This analysis is on “of the entirety of our a priori cognition into the elements of the pure cognition of the understanding.” (A64/B89) This means that all Kant is going to be concerned with here are those pure cognitions of the understanding from which all other concepts are possible. This is, as he puts it, an “analysis of the faculty of understanding itself.” (A66/B90) Accordingly, he gives us four points to keep in mind for properly conducting this investigation:
- The concepts must be pure
- They must belong to thinking and understanding
- The must be elementary concepts and clearly distinguishable from all other subsequent ones
- The table of concepts must be exhaustive
To begin with the first chapter proper, the understanding is not a faculty out of intuition since intuition can exist independently of sensibility. Therefore all cognition of understanding must come out of concepts which are based on functions. What Kant means by function is “the unity of the action of ordering different representations under a common one.” (A68/B93) This common grounding for representations is the spontaneity of thinking.
There is only one purpose for concepts with respect to the understanding at that is judging; add to that point that concepts are never immediately related to objects (for objects are only immediately related to intuition), and we get the conclusion that judgment is the mediate cognition of an object, or “the representation of a representation of it (whether that be an intuition or itself already a concept).” (A68/B93) What Kant is saying here is that in judgments we find a plethora of concepts which are mediately to objects through other concepts. Kant gives us the following example: ““All bodies are divisible,” the concept of the divisible is related to various other concepts; among these, however, it is here particularly related to the concept of body, and this in turn to certain appearances that come before us. These objects are therefore mediately by the concept of divisibility.” (A68/B93) From this we can see that Judgments are unifying functions meant to bring together various representations under different concepts; and since we can trace all the actions of the understanding back to the operation of judging, the understanding, we can thus refer to the understanding generally as a faculty for judging (or alternatively, a faculty of thinking for thinking is cognition through concepts).
With the exposition on judging laid out, Kant’s next move is to demonstrate what the form of judgments in general are once all content has been abstracted away. He lays them out in the following table:
The quantity of judgments consists of:
- Universal (All S is P)
- Particular (Some S is P)
- Singular (This S is P)
Kant first comments on how universal and singular judgments can be treated alike in syllogisms in traditional Aristotelian logic. This has to do with the predicate being connected wholly to the subject rather than merely having some relation to part of the subject regardless if there is a domain or not. If this logic were applied to Kant’s table of judgments, then the singular judgment would be rendered extraneous. However, in transcendental logic comparing singular judgments to universal ones is like comparing unity to infinity. This is because here the comparisons being made are between different forms of judging. If we take the judgment singular and try to apply it to objects that have been related to the judgment universal, we will find a large number of objects which can be represented by one but not the other, hence, the need for both forms of judgments.
The quality of judgments consists of:
- Affirmative (All S are P)
- Negative (No S are P)
- Infinite (All S are non-P)
The same observation made about universal and singular judgments can be applied to infinite and affirmative judgments. Unlike general logic which abstracts all content from the predicate and only focuses on its attribution to the subject, transcendental logic does consider what the content does or does not add to the cognition. In the case of quality, there are cognitions which speak to the affirmation of a representation which also belongs to an infinite class of representations. Kant uses “The soul is non-mortal” as his example. (A72/B97) This statement is an affirmation of the soul as being within the infinite domain of immortal beings, which is itself half a domain it shares with all mortal things. Now, suppose the mortal sphere of the domain was stripped away from the whole, then there would still be the infinite sphere of the immortal to which the soul belongs. In other words, infinite judgments of quality are actual judgments and are limited only with respect to the content of the cognition.
The quality of relations consists of:
- Categorical (S is P)
- Hypothetical (If S, then P)
- Disjunctive (S or P)
Relations of thinking judgments fall into three categories which Kant classifies as being those “a) of the predicate to the subject, b) of the ground to the consequence, and c) between the cognition that is to be divided and all of the members of the division.” (A73/B98) In a) are those pertaining to two concepts, b) are those pertaining to two judgments, and c) are those pertaining to several judgments.
The quality of Modality consists of:
- Problematic (S may be P)
- Assertoric (S is P)
- Apodictic (S is necessarily P)
The judgments are unique in that they contribute nothing to the content of the judgment. What these judgments are concerned with is the truth status of the copular being considered. Problematic judgments only assert only the possibility of truth, assertoric judgments assert that actual truth of a proposition, and apodictic judgments place the claim of necessity on a proposition. Consider the following three examples: Problematic – The rain in Spain falls mainly on the plane, Assertoric – The president of the United States is a man, and Apodictic – For every effect there is a cause.
With the table of judgments laid down, Kant next outlines the table of categories, but first he makes some important comments about synthesis. Synthesis comes about because of the manifold of a priori intuitions receiving representations of objects of sense. These representations are given to us, and the understanding goes about sorting through them and combining them in an appropriate manner so a cognition can be made out of it. It is this process of thought Kant calls synthesis. In Kant’s words, “by synthesis in the most general sense…I understand the action of putting different representations together with each other and comprehending their manifoldness in one cognition.” (A77/B103) Synthesis can either be pure or empirical depending on the content being given, and occurs prior to any analysis of what is being given. For Kant, synthesis is “the mere effect of the imagination” (A78/B103) which blindly combines representations together, which are then analyzed by the understanding, and formed into concepts if appropriate. From what has been said, Kant explains how the process for gaining a cognition works: “The first thing that must be given to us a priori for the cognition of all objects is the manifold of pure intuitions; the synthesis of this manifold by means of the imagination is the second thing, but it still does not yield cognition. The concepts that give this pure synthesis unity, and that consist solely in the representation of this necessary synthetic unity, are the third thing necessary for cognition of an object that comes before us, and they depend on the understanding.” (A79/B105) To put what has been said into an example, I am given a number of representations of a bottle in various forms ranging from completely intact to shattered. From the manifold of pure intuitions I am aware of the concept causality. Once the representations of the bottle and the concept of causality are combined in thought, I realize that the bottle fell off a table and shattered when it hit the ground.
Causality is only one of nine pure concepts of the understanding which apply to objects of intuition a priori. Here is the chart:
These categories, when taken in concert with the forms of judging, exhaust every possibility for how and what we are able to think of. Kant calls them categories as homage to Aristotle who undertook the same task a couple of millennia earlier. Note here that these concepts are pure “ancestral concepts” meaning they are the base concepts from which other pure “derivative concepts” can be built upon. Kant makes several remarks concerning this table that I shall take in order.
First, these four classes of concepts can be split into two divisions. On one side there are the concepts that deal with objects of intuition which Kant calls the mathematical categories. These are the categories of quantity and quality. The second class of concepts deals with the existence of these objects which Kant calls dynamical categories. These are the categories of relation and modality.
Second, the third category is always the result of the first two in its class. For example, “allness (totality) is nothing other than plurality considered as a unity, limitation is nothing other than reality combined with negation, community is the causality of a substance in the reciprocal determination of others, finally necessity is nothing other than the existence that is given to possibility itself.” (B111) However, this does not mean that the third category is not ancestral, for it requires a unique act of the understanding to produce the third category which is not identical with the acts involved with producing the first two. Kant tells us that the “concept of a number (which belongs to the category of allness) is not always possible wherever the concepts of multitude and of unity are (e.g., in the representation of the infinite).” (B111)
From here Kant moves on to make note of the way in which community corresponds to disjunctive judgments and comments briefly on the scholastic thought that every being is one, true, and good.