I have already read past the first book of the Transcendental Analytic, though the consolidation of my notes is lagging a bit.
Transcendental Logic. First Division
Transcendental Analytic
1.
The goal of the Analytic is to study the principles underpinning pure understanding; to accomplish this, the concepts contained in the Analytic must be pure (and not empirical), belong to thought (and not sensibility), elementary (and not deduced), and belong to a complete table of pure concepts. This completeness can only come from an idea of the understanding as a self-sufficient united system, whose parts cannot be added or removed.
The Analytic is divided into two books: the first covers the concepts of pure understanding, while the second covers the principles of pure understanding.
Book I
2. Analytic of Conceptions
This will not be focused on the analysis of some class of concepts, but on the faculty of understanding itself, which alone gives the possibility of a priori conceptions.
Chapter I. Of the Transcendental Clue to the Discovery of all Pure Conceptions of the Understanding
3. Introductory
When we think about the faculty of cognition, we usually do so in a haphazard and unsystematic way; doing so cannot lead to any certainty of judgement thereof, because it does not give any sense of unity or necessity to the conceptions thought, and is dependent on chance. Transcendental philosophy has the advantage that its concepts are pure and unified, and therefore connected by a single idea, which gives us a rule to follow during our investigations.
Section I.
4. Of the Logical Use of the Understanding in general
The understanding is non-sensuous (independent of sensation), and because of this it must not contain any intuitions, since it is in our nature for intuitions to be sensuous. And because there are only two modes of cognition (intuitions and conceptions), the understanding must cogitate through conceptions, that is to say, it is discursive [0], and not intuitive.
Since intuitions are sensuous, they require affection by an object, and so also on the receptivity of the sensibility to impressions. Conceptions, on the other hand, require that different representations be arranged under one common representation (the act of which is called a function), and so also on the spontaneity of thought.
The understanding uses concepts only in order to judge [1] by means of them. Since only intuitions relate immediately to an object, conceptions relate to them mediately (indirectly) as representations of a representation of an object. Judgements are therefore functions of unity, in that many possible representations are joined under one. As the faculty of judgement, the understanding is a faculty of thought (since thought is the cognition by conceptions), and conceptions are predicates of possible judgements. As such, all of the functions of the understanding can be found through the functions of thought, since the understanding just is the faculty of judgement, this being the faculty of thought.
Section II.
5. Of the Logical Function of the Understanding in Judgements
The function of thought in every judgement, when abstracted from all content, has four heads, each of which can be of three moments:
- Quality of judgements
- Universal
- Particular
- Singular
- Quality
- Affirmative
- Negative
- Infinite
- Relation
- Categorical
- Hypothetical
- Disjunctive
- Modality
- Problematical
- Assertorical
- Apodeictical
The following observations will be made to avoid any unnecessary confusion [2]:
1. Singular judgements are not the same as general judgements, so they can be considered to be entirely different from universal judgements.
2. In transcendental logic, infinite judgements are not the same as affirmative judgements, though this is the case in general logic.
3. All judgements are either categorical, hypothetical or disjunctive.
4. The modality of a judgement is peculiar in that it provides no additional content (since this is exhausted by quantity, quality and relation), but is only concerned with the copula (“is”). Problematical judgements may be false, yet still facilitate our cogitation of truth. Problematical judgements concern possibility (objective validity), assertorical judgements concern actuality (objective reality), and apodeictical judgements concern necessity. The mind judges things in this order.
Section III.
6. Of the Pure Conceptions of the Understanding, or Categories.
While general logic abstracts from all content (and expects it to be provided elsewhere in order for it to transform it into conceptions), transcendental logic contains the a priori manifold of intuition, which is used as the matter for pure concepts. Since space and time are the condition of sensibility, they affect how objects are conceived in thought, since these concepts are void without any sensible content, and no concept pertaining to its content can arise before the content is given.
Once this sensibility is delivered to the mind, however, the process called synthesis occurs, in which different representations are examined and joined together into a single cognition. Synthesis in general is merely the operation of the imagination, which is indispensable as a function of thought, yet nevertheless usually not well-understood. The understanding reduces the product of the synthesis to conceptions, from which we attain a proper cognition.
The duty of transcendental logic is to reduce to conceptions, not representations, but the pure synthesis of representations. The diversity of the manifold of pure intuition is first given, then the imagination synthesizes it, before pure conceptions are applied by the understanding to give this synthesis unity, and therefore transform it into a cognition [3].
The pure conceptions of the understanding are the functions which gives unity to both the representations in a judgement, and the synthesis of representations in an intuition. These conceptions, through analytic unity, give rise to the logical forms of judgement, but they also introduce transcendental content through the application of the synthetic unity of the intuitive manifold [8]. Thus there are exactly the same number of pure concepts as there are logical forms, to which they correspond, and are given the name categories. They are:
- Of Quantity
- Unity
- Plurality
- Totality
- Of Quality
- Reality
- Negation
- Limitation
- Of Relation
- Of Inherence and Subsistence (substantia et accidens)
- Of Causality and Dependence (cause and effect)
- Of Community (reciprocity between the agent and patient)
- Of Modality
- Possibility - Impossibility
- Existence - Non-existence
- Necessity - Contingence
It is through these, and only these, pure conceptions that the manifold of intuition is made conceivable - that is to say, thought as an object of intuition. While Aristotle tried to make a catalogue of his own, he went about it unsystematically, and the result was not only uncertain to be correct, but actually indeed contained elements that should not have been included. In comparison, this catalogue has been arrived at by abiding by a rule [4], and so the result is guaranteed to be correct and complete. These pure conceptions themselves have deduced conceptions (called predicables), however these are not included in the present work, as it would distract from its overall purpose, however they would belong in a complete transcendental philosophy.
7.
Here are some observations related to the pure conceptions:
I. The table of categories can be divided into two classes: the first of which relates to objects of intuition (deemed mathematical), the second to the existence of these objects in relation to each other and/or to the understanding (deemed dynamical). Only the latter has correlates [5].
II. There are always three members of each of the four classes. The third is always a product of the combination of the second and first members; but this third member is not a deduced category because of this, since a particular function is required for the first and second members to produce the third.
III. [6]
8.
Ancient transcendental philosophy contained a fifth categorical division, the members of which were the one, the true, and the good (unity, truth, perfection). This would augment the number of categories, which cannot be, because there is a one-to-one relation between a category and a logical function of thought. These supposed-categories are really just surreptitious names for the categories of quantity (unity, plurality and totality) when viewed as general laws of consistency of cognition. In every cognition of an object there is a unity of the manifold (qualitative unity); the truth (objective reality) of a cognition can be indicated by the number of true deductions that are sourced from it (qualitative plurality); and finally when this plurality is fully in accordance with the conceptual unity, it is perfect (qualitative completeness) [7].
Questions/Thoughts
0. By "discursive", I take Kant to mean the process in which the understanding organizes objects by concepts according to their marks.
1. By "judgement", I take Kant to mean basically the mental process of deciding if something is the case.
2. This part was fairly dense to get through, and I felt it was not as important to focus on, so I brushed over some of the parts I found confusing.
3. I don't really understand what the difference is between the synthesis of the imagination (conjoining intuitions) and the operation of the understanding (putting this synthesis under a concept to give it unity). This part was a bit dense for me.
4. It is unclear to me what this rule exactly is.
5. What does Kant mean by "correlate"?
6. Kant's discussion about community and disjunctive judgements is dense, but I recall in Allison's book a good deconstruction of the argument, so I will defer the summary of it to there.
7. I found this section to be incredible dense in areas, though I think I grasp the general idea.