CONCEPT FORMATION
Contents:
Multiple units of the same kind are united by their similarities, but they are also distinguished from units of other kinds by their distinctive similarities, i.e. shared distinctive features. Note that the similarities that distinguish one set of units from another are chosen based on the context of some required subset of one’s knowledge; one cannot relate to what is beyond one’s knowledge, and one need not relate to what is beyond one’s requirement.
Like anything we can retain and focus on, the distinctive similarities can be related to each other to obtain the facts that are the basis of these similarities. In other words, we can treat the distinctive similarities as units and obtain their distinctive similarities. Through this process, we can reduce the number of mental entities required to retain the context in which the units are distinguished.
For higher-level concepts, we can also use identifications and even generalisations of causal relationships to identify the causal relationships among the features of the given units. We can thereby obtain the roots, i.e. causally significant factors that result in the distinctive similarities of the units.
The above processes produce the essentials by which units of one kind can be integrated and distinguished from units of other kinds. By obtaining the essentials, we can reduce the number of conscious units required to retain the units, i.e. perform unit-reduction — “unit” here referring to the conscious units required to be in focus.
Once we have performed enough unit-reduction so that we are able to hold in focus the whole context in which the units were identified, we relate these conscious units and, by extension, the whole context using a single conscious unit; a label, usually a word or a symbol. This, i.e. the integration of multiple conscious units isolated from everything else through abstraction and united to each other by a definition, is a concept. The essence of conceptualisation is the integration of units into one conscious unit by their essential distinctive characteristics.
Note that just as we retain the steps of the process of sensation that leads to a perception even while treating the perception as an inseparable whole, we also retain the steps of the process of abstraction that leads to a unit and then a concept even while treating the unit or concept as an inseparable whole. This enables us to view a potentially unlimited context, i.e. a potentially unlimited range of concretes using a smaller, finite set of conscious units. This also enables us to expand the contents of the context into the relevant specifics by retracing the retained steps of the process of abstraction.
A concept is mental integration of units of a certain kind, integrated by their distinctive similarities. In other words, a single conscious unit — a word, symbol 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 mental integration of a specific — though unlimited — set of concretes into a single conscious unit.
Two or more things can only be differentiated on the basis of mutually exclusive characteristics (since mutually non-exclusive characteristics could both exist in each thing, thereby not helping us in differentiating them from each other). The only way to ensure such mutual exclusivity is to identify characteristics that are different measurements of the same broader characteristic. Hence, as stated in Unit Perception, two or more things can only be differentiated on the basis of a shared commensurable characteristic, wherein each thing contains a different measurement of this characteristic. The set of the essential commensurable characteristics shared by a set of concepts is their conceptual common denominator — CCD. Note that the CCD for everything in existence (considered at once) is existence itself. Hence, we can see that the process of differentiation is scalable to any level of abstraction.
By extension, to differentiate a class of things from everything else requires a broader CCD that unites this class with everything else, and thereby differentiates it based on the different measurements of this 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 that context — i.e. we need a genus. However, to actually differentiate this concept, we need the particular, distinguishing measurements of this CCD that we observe in a given concept — i.e. we need a differentia.
The essence of integrating a concept is measurement omission. Measurement omission is the process of retaining a shared characteristic (a characteristic could also be a set of finer characteristics) that unites a certain kind of unit, i.e. that unites the members of a certain group of similar things, while omitting — not denying but keeping out of focus — the differences in the measurement of this characteristic between members of the same group. This process is implicit to some extent in unit-perception, as you consider and treat various similar entities as similar, i.e. as part of the same group. However, this process is completed when integrating units into a concept, when you only retain their shared distinctive characteristic(s) and omit their particular differences in measurements — not denying their existence but not retaining them in the concept as such. You consider each instance of a concept as an instance of the same concept, i.e. no different in essence — i.e. in terms of shared, distinctive characteristics — to other instances. A tree is a tree is a tree — a man is a man is man, etc.
Obviously, we recognise and retain various particular instances with their particular differences. However, the concept as such is a distilled conscious unit — you may and generally should add details to it with particular information, knowledge, experiences, memories and contexts when needed, but these do not form the essence of the concept.
Identity is not dependent on consciousness, hence the concretes subsumed by a concept do not change; the concept can refer to anything possessing a certain set of characteristics, be it known or unknown, or be it in the past, present, or future, or even as potential. 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 — with respect to its referents — 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 contextual.
SIDE NOTE:
Our grasp of a concept includes the grasp of further shared characteristics of its referents, the fundamentality of the characteristics, and the similarities and differences of its referents from other things in a given context.
FINAL NOTE:
A concept as such designates (1) any and every possible concrete possessing certain characteristics, and (2) any and every piece of knowledge we may learn about its referents — both of these designations are made possible by measurement omission.
Illustrative analogy 1:
A concept is like an arithmetic sequence integrated as an algebraic formulation. Such a formulation would refer 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.
Illustrative analogy 2:
A concept is similar in nature to a proper name. Consider a person named “Aristotle”. Suppose I met Aristotle just a few hours ago, while his mother knew him his whole life. Obviously, the difference in our knowledge of Aristotle is vast. However, when we talk of him, we are — through his name — referring to the same person, i.e. the same concrete entity.
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 — again, this implication is made possible by measurement omission.
Note that a single word may refer to different concepts in different contexts. Furthermore, we may drop a concept that is useless, i.e. that has no practical importance, or we may realise that a concept does not in fact refer to anything in particular (i.e. it is a “floating concept”, which is the result of an invalid process of concept-formation), or we may reassign the same name to a different (maybe related) concept. All these details are irrelevant to the basic nature of concepts.
A concept is an integration of units, but these units need not refer to perceived concretes — they could refer to imaginary, abstract or even conceptual units. In any case, consciousness begins at sense-perception; the material provided by your senses and the first abstractions you make from it form the basis of any further abstraction and imagination.
Imagination is the process of rearranging conscious units — sensations, perceptions, abstractions, mental integrations — into a certain mental integration. Such an integration as a whole may not correspond to anything in reality, but its parts certainly would. Even in this case, such an integration is something, and is thus open to unit-perception and conceptualisation. However, it is key to note that a mental creation or recreation of something is not the same as a concrete, even if imagination corresponds to observation. A thing is not its image, an event is not its memory, and an idea is not its inkling. A is A.
However, we can relate a mental or physical image to a being due to the fact that characteristics are abstractions that can apply to any entity — physical or mental, real-life or representational. In this way, a concept formed from imaginary units can be applied to physical referents and vice versa.
If a concept is formed to include both mentally and physically available referents, then the distinctive characteristics of its units are the abstractions of observable characteristics that can also apply to representations and mental recreations. Such abstractions are in essence concepts whose referents may possess indications of a physical characteristic — observed, imagined, representational, etc. This can expand the range of a concept’s units to include both the physical, mental and representational referents.
Alternatively, we can use the same word, symbol or statement to identify different concepts, each referring to either physical or mental or representational referents. Here, the specific cognitive context would inform you about which version of the concept is in fact being referred to. In this way, we can validly (conditioned by the right context) use the concept of “man” for a real man, a fantasy of a man or a picture of a man.
Observe that we are able to retain a wide range of conscious units, but we can only focus on a few of them at once. When we integrate sensations to perceptions, or perceptions to concepts, we are retaining the relationships between the elements of each. Through integration, however, we can focus on fewer conscious units while retaining a wide context containing many elements, each existing in a retained hierarchy with respect to the conscious units in focus. In this way, we can use our minds to consider a wide context without considering a wide range of conscious units at once.
As an analogy, consider a book divided into chapters, sections, subsections, etc. We cannot focus on the contents of the book at once, but we can focus on the list of chapters, and when required, our focus can shift to within one chapter and its sections, and to within one section and its subsections, etc. This enables us to view the contents of the book in terms of essentials, which can be expanded on demand.
Note that a logical hierarchy of the contents is vital, as it is a hierarchy wherein the derivatives follow the fundamentals logically; this enables us to expand the hierarchy with a well-defined method that is itself easy to retain and apply.
To reiterate in more precise terms: A concept is the integration of multiple units possessing the same distinguishing characteristics, with the separate measurements of the units being omitted. A conceptual common denominator — CCD — is a set of characteristics reducible to one or more units of measurement, by means of which a set of things are differentiated, in a given context, from other things possessing the same characteristics but in different measurements.
As discussed in the essence of concept-formation, the appropriate CCD serves to differentiate a concept from other concepts. To obtain narrower, i.e. more specific concepts from a broader concept, the distinguishing characteristics between the instances of the concepts are used to create a CCD to differentiate the narrower concepts. To obtain broader, i.e. more generalised concepts from narrower concepts, the common characteristics between the concepts are used to create a CCD to differentiate the broader concept from other concepts.
Note that, as per the principle of unit-reduction, i.e. the greatest reduction of conscious units possible to retain a context, we define the CCD in terms of essential characteristics, i.e. characteristics derived by recursively subjecting the distinguishing characteristics of the units of a concept to unit-perception as many times as possible within the relevant context.
Any consciousness has a finite capacity to think and to act. In order to hold in one’s focus the broadest cognitive context that is required to deal with concretes effectively, it is necessary to reduce the amount of observations down to a set of essential characteristics. Why essential characteristics and not any characteristics? Because to be essential is to be the foundation of, i.e. to imply a large number of, or even most or all of the other observed components and attributes of the perceived entities, events, etc.
Note that this fact is due to the nature of necessity, which is the basis of essence; if X is necessary for Y, not-X tells us about the details of Y without even considering Y, and if Y is necessitated by X, then X tells us about Y without even considering the details of Y — we lose no relevant information (relevant to the context) but use fewer mental units (note that unit-economy is achieved even further by repeating the process of abstraction recursively enough times). Hence, by retaining the essentials, you are able to deal with the underlying causes or the formative features of things in reality, thereby enabling more effective action, especially in the long-range and the big-picture.
Hence, we see the interrelation between unit-efficiency and the grasp of essentials. However, we have the relationship in the other direction as well. To be able to grasp the essential characteristics of that which we observe, we need to reduce our data into a smaller set of foundational, i.e. essential information. In this attempt, holding the other observations in our awareness more than necessary is not only an unnecessary mental strain but also a distraction from or the muddling of the essentials.