Pluralism and Criteria:
Minimizing Politicization in Public Service Decision-Making
2000 Edward G. Rozycki

edited 7/2/20

See, also, Model Cases for Analysis



The approach

General notes

i. Describing versus defining: focus, criteria, range

ii a. A condition (criterion) defines a class (set)

ii. b. Conversely, any class (set) can be understood to specify a criterion.

iii.a. Measure of membership (MM)


iii.b. The MM scale reiterated

iv.a. Using the MM with a group

iv.b. Expanding a description to achieve consensus on paradigms

v.a. Paradigms 

v.b. Possible Restrictions on the analysis of paradigms

v. c. Using Case Narrative to Identify Paradigms.

vi. Restricting negative paradigms

vii. Definitions

viii. A metaphor for definition: a net

ix. Counterexamples

x. Differences between paradigms and counterexamples

xi. Developing a definition

xii. Definiens and definiendum. 

xiii. Necessary and sufficient conditions constitute one kind of defintion

xiv. Varieties of definition

xv. Concept families

xvi. Mitigators

xvii. Defeasors

xviii. How to Construct a definition: a procedure

xix. Concluding comments



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 20th 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:

1. It begins by having participants specify "paradigms", i.e. commonly recognized "clear" examples merely acknowledged as such, without requiring justification or elaboration from the participant, and, particularly, without examining or debating each individual's criteria of choice. Nothing controversial for the group engaged in criteria specification will be designated a paradigm.

2. Criteria will be more or less "mechanically" extracted from the paradigms afterwards.

3. Tentative sets of criteria -- proposed "definitions" -- will be tested for accuracy using particular paradigms, called "positive counterexamples" or "negative counterexamples."

Disagreement, if it comes up, can be dealt with early on, during the selection of paradigms. By the time criteria are to be articulated, there is little political maneuvering to be done. What this method preserves are the deeply embedded theoretical and normative traditions which are highly vulnerable to being undermined by special interests when exigencies prompt the articulation of criteria. Yet, it is these traditions of meaning that promote acceptance among a broad public and support the discourse necessary to making fair decisions.

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

Strategy: Using the commonplace activity of describing, to train participants into a more systematic process of definition. The major concern here is pedagogical, bringing newcomers in on a basis that they will find comfortable, i.e. "if you can describe, you can learn to define." 

Counterstrategy: Reject the distinction between describing and defining. 

Comment: This would not be a likely move, since there is no clear political threat from the distinction, which is quite commonsensical (see Searle, 1969), and every reason to avoid provoking the suspicion that one is trying to bias the method so early on. 


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.

NOTE: Description tends to approach being definition when one gives a description of a "typical example" of some class of things, rather than focussing on the characteristics of a particular individual example.

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

DESCRIBE A unique individual Easily recognizable,

Often accidental

Specific, context-bound
DEFINE (A "typical" individual)

A class (or set)

(Normally) Essential

Sometimes difficult to recognize

Strives for universality, free from specific context


c. Consider the difference between the following answers to the question "Who is the town coroner?"
1. He's the elderly man who lives in the white house on Logan Street.

2. He or she is the doctor who is elected to conduct official medical inquiries for the town.

The first answer is a description. It picks out a single individual (we would expect) but does it in a way that is highly bound to the context of a particular situation.

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.

Item for Consideration
Description Only

(Yes, No)

If Definition, List Criteria Mentioned
1. The dog by the gate with the short ears is a terrier.    
2. The only mammal that truly flies is the bat, a nocturnal animal.    
3. The only person in my family licensed to practice medicine is my brother.    
4. Any physically vigorous action that risks injury is violent.    
5. The President of the United States is the man seated third from the left.    
6. Teaching about manners is what the man in the third row is doing with his children.    
7. The President of the United States is the highest ranked elected Federal executive.    
8. Kapelski Hall is the first building directly south of Wolfgram Library.    
9. Education is achieved when a person is knowledgeable and self-motivated.    
10. Discipline means following the rules with no quibbling.    


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

Strategy: Primarily pedagogical: provide linguistic devices with translate either way from condition to class, or vice versa.

Counterstrategy: no likely one

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.

II. b. Conversely, any class or set can be understood to specify a criterion, or criteria.
Strategy: Primarily pedagogical: provide linguistic devices with translate either way from set to criteria, or vice versa.

Counterstrategy: no likely one.

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

Set of Criteria: X is (has) ...
1. small, red house with a chimney X is a house that is small, is red, and has a chimney


X is a small thing that is red, has a chimney and is a house.

2. red sand found in Floridian swamps  
3. flexible glass pipe carrying conducting electricity  
4. large, horned mammal with cloven hoofs  
5. dancer's leap landing on the large toe of one foot  

III. a. Measure of Membership. (MM)

Strategy: Objectify the decision procedure dealing with personal decisions about the acceptability of an example. Permit simplicity in definition for later items. 

Counterstrategy: no likely one. 

Comment: There is no numerical hocus-pocus intended here. The best we will get is a ranking. No interval scale will be assumed. The most we will be concerned with is a mode. 

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

a. X is definitely not an A, i.e. it definitely does not meet the criterion, "is an A." Let us identify this situation with the classification, 1, a measure of membership (MM).

b. X is probably not an A, i.e. it probably does not meet the criterion, "is an A." Let us identify this situation with the measure of membership, (MM), 2.

c. The situation is unclear or confused. X's MM is neither 1 nor 2 yet it is neither probably nor definitely an A. In this situation, X's MM is 3.

d. X is probably an A, i.e. it probably meets the criterion, "is an A." Let us identify this situation with the measure of membership, (MM), 4.

e. X is definitely an A, i.e. it definitely meets the criterion, "is an A." Let us identify this situation with the measure of membership, (MM), 5.

III. b. The MM Scale Reiterated

1 = X is definitely not an A.

2 = X is probably not an A.

3 = It is unclear whether X is an A.

4 = X is probably an A.

5 = X is definitely an A.

How this scale will be used with a group of people is discussed next.

IV. a. Using the Membership Measure in a Group

Strategy: Reduce negotiation by requiring unanimity, or close unanimity, to proceed with process.

Counterstrategy: Reject all items suggested as paradigms as unacceptable.

Comment: See section VI b.

Finding paradigms for everyday objects or situations is generally not problematic (see Wilson, 1999). It is only when terms become controversial, derive from a technical language of a community with restricted usage, or from a discipline which has competing paradigms, that one finds dissensus among group members as to what might be a paradigm case of a class (concept). When disagreement occurs, do the following:

a. When working in a group, accept for use, only positive paradigms where the group mode is MM=5 with nothing below MM=4.

b. When working in a group, accept for use, only negative paradigms where the group mode is MM=1 with nothing above MM=2

Inability to find consensus on paradigms may indicate several things;

1. that the terms used are highly ambiguous (not uncommon); or,

2. that the theoretical disciplines of your field recognize different paradigms (not uncommon in the social sciences -- see Becher, 1989); or

3. that the linguistic communities represented in your group are radically different (rare).

IV. b. Expanding a Description to Achieve Consensus on Paradigms

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,

1. ask the dissenters why they reject them -- this will tend to block what may be mere political maneuvering. If their reasons are plausible, take the next step.

2. Have someone on the low side of the MM scale add to the description of the item being considered so that he or she perceives it to move toward the other side of the scale. (Every addition to the description should be examined later as a necessary condition for definition.)

If this procedure becomes too tedious, look for other items all can agree on.

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

CASE EXAMPLES: Has Arnold been punished?
1. 5 year-old Arnold is bitten by a squirrel after pinching his sister and running out into the backyard.  
2. Mrs. Smith slaps her 5-year old son, Arnold, 3 times on the buttocks vigorously because he pinched his little sister after having been warned not to do it.  
3. Mrs. Smith slaps her 5-year old son, Arnold, 70 times on the buttocks vigorously because he pinched his little sister after having been warned not to do it.  
4. Mrs. Smith slaps her 5-year old son, Arnold, three times on the buttocks vigorously because she enjoys doing it.  
5. Mrs. Smith gives her 5-year old son, Arnold, a cookie after he pinches his little sister.  

V. a. Paradigms.

a. For a given X and A, X is a positive paradigm of A if X's MM = 5.

b. For a given X and A, X is a negative paradigm of A if X's MM = 1

Because anything that is definitely not-A is a negative paradigm, negative paradigms are not very useful unless one restricts them in ways we will discuss next.

V. b. Possible Restrictions on the Analysis of Paradigms
Strategy: Paradigms don't work purely "logically." Forestall domination by group members who are skilled in formal logic. 

Counterstrategy: None to think of. 

Suppose X is a paradigm of a big, white house. According to what we learned above, the criterion, "big, white house" can be analyzed into "big" and "white" and "house." However, we should not jump to the conclusion that, simultaneously:

1. X is a paradigm of something big,

2. X is a paradigm of something white,

3. X is a paradigm of a house

Big things and white things vary much more extremely from one another than do houses. The terms, big, white and house, delimit each other, so to speak, focussing our attention in ways when they are combined that they do not when each term is considered in isolation. For example, consider what a big mouse might look like compared to a big elephant. Or a white stone compared to a white blouse. Typical houses, the kinds we might normally pick for paradigms, would likely look substantially different from the White House in Washington, D. C., clearly a paradigm of a big, white house. A set of paradigms for either "big" or "white" or "house" may not contain the same items as a set of paradigms for "big, white house."

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.

A Case Study Approach: Violence, Imposition, Wrongdoing

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?



1. Sparring at karate, Jack blocks Sam's kick to his stomach and delivers a hard punch to the side of Sam's headgear.      
2. Sam takes little Billy's Walkman from him and runs away. Jack wrestles Sam to the ground, permitting Billy to recover his radio.      
3. "Please watch my seat while I get a soda," says Jack to Sam seated nearby.      
4. Jack, grabbing Sam by the throat, tells him to hand over his wallet.      
5. Jack shoots Sam dead for not paying attention to him.      
6. For the fourth month in a row, Jack fails to pay his share of the rent, forcing Sam, his roomate, to make up the difference.      
7. Jack, having promised to pay for Sam's Walkman should he lose it, loses the radio and refuses to pay.      
8. Jack hands Sam his book.      
9. Jack, while boxing with Sam, knees him in the groin.      
10. Jack "drops in " on Sam just as Sam is preparing dinner.      


VI. Restricting Negative Paradigms.

Strategy: Proceed with a technical adjustment that affects no paradigm choices.

Counterstrategy: No clear counterstrategy.

Comment: If sustained objection is offered to this technique, it can be dispensed with.

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."

Positive Paradigm
Restricted Negative Paradigm
1. A U. S. National Monument    
2. A professional football player    
3. A U. S. citizen    
4. An act of rudeness    
5. A piece of great literature    
6. A good brand of coffee    
7. An economically important city    
8. A teaching act.    
9. An influential woman now living    
10. A discipline problem    
11. An interesting book    
12. A dangerous highway    
13. A bad meal    
14. A famous university    
15. A respected U. S. President    

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).


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.

Proposed Definition
Positive Counterexample
Negative Counterexample
1. A dog is a mammal friendly to human beings.    
2. Theft is taking something without its owner's permission.    
3. Learning is a change of behavior.    
4. Violence is anything that causes harm to the human body.    
5. Great Literature is anything found in public libraries.    
6. Teaching is causing someone to learn something.    
7. Justice means everyone treated equally.    
8. Efficiency means keeping costs low.    
9. Education is the ability to survive in an urban environment.    
10. Discipline means following the rules.    
11. Intelligence means getting it right.    
12. Respect is basically fear.    
13. Fame is a matter of how many other people know your name.    
14. Punishment is cruelty.    
15. Right is whatever the majority approves of.    

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:
1, the definiendum is the term we are trying to define

2. the definiens are those items which we use to do the defining

If we are dealing with definitions constructed using a minimal set of necessary conditions, call them A, B and C, jointly sufficient to identify what we are dealing with, call it X, then the form of our definition is:

"Something is X if it meets conditions A, B and C."

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:

1. each paradigm will be a set of points;

2. on a plane; and

3. each point in the set will be equal to any other point in the set in distance from a center point.,

(It is no coincidence that a mathematical example is used here. All simple examples of definitions tend to be of abstract entities. Real-world objects require some adjustments to the notions of definition, as we will see below.)

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


Strategy: Proceeding with development. 

Counterstrategy: Protest narrow characterization of the notion of definition. 

Comment: Concede same, offer broader examples later. 

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.

XIV. Varieties of Definition

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

Descriptive definition - purporting to capture the common usage of the term

Stipulative definition - specifying a particular formulation as the meaning for a particular purpose with no concern for common usage.

Programmatic definition - a combination of the descriptive and stipulative for argumentative purposes

From Dagobert D. Runes' Dictionary of Philosophy (1960) we get

A. Syntactical (nominal) Definitions- primarily in logic, math

abstract: via relationships, e.g. integers from cardinals

recursive: generated via reflexive application of relationships, e.g. successors to natural numbers

compositional: via multiple recursions, e.g. well-formed formulas

semantic: definiendum = definiens.
B. Real Definitions - attempt to capture "essence" of definiendum.

From Raziel Abelson (1967) we get

A. Essentialist Definitional Types - (Plato, Aristotle, Kant) distinguish between description and definition; seek "essential" characteristics., specifying genus and differentia.

B. Prescriptive Definitional Types- (Hobbes, Russell) Formalisms, e.g. soup = x+water - detergent B, or zx = mRb.

C. Linguistic Definitional Types - (Mill, Moore, early ideal language analysts) - identifying "meaning" of term, e.g. phrase substitutions for terms or operational definitions.

D. Pragmatic Definitional Types - look to context and usage.

Exercise: Consider the following statements. Can they be considered definitions, or not? If so, what kind?

1. Paper is what the text you are now reading is printed on. 

2. A human being is a featherless biped. 

3. A triangle is a three sided polygon. 

4. Property is Theft. 

5. sin2x + cos2x = 1 

6. knowledge = that which can be established by experimental research. 

7. Albert Schweizer is a fascist pig. 

8. Learning is a change of behavior. 

9. John Wilkes Booth is the man who shot Lincoln. 

10. A plucked chicken is a featherless biped. 


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

Strategy: Proceeding with development. 

Counterstrategy: None clear. 

Comment: It is too late to protest at this point. This section is little more than a reiteration of what went before. 

Go through the following steps in order, unless directed otherwise.

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:

A (definiendum) is anything that
(definiens condition 1) and

(definiens condition 2) and ...

Third Step: try to find counterexamples of both kinds.

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.

a. If you can find no counterexamples, your definiens works. Go to the sixth step below.

b. If you find a positive counterexample, your definiens is not exclusive enough. Add characteristics that are shared by the original paradigm set, but which your counterexample does not share. Then go back to the third step given above.

c. If you find negative counterexamples, your definiens is too exclusive. Add the negative to your paradigm set and go back to the second step given above.

Sixth Step: You are finished. (However, even though your definition works, it may be useful to identify mitigators, variants and defeasors for the definiendum.)

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.

Proposed Definition
Additional Condition
1.A political act is any human action that affects other people.    
2. A felony is what the law defines it to be.    
3. A battered spouse is one who has been struck by his or her marital partner.    
4. Perversion is any sexual act involving a non-human living creature.    
5. Insanity is expressed in abnormal behavior.    
6. A person is impoverished if they earn less than $10,000 a year.    
7. Unfairness means unequal treatment.    
8. Obscenity is the depiction of sexual acts..    
9. Equal opportunity means access to publically funded schools..    
10. Culture is the set of values espoused by a group.    
11. Talent is the ability to learn without practice.    
12. Fear is the emotion that motivates flight..    
13. Society means the ruling class of a country.    
14. Punishment is whatever inhibits undesirable behavior.    
15. Beauty is whatever causes sexual desire in a human.    


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.


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

See, also, Edward G. Rozycki, "Measurability and Educational Concerns" available at


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