5. Schematism and Noumenal Ignorance

Aim of the schematism

• Supply the categories with empirical content such that they become homogeneous with intuition and empirical objects

  • Show how the categories actually apply to empirical objects — as pure concepts they have no empirical grounding

  • “In all subsumptions of an object under a concept the representations of the former must be homogeneous with the latter.” (A137/B176)

• It also aims to further establish the restriction thesis

What is schematisation and how does it occur?

• Schematisation is the mediate process which acts to ensure that the categories actually apply to empirical objects

• The schematised categories (schema) are the pure concepts of the understanding supplied with empirical content, the categories embedded in time (time-determinations), making them homogeneous with both the intelligible and the sensible

  • The schema is a time-determined rule which tells us how an empirical intuition - like a dog - must subsume under the categories

    • “a general procedure of the imagination for providing a concept with its image” (B180)

• The pure form of intuition, time, is required for schematisation because it is homogeneous with both the intelligible and sensible — it is intelligible because it is a form of intuition and sensible because it applies to all empirical objects

Examples of schema

• Substance (Pure) — A thing that can be though of as subject without being a predicate of something else — That which endures through change, existence across time (Schema)

• Cause (Pure) — something that allows an inference to the existence of something else — something from which something else follows necessarily in time (Schema)

Quote describing the schema

• “the schemata are nothing but a priori time-determinations in accordance with rules, and these concern, according to the order of the categories, the time-series, the content of time, the order of time, and finally the sum total of time in regard to all possible objects.” (A145)

  • When he says ‘according to the order of the categories’, he refers to quantity, quality, relation, and modality

How is the restriction thesis established by the schematism?

• Building on the restriction thesis established previously, the argument follows:

1. Cognition through concepts requires determining their objective reality

2. This determination requires the temporal schemata

3. Cognition through concepts therefore also requires the temporal schemata

4. Therefore, we cannot cognise things-in-themselves because they require the schema, which are time-determinations — things-in-themselves aren’t temporal

What does Kant mean by objective validity and real possibility?

• In order for a concept to be justified, we must be able to demonstrate that it attaches to an object in intuition (i.e., an empirical object, or figure — like a triangle — constructed by the imagination)

  • One can think whatever they want without contradiction, but for their concept to be justified requires more than mere conceivability

• Kant’s objective reality (metaphysical possibility) lies somewhere between logical possibility (according to the law of noncontradiction) and nomological possibility (according to the laws of nature)

  • Hence, the laws of nature, although not logically necessary, are probably objectively real for Kant

Descartes and Leibniz on logical possibility

• Descartes’ argument for dualism follows the belief that because God can do in reality what is merely conceivable in the mind, what is conceivable in the mind becomes the basis for what is possible — of course, Kant rejects this

  • “Without schemata therefore, the categories are only functions of the understanding for concepts, but do not represent any object. This significance comes to them from sensibility, which realises the understanding at the same time as it restricts it.” (B186)

• Leibniz attempts to prove God through more conceivability, implying, similarly to Descartes, that the grounds for real existence are conceivability

The problem of noumenal affection

• Kant claims that the noumena are fundamentally unknowable, but he also claims that our representations are supported and obtain in some causal relation with mind-independent reality, which seems unjustified

• J.G. Fichte argues that if the categories only apply to the realm of experience, then extending them outside of experience (noumenal affection) contradicts the restriction thesis

  • It is worth pointing out that Kant doesn’t claim the categories don’t apply to things-in-themselves, but merely that these things are unknowable through the schema

    • Somehow, he believes we are able to think of these objects through the unschematised categories (i.e., without determining their objectivity) to use them in practical reasoning

Why is the problem of noumenal affection persistent?

• Even if there is no tension between noumenal affection and the restriction thesis (the categories apply to things-in-themselves but can’t be known through them), noumenal affection is in-built into Kant’s definition of sensibility

  • Kant argues that noumena cause representations, but that this causal relation which must obtain between them is merely a representation

    • If we are unable to perceive whether the noumena actually cause our representations, Kant seems dangerously close to slipping into idealism

What is the divine understanding?

• This is a type of intuitive, rather than discursive intellect, which doesn’t require concepts to cognise objects, it merely grasps them intuitively

  • Here, the categories are understood twofold: (1) as ontological predicates which determine the form of an ontological object and (2) as concepts which represent ontological predicates (this is how they have been conceived so far)

    • Therefore, objects could accord with the categories without one cognising them through concepts

• God would not cognise noumena through the categories as concepts, but he would still intuit objects through the categories as ontological predicates

What is the in-itself?

• This is theoretically disputed, but many scholars, such as Van Cleve, Langton, and Allais, suggest that the in-itself concerns the ‘inner nature of things’ — this is still vague

• To say things-in-themselves are unknowable is to say the inner nature of things is unknowable as are relations-in-themselves

Problems for transcendental idealism

• Kant considers the non-spatiotemporality of things-in-themselves indubitable, but it is obvious he doesn’t have grounds for this conclusion

• He could just say things-in-themselves are possibly non-spatiotemporal and possibly cause representations, but he needs to make this stronger claim to distinguish sensibility and understanding

  • He defines sensibility as the reception of representations caused by external objects (i.e., mind-independent objects)

• Without the stronger claim, he needs to redefine sensibility, and he loses an account of where representations come from

  • This failure to justify that representations are external could cause transcendental idealism to slip back into scepticism and idealism