Operational definition

Operational definition

Overview

An operational definition defines something (e.g. a variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

, term
Terminology
Terminology is the study of terms and their use. Terms are words and compound words that in specific contexts are given specific meanings, meanings that may deviate from the meaning the same words have in other contexts and in everyday language. The discipline Terminology studies among other...

, or object
Object (philosophy)
An object in philosophy is a technical term often used in contrast to the term subject. Consciousness is a state of cognition that includes the subject, which can never be doubted as only it can be the one who doubts, and some object or objects that may or may not have real existence without...

) in terms of the specific process or set of validation tests
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics .- Usage :Formal verification can be...

used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman
Percy Williams Bridgman
Percy Williams Bridgman was an American physicist who won the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other aspects of the philosophy of science.- Biography :Bridgman entered Harvard University in 1900,...

and is a part of the process of operationalization
Operationalization
In humanities, operationalization is the process of defining a fuzzy concept so as to make the concept clearly distinguishable or measurable and to understand it in terms of empirical observations...

. One might use definitions that rely on operations in order to avoid the troubles associated with attempting to define things in terms of some intrinsic essence
Essentialism
In philosophy, essentialism is the view that, for any specific kind of entity, there is a set of characteristics or properties all of which any entity of that kind must possess. Therefore all things can be precisely defined or described...

.

An example of an operational definition might be defining the weight of an object in terms of the numbers that appear when that object is placed on a weighing scale
Weighing scale
A weighing scale is a measuring instrument for determining the weight or mass of an object. A spring scale measures weight by the distance a spring deflects under its load...

.
Discussion

Encyclopedia

An operational definition defines something (e.g. a variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

, term
Terminology
Terminology is the study of terms and their use. Terms are words and compound words that in specific contexts are given specific meanings, meanings that may deviate from the meaning the same words have in other contexts and in everyday language. The discipline Terminology studies among other...

, or object
Object (philosophy)
An object in philosophy is a technical term often used in contrast to the term subject. Consciousness is a state of cognition that includes the subject, which can never be doubted as only it can be the one who doubts, and some object or objects that may or may not have real existence without...

) in terms of the specific process or set of validation tests
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics .- Usage :Formal verification can be...

used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman
Percy Williams Bridgman
Percy Williams Bridgman was an American physicist who won the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other aspects of the philosophy of science.- Biography :Bridgman entered Harvard University in 1900,...

and is a part of the process of operationalization
Operationalization
In humanities, operationalization is the process of defining a fuzzy concept so as to make the concept clearly distinguishable or measurable and to understand it in terms of empirical observations...

. One might use definitions that rely on operations in order to avoid the troubles associated with attempting to define things in terms of some intrinsic essence
Essentialism
In philosophy, essentialism is the view that, for any specific kind of entity, there is a set of characteristics or properties all of which any entity of that kind must possess. Therefore all things can be precisely defined or described...

.

An example of an operational definition might be defining the weight of an object in terms of the numbers that appear when that object is placed on a weighing scale
Weighing scale
A weighing scale is a measuring instrument for determining the weight or mass of an object. A spring scale measures weight by the distance a spring deflects under its load...

. The weight then, is whatever results from following the (weight) measurement procedure, which should be repeatable by anyone. This is in contrast to Operationalization that uses theoretical definition
Theoretical definition
A theoretical definition gives the meaning of a word in terms of the theories of a specific discipline. This type of definition assumes both knowledge and acceptance of the theories that it depends on. To theoretically define is to create a hypothetical construct...

s.

Overview

Properties described in this manner must be sufficiently accessible, so that persons other than the definer may independently measure or test for them at will. An operational definition is generally designed to model a theoretical definition
Theoretical definition
A theoretical definition gives the meaning of a word in terms of the theories of a specific discipline. This type of definition assumes both knowledge and acceptance of the theories that it depends on. To theoretically define is to create a hypothetical construct...

.
The most operational definition is a process for identification
Identity (philosophy)
In philosophy, identity, from , is the relation each thing bears just to itself. According to Leibniz's law two things sharing every attribute are not only similar, but are the same thing. The concept of sameness has given rise to the general concept of identity, as in personal identity and...

of an object by distinguishing it from its background of empirical experience.

The binary version produces either the result that the object exists, or that it doesn't, in the experiential field to which it is applied. The classifier
Classifier
Classifier may refer to:*Classifier *Classifier *Classifier *Hierarchical classifier*Linear classifier...

version results in discrimination between what is part of the object and what is not part of it. This is also discussed in terms of semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

, pattern recognition
Pattern recognition
In machine learning, pattern recognition is the assignment of some sort of output value to a given input value , according to some specific algorithm. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes...

, and operational techniques, such as regression
Calibration (statistics)
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Thus "calibration" can mean...

.

Operationalize means to put into operation. Operational definitions are also used to define system states in terms of a specific, publicly accessible process of preparation or validation testing, which is repeatable at will. For example, 100 degrees Celsius may be crudely defined by describing the process of heating water at sea level until it is observed to boil. An item like a brick, or even a photograph of a brick, may be defined in terms of how it can be made. Likewise, iron may be defined in terms of the results of testing or measuring it in particular ways.

Vandervert (1980/1988) described in scientific detail a simple, every day illustration of an operational definition in terms of making a cake (i.e., its recipe is an operational definition used in a specialized laboratory known as the household kitchen). Similarly, the saying, if it walks like a duck and quacks like a duck, it must be some kind of duck, may be regarded as involving a sort of measurement process or set of tests (see duck test
Duck test
The duck test is a humorous term for a form of inductive reasoning. This is its usual expression:The test implies that a person can identify an unknown subject by observing that subject's habitual characteristics...

).

Limitations

If a definition invokes an historical event, such as having weighed an object sometime in the past, it is no longer repeatable, so it fails to qualify as operational.

Similarly, a specific brick cannot be operationally defined by the process of making it, because that process is historical. (But see the example of the constellation Virgo below for a discussion of how to avoid this difficulty.)

Application

Despite the controversial philosophical origins of the concept, particularly its close association with logical positivism
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...

, operational definitions have undisputed practical applications. This is especially so in the social and medical sciences, where operational definitions of key terms are used to preserve the unambiguous empirical testability of hypothesis and theory. Operational definitions are also important in the physical sciences.

Philosophy

The Stanford Encyclopedia of Philosophy says the following about Operationalism stored at http://plato.stanford.edu/entries/scientific-realism/ and written by Richard Boyd
Richard Boyd
Richard Newell Boyd is an American philosopher who has spent most of his career at Cornell University, though he also taught briefly at Harvard University, the University of Michigan, Ann Arbor, and the University of California, Berkeley...

:
However, this rejection of operationalism as a general project destined ultimately to define all experiential phenomena uniquely did not mean that operational definitions ceased to have any practical use or that they could not be applied in particular cases.

Science

The special theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

can be viewed as the introduction of operational definitions for simultaneity of events
Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...

and of distance
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...

, that is, as providing the operations needed to define these terms.

In quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

the notion of operational definitions is closely related to the idea of observables, that is, definitions based upon what can be measured.

Operational definitions are at their most controversial in the fields of psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...

and psychiatry
Psychiatry
Psychiatry is the medical specialty devoted to the study and treatment of mental disorders. These mental disorders include various affective, behavioural, cognitive and perceptual abnormalities...

, where intuitive concepts, such as intelligence need to be operationally defined before they become amenable to scientific investigation, for example, through processes such as IQ tests. Such definitions are used as a follow up to a theoretical definition
Theoretical definition
A theoretical definition gives the meaning of a word in terms of the theories of a specific discipline. This type of definition assumes both knowledge and acceptance of the theories that it depends on. To theoretically define is to create a hypothetical construct...

, in which the specific concept is defined as a measurable occurrence. John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

pointed out the dangers of believing that anything that could be given a name must refer to a thing and Stephen Jay Gould
Stephen Jay Gould
Stephen Jay Gould was an American paleontologist, evolutionary biologist, and historian of science. He was also one of the most influential and widely read writers of popular science of his generation....

and others have criticized psychologists for doing just that. A committed operationalist would respond that speculation about the thing in itself, or noumenon
Noumenon
The noumenon is a posited object or event that is known without the use of the senses.The term is generally used in contrast with, or in relation to "phenomenon", which refers to anything that appears to, or is an object of, the senses...

, should be resisted as meaningless, and would comment only on phenomena using operationally defined terms and tables of operationally defined measurements.

A behaviorist
Behaviorism
Behaviorism , also called the learning perspective , is a philosophy of psychology based on the proposition that all things that organisms do—including acting, thinking, and feeling—can and should be regarded as behaviors, and that psychological disorders are best treated by altering behavior...

psychologist might (operationally) define intelligence as that score obtained on a specific IQ test (e.g., the Wechsler Adult Intelligence Scale
The Wechsler Adult Intelligence Scale intelligence quotient tests are the primary clinical instruments used to measure adult and adolescent intelligence. The original WAIS was published in February 1955 by David Wechsler, as a revision of the Wechsler-Bellevue Intelligence Scale...

test) by a human subject. The theoretical underpinnings of the WAIS would be completely ignored. This WAIS measurement would only be useful to the extent it could be shown to be related to other operationally defined measurements, e.g., to the measured probability of graduation from university. http://www.wjh.harvard.edu/~cfc/Chabris1998a.html

Operational definitions are the foundation of the diagnostic
Medical diagnosis
Medical diagnosis refers both to the process of attempting to determine or identify a possible disease or disorder , and to the opinion reached by this process...

nomenclature
Nomenclature
Nomenclature is a term that applies to either a list of names or terms, or to the system of principles, procedures and terms related to naming - which is the assigning of a word or phrase to a particular object or property...

of mental disorders (classification of mental disorders
Classification of mental disorders
The classification of mental disorders, also known as psychiatric nosology or taxonomy, is a key aspect of psychiatry and other mental health professions and an important issue for consumers and providers of mental health services...

) from the DSM-III onward.

On October 15, 1970, the West Gate Bridge
West Gate Bridge
The West Gate Bridge is a steel box girder cable-stayed bridge in Melbourne, Victoria, Australia. It spans the Yarra River, just north of its mouth into Port Phillip, and is a vital link between the inner city and Melbourne's western suburbs with the industrial suburbs in the west and with the city...

in Melbourne
Melbourne
Melbourne is the capital and most populous city in the state of Victoria, and the second most populous city in Australia. The Melbourne City Centre is the hub of the greater metropolitan area and the Census statistical division—of which "Melbourne" is the common name. As of June 2009, the greater...

, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

collapsed, killing 35 construction workers. The subsequent enquiry found that the failure arose because engineers had specified the supply of a quantity of flat steel plate. The word flat in this context lacked an operational definition, so there was no test for accepting or rejecting a particular shipment or for controlling quality.

In his managerial and statistical writings, W. Edwards Deming
W. Edwards Deming
William Edwards Deming was an American statistician, professor, author, lecturer and consultant. He is perhaps best known for his work in Japan...

placed great importance on the value of using operational definitions in all agreements in business. As he said:
"An operational definition is a procedure agreed upon for translation of a concept into measurement of some kind." - W. Edwards Deming

"There is no true value of any characteristic, state, or condition that is defined in terms of measurement or observation. Change of procedure for measurement (change of operational definition) or observation produces a new number." - W. Edwards Deming

General process

Operational, in a process context, also can denote a working method or a philosophy that focuses principally on cause and effect relationships (or stimulus/response, behavior, etc.) of specific interest to a particular domain at a particular point in time. As a working method, it does not consider issues related to a domain that are more general, such as the ontological, etc.

The term can be used strictly within the realm of the interactions of humans with advanced computational systems. In this sense, an AI
Ai
AI, A.I., Ai, or ai may refer to:- Computers :* Artificial intelligence, a branch of computer science* Ad impression, in online advertising* .ai, the ISO Internet 2-letter country code for Anguilla...

system cannot be entirely operational (this issue can be used to discuss strong versus weak AI) if learning is involved.

Given that one motive for the operational approach is stability, systems that relax the operational factor can be problematic, for several reasons, as the operational is a means to manage complexity. There will be differences in the nature of the operational as it pertains to degrees along the end-user computing
End-user computing
In computing, End User Computing refer to systems in which non-programmers can create working applications. EUC is a group of approaches to computing that aim at better integrating end users into the computing environment...

axis.

For instance, a knowledge-based engineering
Knowledge-based engineering
Knowledge-based engineering is a discipline with roots in computer-aided design and knowledge-based systems but has several definitions and roles depending upon the context. An early role was support tool for a design engineer generally within the context of product design...

system can enhance its operational aspect and thereby its stability through more involvement by the SME
Subject Matter Expert
A subject matter expert or domain expert is a person who is an expert in a particular area or topic. When spoken, sometimes the acronym "SME" is spelled out and other times voiced as a word ....

, thereby opening up issues of limits that are related to being human, in the sense that, many times, computational results have to be taken at face value due to several factors (hence the duck test
Duck test
The duck test is a humorous term for a form of inductive reasoning. This is its usual expression:The test implies that a person can identify an unknown subject by observing that subject's habitual characteristics...

's necessity arises) that even an expert cannot overcome. The end proof may be the final results (reasonable facsimile by simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

or artifact, working design, etc.) that are not guaranteed to be repeatable, may have been costly to attain (time and money), and so forth.

Many domains, with a numerics
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

focus, use limits logic to overcome the duck test necessity with varying degrees of success. Complex situations may require logic to be more non-monotonic
Non-monotonic logic
A non-monotonic logic is a formal logic whose consequence relation is not monotonic. Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a...

than not raising concerns related to the qualification
Qualification problem
In philosophy and AI , the qualification problem is concerned with the impossibility of listing all the preconditions required for a real-world action to have its intended effect. It might be posed as how to deal with the things that prevent me from achieving my intended result...

, frame
Frame problem
In artificial intelligence, the frame problem was initially formulated as the problem of expressing a dynamical domain in logic without explicitly specifying which conditions are not affected by an action. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, Some...

, and ramification
Ramification problem
In philosophy and artificial intelligence , the ramification problem is concerned with indirect consequences of an action. It might be posed as how to represent what happens implicitly due to an action or to control secondary and tertiary effects within the same period...

problems.

Temperature

The thermodynamic definition of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, due to Nicolas Léonard Sadi Carnot
Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

, refers to heat "flowing" between "infinite reservoirs". This is all highly abstract and unsuited for the day-to-day world of science and trade. In order to make the idea concrete, temperature is defined in terms of operations with the gas thermometer. However, these are sophisticated and delicate instruments, only adapted to the national standardization laboratory.

For day-to-day use, the International Temperature Scale of 1990
International Temperature Scale of 1990
The International Temperature Scale of 1990 is an equipment calibration standard for making measurements on the Kelvin and Celsius temperature scales. ITS–90 is an approximation of the thermodynamic temperature scale that facilitates the comparability and compatibility of temperature measurements...

(ITS) is used, defining temperature in terms of characteristics of the several specific sensor types required to cover the full range. One such is the electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

of a thermistor
Thermistor
A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. The word is a portmanteau of thermal and resistor...

, with specified construction, calibrated
Calibration
Calibration is a comparison between measurements – one of known magnitude or correctness made or set with one device and another measurement made in as similar a way as possible with a second device....

against operationally defined fixed points. Therefore it can be seen that heat is hot.

Electric current

Electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

is defined in terms of the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

between two infinite
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

parallel
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...

conductors, separated by a specified distance. This definition is too abstract for practical measurement, so a device known as a current balance is used to define the ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

operationally.

Mechanical hardness

Unlike temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

and electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

, there is no abstract physical concept of the hardness of a material. It is a slightly vague, subjective idea, somewhat like the idea of intelligence. In fact, it leads to three more specific ideas:
1. Scratch hardness measured on Mohs' scale
Mohs scale of mineral hardness
The Mohs scale of mineral hardness characterizes the scratch resistance of various minerals through the ability of a harder material to scratch a softer material. It was created in 1812 by the German geologist and mineralogist Friedrich Mohs and is one of several definitions of hardness in...

;
2. Indentation hardness; and
3. Rebound, or dynamic, hardness measured with a Shore scleroscope.

Of these, indentation hardness itself leads to many operational definitions, the most important of which are:
1. Brinell hardness test – using a 10 mm steel ball;
2. Vickers hardness test
Vickers hardness test
The Vickers hardness test was developed in 1924 by Smith and Sandland at Vickers Ltd as an alternative to the Brinell method to measure the hardness of materials. The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the...

– using a pyramidal diamond indenter; and
3. Rockwell hardness test – using a diamond cone indenter.

In all these, a process is defined for loading the indenter, measuring the resulting indentation and calculating a hardness number. Each of these three sequences of measurement operations produces numbers that are consistent with our subjective idea of hardness. The harder the material to our informal perception, the greater the number it will achieve on our respective hardness scales. Furthermore, experimental results obtained using these measurement methods has shown that the hardness number can be used to predict the stress required to permanently deform steel, a characteristic that fits in well with our idea of resistance to permanent deformation. However, there is not always a simple relationship between the various hardness scales. Vickers and Rockwell hardness numbers exhibit qualitatively different behaviour when used to describe some materials and phenomena.

The constellation Virgo

The constellation Virgo is a specific constellation of stars in the sky, hence the process of forming Virgo cannot be an operational definition, since it is historical and not repeatable. Nevertheless, the process whereby we locate Virgo in the sky is repeatable, so in this way, Virgo is operationally defined. In fact, Virgo can have any number of definitions (although we can never prove that we are talking about the same Virgo), and any number may be operational.

Duck typing

In advanced modeling, with the requisite computational support such as knowledge-based engineering
Knowledge-based engineering
Knowledge-based engineering is a discipline with roots in computer-aided design and knowledge-based systems but has several definitions and roles depending upon the context. An early role was support tool for a design engineer generally within the context of product design...

, mappings must be maintained between a real-world object, its abstracted counterparts as defined by the domain and its experts, and the computer models. Mismatches between domain models and their computational mirrors can raise issues that are apropos to this topic. Techniques that allow the flexible modeling required for many hard problems must resolve issues of identity, type, etc. which then lead to methods, such as duck typing
Duck typing
In computer programming with object-oriented programming languages, duck typing is a style of dynamic typing in which an object's current set of methods and properties determines the valid semantics, rather than its inheritance from a particular class or implementation of a specific interface...

.

Theoretical vs operational definition

 Theoretical definition Operational definition Weight: a measurement of gravitational force acting on an object a result of measurement of an object on a newton spring scaleSpring scaleThe spring scale apparatus is simply a spring fixed at one end with a hook to attach an object at the other. It works by Hooke's Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position...

• Ballantyne, Paul F. History and Theory of Psychology Course, in Langfeld, H.S. (1945) Introduction to the Symposium on Operationism. Psyc. Rev. 32, 241-243.http://www.comnet.ca/~pballan/operationism(1945).htm
• Bohm, D. (1996). On dialog. N.Y.: Routledge.
• Boyd, Richard. On the Current Status of the Issue of Scientific Realism in Erkenntnis. 19: 45-90.
• Bridgman, P. W. The way things are. Cambridge: Harvard University Press. (1959)
• Carnap, R. The Elimination of Metaphysics Through Logical Analysis of Language in Ayer, A.J. 1959.
• Churchland, Patricia, Neurophilosophy— Toward a unified science of the mind/brain, MIT Press (1986).
• Churchland, Paul., A Neurocomputational Perspective— The Nature of Mind and the Structure of Science, MIT Press (1989).
• Dennett, Daniel C. Consciousness Explained, Little, Brown & Co.. 1992.
• Depraz, N. (1999). "The phenomenological reduction as praxis." Journal of Consciousness Studies, 6(2-3), 95-110.
• Hardcastle, G. L. (1995). "S.S. Stevens and the origins of operationism." Philosophy of Science, 62, 404-424.
• Hermans, H. J. M. (1996). "Voicing the self: from information processing to dialogical interchange." Psychological Bulletin, 119(1), 31-50.
• Hyman, Bronwen, U of Toronto, and Shephard, Alfred H., U of Manitoba, "Zeitgeist: The Development of an Operational Definition", The Journal of Mind and Behavior, 1(2), pps. 227-246 (1980)
• Leahy, Thomas H., Virginia Commonwealth U, The Myth of Operationism, ibid, pps. 127-144 (1980)
• Ribes-Inesta, Emilio "What Is Defined In Operational Definitions? The Case Of Operant Psychology," Behavior and Philosophy, 2003.http://www.findarticles.com/p/articles/mi_qa3814/is_200301/ai_n9222880
• Roepstorff, A. & Jack, A. (2003). "Editorial introduction, Special Issue: Trusting the Subject? (Part 1)." Journal of Consciousness Studies, 10(9-10), v-xx.
• Roepstorff, A. & Jack, A. (2004). "Trust or Interaction? Editorial introduction, Special Issue: Trusting the Subject? (Part 2)." Journal of Consciousness Studies, 11(7-8), v-xxii.
• Stevens, S. S. Operationism and logical positivism, in M. H. Marx (Ed.), Theories in contemporary psychology (pp. 47–76). New York: MacMillan. (1963)
• Thomson — Waddsworth, eds., Learning Psychology: Operational Definitions Research Methods Workshopshttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/res_methd/op_def/op_def_01.html