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An extensional definition, also called a denotative definition, of a concept or term specifies its extension.
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extensional and definition
An extensional definition would be a list of all past, present and future prime ministers.
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.
extensional and also
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 ).
In plate tectonics, a divergent boundary or divergent plate boundary ( also known as a constructive boundary or an extensional boundary ) is a linear feature that exists between two tectonic plates that are moving away from each other.
Other mathematical objects are also constructed in such a way that the intuitive notion of " equality " agrees with set-level extensional equality ; thus, equal ordered pairs have equal elements, and elements of a set which are related by an equivalence relation belong to the same equivalence class.
A non-intensional statement is also known as an extensional statement, since substitution of co-extensive expressions into it always preserves logical value.
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.
Intensional logic is not alone in that: also Gottlob Frege accompanied his ( extensional ) calculus with detailed explanations of the semantical motivations, but the formal foundation of its semantics appeared only in the 20th century.
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.
If E is also assumed extensional, so that:
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.
Whether due to lithospheric cooling also known as thermal subsidence or the compressional activity in the area reactivated some extensional faults the extension is marked by the isotopic ages of the previously mentioned rocks.
See also intensional definition versus extensional definition.
See also extensionality, and also intensional definition versus extensional definition
extensional and called
The study of extensional flows is called extensional rheology.
The techniques Korzybski prescribed to help a person develop consciousness of abstracting he called " extensional devices.
Alternatively such a fault can be called an extensional fault.
The best-known such system is the one called classical extensional mereology, hereinafter abbreviated CEM ( other abbreviations are explained below ).
Simons clarifies something that is very difficult to determine by reading Leśniewski and his students, namely that Polish mereology is a first-order theory isomorphic to what is now called classical extensional mereology.
Such expressions always, or nearly always, produce intensional statements when added ( in some intelligible manner ) to an extensional statement, and thus they ( or more complex expressions like " It is possible that ") are sometimes called intensional operators.
Rheometers that control the applied shear stress or shear strain are called rotational or shear rheometers, whereas rheometers that apply extensional stress or extensional strain are extensional rheometers.
In philosophy of language, a context in which a sub-sentential expression e appears is called extensional if and only if e can be replaced by an expression with the same extension and necessarily preserve truth-value.
extensional and term
Steven Best has coined the term " extensional self-defense " to describe actions carried out in defense of animals by human beings acting as " proxy agents.
Steven Best has coined the term " extensional self-defense " to describe actions carried out in defense of animals by human beings acting as " proxy agents.
extensional and its
In case of a so-called extensional functor we can in a sense abstract from the " material " part of its inputs and output, and regard the functor as a function turning directly the extension of its input ( s ) into the extension of its output.
extensional and extension
See for example extension, and the extensional devices.
The large Basin and Range Province is a basin and range topography resulting from crustal extension ( extensional tectonics ).
Transverse crevasses are the most common crevasse type and they form in a zone of longitudinal extension where the principal stresses are normal to the direction of glacier flow, creating extensional tensile stress.
extensional and .
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.
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.,
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.
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.
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.
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