Concepts, Intraconcept Propositions and Apodictical Propositions

The previous analysis of oneness and sameness points pretty clearly to one possible way to include the concept in the model, and that is by saying that concepts are differentiation trees.

Why?

1. *One and the same* differentiation tree can be done across the time, keeping the concept time-independent (this is different from impossibility of change of concept).

2. Differentiation is abstraction, differentiation trees are abstractions too, so the concept is abstraction as it is clearly seen.

3. *One and the same* concept can be “differentiated” in different cognitive contexts.

4. Different concepts can be “differentiated” in same cognitive context.

5. We get to explain the possibility of the one kind of neccessary true propositions as a relation between branches of differentiation tree and their parts (differentiation trees of parent nodes) as it is shown in what follows…

 Let’s say DT_X is a differentiation tree that serves to differentiate a color from cognitive context. Following our idea, we would say that DT_X is concept of “color”.

On other side, if we got to the certain color context of the cognitive whole (using DT_X), we need additional differentiation (or more of them), to determine it further (e.g. to determine specific color).

Let’s say that we have 3 possible differentiations which can do further – differentiation of green (Diff_G), differentiation of red (Diff_R) and differentiation of blue (Diff_B). Those differentiations can not be directly applied to cognitive whole, it must be applied *after* all DT_X is applied, thus creating new context differentiation tree. (Of course this is simplified model, the actual differentiations of color as we know from psychology experiments are lot more complex, and the color which we perceive of a part depends a lot from the context, but it is I hope clear that any such connection can be made by proposing more complex differentiation or differentiation tree).

Let’s say that after DT_X is applied, it is possible to apply Diff_R on the resulting cognitive context. By the definition of differentiation tree, we thus get new differentiation tree DT_Y. Following our idea, DT_Y would be our concept of “red”. We will call DT_X a *general* differentiation tree (DT_G), and DT_Y – *particular* differentiation tree (DT_P). It is though clear that we can call them such just in their relation, they can by themselves be one or the other in different situations in relation with other differentiation trees.

 It should be obvious now that apodictical truth of “red is color” can be explained in such model as oneness of the DT_G by itself, and DT_G as part of the DT_P. Or that proposition put in other words would be: “For something to be red it must be color first”, or translated further to our model:” When something is differentiated (determined) as red, it is also differentiated (determined) as color”.

The given model would also explain how it is possible to have a concept of color separate from the specific colors, even in our experience we can’t find something as “color” which is not in same time a specific color.

This kind of propositions, where one “general” concept A as differentiation tree is necessary part of “specific” concept B, hence making the proposition “B is A”, necessary or apodictical truth we will call *intraconcept propositions*.

That is normal thing in any reductionist model… we start with more “complex” phenomena for which we have some (certainly vague) ideas, but we expect from the model not just to clear up their behavior, but also to give us an insight in their “nature” or “essence” – to explain their nature in terms of the first principles.

 In such way the concept of “is”, is the possibility to apply certain differentiation tree – a possibility for certain determination. One case is when a differentiation tree is applied on a cognitive context, determining a certain cognitive context as a specific concept. But in second case which is interesting in our last case, a one general DT_G is possible to be applied to a particular DT_P, hence making intraconcept propositions possible.

Although really, there is just one meaning of “is” in sentence “A is B”, which means that there is possibility to determine concept B in the cognitive context already determined with A - it can seem that when we say “that is B” or “this is B”, pointing to the concepts in the direct experience, we have specific case which doesn’t fall under the general concept of “is” we defined up there, but in fact it falls in same case, what should we only have in mind is that indexical concepts like those (“that”, “this” etc…) are also differentiations which determine the cognitive whole in the space/time context of a one who speaks (here), or one to whom it is spoken (there) (more on this later). But in those cases the sentences like “that is a horse” can also hold truth of  two differentiations being one and the same, because what is differentiated by the DT_that is further differentiated by DT_horse, and because of that “that” *is* “horse”.

 Because of the apodictical truth of the both cases, and the same meaning of “is”, we can name those both kind of propositions with one common name and that is “apodictical propositions”.

 Next…the concept of “truth” in this model is nothing else then the comprehension of a connection between concepts- a state of simplicity where there is no contradiction in what Mind have tried and succeeded in comprehending. As such, “truth” probably doesn’t even have some “positive” meaning and there is no reason for such term to exist; it is more of a negation of a possible contradiction in connection between concepts which we call “false”, “lie” or similar, so basically the concept of truth would be only meaningful in the context containing the determination of communication, and possibility for passing false information. So, basically this is compatible with semantic definition of Truth of Tarski, only that it is analyzed here on level of principles of functioning of Mind – the context of communication is necessary, and the possibility of lie or contradiction of what is communicated and what is comprehended must be present in order for someone to have the need for the concept of “truth”.

There is though another (more philosophical?) use of Truth, when it is not used for propositions, but for concept themselves. So, it is said, that God is Truth, Being is Truth or something similar. I think that even in those cases the truth as defined here applies, as those concepts are most often seen as concepts which are in themselves necessary, which doesn’t contain contradictions, so Mind (which of course has put that content of necessity in them), sees them as truth. Seen in this way it isn’t very strange to use “truth” for both individual concepts and propositions, as both are very interrelated and similar in a sense.

 Concepts as presented here address the issue which Plato had in mind when he talked about Forms. For him it was obvious that concepts can’t be built from multitude of experiences alone, as it was noted before here – that concepts can’t be sets.