Definitions

    I.    Tell us what concepts are and how related to other concepts.

        A.    Function of definitions.

                1.    Tell us the criteria for membership in the class of referents and what is and is not included in a concept.

                2.    Clarifies the relationships among concepts.

                3.    Summarizes The referents of our concepts.

        B.    Good definition condenses knowledge we have about the referents.

                1.    Highlights.

                2.    Key points.

        C.    Must have:

                1.    Genus.

                2.     Differentia.

                        a.    Genus names the wider class.

                        b.    Differentia, differentiates concept from other species.

                        c.    Specifies an essential attribute.

        I.    Kinds of definitions.

               A.    There are at least 16 different kinds of definitions. (Try to find some other types)

                        1.    Circular definition presents the meaning of a term either by using the same term with the same meaning in the definiens, or by using

                               grammatical variation of the term. Considered a fallacious means of definition, even though most kinds of definitions are circular themselves.  

                               Circulus in definiendo, Latin for circularity in defining. Examples of circular definition are:

                                a.    A dancer is one who dances.

                                b.    Or A teacher is one who teaches@.

                        2.    Cognitive definition

                        3.    Connotative, or Intensional definition, assigns meaning to a term by indicating the qualities, or attributes that the term connotes. Three kinds of    

                               intensional definition are:

 

                                a.    Synonymous definition, in which one term means, or has the same attributes as the word being defined, or a definition wherein, the

                                      definiendum and definiens are interchangeable. The giving of a list of cognate terms. Or identical meanings. The paradigm for synonymous

                                      definition is the translation from one language into another. As in defining:

                                        1)    Physician means a Doctor,

                                        2)    Lawyer means an Attorney.

                                        3)    To hate means to loathe.

  b.    Operational definition assigns a meaning to a term by specifying certain experimental procedures that determine

        whether, or not the term applies in a particular context. For example: AOne substance is harder than another if and

        only if, one scratches the other when the two are rubbed together@. Also, by indicating the actions, operations,

        activities, or procedures, which the term symbolically implies and which when performed serves as its meaning; as in

        the case of:

        1)    The term length means taking a measuring stick, such as a foot ruler , placing it on an object to be measured, so

               that one end of the stick coincides with one end of the object, then marking where the other end of the stick ends,

               then moving the stick along the object in a straight line until the previous end point coincides with the previous

               position of the second end point. Repeating this process as often as necessary and noting the total number of

               times the operation was performed, constitutes the length of the object being measured@.

                                c.    Definition by Genus and Difference, (L. Genus Et Differentia) assigns meaning to a term by identifying a genus term and one, or more

                                       difference terms, that when combined, convey the meaning of the term being defined, or defining by giving the characteristics, for

                                        differentia of a class that distinguish it from other sub-classes, that also fall within a more general class, the Genus. Some examples are:

  • species                     difference                     genus
  • ice: means                 frozen                          water
  • Human means:          rational                         animal
  • Automobile means:   passenger                     vehicle
  •                     4.    Contextual definition, or Definition in Use, does not give a definition which allows for the substitution of one term for another. Instead, a

                               paraphrase is offered and replaces the term to be defined, by another sentence, or expression in which the term does not occur. As in: A is the

                               brother of B, means A is male and has the same parents as B does. Also a definition which defines a term by establishing a context for it, or

                               indicating the context which gives it meaning. An example would be: X is defined as being soft when it yields easily to the touch. Definition of an

                               expression as it occurs in a larger expression.

                       5.    Co-ordinative definition, The co-ordination of a concept of a physical theory with an actual physical process. As in: In geometry, a straight line may

                              be co-ordinated with the path of a light ray. Definition of a theoretical term using non-theoretical terms. Defining a meter as: A unit of measurement

                              equal to one forty-millionth of the earth's circumference.

                       6.    Denotative, or Extensional definition by naming: Assigns a meaning to a term indicating the members of the class that the definition denotes. There

                             are three kinds of denotative definition, they are:

                            a.    Demonstrative, or Ostensive definition, which is definition by literally pointing out, showing, illustrating, feeling, actual examples of something in

                                   the world. An example: The term chair means: this, point to a chair.

                            b.    Enumerative definition: Assigns meaning to a term by naming the members of the class the term applies to, for instance, Planet means: Mercury,

                                  Venus, Earth, Mars, Saturn, Jupiter, Neptune, Uranus, or Pluto. Listing examples of the term being defined, as in defining U.S. President by

                                  naming some of the presidents: George Washington, Abraham Lincoln, Bill Clinton, George Bush etc. Also, giving a list of examples to which the

                                 term in question can be correctly applied, as in, A bird means such things as: Blue bird, sparrow, pigeon, chicken, hawk, eagle, condor.

                           c.    Definition by Sub-class, assigns meaning to a term by naming subclasses of the class applied by the term, as in, Tree means: Maple, Oak, Pine,

                                 Ohia, Kukui, Koa, or in, Government means: Oligarchy, theocracy, dyarchy, triarchy, duumvirate, triumvirate, gerontocracy, aristocracy,

                                 democracy, etc..

                    7.    Descriptive definition

                    8.    Essential, or Essence, or Real definition, gives the essence of something from among the characteristics possessed by it, one that is unique and

                           hierarchically superior in that it states either, the most important characteristic of the thing, and/or that characteristic upon which the others depend

                           on for their existence. Definition by essence looks for a single, objectively, existing, essence. For example: a human being is a animal that laughs, or

                            an animal that creates and uses tools, or an animal that cooks its food, or an animal that has an opposable thumb. Definition by essence aims for a

                            single objectively existing essence.

                    9.    Explicit definition: Any definition that makes it clear that it is a definition and identifies the term being defined; Father means: male parent, or for any

                               x, x is a father by definition if and only if x is a male parent.

                    10.    Functional definition, defines a term in terms of the functions something performs. Functional definitions are extrinsic, they do not stress the defining

                            characteristics peculiar to the thing itself, but the functions of the thing and its relations to other things. Example: Defining a referee in connection with

                            what he does in the game he is refereeing in, such as blowing a whistle to stop play, assessing penalties, enforcing rules, etc..

                    11.    Grammatical definition,

                    12.    Historical definition, defines a term in reference to the history of the thing being defined. Historical definitions are extrinsic, in that they do not stress

                            the characteristics peculiar to things themselves, but instead, present its external relations to other things and the sequential events involving, or

                            surrounding them.

                    13.    Implicit definition, in a set of axioms which implicitly defines the undefined terms in them by, in effect, confining the references of the terms to the

                            intended ones.

                    14.    Impredicative definition is the definition of an object in terms of a totality of which it is a member.

                    15.    Ideational,

                    16.    Lexical  or Customary or Reportive definition is the Dictionary definition of a term and is used to report meaning that a word already has in

                             common, or ordinary, established language usage. Classifiable as either true, or false, depending on whether it does, or does not report the way the

                             word is actually used in the language.

                    17.    Loaded Definition, gives the meaning of term in a prejudicial, or biased way and is often associated with propaganda. An example would be: A

                            definition of fishing, as a fish on one end of a line and a fool on the other. Or, the only good infidel , is a dead infidel.

                    18.    Nominal definition, or Verbal definition, is a definition, which explains the meaning of a word or symbol, as opposed to a real definition, which gives

                            the definition of an existent thing. Example: A triangle is the name of a plane figure comprised of three, connected, straight sides, that form three

                            angles equaling 180 degrees. Giving the linguistic meaning of the term.

                    19.    Persuasive, or Rhetorical definition is designed to engender a favorable, or unfavorable attitude toward what is being denoted by the definition. This

                            is accomplished by assigning an emotionally charged or value-laden meaning to a word, by making it appear that the word really has that meaning in

                            the language in which it is used. Opposing pairs of persuasive definitions of the term Liberal would be: Liberal means, a bleeding heart do gooder,

                            obsessed with giving away other peoples money. Liberal also means, A genuine humanitarian, committed to the goals of adequate housing, health

                            care and equal opportunity for all Americans. Also, Giving the meaning of terms in an emotive, expressive way in order to influence the attitudes,

                            values, beliefs, emotions, and goals of others. An example: The true meaning of a teacher is one who relates to his students on a personal level and

                            enthusiastically guides them to sources of information. This kind of definition is prevalent in advertising.

                    20.    Phonological

                    21.    Predicative

                    22.    Recursive, or Inductive definition: Contains two parts, a basis clause, in which the definition does not occur and a inductive step in which the

                            definition does occur. An example would be: A direct ancestor would be someone's parents, grand parents, great grand parents etc. Formalizing this

                            we could get: X is a direct ancestor of Y, if X is a parent of Y, or is a parent of a direct ancestor of Y. Also, a definition in which a variation of the

                            word defined occurs in the definiens, thereby avoiding the appearance of circularity, as in defining AA father as a male parent. In mathematics,

                            defining a number, theoretic function, or predicate term, by assigning value or values to the number, theoretic function, or predicate. Recursive

                            definitions are an important variety of contextual definitions.

                    23.    Referential

                    24.     Semantic

                    25.    Semiotic

                    26.    Situational

                    27.    Stipulative, or Legislative, or Precising, or Restricting definition: Assigns meaning to a term for the first time, either by coining a new term like Xerox,

                            for copying machine, or by giving a new meaning to an old term, as in using 'Nuke it', for micro waving something. Also, The definiens is intentionally

                            limited in meaning and/or is assigned a specific meaning for consistency and clarity of communication and as a matter of preference, indicates how

                            the user of the term intends the term to be understood. An example would be: We propose to restrict the meaning of the term, 'college' to a four-

                            year institution of higher learning. Or a new term chosen arbitrarily to assign meaning for the sake of brevity, expressing a new concept, secrecy,

                            added precision, avoidance of emotive connotation, or standardization. An example: When Norbert Weiner coined the term 'cybernetics' he gave it

                            the stipulative definition, As "the science of communication and control systems".

                            1.    Precising or Restricting definition is a specific form of a stipulative definition, where specific and explicit meanings are attached and can only be

                                   attached to a term to reduce the vagueness of a term so a decision can be reached as to the applicability of the term in a specific context: Poor

                                   means, having an annual income below the poverty level or less than $5,000 and a net worth of less than $15,000. Or, for the purpose of this

                                   lecture, the term 'argument' means, a persuasive appeal, or chain of reasoning comprised of two sets of statements, a conclusion and a set of

                                   premises offered in support of the conclusion.

                28.    Syntactical definition, defines the notational conventions that prescribe the ways, or rules, in which certain signs, symbols, or expressions will

                        represent, or be substituted for other particular variables, signs, symbols, or expressions, in a language. In symbolic logic, the logical connectives, or

                        logical operators, and their symbolic notations are defined as follows:

                        NEGATION      ~

                        AND                  •

                        OR                     Ú

                        IF                       É

                        IFF                    º

                29.    Theoretical definition provides a theoretical construct or characterization of the term denoted by the definiendum so as to provide a way of viewing a

                        conceptual framework for the entity, or entities denoted by the term, which suggests deductive consequences, further investigation, experimentation, or

                        anything else that accepting the theory of said entities would entail, as in, The word heat means the energy associated with the random motion of

                        molecules in a given unit of mass. Does more than assign meaning to a term, provides the means to conceive of the physical phenomena of heat itself.

                        (Get examples for each)

                The following kinds of definitions are relevant to the study of Logic:

                30.    DENOTIVE DEFINITION:

                        Term used names particular objects, or instances, in existence. Ostensively point it out.

                        'A chair, this (pointing to it) is a chair'.

                31.    CONNOTATIVE DEFINITION:

                        Terms intensional meaning: Understanding what is intended by the term as it is used.

                        You understand what the intension of the term chair is, so you don't come in and sit on the desk.

                32.    STIPULATIVE DEFINITION:

                        A term that specifics meaning operationally, i.e.:

                        In math, a circle can be defined as the loci of all points equidistant from a center point.

                33.    LEXICAL DEFINITION:

                        The dictionary definition of a term. Classifiable as either true or false.

                        Problem with this is that it is too strong. There is a sub-cultural bias built into all language.

                        Fast

                        Snow Many different meanings.

                        water