Intensional definitions vs extensional definitions Definition

1 intensional definitions vs extensional definitions

1.1 classes of intensional definitions
1.2 classes of extensional definitions
1.3 divisio , partitio
1.4 nominal definitions vs real definitions

intensional definitions vs extensional definitions

an intensional definition, called connotative definition, specifies necessary , sufficient conditions thing being member of specific set. definition attempts set out essence of something, such genus , differentia, intensional definition.

an extensional definition, called denotative definition, of concept or term specifies extension. list naming every object member of specific set.

thus, 7 deadly sins can defined intensionally singled out pope gregory particularly destructive of life of grace , charity within person, creating threat of eternal damnation. extensional definition list of wrath, greed, sloth, pride, lust, envy, , gluttony. in contrast, while intensional definition of prime minister might senior minister of cabinet in executive branch of government in parliamentary system , extensional definition not possible since not known future prime ministers be.

classes of intensional definitions

a genus–differentia definition type of intensional definition takes large category (the genus) , narrows down smaller category distinguishing characteristic (i.e. differentia).

more formally, genus-differentia definition consists of:

for example, consider following genus-differentia definitions:

a triangle: plane figure has 3 straight bounding sides.
a quadrilateral: plane figure has 4 straight bounding sides.

those definitions can expressed genus ( plane figure ) , 2 differentiae ( has 3 straight bounding sides , has 4 straight bounding sides , respectively).

it possible have 2 different genus-differentia definitions describe same term, when term describes overlap of 2 large categories. instance, both of these genus-differentia definitions of square equally acceptable:

a square: rectangle rhombus.
a square: rhombus rectangle.

thus, square member of both genus rectangle , genus rhombus .

classes of extensional definitions

one important form of extensional definition ostensive definition. gives meaning of term pointing, in case of individual, thing itself, or in case of class, examples of right kind. 1 can explain alice (an individual) pointing out another; or rabbit (a class) pointing @ several , expecting understand. process of ostensive definition critically appraised ludwig wittgenstein.

an enumerative definition of concept or term extensional definition gives explicit , exhaustive listing of objects fall under concept or term in question. enumerative definitions possible finite sets , practical relatively small sets.

divisio , partitio

divisio , partitio classical terms definitions. partitio intensional definition. divisio not extensional definition, exhaustive list of subsets of set, in sense every member of divided set member of 1 of subsets. extreme form of divisio lists sets member member of divided set. difference between , extensional definition extensional definitions list members, , not subsets.

nominal definitions vs real definitions

in classical thought, definition taken statement of essence of thing. aristotle had object s essential attributes form essential nature , , definition of object must include these essential attributes.

the idea definition should state essence of thing led distinction between nominal , real essence, originating aristotle. in passage posterior analytics, says meaning of made-up name can known (he gives example goat stag ), without knowing calls essential nature of thing name denote, if there such thing. led medieval logicians distinguish between called quid nominis or whatness of name , , underlying nature common things names, called quid rei or whatness of thing . (early modern philosophers locke used corresponding english terms nominal essence , real essence ). name hobbit , example, meaningful. has quid nominis. 1 not know real nature of hobbits, if there such things, , real nature or quid rei of hobbits cannot known. contrast, name man denotes real things (men) have quid rei. meaning of name distinct nature thing must have in order name apply it.

this leads corresponding distinction between nominal , real definitions. nominal definition definition explaining word means, i.e. says nominal essence is, , definition in classical sense given above. real definition, contrast, 1 expressing real nature or quid rei of thing.

this preoccupation essence dissipated in of modern philosophy. analytic philosophy in particular critical of attempts elucidate essence of thing. russell described hopelessly muddle-headed notion .

more kripke s formalisation of possible world semantics in modal logic led new approach essentialism. insofar essential properties of thing necessary it, things possesses in possible worlds. kripke refers names used in way rigid designators.