An extensional definition, also called a denotative definition, of a concept or term specifies its extension.

One important form of the extensional definition is ostensive definition.

An enumerative definition of a concept or term is an extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question.

A divisio is not an extensional definition.

The difference between this and an extensional definition is that extensional definitions list members, and not sets.

An extensional definition is denoted by enclosing the list of members in curly brackets:

The extensional definition of function equality, discussed above, is commonly used in mathematics.

A similar extensional definition is usually employed for relations: two relations are said to be equal if they have the same extensions.

An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question.

For example, an extensional definition of the term " nation of the world " might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.

But for salva veritate to hold as a definition of something more than extensional agreement, i. e., cognitive synonymy, we need a notion of necessity and thus of analyticity.

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 it works well for sets that are too large to list in an extensional definition.

It is impossible to give an extensional definition for an infinite set, but an intensional one can often be stated concisely — there is an infinite number of even numbers, impossible to list, but they can be defined by saying that even numbers are integer multiples of two.

Such a language would be extensional, in the way that two predicates which are true about the same objects are interchangeable again without altering the truth-value.

Perhaps the above can be made clearer by the discussion of classes in Introduction to the 2nd Edition, which disposes of the Axiom of Reducibility and replaces it with the notion: " All functions of functions are extensional " ( PM 1962: xxxix ), i. e.,

The essence here is that an occasion of experience comprises a finite extent of space time and can be the extensional ' receptacle ' of a process.

* Ultrasound attenuation can be used for extensional rheology measurement.

Satisfactory accounts of general semantics extensional devices can be found easily.

Alternatively such a fault can be called an extensional fault.

In logic, extensionality, or extensional equality refers to principles that judge objects to be equal if they have the same external properties.

" Best argues that the principle of extensional self-defense mirrors the penal code statues known as the " necessity defense ," which can be invoked when a defendant believes that the illegal act was necessary to avoid imminent and great harm.

For example, in extensional mereologies ( defined below ), Parthood can be defined from Overlap as follows:

Many of Royce's writings on logic and mathematics are critical of of the extensional logic of Principia Mathematica, by Bertrand Russell and Alfred North Whitehead, and can be read as an alternative to their approach.

In contrast, setoids may be used when a difference between identity and equivalence must be maintained, often with an interpretation of intensional equality ( the equality on the original set ) and extensional equality ( the equivalence relation, or the equality on the quotient set ).

Predicates may also be defined by facts and rules and therefore neither be purely extensional nor intensional, but any datalog program can be rewritten into an equivalent program without such predicate symbols with duplicate roles.

This was a problem for extensional semantics, where the semantics of a word such as red is to be defined as the set of objects having this property.

Modal logic can be regarded also as the most simple appearance of such studies: it extends extensional logic just with a few sentential functors: these are intensional, and they are interpreted ( in the metarules of semantics ) as quantifying over possible worlds.

En echelon tension gash arrays ( or extensional veins ), characteristic of ductile-brittle shear zones, and sheath folds can also be valuable macroscopic shear-sense indicators.

An " extensional stance " and restriction to a second-order predicate logic means that a propositional function extended to all individuals such as " All ' x ' are blue " now has to list all of the ' x ' that satisfy ( are true in ) the proposition, listing them in a possibly infinite conjunction: e. g. x < sub > 1 </ sub > V x < sub > 2 </ sub > V.

A list of currently and previously marketed commercially available extensional rheometers is shown in the table below.

The production of large quantities of magma, variously attributed to mantle plumes or to extensional tectonics, further pushed sea levels up, so that large areas of the continental crust were covered with shallow seas.

Verbs are composed of a root followed by one or more extensional suffixes.

The longer, more shallow northwestern flank displays extensional features, such as large slumps and normal faults.

As a volcano grows in size, the stress field underneath the volcano changes from compressional to extensional.

The extensional stresses in the detachment zones can produce giant landslides and normal faults on the volcano's flanks, leading to the formation of a basal escarpment.

This change from a quasi-intensional stance to a fully extensional stance also restricts predicate logic to the second order, i. e. functions of functions: " We can decide that mathematics is to confine itself to functions of functions which obey the above assumption " ( PM 2nd Edition p. 401, Appendix C ).

The study of extensional flows is called extensional rheology.

Shear flows are much easier to study and thus much more experimental data are available for shear flows than for extensional flows.

Also, the transition from a continental rift to an oceanic rift is accompanied by block faulting, where blocks of continental crust drop down along extensional faults where the crust is being pulled apart.

See for example extension, and the extensional devices.