Extension (semantics)

Extension and intension (Latin extensio, stretch, span, spread ' and Latin intensio, effort, stress, tension ') are terms of the semantics with which different dimensions of meaning of linguistic expressions ( predicates, sentences ) or logical entities ( amounts, terms, propositions ) are determined. The two terms comes from the environment of Aristotelian logic and has been established as, étendue de l' idee 'and' comprehension de l' idée ' by the logic of Port -Royal. In the philosophy of language, linguistics, various calculi of logic and mathematics extension and intension are often designed differently. For predicates and terms, the expressions term scope and connotation are unproblematic translations.

• 2.1 Extension of a sentence
• 2.2 intension of a sentence

• 3.1 jurisprudence, case law and administrative action
• 3.2 Religious Studies and Theology

• 6.1 Logic History
• 6.2 Modern

Extension and intension of predicates ( concepts )

Extension

In traditional logic ( logic term ) was understood as the extension or the extent of a term the totality of things to which it extends (which fall under it, which he has ). Thus was the extension of the term " person " means all people. Since the Pyrrhonian skepticism, however, there is also doubt about such a term potency. With the advent of empirical sciences, the taxonomies fell more in the individual scientific areas of responsibility and their philosophical or theological- syllogistic administration was obsolete. In traditional logic never a sufficiently complex ontology was able to provide practical review and decision process, as example of this is only the manifold debated question called, which is part of the totality of all human and what is not (eg deceased people, invalids, corpses, future people may only existing people. problem to see presenteeism, actualism ). The last defender of such a term logic was Bruno von Freytag- Löring Hoff.

In classical logic terms we group often as predicates, that is, as forms of expression with a space. From the statement form " ... is a man" then creates a true statement, if you are in the space their own name or the designation of a people begins. Extension of such a predicate the set of references of all those proper names and markings that have been inserted in the blank space is then give a true statement. The same applies to more -place predicates (relations): The extension of the two -digit predicate " ... the same father as ... " consists of the set of all siblings and ( paternal ) half-sibling pairs.

Intension

In what intension and term content, opinions differ in the logic. According to a commonly held view is the intension of a concept of the totality of features or characteristics - the terminology is inconsistent here - which, in fact are the things that he covers together or constituting the intersection of their necessary features. Accordingly contains the intension of the term " man " the characteristics animated, mortal, walking on two legs, ungefiedert, rational, producing tools, etc.

Term characteristics are mainly associated with the definition of a term in appearance:

• People are walking on two legs ungefiederte beings.

Or:

• People are rational beings.

None of these definitions makes use of all the features that are common to all men; both are, for example, without the feature from mortal. Nevertheless, they serve their purpose, namely a universe of discourse that includes only physical things, selective filter out those that fall under the term "man." If, however, a world of the speech, in which is also rational immortal place, for example, for the gods and goddesses of Mount Olympus, so would the second definition in order to fulfill this function be narrowed mortal by the inclusion of the feature.

The examples also show that terms with different intension can have the same extension in the same universe of discourse: "walking on two legs ungefiederte beings " and " rational living " are extensionally equal terms. The reverse does not apply: Terms with different extension have the same universe of discourse always different intension.

Extensional Individuation of terms

As is known, many words are ambiguous: the word "bank" may refer to a seat or a financial institution. Both meanings are different terms. What constitutes the difference between these concepts and how to recognize equality and diversity of concepts? A simple attempt to answer to this question is called extensionality, according to which concepts are completely determined by its extension Alber calibration. Obviously, the set of all seating is a lot different than that of all financial institutions.

This extensionality has among other things to explain the well-known problem, how it behaves in terms such as " Evening Star " and " Morning Star". The extension of both names is the same: both refer to the planet Venus. Still seems plausible that, who thinks of the Evening Star, another term used than that which thinks of the morning star. The difference is, the classical formulation of Gottlob Frege, not in extension, but in the way of reference to the designated object, ie the intension. Frege himself does not speak of extension, but of importance, and not by intention, but of meaning. Subtracting the intension to individuation of concepts approach, the extensionality must be discarded.

Inverse relationship between intension and extension

If one understands the intension as a set of features and the extension as a set of objects which possess these characteristics, then intension and extension behavior evident in the following manner opposite to each other: the more extensive the intension, the smaller the extension and vice versa. A term such as " substance" according to the Aristotelian ontology includes anything at all being, a term such as " physical substance" correspondingly less, and a term such as " rational animated corporeal substance " even less objects. Such examples exist in large numbers and suggest the following basic principle:

If the intension of A is contained ( as a subset ) in the intension of B, then the extension of B is contained ( as a subset ) in the extension of A. B is then a sub-class ( a species) from A, A is a superclass ( a genus ) of B.

With the advent of modern logic the generality of this rule was challenged in various ways. The reason for this lay in the aforementioned vagueness of the notion of intension and in the multitude of ways to translate it into the formal language of a logic calculus. The first successful attempt at such a translation undertook Paul Weingartner. Weingartner was able to show that is a theorem of logic class " with a corresponding definition of intensional containment ", the above formulated principle.

Terminology

Minted is the juxtaposition between extension and intension, trace their roots to the Aristotelian logic, the logic of Port -Royal. By way of example, a compact formulation of Leibniz was quoted: " The living entity comprises more individuals than man, but man has more ideas or shape characteristics; one has more copies, the other more degree of reality; one has more extension, the other more intension. "

Throughout the history of philosophy, the concept of extension and intension of different authors has been applied, you should be extremely careful in equating the pairs of terms, especially since some authors treat them as properties of mental entities ( concepts, judgments ), other than properties of linguistic expressions. The following table shows some of these names.

It should be noted that particularly true in Frege caution to equate the term " significance " with the extension. The distinction between extension and intension is basically in term of the words ( "Planet" ) use, while Frege, the distinction between meaning and significance on proper names (where the meaning is the mode of presentation of an object, the meaning of the corresponding object) and whole sentences ( the point here is the idea that meaning applies the True / false ). In addition, also arise when applied to concept words differences: while the extension of "Planet" includes the planets of the solar system, the meaning of " planet" is for Frege the abstract concept " () is a planet ." In addition, in odd contexts or opaque contexts is the original meaning to the meaning of the expression. What takes the place of sense, Frege leaves.

Extension and intension of sentences

Extension of a sentence

According to widespread, controversial, of Gottlob Frege reasoned opinion, the extension of a declarative sentence is its truth value.

Frege himself: "We have seen that a sentence always a meaning is to be found when it comes to the importance of the components; and that is always and only the case when we ask for the truth values ​​. So we are forced to go to recognize the truth value of a sentence as its meaning. "

Intension of a sentence

The intension of a sentence ( in Frege: the meaning of a sentence ) are according to popular, controversial view its meaning, content, or thought or his proposition. According to Frege, the meaning of a sentence is his idea ( in an objective sense). According to Rudolf Carnap intension of a sentence is indicated by the sentence proposition.

Applications

Jurisprudence, case law and administrative action

For everyday business of lawyers is to link specific cases with legal norms, in which terms, in particular indefinite or vague terms, play a central role belongs. This involves a hand, to determine the intension of an applicable concept so that in practice clear-cut distinctions can be made, and so at the same time indicate the potential extension: cases with the characteristic x ( Intensionsbestimmung ) belong to the set (extension provision) of the term " y" designated standardized situations.

Example: § 242 paragraph 1 of the German Penal Code reads: "Whoever another takes away a foreign movable property with the intention of appropriating the thing itself or a third party unlawfully, shall be punished with imprisonment of up to five years or a monetary penalty. " The term " theft " can not be applied to cases the tapping of electrical energy (limited extension of the term" theft " ), since no current " thing " (limited intension of the term" thing "). The thus created loophole was closed by was inserted into the Criminal Code, § 248c, through which the " withdrawal of electrical energy " is placed under threat of punishment.

Religious Studies and Theology

The question of whether what denotes a term as a linguistic sign, exists or not, can not be treated only as an empirical, but also as onto- or mythological. Then get terms like " God ", " devil ", " angel " is not simply a zero - extension, but a more complex intension. Gods like Zeus " there " in any case as an element of the term " Greek mythology ".