A Critical Outline of Kant’s Analytic of Concepts in the Critique of Pure Reason

The Transcendental Analytic (pp 201..266 of (Guyer/Wood 1998)) is probably the most difficult part of the entire Critique. This “critical outline”, a prologomena if you please to a full-scale paper on this section may help some to understand. I know it helped me where reading the TA section seven times was to no avail.

1. Analytic of concepts
1.1. On the clue to the discovery of all pure concepts of the understanding
1.1.1. On the logical use of the understanding in general
1.1.1.1. Understanding relates to
1.1.1.1.1. The intuition of an object as based on sensibility
1.1.1.1.2. Another understanding of another concept
1.1.1.2. “All bodies are divisible”
1.1.1.2.1. Links the concept body to the concept of divisibility
1.1.1.2.2. Based on appearance but can never be justified by appearance. It’s just that as beings who see three-dimensional space two-dimensionally, a convenient concept is “bounded region (with or without holes: of topological order 0 or above)” and to call this something like a body.
1.1.1.2.2.1. We then find it also convenient to see that any such visible region can be divided as a closed concept into smaller and smaller such regions.
1.1.1.2.2.2. Whence “all bodies are divisible” as a synthetic apriori because “divisibility” adds something to “body” in which “all bodies are bodies” does not. Perhaps by accident, if Kant means by “all bodies are divisible” what I think he means, he means that the division of a body produces two or more bodies: the concept of body is closed under the operation of division.
1.1.1.2.2.3. But an alternative would be that after a finite amount of steps, “bodies” are no longer produced under the operation of division: instead we are given indivisible granular atoms or “pixels”. It’s clear that Kant didn’t have HDTV where in fact this oversold technology resolves continuous bodies into crude and jagged pixels all too soon, making the viewing of art an absurdity on HDTV because of the loss of smooth edges.
1.1.1.3. The understanding is a faculty of judgment. No understanding, no judging, just sensibility and intuition
1.1.2. On the logical function of the understanding in judgments
1.1.2.1. The table of the categories: Kant claims that understanding uses the following categories. Each category is a type of judgement. Note that I have inserted my own, possibly quite flawed, example of each type of judgment.

Note: using modern symbolism and therefore modern concepts to analyze traditional logic’s structures is always a desperate business. Some propositional forms (p and that(p), for example, where there’s little difference between the two) repeat with changes in notation. But in general the symbolisms are variegated enough for us to claim that Kant’s table exhausted all types of judgements and that our symbolism captures the meaning of each entry in the table

1.1.2.1.1. Quantity
1.1.2.1.1.1. Universal
1.1.2.1.1.1.1. (x)[P(x)]
1.1.2.1.1.1.2. For all x, x has the property P
1.1.2.1.1.2. Particular
1.1.2.1.1.2.1. (Ex)[P(x)]
1.1.2.1.1.2.2. There is an x which has the property P
1.1.2.1.1.3. Singular
1.1.2.1.1.3.1. (x)[x=y ⇒ P(x)]
1.1.2.1.1.3.2. y and no other has the property P
1.1.2.1.2. Quality
1.1.2.1.2.1. Affirmative
1.1.2.1.2.1.1. P(x)
1.1.2.1.2.1.2. x has the property p
1.1.2.1.2.2. Negative
1.1.2.1.2.2.1. ~P(x)
1.1.2.1.2.2.2. It is not the case that x has the property p
1.1.2.1.2.3. Infinite
1.1.2.1.2.3.1. (time t)[(x)[P(x)]]: P(x) universally true for all time
1.1.2.1.2.3.2. For all times t P(x) is true at that time for all x
1.1.2.1.3. Relation
1.1.2.1.3.1. Categorical
1.1.2.1.3.1.1. (x)[C(x)⇒P(x)]
1.1.2.1.3.1.2. All x in category C has property P
1.1.2.1.3.2. Hypothetical
1.1.2.1.3.2.1. (x)[H⇒P(x)]
1.1.2.1.3.2.2. For all x when hypothesis H is true then x has the property P
1.1.2.1.3.3. Disjunctive
1.1.2.1.3.3.1. (x)[P(x) v Q(x)]
1.1.2.1.3.3.2. For all x, x has the property P or x has the property Q
1.1.2.1.4. Modality
1.1.2.1.4.1. Problematic
1.1.2.1.4.1.1. possibleThat(p)
1.1.2.1.4.1.2. p is possible
1.1.2.1.4.2. Assertoric
1.1.2.1.4.2.1. that(p)
1.1.2.1.4.2.2. p is contingent
1.1.2.1.4.3. Apodictic
1.1.2.1.4.3.1. necessaryThat(p)
1.1.2.1.4.3.2. p is necessary
1.1.3. On the pure concepts of the understanding or categories
1.1.3.1. Synthesis: three steps
1.1.3.1.1. The manifold of pure intuition
1.1.3.1.1.1. Two or more things or states
1.1.3.1.1.2. Kant is silent on whether one or zero things or states count as degenerate manifolds.
1.1.3.1.1.2.1. When we don’t see something or someone as much as prematurely place that something or someone in a category, perhaps we can understand this to be a source of racism.
1.1.3.1.1.2.1.1. An example would be “Look! A negro!” in (Fanon 2008): for Franz Fanon, part of colonialism consisted in his struggle to be “intuited” (translated from sensibility to understanding) as a professional man (doctor, psychiatrist, person worthy of respect) when in fact he was intuited by children as a “negro”, and their vicious intuition predominated.
1.1.3.1.1.2.1.2. Likewise Ghandi (Attenborough 198): Ghandi innocently expects to be intuited by the porter, conductor and passenger as a professional man (lawyer) from India but with even more fervor than the children of Pieds Noirs in colonial Algeria,
1.2. On the deduction of the pure concepts of the understanding
1.2.1. On the principles of a transcendental deduction in general
1.2.1.1. Transition to the transcendental deduction of the categories
1.2.1.1.1. Best model
1.2.1.1.1.1. Juridical
1.2.1.1.1.2. Fortune? No
1.2.1.1.1.3. Fate? No
1.2.1.2. Transcendental deduction of the pure concepts of the understanding
1.2.1.2.1. Empirical? No
1.2.1.2.2. The TD is an explanation of “the way in which concepts can relate to objects apriori”
1.2.1.2.3. Contrast indeed the empirical deduction which is just (just?) an explanation of how one subject has related a concept to an object
1.2.1.2.4. There might be a general recommended method for relating a given concept to a given object
1.3. References
1.3.1. Attenborough 1982: Richard Attenborough (director), Ghandi (film), 1982
1.3.2 Guyer/Wood (tr) 1998: Critque of Pure Reason. Cambridge University press 1998.
1.3.3. Fanon 2008: Franz Fanon, Black Skin, White Masks. Grove Press 2008.

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