Texts
- The Problem of Learning
- Problemistics Courseware
- Corso su Problemistica
- Resources Management
- Manuale/Intellettuale
- Campagna/Città
Problemistics - Problémistique - Problemistica
The Art & Craft of Problem Dealing
Definitions
Definition (Reference books)
Starting point of a definition (Bertrand Russel)
Good definition (Jean Louis Formey)
Components of a definition (L. Rorabacher, G. Dunbar and C. Dunbar)Classification (Irving M. Copi)
Classification (Deobold B. Van Dalen)
Classification (Philip Brian Bell and Philip James Staines)
Classification (Louise E. Rorabacher, Georgia Dunbar, Clement Dunbar)
Denotation-extension and connotation-intention (Peter Caws)
Denotation-extension and connotation-intention (Gerald Runkle)
Denotation-extension and connotation-intention (Vincent E. Barry and Douglas J. Soccio)
Conceptual definition (C. F. Nachmias and D. Nachmias)
Rules for lexical definitions (Irving M. Copi)Guidelines for definitions (L. Rorabacher, G. Dunbar and C. Dunbar)
Guidelines for definitions (Vincent E. Barry and Douglas J. Soccio)Function (Jean Louis Formey)
Function (C. K. Ogden and I. A. Richards)
Function (Abraham Kaplan)
Function (Irving M. Copi)Classical quotations (Cicero)
Classical quotations (John Locke)
Classical quotations (Ludwig Wittgenstein)
[1981] Webster’s Third New International Dictionary
2. a word or phrase expressing the essential nature of a person or thing or class of persons or of things
3a. a statement of the meaning of a word or word group
[1983] The Shorter Oxford English Dictionary
4. a precise statement of the essential nature of a thing
4b. a declaration of the signification of a word or phrase
[1919] Bertrand Russel, Introduction to Mathematical Philosophy, Graphyco Editions, 2020
“Since all terms that are defined are defined by means of other terms, it is clear that human knowledge must always be content to accept some terms as intelligible without definition, in order to have a starting point for its definitions...[and] since human powers are finite, the definitions known to us must always begin somewhere, with terms undefined for the moment, though perhaps not permanently." (p. 3)
[1751-1772] Jean Louis Formey, Definition in Diderot-D’Alembert, Encyclopédie
"La définition de chose est proprement une énumération qu'on fait des principaux attributs d'une chose, pour expliquer et faire connaître sa nature."
"On demande ordinairement trois choses pour qu'une définition soit bonne :
1) qu'elle soit claire, c'est à dire qu'elle nous serve à avoir une idée plus claire et plus distincte de la chose qu'on définit, et qu'elle nous en fasse, autant qu'il peut, comprendre la nature
2) qu'elle soit universelle ou adéquate, c'est à dire qu'elle convienne à tout ce qui est contenu dans l'espèce définie
3) qu'elle soit propre ou particulière à la chose définie.”
[1988] Louise E. Rorabacher, Georgia Dunbar, Clement Dunbar, Assignments in Exposition, Ninth Edition
“A formal definition is based on a concise, logical pattern that lets the writer give a maximum of information in a minimum of space.
It has three parts:
- the term (word or phrase);
- the class of object or concept to which the term belongs ; and
- the differentiating characteristics that distinguish what the term defines from all others of that class.”
Example : Term Class Differentiating Characteristics
An owl is a bird with large head, strong talons, and nocturnal habits
(Unit 15 Definition - pp. 327-328)
[1953] Irving M. Copi, Introduction to Logic, Macmillan, New York, Sixth edition 1982
1) Stipulative Definition : arbitrary definitions introduced for a variety of reasons (e.g. parsimony as in a scientific formula or transmitting messages using codes).
2) Lexical Definition : to eliminate ambiguity or to increase the vocabulary of the person for whom it is constructed, when the term being defined is not new but has an established usage.
3) Precising Definition : to reduce the vagueness of a term.
4) Theoretical Definition : to formulate an adequate characterization of the objects to which it is applied.
5) Persuasive Definition : to influence attitudes.
(pp. 147-154)
[1962] Deobold B. Van Dalen, Understanding Educational Research, Fourth edition 1979
- Definitions by example : to point to it or to introduce a specimen or picture of it.
- Definitions by genus and differentia : identifying the boundaries and stating the 'essence of a thing' by indicating its genus (i.e. the larger class of things in which the referent is included) and then how it differs from other subclasses of the same genus.
- Definition by stipulation : a researcher is responsible for stipulating precisely how a concept will be applied in a particular study.
- Constitutive definitions : define constructs by describing how they are linked to other constructs in a set (e.g. intelligence is the product of the interaction of a person’s heredity and environment) or by describing their key characteristics (e.g. intelligence is the ability to deal with tasks involving abstractions, to generalize, to learn from experience, or to deal with new situations).
- Operational definitions : ascribe meaning to constructs by specifying the operations necessary to achieve certain objectives, for example (1) measured operational definitions specify the operations necessary to measure instances of constructs; (2) experimental operational definitions specify the operations necessary to manipulate constructs in an experiment to precipitate or prevent their presence.
(from Chapter 7, pp. 180-183)
[1979] Philip Brian Bell and Philip James Staines, Reasoning and Argument in Psychology, Routledge and Kegan Paul, London, 1981
“There are two main classes of definition: descriptive and stipulative. When proposing a descriptive definition, a writer attempts to spell out the usual meaning of a term he is using (e.g. after referring to a conventional dictionary), whereas in a stipulative definition he specifies the meaning he intends for the word or phrase, regardless of more usual or less technically precise possible interpretations. He uses a stipulative definition when he gives a familiar work a new meaning or introduces a new term”. (Chapter 1, p. 9)
[1988] Louise E. Rorabacher, Georgia Dunbar, Clement Dunbar, Assignments in Exposition, Ninth Edition
“You may define ... by means of description, narration, classification, analogy, analysis, or cause and effect”. (p. 346)
[1965] Peter Caws, The Philosophy of Science, D. Van Nostrand, Princeton, New Jersey
Extension (denotation) “The extension of a term is the class of all possible objects, past or future, known or unknown, which if they existed would belong to its denotation.” (p. 45)
Intension (connotation). “A list of the properties which an object must possess if it is to be included in the denotation of some term specifies the intension of the term.” (p. 45)
[1981] Gerald Runkle, Good Thinking, Second Edition
Extension (denotation). “It is sometimes said that ‘the most basic level of meaning’ a word can have is its extension (or denotation). The extension (or denotation) of a word is that whole class of thing to which the word refers.” (Chapter 2, p. 15)
Intension (connotation). “Another kind of ‘meaning’ that words are said to have is intensional. While extension comprises the things a word refers to, intension comprises the characteristics that must be present for the word to be properly applied. The intension of a word is sometimes called its set of defining criteria.” (Chapter 2, p. 17)
[1988] Vincent E. Barry and Douglas J. Soccio, Practical Logic, Holt, Rinehart and Winston, New York, Third Edition
“A definition is an explanation of the meaning of a term. Meaning, in turn, can refer to either to denotation or connotation."
Denotation. "The denotation or extension of a term is the collection or class of objects to which the term may correctly be applied. For example, the denotation of 'chair' would be any example of a chair." "Defining denotatively is defining through example; a term is said to denote the objects it can be applied to."
Connotation. "The objective connotation (or intension) of a term is the collection of properties shared by all and only those objects in a term’s extension (denotation). Thus, the connotation of 'chair' is 'a piece of furniture used to sit on'.” (Chapter 3, p. 48)
[1992] Chava Frankfort Nachmias and David Nachmias, Research Methods in the Social Sciences, Fourth Edition
"Definitions that describe concepts by using other concepts are conceptual definitions."
“Conceptual definitions that enhance communication share the following essential attributes:
- A definition must point out the unique attributes or qualities of whatever is defined. It must be inclusive of all cases it covers and exclusive of all cases not covered.
- A definition should not be circular; that is, it must not contain any part of the thing being defined.
- A definition should be stated positively.
- A definition should use clear terms.”
(Chapter 2 Conceptual Foundations of Research, pp. 30-31)
[1982] Irving M. Copi, Introduction to Logic, Sixth Edition
Rule 1) “A definition should state the essential attributes of the species.”
Rule 2) “A definition must not be circular.”
Rule 3) “A definition must be neither too broad nor too narrow.”
Rule 4) “A definition must not be expressed in ambiguous, obscure, or figurative language.”
Rule 5) "A definition should not be negative where it can be affirmative.”
(Chapter 4 : Definition - pp. 165-169)
[1988] Louise E. Rorabacher, Georgia Dunbar and Clement Dunbar, Assignments in Exposition, Ninth Edition
Guidelines for writing formal definitions:
- Keep your class small but adequate
- Do not define a word by mere repetition
- State the differentiating characteristics precisely
- Define a word in simpler and more familiar terms
- Descriptive details are often valuable
- Examples and positive comparisons may illuminate the unfamiliar
- Negative comparisons (what something is not) may be helpful
- Classification can improve the definition of a term
- Analysis (breaking down the object to be defined into the parts composing it) is another means of clarifying a basic definition
- The description of origin/causes, results/effects and function/uses can assist in producing a clear definition
(Adapted from Unit 15 Definition - pp. 327-332)
[1988] Vincent E. Barry and Douglas J. Soccio, Practical Logic, Holt, Rinehart and Winston, New York, Third Edition
“1 - A good connotative definition should state the essential characteristics of the term being defined.”
“2 - A good connotative definition shouldn’t be circular.”
“3 - A good connotative definition should be neither too broad nor too narrow.”
“4 - A good connotative definition shouldn’t be expressed in obscure or figurative language.”
“5 - A good connotative definition should not be negative where it can be affirmative.”
(Chapter 3, pp. 50-51)
[1751-1772] Jean Louis Formey, Definition, in Diderot-D’Alembert, Encyclopédie
"Une des grandes utilités qu'apporte la définition, c'est de faire comprendre nettement de quoi il s'agit, afin de ne pas disputer inutilement sur des mots, comme on fait si souvent même dans les discours ordinaires.
Mais, outre cette utilité, il y en a encore une autre ; c'est qu'on ne peut souvent avoir une idée distincte d'une chose, qu'en y employant beaucoup de mots pour la désigner. Or il serait importun, surtout dans les livres de science, de répéter toujours cette grande suite de mots : c'est pourquoi, ayant fait comprendre la chose par tous ces mots, on attache à un seul mot l'idée complexe qu'on a conçue, qui tient lieu de toutes les autres."
[1923] C. K. Ogden, I. A Richards, The Meaning of Meaning, 1972
“The reason for using definitions at all is practical. We use them to make discussions more profitable, to bring different thinkers into open agreement or disagreement with one another.” (Chapter VI, p. 121)
“Definitions are of great importance in the construction of deductive, scientific systems, those automatic thinking-machines for which logic and mathematics are, as it were, the rules or instructions. In such a deductive system as mechanics, for example, it is through the definitions employed that the parts of the symbolic system are linked together, so that a given manipulation of the symbolism will yield comparable results even when their precise nature is not foreseen by the manipulator.” (Chapter VI, pp. 121-122)
[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioral Science, Chandler Publishing Co., Scranton
“A real specification has a cognitive content; if we do not speak of it as being strictly ‘true’, we assign some other mark of cognitive worth, like ‘valid’ or ‘sound’, or at least, ‘useful’.” (p. 75)
[1982] Irving M. Copi, Introduction to Logic, Sixth Edition
Five Purposes of Definition.
1) To Increase Vocabulary. “In conversation or in reading, one often comes upon unfamiliar words whose meanings are not made clear by their contexts. To understand what has being said, it is necessary to find out what the words mean; here definitions are required.”
2) To Eliminate Ambiguity. "Fallacious arguments ... result from the unwitting use of ambiguous terms." "When the ambiguity is resolved ... the fallacy is exposed. But to resolve the ambiguity, we require definitions to specify the different meanings of the ambiguous word or phrase. Ambiguous language can lead not only to fallacious argumentation but also to disputes which are merely verbal."
3) To Reduce Vagueness. “Vagueness in sometimes confused with ambiguity. A term is ambiguous in a given context when it has two distinct meanings and the context does not make clear which one is intended. A term is vague when there exist ‘borderline cases’ such that it cannot be determined whether the term applies to them or not.”
4) To Explain Theoretically. Definition, in this case, intends “to formulate a theoretically adequate or scientifically useful characterization of the objects to which it is applied.”
5) To Influence Attitudes. “One often defines a term with the purpose in mind of influencing the attitudes or stirring the emotions of one’s readers or hearers.”
(Chapter 4, pp. 138-143)
[55 B.C.] Cicero, De Oratore, in Richard Robinson, Definition, Clarendon Press, Oxford 1972, First edition 1954
“A certain brief and circumscribed account of the properties of the things we wish to define.”
[1689] John Locke, Concerning Human Understanding
“... the defining of words, which is nothing but declaring their signification ...”
“For, definition, being nothing but making another understand by words what idea the term defined stands for, a definition is best made by enumerating those simple idea that are combined in the signification of the term defined : and if, instead of such an enumeration, men have accustomed themselves to use the next general term, it has not been out of necessity, or for greater clearness, but for quickness and dispatch sake.” (Book III, Chapter 3, § 10)
[1922] Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Routledge, London 1995
“Definitions are rules for the translation of one language into another. Every correct symbolism must be translatable into every other according to such rules. It is this which all have in common.” (3.343)