Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Extensional and intensional definitions
Summary
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term.
An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term.
For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.
This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition – an extensional definition of bachelor would be a listing of all the unmarried men in the world.
As becomes clear, intensional definitions are best used when something has a clearly defined set of properties, and they work well for terms that have too many referents to list in an extensional definition. It is impossible to give an extensional definition for a term with an infinite set of referents, but an intensional one can often be stated concisely – there are infinitely many even numbers, impossible to list, but the term "even numbers" can be defined easily by saying that even numbers are integer multiples of two.
Definition by genus and difference, in which something is defined by first stating the broad category it belongs to and then distinguished by specific properties, is a type of intensional definition. As the name might suggest, this is the type of definition used in Linnaean taxonomy to categorize living things, but is by no means restricted to biology. Suppose one defines a miniskirt as "a skirt with a hemline above the knee".
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (20)
LEARN-602: Designing activities for developing and assessing computational thinking skills
In this course, students will learn how to design, realize, analyse and assess educational activities in formal education, with and without the use of technologies, for the development of computationa
MATH-105(b): Advanced analysis II
Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables.
MATH-213: Differential geometry
Ce cours est une introduction à la géométrie différentielle classique des courbes et des surfaces, principalement dans le plan et l'espace euclidien.
Related lectures (83)
Nonlinear Dynamical Systems: Key Concepts
Covers key concepts in nonlinear dynamical systems, such as existence, uniqueness, and continuous dependence of solutions.
Harmonic Oscillators: Definitions and Dynamics
Covers the definitions and dynamics of harmonic oscillators, including ladder operators and coherent states.
Developable Surfaces and Parametrization
Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.
Related publications (39)
Two statistical regimes in the transition to filamentation
We experimentally investigate fluctuations in the spectrum of ultrashort laser pulses propagating in air, close to the critical power for filamentation. Increasing the laser peak power broadens the spectrum while the beam approaches the filamentation regim ...
Optica Publishing Group2023A Theory of Value for Service Ecosystems
In this thesis, we present a theory of value for the design and analysis of service ecosystems. The theory is based on general systems thinking. The concept of a system is used for relating knowledge from different disciplines (such as software engineering ...
EPFL2022Related people (3)
Related concepts (4)
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.
Intension
In any of several fields of study that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language—an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word plant include properties such as "being composed of cellulose (not always true)", "alive", and "organism", among others. A comprehension is the collection of all such intensions.
Extensionality
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal definitions of objects are the same. Consider the two functions f and g mapping from and to natural numbers, defined as follows: To find f(n), first add 5 to n, then multiply by 2. To find g(n), first multiply n by 2, then add 10.
Related MOOCs (18)
Analyse I
Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond
Analyse I (partie 1) : Prélude, notions de base, les nombres réels
Concepts de base de l'analyse réelle et introduction aux nombres réels.
Analyse I (partie 2) : Introduction aux nombres complexes
Introduction aux nombres complexes