Definition

A definition (Latin definitio " delineation ", from de " (of sth ) down / off " and finis "boundary" ) is depending on the definition of teaching that is followed in this case, either 1 to determine the nature of a thing to be explained, second, the determination of a term, 3 a finding of fact skilled use of language or 4 fixing or agreement of such.

The term, definition ' is also a synonym, in other meanings as a special case of' Declaration ' called.

2.1 Science Scientific classification
2.2 Functions of definitions
2.3 Requirements for definitions 2.3.1 Classical definition rules
2.3.2 Non creativity
2.3.3 eliminability
2.3.4 Circles freedom
2.3.5 appropriateness
2.3.6 soon
2.3.7 Redundancy freedom

Classification of definitions

Connotative and denotative definitions

Intension and extension

In the definition of theory, a distinction between the intension and the extension of an expression. The intension ( connotation, meaning, connotation ) comprises the set of characteristics ( attributes, properties ) that must be met for objects ( people, objects) are denoted by the expression. The extension ( term scope, meaning, denotation ) comprises the set of all objects that are referred to by the expression.

" The extension of the name 'table' is the set of tables that the name ' book' the set of all books, the name, cubist painting ' the set of all Cubist pictures, etc. "

Between intension and extension, there is a reciprocal relation:

"A comparison of the contents and extent of a conception witheachother, Reveals the Following reciprocal relation: The greater the contents, the smaller the extent, and inversely, the smaller the contents, The Greater the extent. The reason is this: to many different object but few attributes belong in common; one the contrary, many attributes belong in common to but few different objects. "

The extension can be empty ( " the present King of France ").

Connotative definitions

A definition that specifies the intension of a word is called intensional or connotative definition.

Definition of equivalence

In the definition of equivalence to the defining expression ( definiendum ) and the defining expression ( definiens ) is connected by means of a copula that expresses that between definiendum and definiens is an equivalence, which means that the first term to the second is intensionsgleich.

The classical Greek term structure (Greek ορίζειν ( ορίζεσθαι ) ορισμός ) was in the translation into Latin split into definire / definitio and determinare / determinatio. Here is the definitio ( concept statement ) to be defined by "Object ", which are determined determinatio ago ( conceptual definition ) by defining "subject". For the classical Greek form of thought both were still collapsed into a single term.

Examples of such copula are " ... we call ... ", " ... means something like ... ", " As ... you should understand ... ", " ... is exactly when ... ".

See also Article: Gender proximum et differentia specifica

In the 19th century the Aristotelian doctrine was common, after which the next higher generic term (genus proximum ) and the artbildende difference ( differentia specifica ) is indicated. But it is basically only useful for classifications and where it is in Aristotle, with its special metaphysics closely related.

Aristotle has prepared the following scheme for such a definition: Each term can be defined as type ( eidos, species)

The classic form of the definition is therefore the stating of a genus proximum ( genus ) and a differentia specifica (specific demarcation criterion ). While it was believed for a long time that it was, this is a universal form, already shows a simple example of " A Norse is a person who comes from Denmark, Norway or Sweden," that meaningful definitions need not necessarily correspond to this scheme.

Definitions of the genus and the difference of species (Latin definitio fit per genus et proximum differentiam specificam ) constitute the most important group of equivalence definitions. The term is determined using a larger expression, and a difference specified, which occurs only in the particular type of goods and absent in all other species of the genus. It first seems to make sense to choose the largest possible number of properties. However, such a list could not be complete. Therefore, one tries to find a feature is sufficient to distinguish the items from other items of the type of the species.

In definitions of the genus and the difference of species, especially in the humanities and social sciences, one often finds the error that there are several species. It's called definitions with this definition error definition with multiple genres.

A word can be defined by specifying a synonym for the word. The problem with this method is that rare actual full synonyms are available. John Stuart Mill points out that this form of definition is not universally accepted:

Denotative definition

A definition that specifies the extension of a word is referred to as extensional or denotative definition.

Deictic definition

A " deictic " (or " epideictic " ) definition is a definition of terms, say a " elephant ", which consists in pointing pointing to a copy of the relevant class designated by the term (see deixis ).

Example: This here is red: red

Descriptive, caging and stipulative definition

Descriptive definition

As a descriptive definition (or declaratory definition) refers to a definition that holds a familiar language.

Immobilizing end definition

As caging definition refers to a definition in which a new term is introduced.

Thomas Hobbes was one of the first who decided a definition as fixing the meaning construed. For him, as for Spinoza, but were "correct" definition of the starting point for any real science.

Blaise Pascal (L' Esprit Géométrique, Logic of Port- Royal) was then the first person who has carried out the doctrine of logically defining clean as a term setting.

Christoph Sigwart

Christoph von Sigwart (1830 - 1904) wanted to "Definition" just call the sentence that equates the meaning of two expressions.

Gottlob Frege

The " Frege's theory " - the Dubislav so called because it was Gottlob Frege, who developed the distinction between signifier and signified - understands definitions as substitution rules about signs. One definition refers to the importance of a character by specifying the manner in which a sign is to be replaced by another in a logically equivalent manner.

Karl R. Popper

The conventional view definitions form the basic building blocks of every science. For Karl Popper, however, definitions are rather unimportant to the problems and theories. Because words in their logical function statements and theories subordinate in connection with which they are used.

"Not by the definition of the application of a term is defined, but the use of the term defines the set what is called his ' definition ' or its 'meaning'. In other words, there are only definitions in use ".

The traditional view that one must before one starts a discussion, first define the terms, ie achieve compliance over the vocabulary to be used, Popper holds fundamentally wrong. For all definitions, including operational definitions, only the problem of one side of the relation definition can move to the other side. This leads to an infinite regress; ultimately remain always undefined terms. It was impossible for logical reasons, to define scientific terms empirically or " constitute " to. However, in order to eliminate confusion, often necessary terms (such as " truth -like" or "probably " ) to distinguish.

The terms of empirical science are only defined implicitly, by the sentences in which they occur. This implicit definition as such is only a logical- formal; they are the implicitly defined terms no specific meaning (implicitly defined terms are variable). A " specific meaning " namely an empirical "meaning" get the implicitly defined terms only through the empirical use of the sentences in which they occur.

The erroneous view that it is possible to define terms, either explicitly ( by constitution ) or by reference ( through a so-called " coordinative definition " ) empirically, by pointing out the unbridgeable gap between universals ( universals ) and individual names ( proper names) be refuted. It is trivial that one can not define by a class of proper names a universal concept, nor a proper name by specification of universal terms. Between individual and universal terms so there is no transition in the sense that individual names can be defined by individual names by universals, or universals; there is only a substitution relationship between them: Each individual concept can occur not only as an element of your own special, but also as an element of a universal class ( but not vice versa).

A similar ratio as between concept and object between sentence and fact. The sentence is a matter hereof This situation can be from the fact ( an irrational piece of reality ) that identifies the record and from which the facts constituting a "rational part Moment" differ.

From each subject can testify its characteristics. Each sentence which says a feature represents a matter hereof that an object has infinitely many features, thus corresponds to the fact that a fact has infinitely many facts as rational part moments.

This second expression, which refers to facts, facts and phrases, is undoubtedly more important than the language that speaks of objects, features and terms. However, just as an object does not consist of features, and how the characteristics of the very fact prove to be brought by us to the subject that they are - logically - always singled out as arbitrary prove ( extracted from an infinite set of possible features ), as well prove the facts as rational, we carried into the non- rationalized reality coordinates.

The naive inductivist empiricism holds the records for pictures of reality. So he believes that the sets represent what is referred to herein as "facts"; and thus he sees the difference between " facts " and "fact". He does not the facts but the facts for in some sense "given" or " observable ". A less naive view of the facts and the fact is different, is if he 's going induktivistisch, before the mystery of how to stand out from the irrational facts, the rational facts.

Here exists no fundamental difficulty for the deductivism. His theory approaches, etc. are all rational constructions. That a situation turns out to be rational part moment of a fact for him means nothing more than the possibility that the facts may contradict rational facts - in other words, namely bio- pragmatic: that reactions may prove expedient and inexpedient.

" The principles of the theories ( nichtempirischer as empirical ) can be interpreted as implicit definitions of the basic concepts occurring This is recognized for non-empirical theories. Upon empirical theories are, however, mostly of the opinion that the basic concepts are understood as not logical constants or the like and that they is anything associated with in reality. this view is in this form untenable (especially the specified view of the mapping definitions ). the fact that a basic concept can be associated with its subject in reality, would indicate that denote general concepts demonstrable objects ( that is, the These " universals sunt realia " in the most primitive form). the case is this, that even the basic concepts of the empirical sciences are defined implicitly. allocation to the reality does not happen for the basic concepts, but for the theory as a whole, with all its terms ( the fact that is specified under which circumstances it is to be regarded as refuted ). In other words: The assignment is done by the method of deciding the specific corollaries of the theory, by decision of the derived predictions, in which no longer occur, the basic concepts. ( The assignment is application of the theory, practice is, it is based on practical decisions, - a remark which makes a discussion of the difference of the transcendental and the cognitive psychology thus urgent. ). "

While the logic of the research proposes a methodology for the purposes of empiricism, Popper borders latter on another, for each a scientific system mainly consists of definitions. The conventionalism is by Popper likewise a deductivist methodology; but these are statements of law any statements that relate to the reality or experience, but analytical judgments that are based on definitions. In a broader sense are also " implicit definitions " by the interpretation and conceptual networking within an axiomatic system can take the place of explicit definitions. Here, the terms are therefore not explicitly, but defined by the axiomatic theory.

The fundamental difference, however, between conventionalism and empiricism advocated by Popper is not moor cognitive logical, but based on a difference in the decision for a certain methodological orientation: wants to fail during the empiricism scientific statements on the experience, the conventionalist can by a " conventionalist twist " his favorite theory is always maintained in the wide variety of ways. Because this is already due to definitional reduction (logically) true; it then sets its part, for example by measurement method, what are the relevant data for them.

Stipulative definition and its explication

As a stipulative definition ( or even regulatory, rule -giving or prescriptive definition) refers to a definition that takes a familiar use of language as a basis, but new rules for the use. The analysis of language usage with the aim of stipulativen definition is referred to as explicitation.

C. G. Hempel

Carl Gustav Hempel recommends to undergo real definitions as well as the natural or everyday language terms and concepts taken from the process of explication or conceptual analysis. Only then they can be appropriately used according to scientific statements contexts. Here, it is clearly a parallel to Karl Popper's " diacritical analysis / Dialysis ".

Explikationsverfahren

As an explication is the process, will come in from an expression whose meaning is not clear to a science-based expression. Often, the result will be a stipulative, ie regulating, definition. It is different Explikationsverfahren have established.

The starting point of this method is the word origin. The reference can be made to the origin in the same language or the origin in another language. The word origin is often only one element in explicating and unreliable, but it can certainly provide surprising results and change of perspective. In particular, they can help developing trends in the use of the phrase to be recognized.

The etymological method

Another method is the analysis (in particular, the comparison ) of many applications of the analyzed expression. The method is also called the Socratic method because Socrates allegedly systematically apply finished first in his reflections on the meaning of different words. The term Socratic method is, however, problematic since this term in the history of philosophy terminology not only includes the induction.

In analytic philosophy is often trying to gain as much linguistic material to go into the analysis of a word. There are several systematic tool for finding a sufficient language material. One group of these methods form the lexicon methods.

In analytic philosophy another Explikationsverfahren has established, the transition to other parts of speech. A typical case is the transition from a noun to the corresponding verb in many cases, eg, when one examines instead the language speaking or instead of determining the detection, increasing with this approach, the emphasis on the action character of the object of investigation. In other cases, at least the perspective changes to be explicated expression.

Nominal and real definition

Following the Topics of Aristotle nominal and real definition can be distinguished.

Nominal definition

By means of a nominal definition sets the respective speaker fixed by his own decision, what a name should mean or designate a linguistic expression. A nominal definition is the same, what is called today "explicit definition " in use.

Example: In the " AWT " is to be understood in the following text " labor theory of value ".

Real definition

A real definition includes in the Aristotelian understanding a statement as to what a thing is in reality. In addition, it contains certain theoretical and philosophical conditions, about what certain things are, or what there is any, and how they are ordered (ontology ). There are hereby made and differences of style and genre according to Aristotle, or in an order under disorganized (taxonomy ) terms.

Example: " Lagmy " ≡ wine, which is produced by the fermentation of the juice of the date palm.

Behind the use of real definitions is thus more or less pronounced a certain philosophical conception of being and essence ( essentialism ) or assumptions about the existence of a specific law which finds its expression in the heart of the matter. Usually a truth claim is made with a real definition.

Less philosophically awkward to undergo real definitions to the process of meaning analysis or explication is. The result of such Explikationsversuchs can then be treated as an explicitly introduced definition without having thereby necessarily down to a certain philosophical position.

Aristotle

The logic of Aristotle is never "formal" in the sense that they would be of all metaphysical assumptions or other factual assumptions freely. Methodologically is important that the highest task of definition is according to Aristotle, is to complete the scientific investigation and thereby determine the nature of the objects studied.

G. W. F. Hegel

In traditional philosophy, the General Aristotle is treated following within the logic of concept, judgment and conclusion. For Hegel ( Jena Logic, Science of Logic ) but now these logical forms and processes reflect those of reality, ie they are interpreted ontologically from him.

Conventionally covered by the definition thinking the general nature of an object in its essential difference from other objects. According to Hegel, the definition can do this only because it reflects the real process in which the object of different type is different: the definition expresses the movement, one being preserved in its identity in the movement.

Thus, a real definition not be given in a single sentence, but actually as well as receives only by the real story of the object itself, as it defends against both other special and extended.

The General is framed by the negation of the particular, ie the term is dialectically constructed. The process of dissolution and destruction of the stable world of common sense results in the construction of a universal which is concrete in itself. Because it is carried out in particular, and by the special, ie. In the totality of the special moments

Heinrich Rickert and Emil Lask

Within the Baden neo-Kantian Heinrich Rickert and especially Emil Lask have endeavored to elaborate a definition of teaching.

Define is a unique possible definition of a term, being separated from adjacent other terms.

Rickert is the Doctrine of the definition of dissertation dar. Within limits of scientific concept formation, he then further elaborated his theory of the term without regard to the definition. The general confusion in the definition of teaching is based on a false conception of the term. Rickert wants to stick to the "Definition" as a " definition ".

On the question of the relationship between experience and thought and of intuition and concept Rickert says, citing the " visual people " Goethe, who says in his color theory, we theorize that even with every attentive look at the world:

"Every expressly brought to consciousness or known truth is in the form of the judgment, and necessary to its logical content include both an ' intuitive ' and a ' discursive ' moment. "

Rickert treated define as concept formation and concept of decomposition and tested against intuitionism about Jakob Friedrich Fries, who believe that it is possible to detect a truth theory to show just by seeing already, that the term finished defined not as logically earlier than the judgment is, but its logical content must be understood as a by product of judgment. The judgment is therefore not mere conjunction of concepts as ideas, but is an essential carrier discursive element.

Ernst Cassirer

Ernst Cassirer rises against the nominalism the objection that this could not explain why a particular concept (eg, the atomic term ) could lead to the discovery of new, previously unexplored facts.

Definitions according explicitness

Context definition ( implicit definition )

While in explicit definitions of the defined term appears alone on the left side, this does not apply for context definitions (or implicit definitions). In the context definition of the term defined thus occurs not only on the left side, but in a characteristic context for him. The use in other contexts is not permitted.

If, for example, a general definition of the predicate " adequate" heavy so can be defined easily, that the statement " X is an adequate calculus " iff is true if X is a calculus that is complete and correct.

Adequacy was thus defined only in the context of " calculus ", and the question of when anything is adequate, and what things fall under this definition, does not arise. This ontological difference saves about modern mathematics, the philosophical question of the nature of the number ( empirically psychologistically or logical). Because the mathematical axioms do not say what is a number, but when a little number may call and what arithmetic properties then apply for this.

Spinoza

Baruch Spinoza confused in his " Ethics" definitions with axioms.

As an example: He draws the following two statements, which he calls the "Definitions", the conclusion:

The substance is naturally earlier than their affections.

It is clear, at (1 ) and (2) to agreements on the language or character use. From such can not even the existence of the so signified conclude, let alone derive another existence assertion logically correct. If it succeeds Spinoza to come to an interesting thesis, then only because he uses his definitions secretly as Existenzialaxiome.

" Omnia determinatio negatio est. " (Eng.: Each determination is a negation. )

Partial definitions

Partial definitions apply only to a specific part of the field. They are applicable only for the case that a certain condition is satisfied.

The most important group of partial definitions form the definitions of " disposition terms", such as " water-soluble". Such definitions do not describe properties that are directly readable by observation, but those that are subject to a condition (test ).

Operational definition

Sometimes terms are defined by a method by which one can determine whether it can be applied in a particular case the expression. In this case one speaks of operational definitions. Operational definitions are often partial.

Recursive definition

Persuasive definitions

Persuasive definitions are definitions that have next to their descriptive content and emotional meanings (English emotive meaning). Charles L. Stevenson, who introduced the term in 1938 in a Mind- article, writes:

"A persuasive definition changes descriptive meaning without Substantially changing emotive meaning; and a quasi- persuasive definition changes emotive meaning without Substantially changing descriptive meaning. "

Persuasive definitions are very common in philosophy and the social sciences.

Type terms

Max Weber

For the development of the theory of type terms the considerations of Max Weber's ideal type of the theory have been making.

C. G. Hempel

The logical studies of CG Hempel type term are not only in terms of Max Weber's ideal type of interest, but in general the question of how a taxonomy is to create.

Theoretical problems of definitions

Science Scientific classification

The definition of teaching forms part of the logic, if this is seen as a methodology. The logical character of " definition " arises here " teleological " from the resulting finite methodological function.

Functions of definitions

Scientific definitions are usually required if hypotheses and theories erected or models are constructed, which can be examined and discussed by other researchers to. To meet the criteria of intersubjectivity, this agreement should be reached on the meaning of the terms used.

After defining doctrine of Karl Popper, however, the question of definition is thus miterledigt that applying the theory as a whole on an object region and individual inferences therefrom reviewed to observation sentences.

In the social sciences, the boundary between definitions and terms that are no definition is often blurred. If the outer shape is not very clear is whether there is a definition, ie when the author has either explicitly or implicitly expressed its intention, it depends on the intention of the author, which can not be clarified in this case. In this case, there may be confusion of definitions and in particular empirical generalizations that can lead to misunderstanding of the text.

Similar problems can occur if it is not clear to which class of definitions presented a definition should belong.

A definition of teaching is a methodological design of what a " definition " and after which they must be assessed, ie the meaning and purpose they 've the view of philosophy of science and logic. As in the case of a jargon definitions are created and handled, is investigated by the terminology theory and precisely defined. When classified by definitions objects are thus classified in a particular class, a taxonomy is created.

One of each particular definition doctrine is based on a particular conception of theory of concepts or a conception of the relations between concept, judgment, and theory; it thus has a certain conception of epistemology and / or methodology for ( more or less explicitly made ) condition. Therefore, the views on the role of definitions in the language and also in academic contexts often differ greatly.

After a definition of nominalism opinion is nothing more useful than a definition of that expression or the respective characters use and may not be a matter for agreement as " true or false ", only more or less. Definitions in this sense, represent merely a technical tool, by allowing to shorten the speech. Anyone who thinks the other hand, for each term there is a " correct" definition, an appropriate statement could therefore be true or false, thus turns to the side of essentialism as one of the possible answer attempts on the problem of universals.

The most important definition teachings are:

A) A definition determines the nature ( tangible explanation).

B) A definition defines the concept ( or concept design - decomposition ).

C) A definition determines how and with what meaning a mark is actually used.

This view is rarely explicitly represented in the older philosophical tradition. It is often only implicitly represented. For example, such authors can be interpreted as the search for the claim to truth that makes a real definition to transfer to a nominal definition.

At times, such as by Christoph von Sigwart, only an indication of the meaning of an expression is understood under "Definition".

D) A definition sets how and with what meaning a sign should be used.

Considerable confusion has arisen thereby that even philosophers such as Aristotle, Leibniz and Immanuel Kant, these four concepts conceptually not always strictly kept apart and have come up in their arguments to inconsistencies.

Requirements definitions

Classical definition rules

What are the rules of definition is maintained, is basically depending on what definition to follow teaching it was decided.

The classic definition of rules can be traced back to Aristotle; today they are often mostly considered obsolete and in modern science as not very helpful.

Not creativity

Some authors the non- creativity of definitions is required. This means that with the addition of the definition of a theory nothing can be developed, which would not deducible even without that definition.

Eliminability

If a definition of equivalence is correctly formed, the definiendum can be replaced by the Definiens Definiens or by the definiendum in all sets, without changing the truth value of the statement. However, this property does not apply to all definition types, eg not for partial or recursive definitions.

The removability also does not apply if you are on the meta-level. For example, it follows from the definition of " A mold is a white horse " and the phrase " The term ' mold ' has eight letters " not " ' white horse ' has eight letters ."

Circle freedom

Karl Christian Friedrich Krause formulated as the first " Basic Law of the definition ":

" The first requirement is that can not be Definirende again in the definition occur ( terminus definitus non debet ingredi definition ), as would be Diess, so you do not might know yes, What is that to Definirende, it would be The same is declared by Him, idem per idem. as they say. "

And Krause also provides two examples:

" Z. As it is to be denned the term: basic, as is commonly said: the reason of something is The one, which makes this something is. This, however, learns nothing, because it is idem idem per denned; you have inserted only one other word instead of reason, that is, the word by, which is synonymous with reason, or if one is denned the room, and they say: the space is the form, after which the Physically next - and with each other here is explained by idem idem; because then the word: in addition, already spatially understands ".

Adequacy

The third fundamental law of the definition Krause refers to the rule that a definition neither too tight may still be too far.

An excessively wide definition would be " A bird is an oviparous animal ", as well as crocodiles lay eggs.

Aristotle and Cicero have requested that a definition should be short. That conclusion is contrary to that definitions are usually very long. Frequently, however, indicate long definitions suggest that they contain ingredients that do not explain the use of a term, but to investigate the expression belong to the signified.

Redundancy freedom

Closely related to the need for brevity is the requirement of redundancy freedom. According to this requirement, a definition must not contain any ingredients that follow logically from the rest of the definition.

Example: " A parallelogram is a quadrilateral in which the opposite sides are parallel and equal in length and the diagonals bisect each other" is redundant, since this set already from the phrase " A parallelogram is a quadrilateral in which the opposite sides are parallel " follows.

Is not redundancy-free definition, we speak of a definition with pleonasm ( definitio Abundans ).

Declaration (computer programming) Port-Royal Logic The Logic of Scientific Discovery Topics (Aristotle) Theory of Colours Intuitionistic logic Psychologism Structural induction Charles Stevenson Mind (journal) Hypothesis Convention (norm) Herbert Marcuse Posterior Analytics Richard Robinson (philosopher) Stanford Encyclopedia of Philosophy Internet Encyclopedia of Philosophy Integrated Authority File

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