7/29/2019 AERJ Operational Definitions http://slidepdf.com/reader/full/aerj-operational-definitions 1/20 American Educational Research Association Operational Definitions Author(s): Robert H. Ennis Source: American Educational Research Journal, Vol. 1, No. 3 (May, 1964), pp. 183-201 Published by: American Educational Research Association Stable URL: http://www.jstor.org/stable/1162219 Accessed: 02/06/2009 19:48 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aera . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. American Educational Research Associationis collaborating with JSTOR to digitize, preserve and extend access to American Educational Research Journal. http://www.jstor.org
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Operational DefinitionsAuthor(s): Robert H. EnnisSource: American Educational Research Journal, Vol. 1, No. 3 (May, 1964), pp. 183-201Published by: American Educational Research AssociationStable URL: http://www.jstor.org/stable/1162219
Accessed: 02/06/2009 19:48
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
on theinstrumentsand procedures used, and we are admonished to define our terms in a
manner that takes account of these instruments and procedures (oftenthis admonition specifies that the definition should be operational); yetwe want to express our conclusions in terms that are not limited to the
particular instruments and procedures. That sets my problem: Howcan we give operational definitions without unduly restricting the mean-
ing of the terms in which we state our conclusions?
In this paper I shall examine various forms that operational defi-
nitions might take and shall develop and defend a set of guides formaking these definitions. These guides will enable us to connect ourabstract terms to our instruments and procedures without completelylimiting the meaning of the terms to these instruments and procedures.
THE SPIRIT OF OPERATIONISM
An early expression of what has come to be called "operationism"is found in P. W. Bridgman's The Logic of Modern Physics: "The con-
cept of length involves as much as and nothing more than the set of
operations by which length is determined. In general, we mean by anyconcept nothing more than a set of operations; the concept is synony-mouswith the correspondinget of operations"(Bridgman,1927;p. 5).Although Bridgman, who is regarded as the father of operationism, goestoo far in this statement, the focus on instruments and procedures, whichis the essence of operationism, comes through clearly. This focus may beviewed as one of the empiricist and pragmatic trends of recent years,as A. C. Benjamin has shown in his interesting summary and appraisalof
Bridgman'sideas and their
development under criticism (Benjamin,1955).
* The preparationof this paper was supported through the Cooperative ResearchProgram of the Office of Education, United States Department of Health, Educa-tion, and Welfare. An earlier version was presented to the Philosophy of EducationSociety in San Francisco on April 8, 1963. I have profited from the criticisms ofProfessorsH. Broudy, H. Burns, J. Canfield,D. B. Gowin, J. Millman, F. Neff, andN. Champlin,and a number of my studentsat CornellUniversity.
As a thesis, the spirit of operationism can be loosely put as follows:
There s an importantrelationshipbetweenthe meaningof a termand the
instrumentsand procedures hat one would use to see whetherthe termappliesto a particular ituationand, if so, how.
FORMS IN WHICH THIS SPIRIT HAS BEEN EXPRESSED
In the literature on operationism one finds four basic approaches to
operational definitions: 1) giving examples; 2) giving a set of operationsas the meaning of a concept; 3) equating a phrase or sentence containingthe term in question with a phrase or sentence about a combination of
operations and observations; and 4) providing implication relationshipsamong operations, observations, and the concept in question. The pro-
posed guides fit under the fourth approach, the description of which has
been vague because of the several variations possible.Since the defense of these guides rests heavily on showing the diffi-
culties of the first three approaches, difficulties that are avoided if one
follows the guides, we must look carefully at all four approaches.
1. GivingExamples
Although Bridgman had something more rigorous in mind, the use of
examples of abstract concepts sometimes indicates the instruments and
procedures involved when using the concepts and, at an unsophisticated
level, does provide an empirical interpretation. G. A. Lundberg, the
sociologist, indicates endorsement of the example approach in the followingstatement: "The simplest form of an operational definition of a wordis to point to its referent while enunciating the word. Thus we define theword 'cat' to a child by pointing to a certain kind of animal or a succession
of animals denoted by the word in our language" (Lundberg, 1942a; p.730).
Examples are very useful in clarifying terms because they connectthem to the concrete world-concreteness is one of the virtues of opera-tional definitions. But in giving an example, one does not necessarilyspecify a manipulation by an investigator, and thus exemplification missessome of the spirit of operationism. The "cat" example above does not
specify a manipulation by an investigator; instead it specifies particularcats.
Nevertheless, it would not be a serious error to treat examples as
operational definitions-provided that we have distinct names for whatwould then be two different kinds of operational definitions. Obvious,though rather wordy, names are "example-type operational definitions"and "manipulative operational definitions." For verbal economy I preferto mark the distinction with the terms "example" and "operational defi-
nition," both of which have established usages. Accordingly, exampleswould not be operational definitions.
2. Giving a Set of Operations as the Meaning of a Concept
(Form: Concept = Operations)
This approach is suggested by a strict interpretation of Bridgman'sstatement quoted earlier. According to this approach, length means a set
of operations, such as putting down a ruler end over end and (presumably)
counting the number of times this is done. Length means what you do; it is
not a property of the thing you do it to. It does not mean what you find
out; it means what you do when finding out.
If we apply this approach strictly to a concept often used in social-
science research, IQ might mean administering and (presumably) scor-
ing the California Test of Mental Maturity* (henceforth referred to asCTMM). An IQ would not then be a quality of a child; the child's IQwould mean what you had done to him.
Another feature of this approach is that it implies as many concepts of
length (IQ, etc.) as there are ways of measuring it. According to Bridg-
man, the concept length in length of a city lot is different from the concept
length in length of a large piece of land if measuring sticks alone are used
for determining the first and measuring sticks plus triangulation for the
second, because the sets of operations are different (Bridgman, 1927; p.14). Similarly, there would be as many concepts of IQ as there are tests
for IQ and ways of administering them. If meaning is identical with
a set of operations, different operations imply different meanings. Bridg-man says, "If we have more than one set of operations, we have more
than one concept, and strictly there should be a separate name to cor-
respond to each different set of operations" (Bridgman, 1927; p. 10).
Thus, there are these two distinguishing features of this, the second,
approach to operationism: (a) the meaning of a concept is limited to the
operations, and (b) different operations imply different concepts. I shallcriticize each feature.
(a) To treat the meaning of a concept (or term) as limited to set of
operations seems odd, to say the least. When I say that the length of a
bench is five feet, I intend to be talking about the bench-not about what
I did. When I say that Johnny has a low IQ, I intend to be talking about
Johnny-not about what I did. If one interprets Bridgman's originalformula strictly, there seems no way to include the observations that one
makes, observations that reveal the qualities measured. One cannot talk
about the things measured; one can talk only about what the experimenterdoes-not about what he perceives.
It may be held that this reading of Bridgman's statements is unfair-that he did not mean them as I have presented them. Perhaps so. I do notsee how anyone could really mean them that way although some soci-
"* o simplify the presentation,I have not given the form, edition, or level of thetests discussed.
ologists and psychologists may appear to have so taken them.* An ex-
amination of The Logic of Modern Physics and the works of these social
scientists reveals that it is hard to be sure just what they do mean. How-ever, my purpose here is not to criticize them but to clarify the ad-
vantages and disadvantages of various expressions of the operationist
spirit. Strictly interpreted, this, the second, approach to operationism
neglects the results one gets after doing the operations.
(b) There is no doubt that people (including Bridgman in The Logic ofModern Physics and most social scientists that I have read on the sub-
ject) have taken seriously the second feature of the second approachto operationism (that different operations imply different concepts), and
there has been considerable dispute on this point. I shall not go into it
thoroughly here because to do so would require systematic treatment of
the nature and content of scientific theories, about which there is a vast
literature. I shall only comment on the serious difficulties of this view.
These comments are carefully elaborated, however, because they con-
tribute substantially to refuting the third (and most popular) approachto operationism.
The first point to clarify is how to tell if two operations are actuallydifferent. Is
myadministration of the CTMM at 9:00 a.m. on
Monday,April 6, 1964, in Fall Creek School a different operation from my admin-
istration of the CTMM at 10:00 a.m. on Monday, April 6, 1964, in Belle
Sherman School? The only differences are the time and place of admin-
istration. To my knowledge, no satisfactory criterion, operational or
otherwise, has been provided by operationists of the concept different
operation. This is a significant weakness of the thesis that different opera-tions require different concepts. We do not know how different, or in what
respects different, the operations have to be to require different concepts.
Let us, however, assume that different times and places do not re-quire a judgment of different operations. But presumably the use of
measuring sticks and that of measuring sticks plus triangulation would
be different operations, as would the use of the CTMM and that of the
Lorge-Thorndike Intelligence Tests. Similarly, using the mercury ther-
mometer, the alcohol thermometer, and the resistance thermometer would
be three different operations.But why should there be two concepts of length, two concepts of IQ,
and three concepts of temperature to correspond to the various opera-
tions mentioned in the previous paragraph? Why not one concept of
length and two ways of measuring it? One concept of IQ and two waysof estimating it? One concept of temperature and three ways of deter-
mining it?
Let us consider the concept temperature. (Analogous things could be
said about length, but these things would be considerably more difficult.)
"*or examples, see Lundberg (1942b, p. 89), Stevens (1951, p. 28), and Marx(1951,p. 11).
What would be the consequences of having three concepts of temperature,
say M-temperature for the mercury thermometer, A-temperature for the
alcohol thermometer, and R-temperature for the resistance thermometer?Since there are many more ways of measuring temperature, there would,of course, have to be many more concepts.
One difficulty is that people would misunderstand someone who heldthis view since people think of temperature as one quality, which ismeasured in various ways. But this is not an insuperable objection. One
might stipulate three senses for the word "temperature" that represent
qualities highly correlated with one another and hold that these sensesshould be distinguished for scientists and sloppily merged for laymen.
This is a plausible answer; scientists are not bound by ordinary usage intheir research.
A second difficulty, however, is that physics itself would become im-
mensely more complicated. The law of thermal expansion would becomethree laws, one for each concept. (And since there are many more ways of
measuring temperature, there would have to be many more laws, where
previously we managed with only one.) Furthermore, the law based on
M-temperature would extend over a different range from that of the lawbased on R-temperature since the two thermometers have different
ranges. Not only convenience would be sacrificed, but also simplicity and
elegance.The attempt to explain differences in temperature would run into
difficulty. The model provided by the kinetic theory of heat explains them
by means of differences in the mean kinetic energy of molecules. Thereis just this one phenomenon, the mean kinetic energy of molecules, to
explain differences in temperature. Minor aberrations and inconsistenciesbetween instruments at extreme points have auxilary explanations, but
the fact remains that there is one underlying phenomenon associated withtemperature in physical theory, which implies that temperature is justone thing. (This discussion assumes ordinary contexts; later on, we shallconsider a special context with somewhat different results.)
Of course, we could conceivably elevate what I have called "auxiliaryexplanations" to the status of central explanations, in which case wecould have a different central explanation for the phenomenon associatedwith each instrument, but to do so would be inconvenient. The simplest ex-
planation, and the one that suffices in most cases, is the one that refers
only to the mean kinetic energy of the molecules.What about fruitfulness-the ability of theory to generate new pre-
dictions and to suggest new ways of looking at other fields? It is difficultto see how the complex structure that is implicit in the requirement thatdifferent operations imply different concepts could be a provoker of newideas or an aid to seeing new applications; it would be so hard to see thestructure as a whole, to see it intuitively.
While there is ordinarily only one concept of temperature functioning
within our normal range of experience, the concept does become elusive
in extreme situations. When we try to measure temperature at points suc-
cessively farther from the earth's surface, different operations tend to callfor different concepts because different operations produce radically dif-
ferent readings at the same point and because our interest in hotness and
coldness out in space calls for great attention to sources of radiant heat.
The reading on a thermometer depends on whether the thermometer is
exposed to radiant heat and, if so, on the direction in which the thermom-
eter is aimed. This is something like the dependence of a reading on
whether a thermometer is in the sun or in the shade. There are needed,so to speak, a concept, shade-temperature, and a concept, directional-
radiant-temperature. A thermometer suspended in a reflecting spherewould indicate shade-temperature (to the extent that the sphere success-
fully reflects radiant energy). A thermometer in a reflecting tube openat one end (thus admitting radiant energy from one direction) would
indicate directional-radiant-temperature. Thus, under conditions that ob-
tain as we leave the earth, it becomes convenient to have two concepts of
temperature since different operations give answers that at times are
radically different and since our fundamental concern, hotness and cold-
ness,is
radicallyaffected
byradiant heat.
In summary, once we are willing to bypass the difficulties attendant
upon violating the conventions of everyday speech and ordinary technical
language, the difficulty with having a different concept for each operationof temperature measurement is the inconvenience. But under certain
conditions, given our interests, we have to accept this inconvenience be-
cause the results from two different methods of measurement disagree so
greatly. The conclusion is that different operations do not by themselves
imply different concepts although, under certain circumstances for cer-
tain purposes, they may call for different concepts.Now, do the same considerations apply to IQ? In ordinary use (among
teachers and others who use the concept but who are not scientists), IQis held to be one thing, estimated with varying degrees of validity by the
various intelligence tests. But this in itself is not sufficient reason for edu-
cational scientists to adopt a unitary concept. They might hold that the
matter is not that simple-the measures we have differ so much that, al-
though they contain common elements, they are not enough alike to war-
rant calling them measures of the same thing. At best, IQ tests correlate
around .8. Thus they have much in common, but not everything in com-
mon, and we know from analyzing them that they emphasize different
abilities, such as spatial reasoning, verbal facility, and numerical skill.
Furthermore, there is not yet an explanatory theory for IQ comparableto the kinetic theory of heat. In view of these facts, it would be safestto develop a number of concepts of IQ, one for each test. (This, in effect,is part of what people are doing who say that "intelligence" means what
pear in either a phrase or a sentence that is equated to another phrase or
sentence:
3.lb. "Tx"meansthe sameas "OPxandOBSx,"
where Tx is a phrase or sentence containing the term T to be defined;
OPx is a phrase or sentence about the performance of operations; and
OBSx is a phrase or sentence about observations. OPx and OBSx maybe merged into one phrase or sentence. Example 1 fits Form 3.1b, as does
example 2 below.
Example2: "A person's Q"means the sameas "a person'sscoreresulting
from the administration f the CTMM"(or, more simply, "a person'sscoreonthe CTMM").
The term (or concept) IQ is tied down to a particular intelligence test
in this, the third, approach to operational definitions; but, in contrast to
the second approach, an IQ is a characteristic of a person, not of the
operations performed, though it is still dependent on those operations.An immediate objection presents itself. In example 1, let us assume
that X actually has an IQ of, say, 120. If this is not known because he has
not yet taken the test, one is obliged to say that it is false that he has anIQ of 120 since the statement alleged to be identical in meaning is false;that is, it is false that X was given the CTMM, so it is false that he was
given it and got a score of 120. Hence, by this interpretation, it must be
false that he has an IQ of 120. This contradicts our assumption that he
has an IQ of 120. No matter what IQ we assume X to have, a contradic-
tion develops. Since he must have some IQ, the definition is faulty.A similar problem exists for the phrase approach. According to ex-
ample 2, a person who does not have a score on the CTMM does not have
an IQ at all since "score on the CTMM" and IQ mean the same thing. Ifthat were so, it would make no sense for a principal to ask his guidancecounselor to obtain IQ's for new students who had never before been
tested since, by this interpretation, they have no IQ's (because they have
no scores on the CTMM).A way out of this difficulty is to use between OPx and OBSx an im-
plication relationship that is expressed conditionally and can be put in
the subjunctive mood. The revised form is:
3.2. "Tx" means the same as "If OPx, then OBSx." Our sentence ex-amplebecomes:
Example3: "X has an IQ of n" meansthe same as "If X is (were) giventhe CTMM,he will (would)get a scoreof n."
Ourphrase example becomes:
Example 4: "A person's IQ" means the same as "the score he will
There are problems remaining, but the use of implications that canbe put in the subjunctive* solves this first one. If a person has never
taken the CTMM-even if he is never going to take it, he neverthelesshas an IQ, perhaps never to be known. And if he has taken it and has a
score, there still is no inconsistency, for that does not preclude his being
given it again.In future examples, reference to the subjunctive will be omitted for
simplicity's sake. But it should be understood that each example is in-
tended to be convertible to the subjunctive-if need be. Furthermore,
phrase-type examples will no longer be given; with appropriate modifi-
cations, the general points to be made apply also to them.
Let us now consider another difficulty with the third approach. Itlimits the meaning of a concept to a particular set of operations (in the
case discussed above, the administration of the CTMM) together withthe results of this set of operations. Thus, like the second approach, it
implies that different operations require different concepts. As indicated
earlier, this view is generally false-although, under certain circumstancesand purposes, different operations do require different concepts.
What is needed is a format that will not commit us to having different
operations requiredifferent
conceptsin all
cases but will permit someleeway. We must replace the relationship, means the same as, with onethat does not limit the meaning to a particular set of operations. An im-
plication relationship that does not claim equivalence of meaning willmeet this requirement. This idea leads us to the fourth approach.
4. Providing Implication Relationships Among Operations, Observations,and the Concept
We can avoid thedifficulty
causedby
therelationship, means thesame as, by replacing it with the relationship, if and only if.t The
amended form follows:
4.1. Tx; if andonly if; if OPx,then OBSx.
The use of "if and only if" permits us to have two, or more, different
* See Chisholm (1949), Goodman (1952), von Wright (1957), and Will (1947) forinteresting discussions of counter-factualconditionals. This problem need not bother
us here unless we try to reduce all logical relationshipsto conjunction and negation(or somethingsimilar)-an unwise course,in my opinion.t This approach is along the lines recommended by Carl Hempel (1952, 1961),
who has applied Rudolph Carnap's (1953) notion of the reduction sentence to theformulation of operational definitions. My approachdiffers from theirs primarily inthe interpretation of the if-then relationship, theirs being a truth-functional inter-pretation and mine being an ordinary-language nterpretation.See P. F. Strawson'sIntroduction to Logical Theory (1952) for a discussion of the difference. If thereaderwho is unacquainted with this differencein approachsimply interpretsif-thensentences in the way to which he is accustomed, he will be interpreting these sen-tences as they are here intended.
kinds of operations to measure the same thing. The following examplescan both be operational definitions of the same concept, temperature:
Example 5: X has a temperatureof t; if and only if; if a mercurythermometers inserted n X, the thermometerwillreadt.
Example 6: X has a temperatureof t; if and only if; if an alcohol
thermometers inserted n X, the thermometerwill readt.
If "means the same as" appeared in these definitions instead of "if and
only if," we should be committed to saying that "mercury thermometer"
means the same as "alcohol thermometer." In effect, the if-and-only-ifformulation allows several accurate ways of measuring the same thing.
If we apply this approach to the measurement of IQ, another prob-lem becomes prominent. There is much less agreement among IQ tests
than there is among thermometers. Even the if-and-only-if formulation
seems too rigid. Consider these two possible definitions of the concept
IQ:
Example7: X has an IQ of n; if and only if; if the CTMM is admin-isteredto X, X willget a scoreof n.
Example8: X has an IQ of n; if and only if; if the Lorge-Thorndike
IntelligenceTests are administeredo X, X will get a score of n.
Together these definitions commit us to saying that a person will getthe same score on the CTMM as on the Lorge-Thorndike. For at least
two reasons we do not want to be fully committed to this.
First, the conditions of administration may not be standard for both
tests in any given pair of situations. If one test is administered under
standard conditions and the other is not, we can hardly expect the same
scores. This difficulty can be handled by adding some such phrase as
"under standard conditions." It is desirable that a list of standard condi-tions be available, perhaps in the test manual. Incidentally, this same
qualification holds for thermometers when precision is necessary.
Second, each instrument has its idiosyncrasies, which inevitablyinterfere with measurement at some level of precision. If these are large
enough to make a practical difference, some word like "approximately"should be added to the operational definition. Since the idiosyncracies of
IQ tests do make a practical difference at the level of precision at which
they are used, "approximately" should probably be added to operational
definitions of IQ. I should not ordinarily add it to operational definitionsof temperature since the idiosyncracies of thermometers do not make a
significant difference in the contexts with which I am familiar. However,for certain purposes and situations, some qualifying word should beadded for thermometers also.
To remind us of the qualifications, we can add "(WQ)," which standsfor "with qualifications," to Form 4.1:
An operational definition of IQ might look like this:
Example9: X has an IQ of approximatelyn; if andonly if; if the CTMM
is administeredo X understandardconditions,X willget a scoreof n.
In this example, "approximately" was inserted in the clause containingthe concept being defined, IQ. This is the proper place for the qualifierwhen we are trying to judge what someone's IQ is; the method of deter-
mination gives an approximation. On the other hand, when we are reason-
ing from an assumption about what someone's IQ is to a predicted
score, "approximately" should appear in the clause about the score:
Example10: X has an IQ of n; if and only if; if the CTMMis adminis-
tered to X understandardconditions,X will get a scoreof approximatelyn.
Thus, the location of the qualifiers, as well as the decision about whether
to make them explicit, depends to some extent on the situation. Hence-
forth I shall use "(WQ)" in the examples, leaving placement of the
qualifiers to be determined by the context.
People who are not adept at dealing with complicated if-then rela-
tionships tend to find Form 4.2 hard to understand. Some read into it
the suggestion that a person who has not been given the test does not
have an IQ. They also are puzzled by the three occurrences of the word"if" so close together. A more understandable formulation follows:
4.3. If OPx; then Tx,if andonlyif, OBSx(WQ).
Example 11: If the CTMM is administered o X under standardcondi-
tions; then X has an IQ of n, if and only if, he gets a scoreof n (WQ).
Although this new formulation is easier to understand, it does not
say quite the same thing as Form 4.2. To see this, consider the situation
in which we are trying to make a judgment about an individual's IQ onthe basis of his score on the CTMM. Using 4.3, we can conclude that X
probably has an IQ of approximately n, where n is the score that we
have. However, using 4.2, we cannot draw that conclusion without an
auxiliary assumption: our conclusion that X has an IQ of approximatelyn depends on the generalization that n is the score he gets whenever he
takes the test; it does not rest simply on his getting the score of n this
time. To make this generalization, one would probably assume that thescore we have is typical for him, an assumption we often make in dealing
with test scores. Form 4.3 has this assumption built in, so we should notuse 4.3 unless we are fairly confident that the scores on which we are
basing our judgments are typical.Neither formulation allows us to escape the problem of typicality.
The problem is faced in applying 4.2 and in adopting 4.3. Since we shallwant to adopt 4.3 without being completely committed to the belief thatall the scores are typical, the word "probably" should be included amongthe qualifiers referred to by "(WQ)."
an operational definition of 'degree of mastery of the principle thatdenial of the consequent implies denial of the antecedent'?" We can
answer that question with the following operational definition:
Example 12: If X is given The Cornell ConditionalReasoning Test,Form X; then X has masteredto the degreek the principlethat denial ofthe consequent mplies denial of the antecedent,if and only if, he gets ascoreof k righton the following tems: 8, 16, 22, 29, 35, and 39 (WQ).
Using this definition, we obtain a score that can vary from zero tosix and that indicates degree of mastery of the principle. But this scorehas limitations. It means little to people who are not well acquainted
with the test or with the scores of other individuals whose degree ofmastery of this principle is known. Yet the audience for our results is
likely to consist largely of such people.Another drawback is that one of our interests is the determination
of the per cent of students of a given description who have mastered the
principle. This interest calls for the judgment that a particular student
has or has not done so; it does not call for a judgment about his degreeof knowledge. We need a definition that will fit our attempts to judgewith some assurance whether a student has mastered this
principle.One might suppose that these difficulties could be handled by a defi-nition that gave a certain minimum score as a necessary and sufficientcondition for having mastered the principle. For example,
Example13: If X is given The CornellConditionalReasoningTest, Form
X; then X has masteredthe principlethat denial of the consequent mpliesdenial of the antecedent, f and only if, X answerscorrectlyat least four oftheseitems: 8, 16, 22,29, 35,and39 (WQ).
In thisexample, getting at least four items right is a rough necessary-and-sufficient condition for a person's knowing the principle (we assume
that he takes the test). However, we do not want to be committed to
any one minimum score as both necessary and sufficient; we do not wantto draw that sharp a line between mastery and nonmastery. What weshould like to say is something to the effect that getting at least five rightis a probable sufficient condition and getting at least four right is a
probable necessary condition. That is, we should like to say of a studentwho gets at least five right that he probably has mastered the principle
and of a student who gets fewer than four right that he probably has notmastered it. About the students who get exactly four right, we are notsure what to say. They are borderline cases-and we should like a defi-nition form that will allow us to leave them that way.
The following form permits us to present the sufficient condition:
4.4. If OPx; then, if OBSx, then Tx (WQ).** The sufficient-conditionform correspondingto 4.2 is: Tx; if; if OPx, then
OBSx (WQ). This form, with the adjacent "if's,"is harderto understand.
The operational definition corresponding to this sufficient-condition
form follows:
Example 14: If X is given The Cornell ConditionalReasoning Test,FormX; then, if X answerscorrectlyat least five of items 8, 16, 22, 29, 35,and 39, X has mastered the principlethat denial of the consequent mpliesdenialof the antecedent(WQ).
The following form permits us to present the necessary condition:
4.5. If OPx; then, Tx,only if OBSx(WQ).*
The operational definition corresponding to this necessary-conditionform follows:
Example 15: If X is given The Cornell ConditionalReasoning Test,Form X; then X has masteredthe principlethat denial of the consequentimpliesdenialof the antecedent,only if X answerscorrectlyat least four oftheseitems: 8, 16,22,29, 35,and 39 (WQ).
To give an operational interpretation of the concept, knowledge that
denial of the consequent implies denial of the antecedent, we supply both
operational definitions, each of which provides a partial interpretation.
Combined, they still do not provide a complete interpretation of the
concept, but they give a basis on which to work and reason.It is not necessary to agree with our specific decisions in the case
above to see the need for Forms 4.4 and 4.5. That is, without contradict-
ing my basic thesis, one can hold that answering correctly a minimum of
one certain number of the items should be considered both necessary and
sufficient, or one can hold that the number of items in the necessarycondition should differ from that in the sufficient condition but that fourand five are not the proper numbers. It is necessary only to see that these
formsmay
sometimes be needed.
In summary, I recommend that operational definitions start with an
if-clause that specifies an operation or a set of operations and that this
clause be followed by an implication relationship between a phrase or
sentence containing the concept (or term) to be defined and a phrase or
sentence specifying an observation or a set of observations. Appropriatequalifications should be implicit or explicit.
OPERATIONAL INTERPRETATION VERSUS OPERATIONAL DEFINITION
Now that all these qualifications have been introduced, one maywonder if the result is a definition at all. It does not exhaust the meaningof a concept; it is loose; and a pair of operational definitions of the same
concept sometimes implies an empirical fact. For example, the two defi-nitions of IQ using the CTMM and the Lorge-Thorndike imply a highcorrelation between the tests; this is certainly an empirical matter. Some
"*The necessary-conditionform corresponding to 4.2, which again is harder tounderstand, s: Tx; only if; if OPx, then OBSx (WQ).
people regard the implication of empirical facts as a serious defect, for
presumably definitions should give the meaning of concepts, not give
facts.Fortunately, the utility of the guides that I am proposing does not
depend on the resolution of this difficult question. If one boggles at callingthe examples I have given "operational definitions," call them "opera-tional interpretations." In either case they help indicate the meaning ofa concept, and they do so by focusing on concrete things, especially the
manipulations of investigators. They help both to delimit and to fill inthe meaning of a concept. What harm is there in calling them "defini-tions" so long as we remember that they differ from the classical type
of definition, which provides expressions that are equivalent in meaning?Since their purpose and function is to indicate meaning, the most reason-able term for them, it seems to me, is "operational definitions." But Ido not insist on this, for not much turns on the terminology.*
THENECESSITYORDELIBERATEANIPULATION
Carl Hempel, among others, has suggested that a deliberate manipula-tion by an investigator is not really necessary for an operational defini-
nition-that all we need is some condition, whether it be a deliberatemanipulation or not. He points out that although emphasis on deliberate
operations "is of great interest for the practice of scientific research,...it is inessential in securing experimental import for the defined term"
(Hempel, 1961; p. 59). It is true that a deliberate manipulation is not a
necessary condition for experimental import, but there is an importantdistinction in discussions of the methodology of scientific research be-tween those definitions that specify manipulations and those that specifyother conditions.
If we were proceeding on the assumption that all terms must be
operationally defined, Hempel's advice should be heeded because notall terms require manipulation by an experimenter as part of their
interpretation (unless such activities as looking are regarded as manip-ulations, in which case operationism reduces to empiricism). PerhapsHempel offered his advice in the context of an assumed recommendationthat all terms be operationally definable. If one does not make that
recommendation, one can preserve an independent meaning for theterm
"operationism,"a
meaning that emphasizes the manipulations ofan investigator. In this case, a recommendation that a term be defined
* The philosopher would say that the sharp distinction between analytic andsynthetic statements is blurred by using the term "definitions." The question is adifficult and subtle one, but I might note that the sharpness of this distinction inthe area of empirical science has been questioned recently even in the writings ofCarl Hempel, who says (1961, p. 66), "It . . appears doubtful whether the dis-tinction between analytic and synthetic sentences can be effectively maintained ina formal model of the language of empirical science." Keith Donnellan (1962) hasprovideda valuable discussion of this question.
operationally would imply that the definition should specify some bona
fide manipulations by the research worker.
As with the case in which it was possible (but not preferable) to callexamples "operational definitions," I recommend that we preserve the
independent meaning of "operational definition" and that some other
term, perhaps "conditional definition," be used to cover both operationaldefinitions and definitions that are similar in form but contain a non-
manipulative condition in the first if-clause. This approach will preservethe necessary distinctions without violating the original spirit of opera-tionism as expressed by Bridgman and recognized for its value by many
empirical scientists.
SUMMARY
In this paper I have examined various forms for the operational defi-
nition of concepts, or terms, and have formulated the following set of
guides:
A. Operational definitions should
1. start with an if-clause specifying the nature of the operation
performable bythe investigator.
2. contain an implication relationship that holds when a given
operation has been performed. This relationship can be
necessary (but not sufficient), sufficient (but not necessary),or both necessary and sufficient.
3. be convertible to the subjunctive mood if they are not
already in the subjunctive.4. not be taken to require a separate concept for each opera-
tional definition. Some concepts will have many operational
definitions.5. contain, either explicitly or implicitly, qualifying words or
phrases like "approximately," "probably," and "under stand-
ard conditions."
B. Three useful forms for operational definitions follow:
Let: Tx represent a phrase or sentence containing the term
(or concept) T being defined. For example, "X has
an IQ of n," in which IQ is the concept.
OPx represent a phrase or sentence about the perform-ance of an operation or a set of operations. For ex-
ample, "X is (were) given the CTMM."
"*Rudolph Carnap (1953) has suggested "reduction sentence," a term in wide-spread use among philosophers. Because this term is closely associated with truth-functional logic and suggests that abstract concepts are reduced to concrete termswithout loss (this is not Carnap's intent), I prefer "conditional definition." Thisterm is free from these connotations and indicates the conditional aspect of thedefinition.
OBSx represent a phrase or sentence about an observa-
tion or a set of observations. For example, "X's
score is (will be, would be) n."WQ indicate that certain qualifications like "approx-
imately" and "probably" should be included in the
definition.
Form 1. In which OBSx is a necessary and sufficient condition,
given OPx:
If OPx; then Tx, if and only if, OBSx (WQ). (4.3)
Example: If X is given the CTMM; then X has an IQ of n, if
and only if, X's score is n (WQ).
Form 2. In which OBSx is a sufficient condition, given OPx:
If OPx; then, if OBSx, then Tx (WQ). (4.4)
Form 3. In which OBSx is a necessary condition, given OPx:
If OPx; then Tx, only if OBSx (WQ). (4.5)
It was not claimed that all definitions in the empirical sciences should
be operational. It was assumed that it is often a good idea to define
concepts (or terms) operationally because the specific connections al-leged between the concrete world and an abstract concept are importantand because an especially important set of these connections involves
the particular instruments and procedures used by the investigator.
REFERENCES
BENJAMIN, A. CORNELIUS. Operationism. Springfield, Ill.: Charles C.
Thomas, 1955. 154 pp.
BERGMANN, GUSTAV. "Sense and Nonsense in Operationism." The Vali-dation of Scientific Theories. (Edited by Philipp G. Frank.) New
York: Collier Books, 1961, pp. 46-56.
BERGMANN, GUSTAV, and SPENCE, KENNETH W. "Operationismand
Theory Construction." Psychological Theory. (Edited by Melvin H.
Marx.) New York: Macmillan Co., 1951, pp. 54-66.
BRIDGMAN, PERCY W. The Logic of Modern Physics. New York: Mac-
millan Co., 1927. 228 pp.
BRIDGMAN, PERCY W. "The Present State of Operationalism." The Vali-
dation of Scientific Theories. (Edited by Philipp G. Frank.) New York:Collier Books, 1961, pp. 75-80.
BRODBECK,MAY."Logic and Scientific Method in Research on Teaching."Handbook of Research on Teaching. (Edited by Nathaniel L. Gage.)
Chicago: Rand McNally and Co., 1963, pp. 44-93.
CARNAP, RUDOLPH. "Testability and Meaning." Readings in the Philos-
ophy of Science. (Edited by Herbert Feigl and May Brodbeck.) New