DEFINITION
Contents:
A definition is a statement that identifies the nature of the units subsumed under a concept. In other terms, definitions serve to give each concept a clear, specific identity in one’s cognitive context, and thus, identify its essence, its referents in reality, and its distinctness from other concepts. For this discussion, the valid method of concept formation and the meaning of concepts is taken for granted.
The fundamental tool of reason, and thus, of logic, is concepts. Concepts are the link between perceptual information and knowledge, i.e. the grasp of (1) the key facts that unite and divide relevant parts of reality – relevant with respect to us and our purposes, of course, and (2) he core causes, attributes and relationships – of and between entities – underlying perceived facts – i.e. the essentials and the fundamentals of perceived reality, i.e. the nature (i.e. identity) of entities, and the derived nature of their actions and interactions. Note that the nature of entities is the cause, their actions the effect.
Concepts are the basic, indispensable means of expanding the range and depth of our cognition, and the primary means to efficiently and effectively expand the use of our finite capacity. A definition is – in essence – an effective condensation of a concept, i.e. a statement that captures the whole relevant context of knowledge conveyed by a concept while minimising the mental units required to hold this context in focus. Hence, definitions are indispensable in the proper grasp, retention and application of concepts. Due to its vital role in cognition in general and logic in particular, we shall explore the rules that enable us to form and validate effective definitions.
(Credits to: Ayn Rand)
A unit is a member of a group of similar beings. It is the result of viewing an being in relation to similar beings, retaining the similarities and omitting the differences between them. Note that by omitting differences, we do not deny that they exist; rather, we are saying that differences exist but may exist in any quantity – it is only that these particular differences are not considered.
The mental integration of units of a certain kind. In other words, a single mental unit – a word or statement – is used to refer to any unit of that kind. Units are identification of a specific – though unlimited – set of concretes, and thus, concepts are the integration of a range of concretes into a single mental unit.
The key aspect of concept-formation is measurement omission, i.e. the process of retaining the shared, distinctive characteristics that unite the members of a group while omitting – not denying but keeping out of focus – the differences in measurements of these characteristics between members of the same group.
Since identity is not dependent on consciousness, the referents of a concept do not change; the concept can refer to any being possessing a certain set of characteristics. In other words, while our knowledge of the referents of a concept – and thus the concept’s definition – is contextual and can change with one’s cognitive context, the referents themselves are what they are – or were, or can be – independent of consciousness. Hence, the concept remains the same for any context.
In other words…
Since a concept is the mental integration of a fixed – albeit unlimited – set of referents, a concept as such is not contextual; only our grasp of it is. A concept as such implies any and every piece of knowledge we may learn about its referents – this is made possible by measurement omission. In this regard, a concept is like an arithmetic sequence integrated as an algebraic formulation. Such a formulation refers to an unlimited range of terms possessing a certain characteristic and implies anything we may learn about these terms – either individually or as a whole.
However, we do not form any knowledge, including concepts, in a vacuum. To form a concept, we first need some cognitive context from which we can begin abstracting perceptions into units and integrating these units into concepts. Hence, every concept is grasped in a specific cognitive context. Therefore, the process of conceptualisation is contextual. However, the end product of this process is not simply a sum of our knowledge but a reference to an unlimited range of concretes by implication (mainly through measurement omission).
That which is necessary for a being to be what it is, i.e. necessary for its nature and existence. In other terms, if a feature P is essential to an being S, then the existence of S presupposes P.
That which is necessary and sufficient for an being to be what it is for an being to be what it is, i.e. necessary and sufficient for its nature and existence. In other terms, if a feature P is fundamental to an being S, then P leads to S, and the existence of S presupposes P.
The difference between an essential and a fundamental can be summarised as a difference between a necessary condition and a necessary cause. Hence, all fundamentals are essentials but not all essentials are fundamental.
Essential characteristic:
The characteristic that makes the units of a concept the kind of beings they are, and differentiates it from other kinds of beings. Note that based on the definition of a unit, i.e. a member of a group of similar beings, what makes a unit distinctive, i.e. what makes it similar to each member of its group and also different from each member of other groups. Hence, an essential characteristic is a distinctive characteristic that is necessary to unite the members of a group of similar beings.
Fundamental characteristic:
The characteristic which is responsible for the greatest number of a being’s distinctive characteristics; it may not explain everything, but it does explain more than any other.
Property:
A characteristic that is the effect, i.e. the derivative of an essential characteristic.
Essentials or fundamentals can only be identified in a certain cognitive context; we cannot identify more than we know. Furthermore, the required context in which we need to retain the nature of the units subsumed by a concept may necessitate a more limited cognitive context, thereby limiting what we may identify as essentials or fundamentals. In either case, we see that essentials and fundamentals are defined with respect to a certain context.
Metaphysically, beings have no essentials and fundamentals as such. Metaphysically – i.e. independent of consciousness – only concretes exist, and the identity of a concrete consists of everything that it is and not just some set of basic features. Essentials and fundamentals are identified based on our conscious purpose and knowledge – they are only relevant to unit-perception. They do refer to reality and are objective, but they are not independent of consciousness as they are the products of a conscious, selective focus on reality.
A definition is a statement that identifies the nature of the units subsumed under a concept by means of specifying their essential characteristics. In other words, a definition is the statement of essence. Given that essentials are contextual, so are definitions. A statement that merely identifies facts or truths about the units of a concept or the concept as a whole is not necessarily a definition. To be a definition, the statement has to specify and be limited to the essentials. This restriction arises from the role of definitions in cognition; an effective condensation of a concept that minimises the mental units required to hold the whole context of a concept in focus.
A definition has to (1) specify the fundamentals that make the referents of a concept what they are, (2) differentiate the units of a concept from everything else in the relevant cognitive context, and (3) delimit, fix or guide the use and application of a concept in the relevant context.
Given their contextual nature, definitions can change with the cognitive context. They are not concepts but means of retaining a concept in a given context. In other words, a concept is not its definition; a definition is the identification of a concept in a given cognitive context, not the concept itself.
A definition is a conceptual statement and not the mere presentation of instances or examples of a concept. For certain concepts which form the basis of – and are presupposed by – any other concept, we obviously cannot provide conceptual statements to define them as that would result in a circular definition. Examples of such concepts are:
In such cases, we have to point to instances and examples to prompt the formation of a concept; this is called an ostensive definition. However, this is not strictly a definition in the way we are using the term.
A definition is also not an etymological report. Etymology may provide the definition or may at least provide a guide to form, contextualise or clarify the definition. However, etymology by itself is not a reliable means to reach a definition.
Credits:
A valid definition must contain a genus and a differentia.
Genus (plural - genera):
A class wider than the concept to be defined, which represents the basic identity of the concretes / referents in question.
Differentia (plural - differentiae):
The characteristic(s) which distinguish the concretes / referents in question from all other members of the genus.
For example, consider the definition of “human”:
Rational (differentia) animal (genus)
Concepts are a form of organising perceptual material, which means not just discovering in what ways a class of entities is different from others, but also in what ways this group is similar to others. Hence, whenever a given class is a part of a wider field of entities, the definition must encompass this fact; otherwise, you are defaulting on one of the cognitive functions of concepts.
2 or more existents can only be differentiated on the basis of mutually exclusive characteristics (since mutually non-exclusive characteristics could exist in both at once, thereby not differentiating them). The only way to ensure such mutual exclusivity is to identify characteristics that are different measurements of the same broader characteristic.
Hence, 2 or more existents can only be differentiated on the basis of a shared commensurable characteristic, wherein each existent contains a different measurement of this characteristic. The set of the essential commensurable characteristics shared by a set of existents is their conceptual common denominator – CCD. Note that the CCD for everything in existence (considered at once) is existence itself. Hence, the process of differentiation is scalable to any level.
By extension, to differentiate a class of beings from everything else requires a broader CCD that unites this class with everything else and thereby differentiates it based on having different measurements of the CCD. Hence, to differentiate a concept from everything else in a given context, we need a broader CCD that unites it with everything else in the context – i.e. we need a genus. However, to actually differentiate this concept, we need the particular distinguishing measurements of the CCD that are present in the concept – i.e. we need a differentia.
Knowledge is contextual, and one’s grasp of a concept necessarily exists in a cognitive context that – ultimately – relates to the sum of our knowledge. To hold the proper context in which a concept is to be grasped, we must understand how it relates to the rest of our knowledge, while also being distinct from the rest of our knowledge. Hence, since a concept integrates a class of beings, we must discover how (1) this class of beings is similar to other classes or kinds of beings, i.e. we must discover the CCD that unites this class to other classes in a sufficiently broad context (sufficiency is based on relevance), and (2) this class of beings is different from other classes or kinds of beings, i.e. we must discover the particular measurements of the CCD of the broader context that differentiate this class from other classes in the given context. (1) implies the need for a genus, while (2) implies the need for a differentia.
Since all knowledge is hierarchical, genera also exist in a hierarchy. For example, consider the classes human, animal and organism.
| Class | Genus of… | Species of… |
|---|---|---|
| Human | - | Animal |
| Animal | Human | Organism |
| Organism | Animal | - |
The genus of a class must be identified with respect to the relevant cognitive context – this may be the general available context, or simply the specific required context. For the highest cognitive efficacy, you must select as a genus the wider class that shares the greatest number of characteristics with the definiendum (i.e. the class being defined) in the relevant cognitive context.
Specific genus:
The wider class that shares the greatest number of non-distinctive characteristics with the definiendum.
Fundamental differentia:
The distinctive characteristic(s) that leads to or is responsible for the greatest number of distinctive characteristics – distinctive within the specific genus.
In simple terms, the purpose of definitions dictates that we must (1) choose the most specific genus possible – in the relevant context, and (2) choose the broadest, i.e. most fundamental differentia possible – in the relevant context.
NOTE: The fundamentality of the differentia is elaborated in the rule of fundamentality.
Always note that the required or relevant context determines the specificity required. For example, regarding the definition of “human,” “rational animal” is sufficient for philosophical discussion; it defines the fundamental characteristics required to discuss human nature in broad philosophical terms. Here, “rational mammal” would entail needless specificity; there is nothing philosophically relevant in the genus “mammal” that is not also present in the genus “animal.” However, for the purposes of biology, we may require more specificity, and thereby define “human” as “rational mammal,” “rational primate,” etc.
In other words, define the genus based on the specific category of beings you want to or need to distinguish your concept from, i.e. find the minimum conceptual common denominator (CCD) required. For example, when defining “socialism,” we need to define it within the broader category of “political systems” rather than overly broad categories such as “ideas” or “systems.”
The definiendum (the class being defined) and the definiens (the definition offered) must be logically equivalent in the given context. In other words, for the given context, the definition must be true (a) for all members of the definiendum and it must be true (b) only of the members of the definiendum.
Note that (a) is necessary to integrate the class – to specify what makes each member of the class a part of the same class – and (b) is necessary to differentiate the class – to specify what makes each member of the class distinct from members of other classes.
Violating this rule can result in one of 2 fallacies:
To avoid making these fallacies, here are some tips. (1) Let your mind range over a wide variety of examples, both within the class being defined, and outside the class being defined; variety is key. (2) To avoid violating condition (b) in particular, keep in mind the specific broader category of beings you want to differentiate your concept from (by keeping in mind a certain cluster of associated concepts) – i.e. keep the appropriately defined genus in mind (not too narrow or too broad).
Your definition is logically equivalent when you can assert it as an A-proposition which is simply convertible. Note that an A-proposition is a categorical statement of the form “all S is P”. This proposition is not simply convertible by itself, since from “all S is P”, you can only determine that “some P is S “and not that “all P is S”. A simply convertible A-proposition is such that you can say from “all S is P” that “all P is S”. In other words, you should be able to assert your definition in both ways:
The definition must state fundamental characteristics. In other words, the essential characteristics used in the definition must also be the fundamental characteristics (in the given context).
This rule becomes crucial if the units of a given concept have a number of distinctive characteristics, each true for all units and only true for those units in the given context. The purpose of a definition is, in essence, unit-economy in cognition. This means that a definition must be a proper condensation of a concept and not a catalogue of its distinctive characteristics.
In short, the fundamental characteristics, due to their relatively wide-ranging implications about the nature of the units of a concept, makes them the only rational choice of differentia. In other words, fundamental characteristics have the most causal significance, and thus, imply the widest context possible with the fewest possible mental units. Consequently, grasping the fundamental characteristics enables you to understand the properties and behaviour of a being in the widest range of situations and circumstances.
If we have one or more distinctive characteristics, find out what distinctive character (either among them or some other) is the root or cause of them that is itself a distinctive characteristic. Note that if a distinctive characteristic does not have any roots that are also distinctive to the class, this does not mean this characteristic is fundamental.
The rule of fundamentality is implicit in every other rule, i.e. the violation of any other rule automatically violates this one. Hence, to pinpoint the flaws in a definition, first check with every other rule.
The definition must not – directly or indirectly – define the subject by the subject itself. In other words, the definition must not contain any content that, to understand, presupposes the definition you are supposed to be providing.
1.
Naming the concept being defined or its derivatives. For example: Democracy being defined as “a system of governance in which leaders are elected democratically”.
2.
Use of synonyms or synonymous expressions for the concept being defined or its derivatives. For example: Lateness being defined as “the state of tardiness”. Note that synonyms can help if you already have a definition for the concept and just need to connect this definition with the synonyms.
3.
Use of concepts whose own definitions require the concept being defined.
4.
Use of correlatives, i.e. 2 things so related that the existence of either implies the existence of the other. For example: Cause being defined as “that which creates an effect”, and effect being defined as “that which is caused by something”. As another example: Husband being defined as “a man who has a wife”, and wife being defined as “a woman who has a husband”.
In defining correlatives, do not define one correlative in terms of the other – the 2-way implication between them means no new information is conveyed. Instead, define the actual essence of the correlatives, i.e. define the relationship between the correlatives. So, for example, to define “husband” or “wife,” first define the underlying relationship, i.e. “marriage.” Thus, define the correlatives with respect to their relationship.
Where possible, a definition must be positive not negative. In other words, as far as possible, a definition must identify what something is rather than what it is not.
Identity is defined by the existence of specific attributes. Thus, identification of concepts, i.e. definitions, must involve identification of what exists. Note that even when identifying a concept in negatives, you are necessarily identifying it with respect to positives; an absence can only be identified if you know what could be present but is not. Furthermore, confirming a positive is far easier than confirming a negative, since a positive is immediately identifiable while a negative can only be identified by first confirming what is in fact present.
Hence, positive definitions must precede negative ones, and choosing a negative definition where a positive one is available reduces your ability – in terms of efficiency and effectiveness – to identify and apply the concept.
NOTE: Valid negative definitions:
There are certain concepts that can only be defined in terms of negatives, due to the only differentia possible in the given context being the absence of certain characteristics. Some examples are:
(This is a general rule for thought, not just definitions)
Definition must be stated literally (i.e. with exact meaning), clearly and simply and economically as possible – for the relevant context. In other words, say what you mean and mean what you say, directly, clearly, exactly and simply as possible, for the relevant context.
An unnecessarily complicated, difficult-to-retain definition defeats the essential purpose of a definition: achieving unit-economy by effectively condensing the nature of a concept in a given context. Note that legitimate technicality or specificity in the appropriate context is not necessarily a violation of this rule, even if the definitions seem overly complicated for someone outside this context. For example, the definitions of organs in medical terms would be far more specific and detailed than a layman’s definitions due to the different requirements of their respective contexts. Hence, the rule of obscurity, like every other rule, applies within a given context.
Invalidating a definition does not mean you will be presented with a valid one. Furthermore, to invalidate a definition, you do not need to know the valid one. Lastly, you can neither make nor validate definitions out-of-context. Hence, every rule for the validity of definitions is to be applied within a given cognitive context.
1.
If unsure about how to define a concept in your specific context, start with a simpler, broader context and then narrow down.
2.
Note the purpose of a definition in any area of study: to integrate and isolate an unlimited range of concretes for the purposes of specialised study. With this in mind, ask: is the definition too generalised so as to be useless for specialised study? In other words, does the definition name a fundamental similarity that warrants a specialised study, or does it integrate too disparate a set of things so that it is not meaningful to study the concept in a more intensive context?
NOTE: The broader the scope of a definition, the less useful it is in a more intensive context.