4.3 Explicit definitions in logic and requirements for them

Explicit Definitions

In explicit definitions, two concepts are identified, equated to each other. One of them is a defined concept, the content of which is required to be disclosed, the other is a defining concept that solves this problem.

The usual definition of a metaphor: "Metaphor is a turn of speech, enclosing a hidden assimilation, figurative convergence of words on the basis of their figurative meaning." The defining part is expressed by the words “the turn of speech concluding ...” and consists of two parts. First, the concept of metaphor is brought under the broader concept of “turn of speech”. Then the metaphor is delimited from all other turns of speech. This is achieved by indicating the signs inherent only in the metaphor and absent in the epithet, metonymy and all other turns with which it would be possible to dream the metaphor.

Definitions of this type are usually called definitions through the genus and species difference. Their general scheme: "A is B and C." Here A is a defined concept, B is a concept more general in relation to A (genus), C are such signs that distinguish objects, denoted by A, among all objects denoted by B (species difference).

Generic definition - one of the most simple and common methods of determination. In dictionaries and encyclopedias, the vast majority of definitions refer to this type. Sometimes they even think - which, of course, is wrong - as if every definition is generic.

Requirements for explicit definition

There are a number of fairly simple and obvious requirements for explicit definitions, and in particular for generic ones. They are usually called definition rules.

First of all, defined and defining concepts should be interchangeable. If one of these concepts is found in a sentence, it should always be possible to replace it with another. At the same time, the proposal, which is true before replacement, must remain true after it.

For definitions through genus and species difference, this rule is formulated as a rule of proportionality of the defined and defining concepts: the sets of objects covered by them must be the same.

For example, the concepts of “high relief” and “a sculptural image protruding above the background plane by more than half of its volume” are commensurate. “Bas-relief” and “a sculptural image or ornament protruding on a flat surface in less than half the volume of the depicted object” are also commensurate. “Absurd” and “nonsense” are commensurate. Having met the notion of “absurdity” in some sentence, we have the right to replace it with “nonsense,” and vice versa.

If the volume of the defining concept is wider than the volume of the determined one, then an error of a too broad definition is indicated. We would make such a mistake by defining, for example, “high relief” simply as “a sculptural image protruding above the background plane”. The bas-reliefs would be classified in this case as high reliefs.

If the scope of the defining concept is already defined, there is an error of too narrow a definition. Such an error is made, in particular, by one who defines the “bas-relief” as “a sculptural image made of stone and protruding on a flat surface in less than half the volume of the depicted object”. From the number of bas-reliefs, this definition excludes all those that are not made of stone, but, say, of metal or other materials.

The second rule of definition prohibits a vicious circle: it is impossible to define a concept through itself or to define it through such another concept, which, in turn, is defined through it.

They contain an obvious definition of “Life is life” and “Poetry is poetry, not prose.” The task of the definition is to reveal the content of a previously unknown concept and make it known. The definition containing the circle clarifies the unknown through it. As a result, the unknown remains unknown. Truth can, for example, be defined as a true reflection of reality, but only under the condition that before this a true reflection of reality was not defined as such which gives truth.

The third rule says that the definition should be clear. This means that in the defining part only the concepts known and understood by those on whom the definition is intended can be used. It is also desirable that images, metaphors, comparisons, i.e. all that does not imply a clear and unambiguous interpretation.

You can define, for example, pro-domains as propedeutics. But such a definition will be clear only for those who know that propedeutics is an introduction to any science.

Definitions such as “Children are the flowers of life”, “Architecture is frozen music”, “Oval is a circle in constrained circumstances”, “Arba is a cart with the third wheel as the fifth wheel”, etc. are not particularly clear. They are figurative, allegorical, do not say anything about the object being defined directly and in essence, each person can understand them in his own way.

Clarity is not, of course, an absolute and unchanging characteristic. Clear for one may not be completely understandable for the other and completely dark and unintelligible for the third. Ideas about clarity are changing with the deepening of knowledge. At first, the study of any objects, even ns, a completely perfect definition of them can be perceived as a success. But in the future, the initial definitions begin to seem increasingly foggy. The question arises of replacing them with clearer definitions that correspond to a new, higher level of knowledge.

The definition always exists in some context. It unequivocally identifies and delimits many of the things in question, but does so only in relation to their environment. To delimit, one must know not only what remains within the border, but also what will be outside it. You can, for example, say that ungulates are animals that "walk on their fingertips, or tiptoe." At the same time, no one, of course, confuses horses, cows and other animals with ballerinas, who sometimes move around the stage at their fingertips.

It is interesting to note that our usual riddles are, in essence, peculiar definitions. The formulation of the riddle is half the definition, its defining part. The otgadka is the second half of it, the determined part.

“In the morning - on four legs, in the afternoon - on two, in the evening - on three. What is this? ”It is clear that this is a man. The riddle itself can be reformulated in such a way that it will become one of its possible definitions.

The contextual nature of the definitions is clearly visible on some issues like riddles. Formulated for a specific circle of people, they may seem strange or even incomprehensible beyond it.

The ancient Chinese Buddhist Dan Yinfeng once asked such a “riddle”: “People die sitting and lying down, some die even standing. And who died upside down? "-" We do not know this, "- they answered him. Then Dan got up on his head and ... died.

Now this kind of "mystery" seems absurd. But at that long time when Dan lived, in an atmosphere of controversy with existing customs and ritual, his “riddle” and the “clue” suggested by him seemed completely natural.

In any case, his sister, who was present at the same time, remarked only: "You are alive, Dan, neglected customs and rules, and now, being dead, you are again breaking public order!"