In order to further develop the meaning of the term ‘concept’, this chapter defines four properties: discretion, strength, longevity and sharpness.
9.1 Concepts are discrete
The notion concept as used in general philosophy has a structure, which means that it contains sub concepts, corresponding to the structure of the object the concept is referring to. The concept CHAIR for example contains the sub concepts SEAT and LEG, in the usual notation. Does it also apply to the concepts as defined here? A meadow includes grass. Can we say that the concept of ‘grass’, in my notation, is a sub concept of the concept of ‘meadow’?
The concepts ‘meadow’ and ‘grass’ each consist of a number of types, represented by CMEADOW {T1, …. Tn} and CGRASS {T1, …. Tm}. Because a meadow, besides many other aspects, consists of grass, it seems obvious that all types that are part of CGRASS belong to CMEADOW too. In that case, CGRASS could be called a sub concept of CMEADOW.
However, this makes a mistake. This reasoning assumes that because a meadow consists of grass, all types that belong to the concept ‘grass’ also form part of the concept ‘meadow’. That is incorrect, the term ‘grass’ contains aspects that do not contain the term ‘meadow’. For example, cows eat grass, but no meadow. ‘Eating grass’ can therefore be part of ‘grass’, but not ‘meadow’. Another example: grass is monocotyledonous, so the concept of ‘grass’ can contain the type ‘monocotyledon’ for a person with sufficient biological training. It is clear that ‘meadow’ will normally not be connected to monocotyledon. In a meadow clover grows and grass meadow birds breed, cows or sheep graze. On the same basis one can assume that the concept ‘meadow’ generally does not contain all types that belong to the concepts ‘clover’, ‘meadow birds’, ‘brood’, ‘cow’ and ‘sheep’.
This phenomenon is a general law and is related to the fact that the two concepts ‘grass’ and ‘meadow’ are experienced as separate concepts. Should all types of ‘grass’ also belong to the concept ‘meadow’, ‘grass’ would not be a separate concept and only ‘meadow’ would be known. The fact that ‘grass’ is a different concept than ‘meadow’ implies that ‘grass’ contains types that are not part of the ‘meadow’ concept, despite the fact that every meadow consists of at least grass. The opposite also applies: the concept ‘meadow’ contains types that are not part of the ‘grass’ concept.
This law is connected with the fact that the mind arranges matters in such a way that one can deal with it. Without this arrangement one would be confronted with a structureless mush of impressions and thoughts.
So:
9.1.1 Every concept is discrete: separate and distinguishable from any other concept
This law is also formulated differently:
9.1.2 For each two concepts C1 and C2 holds that C1 contains types that are not part of C2and that C2 contains types that are not part of C1
Graphically the law can be represented as follows:
Concepts can overlap but never fully coincide with other concepts.
9.2 Concepts have power
A concept is a connection of a number of types. This connection means that if one or more of the constituent types of a concept is actualised, there is a chance that the entire concept will be realized. For example, if I look at the front end of a coin of one Euro, it may happen that I focus on the image of the Dutch king and think of the concept of ‘King Willem Alexander’, but it may well be that my attention is drawn by the yellowish material in the ring around the coin whereupon the concept of ‘copper-nickel alloy’ may arise in my consciousness. Because a type is usually part of multiple concepts, each of these concepts can be realized when a constituent type is activated. The question then arises what are the odds that a concept C {T1 … Tn} will be realised upon actualisation of one of the constituent types.
On the basis of the conceptual model it can be assumed that this probability depends on the strength of the bond between the types T1 … Tn and the relevant concept. If Ta is more strongly bound to Cx than to Cy, the chance of realization of Cx will be greater than that of Cy. Either, the chance that a certain concept C is realized depends on the strength of the interconnections between all types that belong to C. The connection between the different types is not the same, one type is more strongly tied to the concept than the other.
9.2.1. If one or more types that are more strongly bound to a concept are actualised, the chance of realization of the concept is greater than if it concerns weakly bound types
A second factor that influences the chance that a concept is realized by actualizing one or more specific types is related to the number of concepts of which certain types are part. If one or a few types are only bound to one concept, then the chance of realizing that concept is greater than in the case that the types are part of more concepts.
9.2.2. The more concepts a type is part of, the less likely one specific of those concepts is realized when the type is actualised
The bonds to the different concepts of which a type is part can be different in strength. Those concepts to which the type is most strongly connected have the greatest chance of realization.
According to the definition, a type is a connection between elementary components of patterns stored in the past. In general, these connections will not all be equally strong. Some represent powerful experiences, others are weak patterns that hardly impressed at the time. Past experience will also be weaker than more recent. Therefore It’s obvious to assume the occurrence of weaker and stronger types.
9.2.3. The chance of realizing a concept is smaller if the concept consists of relatively weak types. Conversely, a concept that consists of strong types has a greater chance of realization if one or more of the constituent types are actualised
A concept can be realized by actualising one or more of the constituent types. It is therefore obvious that the probability a particular concept is realized depends in part on the number of constituent types that are simultaneously actualised.
9.2.4. The chance of realizing of a concept is greater as more of the constituent types are actualised at the same time
In summary, the probability that a certain concept is realized if one or more of the constituent types is actualised depends on a number of factors:
- The strength of the binding of the types to the concept
- The number of other concepts to which these types are also bound
- The strength of the relevant types (= the strength of the bonds between the elements of experienced patterns from which the types originates)
- The number of constituent types that are simultaneously actualised
The chance that a concept will be realized at any moment is therefore dependent on the structure of the concept as well as on random external or internal actualisations of types. If only the structure factor is considered, i.e. the chance that a concept can be realized independently of random factors, then the chance of realization can be defined as a characteristic of that concept. I call it the power of the concept.
9.2.5. A concept has more power as the concept has a greater chance of being realized, independently of accidental actualising of its constituent types
A strong concept will be easily realized, a weak concept difficult. One can imagine a concept is so weak that it is no longer realized, even if all its constituent types are being updated at the same time. In that case we define the power of the concept equal to zero.
9.2.6. A concept has zero power if it is not realized in any situation
A concept with power zero can still exist, there can still be links between the constituent types, but the concept can no longer be realized, the concept is completely forgotten. It is not inconceivable that the power will become stronger again at a certain moment, for example by the realization of congruent concepts.
9.3 Concepts have a lifespan
A concept can arise and disappear again. For example: the place where I parked my car in the city. Normally this is my individual concept that continues until I want to pick up the car again. The next day I park in a different place, which I remember as a new concept. If I park my car at a similar location in the same neighbourhood every day, I will soon forget where some time ago I parked the car exactly and I only remember the last parking space or the last few parking spaces. The old concepts lose their strength.
However, something special can happen one day: when I get back to the car I see a big scratch in the side of the car. Or the engine will not start and I call the roadside assistance. In such cases, the concept of the place of the car will be retain power for longer. When I walk past those places, I often see it for me again. But even if oly a friend tells us that his car has been scratched at night, chances are my concept of the place where my car was scratched at the time is immediately realized again.
So a concept arises at a certain moment with a certain power. Over time its power can both increase and decrease, even to zero, in which case the concept can no longer be realized in any way. How decreasing of the power of the concept works will be discussed later. Thus a concept can exist for a long time, maximally during my entire life, but also very briefly. As I stated the structure of a concept may continue to exist even if its power is zero. Therefore I define the lifespan of a concept not as the period the concept exists, rather as the period that elapses between the moment the concept arises and the time at which its power has become zero.
However, this definition is problematic. It may be already hard to determine the moment of creation properly, the time at which the power is zero can essentially not be measured. To do the latter, it would be necessary to periodically actualize a number of constituent types artificially to see whether the concept is still being realized. In the case of the parking lot of my car some time ago, for example I can take a picture of that place and put it next to my breakfast plate every day. But then the strength of the concept, the chance that it will be realized, will increase sharply through this daily ‘measurement’ and thus also the lifespan of the concept.
In the morning one often remembers a dream shortly after waking up, while an hour or so later one only knows one has dreamed but no longer remembers the dream itself. The concept of that dream can no longer be realized, its power has become zero. When that has exactly happened, one does not know, but it is clear the lifespan of this concept, as defined above, is no longer than, for example, one and a half hours. For many people the concept ‘my mother’, however, will be a concept with a long lifespan, almost as long as they themselves live.
As a concept is individual, the lifespan of a concept is also an individual quality. Well known is the phenomenon that acquaintances recall memories of events they have experienced together, some of which are remembered vividly by one of them but in the other’s mind don’t trigger any recollection. I tell a friend: “Do you remember that time when we left school and we stole an apple at the greengrocer’s and the shopkeeper angrily ran after us?” Where after he looks glassy at me without any sign of recognition, from which I conclude that my concept of the incident, for whatever reason, had a longer life span than his own. By the way another possibility is my concept of what happened during the course of my life has changed a lot and the friend in question has not been present at all at the ‘remembered’ event, in which case he never could possess the concept.
So determining a moment when the power of a concept has decreased to zero is impossible. However, it is not clear how this problem can be avoided. Even if one were to define something like a half-life, such as at the decay of radioactive substances, one runs up against the problem that every measurement of the power of a concept increases the same force, which prolongs the lifetime. Although, in principle it’s not possible to measure it, I define the lifespan of a concept as follows:
9.3.1 The lifespan of a concept is the period between the origin of the concept and the decrease of its power to zero or to almost zero
9.4 A concept possess sharpness
In 9.1 I stated that concepts are discrete, i.e. that each concept can be distinguished from all other concepts. At the same time it turned out that a concept can have an overlap with other concepts when they share a number of types. For example, the concept of ‘leather football’ includes types which are also part of the ‘leather shoe’ concept, Also the concepts ‘leather soccer ball’ and ‘leather handball’ have a large number of types in common. This phenomenon is not a rarity, most types are part of many different concepts.
If two concepts have many different types in common, one says they are very similar. In chapter 8 I called them congruent. For example, many people will not find it so easy to distinguish a handball from a football. If someone comes cycling along, it is often difficult to say whether it was a regular or an electric bike: those two are very similar and are only to distinguish by looking at certain aspects, for example the size of the front or rear hub or a special little box on the handle bar. But if an elderly person cycles into the wind at great speed without much visible effort it’s not hard to come to the conclusion it must be an electric bicycle without looking further at the vehicle.
I now define the concept of sharpness as follows:
9.4.1. A concept C1 is sharper than concept C2 if C1 has fewer types than C2 in common with any other concept
In ordinary terms: a concept is sharp if it shows little resemblance to any other concept, it is less sharp if it is very similar to one other concept and it is very out of focus if it is very similar to many other concepts. I once again recall that a concept is individual, which means the sharpness of a concept is an individual characteristic too. It is quite possible I do not see the difference between two flowers, they have too many matching types for me, while the educated biologist is stunned by so much ignorance: the differences are especially striking to him. Traditionally Amsterdam people are said to know only two species of birds: siskins and floating siskins, while the Amsterdam City Ecology Bureau distinguishes between more than 145 bird species that breed in Amsterdam.