Comprehension

Any experiences come to us serially in time. Experiences here may be the steps of an inference, a proof, a melody or the words of a sentence, all of which can be embedded in a situoid. Any of those events are experienced one after another, but must be considered in a single mental act, before they can bear any meaning at all. Such an act is what we will call ``comprehension''. This act differs from inference or judgement, it comes before both. Judgement, the assertion or denial of a relation between concepts, presupposes considering both concepts together. Where inference refers to the drawing of conclusions from premises, comprehension refers to considering the premises together with the conclusion, as in mathematics, where we do not see a proof as a series of manipulations according to rules, but rather as something whole.

In comprehension, Mink writes:

[...] comprehension operates on all levels of reflection and inquiry. At the lowest level, it is a grasping of the data of experience and issues in the perception and recognition of objects. At an intermediate level, it is the classification together of a set of objects and issues in the formation of concepts. At the highest level, it is the attempt to order our knowledge of the world into a single object of understanding.

This suggests, that there are fundamentally different modes of comprehension. A number of entities may be comprehended as instances of the same law or formula or generalization. This kind of comprehension refers to some entities in virtue of their possession of certain common characteristics, omitting everything else. This specific kind of comprehension, that Mink in comprehension called ``theoretical'' or ``hypothetico-deductive comprehension'', lets us understand all instances of the consequence of some hypothesis.

Another mode of comprehension is understanding a number of entities as elements of a single complex of concrete relations. It is this mode, that lets us understand the multiple lines, multiple images of a song or poem, or a sentence in this thesis. Mink called this ``configurational comprehension'', described by Pascal as ``the ability to hold together a number of elements in nice balance''.

Plato envisioned another mode of comprehension: ``to hold together a number of things as examples of some category, and in fact a system of categories incapable of abstraction from each other.'' The question arises, if this subsumption under categories falls together with deduction from hypotheses. As Mink points out, there are a number of differences why these two views are not identical. First, hypotheses are meaningful even independent of each other, while the meaning of categories is dependant on their interconnection. Also, according to Kant, categorical connections are not falsifiable by experience, since they give form to experience itself. This mode of comprehension is called ``categorical comprehension''.

Theoretical comprehension therefore is the understanding of relations between universals and particulars. Comprehending a particular at this mode lets us identify an universal, of which this particular is an instance. Theoretical comprehension of a universal lets us identify the class of all particulars, that are instances of this universal. Configurational comprehension is understanding of the relation between particular and particular. Configurational comprehension of some particular lets us identify the roles this particular takes in the relations to other entities in some whole, as well as the relations this particular is in. Categorical comprehension is understanding the relations holding between universal and universal. It lets us identify relations like $part-of$ or existential dependence of categories. Comprehending a number of categories is understanding them as a web of categories with relations holding amongst them.

None of these modes is primal to another. They are self-justifying, and when we speak of comprehension we will have to consider all three modes.

Let us apply our knowledge of comprehension to situoids, now. What is meant by comprehending a situoid in the various senses?

Let us start with theoretical comprehension. For a situoid to be comprehensible in this sense we have to be able to find a universal this situoid is an instance of. Therefore we state that a situoid is an instance of at least one universal. We can formulate this as an axiom:

Axiom 5.20  

$$\forall s \left( Situoid(s) \rightarrow \exists u \left( Universal(u) \land s::u \right)\right)$$

Objects can be treated as situoid. Therefore a universal ``house'' may have situoids as well as substances, processes, concepts, etc. as its instances. Because universals in our background ontology General Formal Ontology are intentional entities, all those universals are different, because they have different intentions. There exists only one universal ``house'' with house-situoids as its instances.

In herre3, situoids are associated with a set of universals. Therefore, if we consider a house as a situoid, it may be associated with the universals $Building$, $House$, $Window$, $Door$, et cetera. However, in herre3 it never becomes clear what this association relation between situoids and sets of universals really is, in an ontological sense.

It is obvious, that these universals are needed to describe a situoid of some kind, and that there are entities in the situoid, that are instances of these universals. We consider the description in herre3 insufficient and unnecessary. We cannot deny the existence of a set of universals in a situoid, so we state that every situoid is an instance of the complex universal that is formed by all universals, that are said to be associated with it in herre3. After all, universals are intentional entities, and they define properties and structure of their instances.

However, we will associate with situoids what we will call ``categorization devices''. A categorization device is a universal with universals as its instances, and they specify a context for a situoid. They are needed to give semantic to natural language, especially referring terms, in situoid theory, and are discussed in section 6.1.1.

Let us turn our attention to the second kind of comprehension, configurational comprehension. For a situoid to be comprehensible in this sense, we have to be able to identify the relations it is in with other entities ``in some whole''. We will proceed with a discussion of wholes in the next section. For now we will consider at least every situoid as some whole. We state, that every situoid can be embedded in another situoid, in which more infons obtain. This captures the ability of the human mind and speech, to add more and more qualities, properties or entities, and therefore more information, to some whole. Image a stone laying in a desert as a situoid. We can add, in mind or speech, more and more information about this situoid. We could start by stating the color, shape or weight of the stone. Then we can add some other entities, maybe the stone is part of a pile of stones. We can go on by adding information about the desert or the history of the stone, up to its position in the universe. Let us summarize this with the following axiom:

Axiom 5.21  

$$\forall s ( Situoid(s) \rightarrow \exists t (Situoid(t) \land s \leq t) \land t \not= s)$$

Now the remaining problem is, finding the relations of some entity in the larger situoid. If this is possible our task is done, because then we can identify the relations and roles a situoid plays in some whole by identifying the relations that obtain in some larger situoid. How can we assure that this is possible? There is a set having all the infons that obtain in some situoid as elements. If we are able to decide, if some infon is an element of this set, we can identify all the relations that hold for any entity in a structured whole (situoid). Therefore, we request the following to be true for situoids:

Axiom 5.22   The set $S(s)$ of all infons obtaining in a situoid $s$ is decidable.

This axiom is required for comprehending a situoid. It also captures the feeling we had, when the phrase ``can be comprehended as a whole'' came into being. Because infons are the means we use to express knowledge about situoids, we have to be able to say what these infons are for a particular situoid. If we are not able to do this, then we have not comprehended the situoid. And even stronger, if we are not able to say what infons in the relevant part of reality exist, then this part of reality cannot be regarded a situoid.

Categorical comprehension can be disregarded in this discussion, because universals and categories are not at issue here. However, let us point out, that this entire work is dedicated to comprehension of the categories ``situoid'' and ``situation'' in the system of the General Formal Ontology.

We will proceed with a discussion of wholes in general and whole situoids in specific.