Definition is a statement that delimits a concept in its exact extension and understanding, univocally in a given context, intelligible for a given background and effectively for a given function.
How to delimit a concept
We could make the concept of definition narrower and more rigorous to get more concise definitions by adding conditions like:
- Necessity for the parties. Each part that makes up the definition must be required.
- Sufficiency of the set. The conjunction of the parts is sufficient to delimit the concept.
- Non-triviality in the given background, that is, not including in the definition what is supposed to be known.
- Essential for the definition. Demand that the definition refer to the essence of the concept.
Such restrictions, however, are dispensable. They may or may not be required on a case-by-case basis.
From what has been said we can conclude:
- If an utterance defines X, it only defines X in context. He cannot be ambiguous.
- Another statement can also define X.
- The given background is not extrapolated.
- A good definition for one context may not be good for another.
- A good definition for one function may not be good for another.
There are several ways to delimit a concept, such as:
- Relate its properties, say what it is, in an absolute and non-comparative way.
- Show how it differs from other objects considered in the context.
- Establish the position occupied by the concept in a taxonomy for the concepts of the considered universe.
The chosen mode must be relevant to make the definition effective for its intended purpose.
It can have one or more of the following functions:
- Name the concept, if the definition is name.
- Establish the concept, if it is by definition that it is made public.
- Make known the characteristics of the concept. In this case, its function is to transmit knowledge.
- Distinguish the concept in a given universe.
- Evidencing the relationship of the concept with other concepts of the context universe.
Contextuality of definitions : An utterance is only a definition if the context in which it is applied is established and a minimum background of the person who uses it is assumed. ‘Rational animal’ is a definition for man in a zoology context, which may have little value in a metaphysical context. Furthermore, it is necessary to know what is ‘animal’ and what is ‘rational‘.
It is a word or phrase that defines a concept, is a definition, and has a symbolic relationship with the concept. The name is a sign for the concept, therefore, it has permanence, reproducibility and acceptance.
It is the one that delimits the concept relating its attributes, its properties. The form of an analytic definition is a conjunction of propositions.
It is a type of analytical definition that uses the criteria of a taxonomy. The most notable particular case is the Aristotelian definition, in which the concept is defined by citing the proximate genus and the specific difference. A proximate genus is the most restricted taxonomic class to which the concept and specific difference belongs, which differentiates it within the genus essentially.
Classification definition should not be confused with definition within the taxonomy. Defining a class within a taxonomy is determining its position within the taxonomy, which may not be enough for the receiver to delimit the concept.
4-Definition by exclusion
5-Equivalence of definitions
Two definitions are equivalent when referring to the same concept.
Statements that show definitional equivalence are very common. The most practiced equivalence is the one that relates the name to an analytic definition. Example: ‘Man is a rational animal.’
It is a category that differs in nature from the definitions discussed so far. It is the act of making known in the objectivity to which the name refers. Example: ‘A cow? Cow is that animal in the pasture. See?’
‘Being’ and ‘nothing’ are indefinable.
- Periphrasis : It is the citation of one or another essential attribute of the concept. It is an incomplete analytical definition.
- Exemplification : A case of occurrence of the concept is cited.
- Contextual : Applies the concept to a context in which it fits.
- Intuitive : It is a mere approximation without rigor.
The prefix pseudo should not be understood as pejorative. Pseudo-definitions, for given contexts, are sufficient and practical.
Circular definition is the statement in which a concept is defined using the concept in the attempt to define it. Otherwise, to understand a circular definition, the defined concept has to be known in the terms in which the definition should be making known. Example:
- Precision is the precise delimitation of boundaries.
There is no circular definition when, for example, the connective ‘e’ is defined as a linguistic category through an utterance where ‘e’ is used. In this case, we have the difference between usage and mention.
There is a special case of circular definition, which is the one in which it is necessary to know concepts that form groups with the same conceptual root.
Let the statement be: ‘The strategist is the one who takes care of the strategy’. The concepts delimited by ‘strategy’, ‘strategic’, ‘strategist’ belong to the same conceptual root. If anyone who reads the above statement knows what ‘strategy’ refers to and does not know what ‘strategist’ refers to, he will judge the above definition to be valid. Now, if the receiver lacks knowledge of the common root of the concepts, there is a circular definition of ‘strategist’.
This kind of definition is typical of the dictionary. In the dictionary, you choose a word in a group with the same root. A definition is given for this word using references that do not depend on prior knowledge of the root. The other words in the group are defined according to this one. If anyone who uses the dictionary finds a definition with this type of circularity, he will have to look for the lexical entry in which it breaks.
Circular equivalence of definitions: When an equivalence of definitions is practiced, most of the time, what is intended is to present an alternative to who receives the speech so that he can delimit the concept. When you say: ‘Gastritis is an inflammation of the stomach’, you are establishing an equivalence between a name, ‘gastritis’, and an analytical definition, ‘inflammation of the stomach’, probably because not everyone knows that the name gastritis defines an inflammation of the stomach. stomach. A circular equivalence, or circumlocution, is one in which the new information that the receiver lacks is not added. In circular equivalence, only a cosmetic mutation of the definition occurs. The information on each side of the equivalence is basically the same. No new information happens.
The usefulness of equivalence of definitions: There is a fallacy that says that all equivalence of definitions is useless because they reduce to the formula ‘A is A’, which adds nothing to knowledge. There really is a reduction. When you say ‘Gastritis is an inflammation of the stomach’ you are practicing an equivalence that boils down to the principle of identity. But to say that practices of this type are useless is a mistake, as not everyone knows that gastritis is an inflammation of the stomach. The fallacy starts from the premise that everyone knows the nature of things and the meaning of names and accepting it we conclude that dictionaries and textbooks are useless. Today, to say: ‘The Earth is a round planet’ is a redundancy. At the time when the Earth was thought to be flat, it was heresy.
The fallacy of the circularity of the search for meanings: It consists in thinking that it is impossible to know the meaning of words because they are elucidated by the practice of definition equivalences, as is done in dictionaries. That is, the meaning of a word is explained with other words, which are explained by others, until we return to the initial word. The fallacy exists when the existence of the ostensive definition is disregarded, which at some point in the chain of definitional equivalences is interposed to take the receiver out of the labyrinth of words that refer to other words.
Groups of concatenated definitions: These are an ordered set of definitions and commonly occur in scientific and mathematical theories. One or more concepts are usually considered primary, that is, they are introduced without definition. The first definition of the group is established with references only to primary concepts. The second definition can refer to primary concepts and the concept delimited by definition 1. The definition n can be made with references to primary concepts and to any concepts delimited by the preceding definitions.
The concatenated definition groups are organized by increasing background. Generally, the most obvious and simple primary concepts are chosen, which is not absolutely necessary, but generally convenient.
Other particular cases
- Extensive definition: occurs when there are all possible types of the defined. For example: ‘European is English, French, German, Italian, etc.’
- Comprehensive definition : when the generic attributes of the defined are mentioned. Ex.: ‘European is born in Europe’.
- Essential definition : when the essential characteristics of the defined are mentioned.
- Recursive definition : used to define the generic n element of an ordered sequence. The element is defined by referring to the element of order immediately lower or higher, as the case may be, for which the recursive definition also serves. An element lends itself to the definition of the next or predecessor element, forming a chain of definitions until it reaches the first or last element of the series when, then, by the logic of the recursive definition, a condition of closing the procedure is reached. An example of this is the way we define taxonomic level on this site.
Definition of meaning of signs
By asking yourself ‘What is a car?’ and ‘What does ‘car’ mean?’ in the first case a conceptual definition is being asked and in the second case a definition of meaning.
To answer the second question, one can say: ‘A car is an automobile’, that is, we practice an equivalence of meanings, also called synonymy, when practiced between names. With such an answer, the questioner may have enriched their knowledge of the Portuguese lexicon, but it did not add anything to their knowledge of machines, which are called ‘cars’ and also ‘automobiles’.
In an equivalence of definitions of a concept, two definitions are pertinent to the same concept and in an equivalence of meanings, two signs designate the same concept.
There are cases in which the equivalence of meanings is confused with that of concepts. There is no way to say whether in the sentence ‘Car is a four-wheeled motor vehicle’ there is an equivalence of meanings or concepts, as both are formally identical.
Synonymy is often used more as an equivalence of meanings than as an equivalence of concepts.
It is not for all utterances that the establishment of equivalence of meaning is as simple as the one mentioned above.
Grammatical words, such as connectives, articles and pronouns, for example, generally do not offer means of equivalence by synonymy. Of the interjections it can be said that they do not signify, but that they express emotional states. Of the ceremonial and protocol phrases it can be said that they do not mean like lexical words, but that they have a social function in certain situations.
So how can one answer the question ‘What does ‘and’ mean?’ The connective ‘e’ has no synonyms in Portuguese. There is also no object related to the sign ‘e’ as there is an object related to the sign ‘car‘. In the dictionary we will find in the entry ‘and’: ‘conjunction that represents the logical operation of conjunction between syntactic terms, etc.’ What the dictionary does in this case is to give an equivalence of concepts, rather than an equivalence of meanings. The dictionary assumes that ‘e’ is understood as a sign, therefore as a concept, and proposes the equivalence with an analytical definition for a linguistic category.
Another solution that the dictionary adopts is the contextual definition, which here we consider a pseudo-definition. Several typical contexts for the use of ‘e’ are presented.
Finally, it is good to remember that when the equivalence of meaning between ‘car‘ and ‘automobile’ is established, this equivalence is limited to the reference. The connotative aspects of each sign are not being considered, which breaks with the synonymy if total similarity between the signs is required.