The Definition of Definitions
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The sentence “all cats are black” is evidently untrue even if only one cat in the whole universe were to be white. Thus, the property “being black” cannot form a part of the definition of a cat. The lesson to be learnt is that definitions must be universal. They must apply to all the members of a defined set (the set of “all cats” in our example).
Let us try to define a chair. In doing so we are trying to capture the essence of being a chair, its “chairness”. It is chairness that is defined – not this or that specific chair. We want to be able to identify chairness whenever and wherever we come across it. But chairness cannot be captured without somehow tackling and including the uses of a chair – what is it made for, what does it do or help to do. In other words, a definition must include an operative part, a function. In many cases the function of the Definiendum (the term defined) constitutes its meaning. The function of a vinyl record is its meaning. It has no meaning outside its function. The Definiens (the expression supplying the definition) of a vinyl record both encompasses and consists of its function or use.
Yet, can a vinyl record be defined in vacuum, without incorporating the record player in the definiens? After all, a vinyl record is an object containing audio information decoded by a record player. Without the “record player” bit, the definiens becomes ambiguous. It can fit an audio cassette, or a compact disc. So, the context is essential. A good definition includes a context, which serves to alleviate ambiguity.
Ostensibly, the more details provided in the definition – the less ambiguous it becomes. But this is not true. Actually, the more details provided the more prone is the definition to be ambiguous. A definition must strive to be both minimal and aesthetic. In this sense it is much like a scientific theory. It talks about the match or the correlation between language and reality. Reality is parsimonious and to reflect it, definitions must be as parsimonious as it is.
Let us summarize the characteristics of a good definition and then apply them and try to define a few very mundane terms.
First, a definition must reveal the meaning of the term or concept defined. By “meaning” I mean the independent and invariant meaning – not the culturally dependent, narrative derived, type. The invariant meaning has to do with a function, or a use. A term or a concept can have several uses or functions, even conflicting ones. But all of the uses and functions must be universally recognized. Think about Marijuana or tobacco. They have medical uses and recreational uses. These uses are expressly contradictory. But both are universally acknowledged, so both define the meaning of marijuana or tobacco and form a part of their definitions.
Let us try to construct the first, indisputable, functional, part of the definitions of a few terms.
“Chair” – Intended for sitting
“Game” – Deals with the accomplishment of goals
“Window” – Allows to look through it, or for the penetration of light or air (when open or not covered)
“Table” – Intended for laying things on its surface
It is only when we know the function or use of the definiendum that we can begin to look for it. The function/use FILTERS the world and narrows the set of candidates to the definiendum. A definition is a series of superimposed language filters. Only the definendum can penetrate this lineup of filters. It is like a high-specificity membrane: only one term can slip in.
The next parameter to look for is the characteristics of the definiendum. In the case of physical objects, we will be looking for physical characteristics, of course. Otherwise, we will be looking for more ephemeral traits.
“Chair” – Solid structure Intended for sitting
“Game” – Mental or physical activity of one or more people (the players), which deals with the accomplishment of goals
“Window” – Planar discontinuity in a solid surface, which allows to look through it, or for the penetration of light or air (when open or not covered)
“Table” – Structure with at least one leg and one flat surface, intended for laying things on its surface.
A contrast begins to emerge between a rigorous “dictionary-language-lexical definition” and a “stipulative definition” (explaining how the term is to be used). The first might not be immediately recognizable, the second may be inaccurate, non-universal or otherwise lacking.
Every definition contrasts the general with the particular. The first part of the definiens is almost always the genus (the wider class to which the term belongs). It is only as we refine the definition that we introduce the differentia (the distinguishing features). A good definition allows for the substitution of the defined by its definition (a bit awkward if we are trying to define God, for instance, or love). This would be impossible without a union of the general and the particular. A case could be made that the genus is more “lexical” while the differentia are more stipulative. But whatever the case, a definition must include a genus and a differentia because, as we said, it is bound to reflect reality and reality is hierarchical and inclusive (“The Matriushka Doll Principle”).
“Chair” – Solid structure Intended for sitting (genus). Makes use of at least one bodily axis of the sitter (differentia). Without the differentia – with the genus alone – the definition can well fit a bed or a divan.
“Game” – Mental or physical activity of one or more people (the players), which deals with the accomplishment of goals (genus), in which both the activities and the goals accomplished are reversible (differentia). Without the differentia – with the genus alone – the definition can well fit most other human activities.
“Window” – Planar discontinuity in a solid surface (genus), which allows to look through it, or for the penetration of light or air (when open or not covered) (differentia). Without the differentia – with the genus alone – the definition can well fit a door.
“Table” – Structure with at least one leg and one flat surface (genus), intended for laying things on its surface(s) (differentia). Without the differentia – with the genus alone – the definition can well fit the statue of a one-legged soldier holding a tray.
It was Locke who realized that there are words whose meaning can be precisely explained but which cannot be DEFINED in this sense. This is either because the explanatory equivalent may require more than genus and differentia – or because some words cannot be defined by means of others (because those other words also have to be defined and this leads to infinite regression). If we adopt the broad view that a definition is the explanation of meaning by other words, how can we define “blue”? Only by pointing out examples of blue. Thus, names of elementary ideas (colors, for instance) cannot be defined by words. They require an “ostensive definition” (definition by pointing out examples). This is because elementary concepts apply to our experiences (emotions, sensations, or impressions) and to sensa (sense data). These are usually words in a private language, our private language. How does one communicate (let alone define) the emotions one experiences during an epiphany? On the contrary: dictionary definitions suffer from gross inaccuracies precisely because they are confined to established meanings. They usually include in the definition things that they should have excluded, exclude things that they should have included or get it altogether wrong. Stipulative or ostensive definitions cannot be wrong (by definition). They may conflict with the lexical (dictionary) definition and diverge from established meanings. This may prove to be both confusing and costly (for instance, in legal matters). But this has nothing to do with their accuracy or truthfulness. Additionally, both types of definition may be insufficiently explanatory. They may be circular, or obscure, leaving more than one possibility open (ambiguous or equivocal).
Many of these problems are solved when we introduce context to the definition. Context has four conceptual pillars: time, place, cultural context and mental context (or mental characteristics). A definition, which is able to incorporate all four elements is monovalent, unequivocal, unambiguous, precise, universal, appropriately exclusive and inclusive, aesthetic and parsimonious.
“Chair” – Artificial (context) solid structure Intended for sitting (genus). Makes use of at least one bodily axis of the sitter (differentia). Without the context, the definition can well fit an appropriately shaped rock.
“Game” – Mental or physical activity of one or more people (the players), subject to agreed rules of confrontation, collaboration and scoring (context), which deals with the accomplishment of goals (genus), in which both the activities and the goals accomplished are reversible (differentia). Without the context, the definition can well fit most other non-playing human activities.
“Window” – Planar discontinuity in a solid artificial (context) surface (genus), which allows to look through it, or for the penetration of light or air (when not covered or open) (differentia). Without the context, the definition can well fit a hole in a rock.
It is easy to notice that the distinction between the differentia and the context is rather blurred. Many of the diffrerentia are the result of cultural and historical context. A lot of the context emerges from the critical mass of differentia.
We have confined our discussion hitherto to the structural elements of a definition. But a definition is a dynamic process. It involves the sentence doing the defining, the process of defining and the resulting defining expression (definiens). This interaction between different definitions of definition gives rise to numerous forms of equivalence, all called “definitions”. Real definitions, nominal definitions, prescriptive, contextual, recursive, inductive, persuasive, impredicative, extensional and intensional definitions, are stars in a galaxy of alternative modes of explanation.
But it all boils down to the same truth: it is the type of definition chosen and the rigorousness with which we understand the meaning of “definition” that determine which words can and cannot be defined. In my view, there is still a mistaken belief that there are terms which can be defined without going outside a specified realm(=set of terms). People are trying to define life or love by resorting to chemical reactions. This reductionism inevitably and invariably leads to the Locke paradoxes. It is true that a definition must include all the necessary conditions to the definiendum. Chemical reactions are a necessary condition to life. But they are not sufficient conditions. A definition must include all the sufficient conditions as well.
Now we can try to define “definition” itself:
“Definition” – A statement which captures the meaning,
the use, the function and the essence of a term or a concept.