Additional remarks about individuals and categories
1. What else to pay attention to in names
When forming names for individuals, you may have noticed that the construction of a name often (but not always) follows a certain principle: the name of the individual includes the name of its category, plus an additional identifier.
"screwdriver inventory number 1250564-678" - this is a "Screwdriver"
Similarly, the name of a category often (but not always) includes the name of a broader category, plus additional information narrowing down the category:
"Screwdriver Makita" - this is a "Screwdriver".
It is convenient to associate names in this way when the functions of objects roughly correspond to each other. If the objects are distinguished and grouped into categories based on principles other than function, or if the functions of the objects are not very similar, this principle is unlikely to be used in naming.
"Ivan Ivanovich Ivanov" - this is a "Man"
"Screwdriver Makita" - this is a "Tool".
2. Note for programmers
If you know what a relational database is, you can already link our concepts from the field of ontological modeling to the structure of a database.
Individuals (usually) correspond to rows in database tables - one row per individual.
Primary key - this is the identifier that ensures the unique name of the individual. Sometimes a primary key is formed by combining a number of meaningful fields to ensure uniqueness, as in our examples, and sometimes a meaningless unreadable unique identifier (GUID, UUID) is used.
Categories in the database exist in two forms.
- First, the category is the name of a specific table. The "Employees" table contains rows corresponding to individual employees.
- Secondly, categories exist in all cells of the database where the selection is made from a predefined set of values. The "Gender" column in the "Employees" table is filled for each employee with categories "Male" or "Female".
3. "Completely abstract" concepts
An attentive reader may notice that one important type of abstract objects seems to have fallen out of our considerations: completely abstract concepts that are difficult to perceive as categories - because it is unclear which individuals are even included in them? For example, objects like "justice" or "beauty" - what are they? Our thinking is perfectly capable of distinguishing these objects from the background, or else they would not arise in our consciousness. But how does their existence align with the function of categories, which is to group objects?
A precise formal answer to this question within the framework of a formal-logical 4D extensional ontological approach will be provided later. For now, you may find it interesting to explore the origins of concepts (including abstract ones) that have been developed within a framework closer to the science of cognitive psychology.
What is briefly outlined below are two hypotheses that do not exclude each other and may be correct in some aspects simultaneously.
3.1. Prototype theory
The prototype theory states that for each concept (category), there is one, uniquely true physical embodiment in space-time that is the most typical for it. To discover it, we can survey those who use this concept, literally ask them to show what kind of thing in the real world is the most typical representative of this concept.
For example, ask a few people what a typical object for a "bird" is.
We will collect the answers, identify the most typical embodiment (for example, a pigeon), and place it at the center. This will be our prototype. All other objects mentioned during the survey are more or less distant from this prototype. The next time we want to classify a new object as a bird, we will gauge how similar this new object is to the central one we identified.
Overall, this is good and convenient, but there may be difficulties with composite concepts.
An example of a composite concept would be a pet fish. Let's say a herring turns out to be the prototype fish for us. A cocker spaniel might be the prototype for a pet. When we hear "pet fish," we get a strange feeling. A pet that is a fish, how does that even work? Is it like a fluffy dog or like a herring?
3.2. Exemplar theory
The exemplar theory assumes that there are multiple exemplars of a category (concept) (in contrast to prototype theory, which asserts the existence of a single central object). You classify objects into a category based on some similarity. Each object resembles exemplars in some way, possibly with different traits. When you want to assign a new object to a category, you look at its resemblance to previously encountered exemplars. If you classified a new object into the category, it can itself become an exemplar for the next object.
People learn based on a relatively small number of such exemplars. Sometimes even on a very small number, and sometimes people even see similarity where it was not expected (this can sometimes be very inconvenient, but that's another story).
Research shows that if there are very few typical objects, then prototype theory better describes how the brain works, with the brain focusing on a single central object. But if the number of typical objects increases, exemplar theory starts to work better, and the example with the pet fish no longer poses such difficulties. However, there are studies that show the opposite. Keep in mind that both models work well enough to describe fast associative brain function, but do not describe slow formal thinking.
For transitioning from analyzing brain function to formal computer-supported modeling, prototype theory is still more promising - making it easier to move to object features for formal category identification.
Moreover, these two theories unexpectedly turned out to be useful in studying how neural networks work. Mathematically, the apparatus of multidimensional representations (embeddings) is very similar in principle both to searching for proximity to a prototype and to searching for analogs among exemplars. You can look up the details yourself.