Critique of Pure Reason – Analytic of Concepts


How to discover the pure concepts of the understanding

By Analytic of Concepts, Kant refers to the analysis of the faculty of the understading itself. When we study the faculty of knowledge, different concepts spring up in order to help us understand it. These concepts can then be gathered into a more or less complete collection. Kant however acknowledges that it may be impossible to determine reliably when it is complete. The concepts Kant claims do not share a systematic unity, but rather are paired to what is deemed similar. Kant tries to make a rough system for eases sake, with a certain methodological rigor. It may not be 100% correct, but it’s easier.

Our Understanding organizes our experiences

Understanding is a non-sensible faculty of knowledge i.e. it is the mechanism which allows us to make our experience intelligible. It is not the facility that makes intuition possible, but what makes intelligible intuitions possible. Without it, everything would be a chaotic blur.

Knowledge of the human understanding is done via the means of concepts. While intuitions rest on how we are affected by objects, concepts rest on functions i.e. arranging many representations under one common representation. Concepts do not refer to an object immediately, but indirectly through some other representation, concept or intuition. Judgment, is therefore the mediate knowledge of an object. To use an example from Hume:

If we had two concept of two shades of blue: one lighter, one darker than the other. Both of these came from intuitions of sensibility and hence, are derived from experience. Hume argued that it is possible that we could mediate between the two different concepts of blue to create a new shade of blue which is a mixture between the two colours.

Understanding can be said to be in general, the faculty of judgment. While it is also the faculty of thought, it goes between and comprehends other representations, intuitions and concepts.

The ways in which the Understanding organizes our experiences in Judgements

The function of thought can be bought under four heads:

  1. Quantity of Judgements
    • Universal
    • Particular
    • Singular
  2. Quality of Judgments
    • Affermitive
    • Negative
    • Infinite
  3. Modality of Judgements
    • Problematic
    • Assertoric
    • Apodictic
  4. Relation of Judgements
    • Categorical
    • Hypothetical
    • Disjunctive

Let us now go over the various functions of thought and particular aspects for that matter, in more details:

Singular Judgements

In logical arguments which use deduction to come to a conclusions, singular judgements are treated as universal ones. This is because they do not go outside logical structures, but stay contained within it. But when we compare a singular judgment with a generally valid judgment in terms of quantity, then it relates to the generally valid judgment in terms of infinity. Therefore, giving it a state of difference in relation to it. They therefore do not relate only to their inner validity, but knowledge in general.

Infinite Judgements

These must be separated from affirmative judgments, which at times may seem infinite. For example:

‘The soul is non-mortal’

The sentence is affirmative, as it puts the soul in the unlimited sphere of non-mortal beings. Yet the sphere is limited, insofar as it does not contain beings which aren’t mortal. This space where the soul resides, is still infinite. Though the judgment is unlimited in regards to its logical range, is limited by its qualities. The quality of being an immortal soul cannot contain the essence of being mortal.

Relations of Thought in Judgements:

When we utter the hypothesis, ‘If there is perfect justice, then the obstinately wicked get punished’, we are uttering two separate propositions which relate to each other within the sentence. Namely, ‘There is perfect justice’ and ‘The obstinately wicked get punished’. Kant also gives us these following examples:

Relation of the predicate to the subject

In this judgment, we only consider two concepts.

Relation to the ground of its consequence

In this judgment, we consider two judgements.

Relation of the subdivided knowledge and the collected members of the subdivision to one and other

In this judgment, we consider several judgments in relation to one and other.

Disjunctive Judgements

Disjunctive Judgements refers to the relationship of two or more propositions to each other. This is not a relation of consequences, but of logical opposition i.e. where one proposition contradicts the other. There is however, a community between the propositions, which fill the space of knowledge proper. When we say that the world exists either through ‘blind chance’ or ‘inner necessity’ or ‘outer cause’, each of these propositions occupies a sphere of all possible knowledge concerning the existence of the world, while simultaneously occupying its space. If we take away the knowledge from one of these spheres, we place it in another sphere. But through placing it in another sphere, we take away some of the knowledge in that sphere.

The Modality of Judgements:

The modality of a judgment contributes nothing to the content of a judgment, but rather concerns the value of linking subjects and predicates to thought in general.

Problematic Judgements:

Where affirmation or negation are taking as being merely possible.

Assertoric Judgements:

Where affirmation or negation are taken to be true.

Apodictic Judgements:

The statement ‘If there is perfect justice…’ is not stated as an Assertoric judgment, yet we assume if the conditions are met it is true.

Of the Pure concepts of the Understanding or Categories

While General Logic abstracts all content from itself, Transcendental Logic, needs content and material to make itself intelligible. Synthesis is needed (by which Kant means, putting contrasting representations together, and of comprehending their manifoldness in one item of knowledge). This synthesis used in Transcendental Logic is pure, in that, it is not derived from the realm of empirical senses. Rather, it is a manifestation of mind which makes information intelligible to us. Knowledge is produced by synthesis. When we count, we use Pure Synthesis (see Kant’s 5+7=12 example). Applying a priori functions to objects creates pure concepts.

Table of Categories:

  • Mathematical
    • Quantity
      • Unity
      • Plurality
      • Totality
    •  Quality
      •  Reality
      •  Negation
      • Limitation
  • Dynamic
    • Relation
      • Inheritance and Subsistence
      • Causality and Dependence
      • Community (reciprocity)
    • Modality
      • Possibility – Impossibility
      • Existence – Non-existence
      • Necessity – Contingency

This is the list of all original concepts of synthesis that the understanding contains a priori. Yet these concepts also have pure derivative concepts. Kant here, is not demonstrating the system of the understanding itself. But rather, the principles of the system. The first two concepts (quality and quantity) are directed at objects of intuition, whereas the second section (Relation and Modality) are directed to how the understanding depicts how they are or not to us as phenomena, and how they relate to other phenomena.  The first section Kant calls Mathematical, while the second he refers to as Dynamic. The first section meets with the second section. Totality, Limitation, Community and Necessity are nothing more than the combined synthesis of the other two categories in their tiers.