify and leaves behind those things we want to exclude, it constitutes a definition.

We will develop definitions by suggesting criteria for the object or objects we wish to isolate, examining whether these criteria "catch" what we want, and, if not, adding or modifying the criteria to yield a better "catch."

Definitions should catch paradigms of the concept we are concerned to define. We will see below how to deal with real-world variants of paradigms that definitions might miss.

IX. Counterexamples
 

a. For a proposed definition of some class, B, a positive counterexample is an object that meets the criteria of the definition, (MM=4 or MM=5) but is not what we would recognize to be a B, (MM=1 or MM=2). In considering counterexamples, our normal traditions of identification, our "intuitions," even, take precedence over the proposed definition.

b. For a proposed definition of some class, B, a negative counterexample is an object that does not meet the criteria of the definition, (MM=1 or MM=2) by is what we would recognize to be a B, (MM=4 or MM=5).

 

See, also, Using Counterexamples

X. Differences between paradigms and counterexamples.

 
a. Paradigms relate to classes. Their MM=5 (positive paradigm) or MM=1, negative paradigm. For example, of the class we are concerned with is "kind treatment" then:

1. helping someone is a positive paradigm; whereas,

2. torturing someone is a negative paradigm.

b. Counterexamples relate to a proposed definition. Suppose, for example, we wanted to develop a definition for theft. Someone might propose a definition that it is theft when

Sam takes something, say, a wallet, that belongs to Harry.

(This can be generalized as follows: It is theft when a person takes a wallet that belongs to another person.)

c. We can break B down into two conditions:

1. Sam takes a wallet

2. The wallet belongs to Harry.

d. A positive paradigm for condition 1 would be if Sam sees a wallet on desk, picks it up, puts it into his pocket and leaves the scene. A positive paradigm for condition 2 would be if the wallet, containing many of Harry's important documents, money and credit cards, had been purchased and was normally carried by Harry.

e. Counterexamples show what is wrong with the proposed definition. Suppose Harry had lost his wallet and had asked Sam to pick it up, should Sam find it anywhere. This would not be theft, but it meets the conditions of the proposed definition. It is a positive counterexample. Another positive counterexample would be where Harry had left his wallet on the desk and told Sam to go get it for him

f. Suppose Sam doesn't take the wallet, but covers it with a cloth so Harry won't notice it should he come looking for it. Later, Sam's accomplice, Mary, comes by and removes Harry's wallet. This is theft and Sam is involved in it, yet the proposed definition doesn't "catch it."

Do the exercise below using counterexamples to test proposed definitions.

Exercise: For each proposed definition give counterexamples as indicated.
 

XI. Developing a Definition

As a social institutions change, so do definitions. Definitions are only as stable as the institutions that maintain them. If we approach our task of defining concepts knowing that our efforts will be normally incomplete, or, at best, temporary -- when considered over years -- we can devise practical definitions that meet our needs in the short run.

Definitions or developed by comparing positive paradigms and looking for common characteristics. These are they treated as necessary conditions and the proposed definition is examined for the counterexamples, positive and negative, that it generates.

Negative paradigms may be contrasted with positive paradigms to see what differences exist between them. These may also yield necessary conditions and the proposed definition is examined for the counterexamples, positive and negative, that it generates.

The existence of counterexamples indicates that the present formulation of the definition has to be modified. (See Wilson, 1999.)

XII. Definiens and Definiendum
 

a. It is necessary to introduce two terms at this point:

X is the definiendum; and, A, B and C together constitute the definiens.

b. Let's recast our notions of paradigm and counterexample using these two traditional technical terms.

A paradigm is an example, MM=5, of either a definiendum, or a definiens. If X is a paradigm of a definiendum, then it is a paradigm of the X we are looking to define. On the other hand, if something is a paradigm of A, B and C jointly, then it is a paradigm of the definiens. For good definitions, the set of definiendum paradigms will be identical with the set of definiens paradigms. Example, the set of all paradigm circles will be identical with the set of all paradigms meeting the following conditions:
 

A positive counter-example is a paradigm of the definiens that is not a paradigm of the definiendum. For example, a once-popular definition of learning used to be, "Learning is a change in behavior." Now, death is certainly a change in behavior, but it is not learning.

A negative counter-example is a paradigm of the definiendum that is not a paradigm of the definiens. Learning a number by committing it to memory is certainly learning, but no change of behavior need ever occur. One can have learned a number, then forgotten it, without ever having put that knowledge to use in a demonstrable way.

XIII. Necessary and sufficient conditions constitute one kind of definition
 

a. A definition consists of a definiendum paired with a definiens.

b. The model of definition as a set of necessary and sufficient conditions constructs a definiens as a list of conditions, each individually necessary and together sufficient to isolate all instances of the definiendum from everything else the universe. This model tends to work best for abstract entities, although we can sometimes use them for real-world items.

c. An example of such a definition is this:

A mammal is anything that
 

1. has hair;

2. suckles its young

3. is warm-blooded.

d. If something is missing one of the conditions of the definiens, then it is not a mammal. If we know that something meets all the conditions of the definiens, then we know it is a mammal.

Different philosophers have recognized a wide variety of definitions. We get, for example, from Israel Scheffler in The Language of Education (1968):

XV. Concept Families

For most real-world applications, a definiendum admits of some alternatives in its definiens. Words have different senses, that is, several distinct sets of paradigms each of which may share little in common. (See Wittgenstein, 1967, throughout) In education, for example, "teach" sometimes is defined in terms of the intentions of the teacher and the circumstances of his or her performance, as when we distinguish between the teacher's presenting a lesson (teaching) as contrasted with taking roll, or collecting book slips, or handing out materials.

By way of contrast, sometimes "teach" means no more than "being in the classroom with students" as when we say that a teacher is teaching, as opposed to being at lunch, supervising an assembly, or conferring with a parent.

We could mark this distinction by calling the former, "teaching acts" and the latter, "teacher activities," if we found it useful to do so.

XVI. Mitigators

A mitigating condition, or mitigators, connects definitions to real objects in the world. Definitions capture paradigms. Not everything is a paradigm of some kind or another. A chair that has lost a leg so that it cannot function anymore is still a chair, a broken chair. Broken is a mitigator in this case so that we can still acknowledge the object to be a chair, even if it fails to meet several of the conditions that a paradigms example does. A chair made to look like a table will not be a paradigm chair. The mitigating phrase here is made to look like a table and helps explain both why the chair looks so odd, and why we can still sit on it.

Mitigators explain and excuse, even permit, variance. All chairs are either chair-paradigms of chair-variants. Groups of variants are often recognized as types. Types may have their own paradigms and variants.

Phrases and words that indicate changes, variations through time, of all kinds, breakage, corruption, enhancement, development, can be used a mitigators: e.g. broken, repainted, worn out, refurbished, torn, expanded, twisted, replicated, etc. Also, human intentions may be called upon to define things, "This is a chair because its maker intended people to sit on it." However, we may reject such intentions as definitive if, for example, the object is, say, made of barbed wire and shaped like a kite. In any case, we would not be dealing with a paradigm here.

XVII. Defeasors

A defeating condition, or defeasor, calls off all bets. Defeasors are used wherever, despite present appearance, or even upon much later reconsideration, historical or other conditions are seen relevant to reject the definiendum. Addended to the conditions of the definiens, it causes us to reject an item as a paradigm, or even a mitigated paradigm. The conditions of definition are said to be "defeated." Definitions for which recognized defeasors exist are called "defeasible." (See Hart, 1965)

Suppose we have a painting we believe to be an original Rembrandt, because skilled experts in detecting forgery have declared it to be authentic. A year later we find an indistinguishable replica. Which is the original and which is the forgery?

Now, an "indistinguishable replica" of a particular real Rembrandt is not a Rembrandt -- suppose it not to be a copy made by Rembrandt himself -- even though it is the case that those experts cannot tell which is which, if they look at each copy by itself. They would only know, when confronted with both paintings simultaneously, that one had to be a copy. The phrase, "indistinguishable replica," is a defeasor.

Defeasors are often introduced to ward off consequences subsequent to a particular identification, e.g. murder, theft, etc. The following list consists of words or phrases that when added to descriptions of human action, defeat their strongest criminal characterization: unintentional, inadvertant, accidental, unthinking, unconscious, unwilling, under compulsion.

There are defeasors for positive descriptions also. Suppose you have witnessed what appears to have been a particularly well-executed vault on a gymnastic horse. Terms like lucky, serendipitous, or fortuitous deprive the vaulter of an attribution of skill.

Not of sound mind, or coerced are defeasors that undermine the validity of a contract. Cheated and crammed attack the validity of a test result.

XVIII. How to Construct a Definition: a procedure
 
 

First Step: agree on a set of paradigms for the definiendum. Use examples you think would be good ones to teach to a beginner being introduced to the concept. Look for as wide a variation among paradigms as possible.

Second Step: list the characteristics that are shared by each paradigm example. This is your tentative definiens. Make a list as short as seems reasonable; it can be lengthened if necessary after it is tested. Put definiendum and definiens in the following form:

Fourth Step: make sure, if you think you have counterexamples, you haven't just chosen mitigated or defeated variants. Counterexamples should be paradigms, if they are positive, of the definiens; or, if they are negative, of the definiendum.

Fifth Step: adjust your prospective definiens, if necessary.

Congratulations. You have done a lot of work.

Exercise: For each proposed definition give a counterexample and a condition which expands the original definition to include (or exclude) it.
 

XIX. Concluding Comments

The technique given above helps to articulate meanings embedded in the linguistic usage of communities indifferent to any particular controversy. The question,"What does that mean?" need not result in a struggle among partisans to steer decisions with criteria contrived to suit their particular interests. By carefully observing the distinctions practitioners actually make and articulating the criteria of judgment derived from the paradigms they employ, the spectre of inexorable politicization that threatens our public discourse can be exorcised.

Footnotes

1a. Dispute name: I.P. and Centennial, DP 00-115 Hearing Officer: W. Mize. Date of Order: 12/13/00. Document no long available (2020) at http://www.ode.state.or.us/services/disputeresolution/dueprocess/searchable/iepmeasurgoals.aspx

See, also, Edward G. Rozycki, "Measurability and Educational Concerns" available at http://www.newfoundations.com/EGR/Measurability.html

Bibliography