Type-I and Type-II Units

[SpookyKitty]

In the following, I use the term "entity" to refer to both mental and non-mental entities.

Concepts are integrations of facts. A concept integrates all of the facts about its units. But, a concept of a property P therefore necessarily also integrates any universal facts about its units which can be deduced by assuming that there is some thing which is P but without assuming any particular measurements of that thing (except for those which are necessary for being P). This is just measurement omission applied to deduction. So, for example, considering the concept of "triangle", if we assume that we have a triangle without specifying any particular side lengths, or angles, etc. we can deduce that it has three sides, and that, therefore, all triangles have three sides. Such facts are necessarily true. You can have a triangle that is red or blue or rough or smooth, but you cannot have a four-sided triangle. We will call facts of the aforementioned sort conceptual facts. Now, the properties presupposed by those conceptual facts we will say are necessarily integrated (n-integrated from now on) by the concept of P.

Each property P can relate to an entity in two different ways. Firstly, an entity x might actually have the property P. For example, some particular car might actually be red. But also, an entity can n-integrate a property P. For example, the concept "triangularity" n-integrates the property of being three-sided. Obviously, concretes cannot n-integrate anything. Only concepts can. Unlike concretes, concepts can therefore relate to properties in both ways. Concepts not only n-integrate properties but also have properties.

Now, something interesting happens when you look at things from the point of view of the units. When an entity has a property P, it is a unit of the concept of P. We will call this type of unit a type-I unit. But the concept of P n-integrates some other properties, and since those properties have their corresponding concepts, we will consider those concepts to be type-II units of P (this justified by the fact that concepts themselves are also entities). Type-II units are important because the type-I units of P are also type-I units of each type-II unit of P. And they are so necessarily. For example, the type-I units of the concept "triangle" are necessarily type-I units of the concept "polygon" (which is a type-II unit of "triangle"), because being a triangle necessarily implies being a polygon, while being a polygon doesn't even imply being a triangle, much less necessarily so.

But as we said before, concepts can also have properties. So concepts themselves can also appear as both type-I and type-II units of other concepts. In particular, the concept "abstraction" is very interesting because it is both a type-I and a type-II unit of itself. In fact, every concept is a type-II unit of itself (something which is easily proved), but not every concept is both a type-I and a type-II unit of itself.

Concepts such as "abstraction" which are both type-I and type-II units of themselves I will call philosophical concepts. Let us look closely at the concept "abstraction". Since "abstraction" is a type-I unit of "abstraction", it is abstract. Now, given an abstraction without specifying anything else about it, we can deduce that it cannot be touched. Therefore, the property of being untouchable is n-integrated by the concept "abstraction", and the concept of "untouchableness" is a type-II unit of "abstraction". It follows then that, necessarily, every abstraction is untouchable. Since "abstraction" is itself abstract, it follows that "abstraction" not only n-integrates "untouchableness" but it actually has the property of being untouchable.

The above argument can be generalized to any philosophical concept and any property that the philosophical concept n-integrates. That is, each philosophical concept actually has every property that it n-integrates. But we can deduce an even stronger claim by applying this reasoning to the concept "abstraction". Then we get that if "abstraction" n-integrates some property Q, since every abstraction is a unit of abstraction, it follows that every abstraction actually has the property Q.

I think that the above arguments give us a powerful means to deduce the properties of concepts.

AN ASIDE ON RUSSELL'S PARADOX:

Consider the concept R of concepts that are not type-I units of themselves. Is R a type-I unit of itself? Answering either way results in a contradiction. I've pointed out this problem before, but I think I now have a resolution of this paradox. The key is to reject the law of excluded middle as applied to abstracta. Therefore, with regard to the philosophical conceptness of R we must remain agnostic so as to avoid the paradox.

 

Edited December 17, 2021 by SpookyKitty

[Doug Morris]

2 hours ago, SpookyKitty said:

AN ASIDE ON RUSSELL'S PARADOX:

Consider the concept R of concepts that are not type-I units of themselves. Is R a type-I unit of itself? Answering either way results in a contradiction. I've pointed out this problem before, but I think I now have a resolution of this paradox. The key is to reject the law of excluded middle as applied to abstracta. Therefore, with regard to the philosophical conceptness of R we must remain agnostic so as to avoid the paradox.

Or we could argue as follows.  We ask "Is R a type-I unit of itself?"  By the definition of R, this reduces to the question, "Is R not a type-I unit of itself?".  Thus, to determine whether R is a type-I unit of itself, we must first determine whether R is a type-I unit of itself.  This circularity makes it logically impossible to answer the question, which invalidates the question.

[SpookyKitty]

12 minutes ago, Doug Morris said:

Or we could argue as follows.  We ask "Is R a type-I unit of itself?"  By the definition of R, this reduces to the question, "Is R not a type-I unit of itself?".  Thus, to determine whether R is a type-I unit of itself, we must first determine whether R is a type-I unit of itself.  This circularity makes it logically impossible to answer the question, which invalidates the question.

But the problem with this is that there might be ways of showing that "R is (not) a type-I unit of itself" other than trying to demonstrate the negation. You are not limited to only applying the definition.

Edited December 17, 2021 by SpookyKitty