Twelve rounds with Kant (part 2)

Vasily Kandinsky, Examination (1930)

Okay.

What we're going to do today is take an uncritical look at the ideas Kant devises and attempts to substantiate in the first half of his Critique of Pure Reason (in the Transcendental Aesthetic and Transcendental Analytic sections). I am doing this, firstly, because I'll never understand Kant's theories unless I try to articulate them for myself. And secondly, I do it in the hope that maybe somebody else will find it useful.

Even before reading the Critique, I found Kant frustrating because people who write about him on the internet usually provide a either summary that's too vague and too abbreviated to communicate much of anything at all, or commentary that's far too technical to be of use to anyone who isn't already sitting with Kant's book in their lap. I'd like to imagine this could be a serviceable middle ground between "Kant says we make our reality iirc" and any given Kant page on plato.stanford.edu: useful to somebody who wants to dip in more than just one toe, but isn't yet ready to get his ankles wet.

Please bear in mind that I am a mere layman trying his best; anything I say here is subject to error.

The bullet points will be interspersed with pretty paintings by Kandinsky in order to break up the visual monotony of the text and refresh your mind. (I know they help me.)

Vasily Kandinsky, Disintegrated Tension (1930)

• First—and again, this is for my own benefit—let's define some terms. Kant's jargon is idiosyncratic and teeth-grindingly wonky. What's really scary is that what we're going to read here doesn't take us any deeper than the epipelagic zone of the Kantian system. All quotes are from the Critique.

◦ Knowledge: Cf. Plato, Theaetetus.¹ "...consists in a determinate relation of given representations to an object." "...involves two parts: first, the concept, through which an object is thought at all (the category); and secondly, the intuition, through which it is given." 

 

◦ Object: Things that are capable of being known. "...that in the concept of which the manifold of a given intuition is united." 

 

◦ Representation: Any of the following: perceptions, sensations, knowledge, intuitions, concepts, notions, ideas. Basically anything that crosses our mind, as they say. 

 

◦ Intuition: Immediate sense-perception. The matter of an appearance. "That through which [knowledge] refers to [objects] immediately." "The representation which can be given prior to all thought."  

 

◦ Sensibility: Passive receptivity to sense-impressions. Supplies us with intuitions. "The capacity (receptivity) to obtain representations through the way in which we are affected by objects." 

 
◦ Concept: Arises from the understanding's processing of intuitions. The form of an appearance. Discursive. "...rest[s]...on the unity of the act of arranging various representations under one common representation." "...refers mediately to the object, that is, by means of a characteristic mark that several things have in common."  

 

◦ Judgement: That to which all acts of the understanding can be referred.² Its faculty is the same as the faculty of thinking. "..functions of unity among representations." "...the mediate knowledge of an object, that is, the representation of a representation of it."

 
◦ Inner sense: Empirical apperception. "Dispersed" awareness. "Consciousness of oneself according to the determinations of our state in inner perception...merely empirical and always transient." 

 

◦ [Transcendental] apperception: Subjective unity and continuity of self; the unity from which a priori knowledge can be obtained. "...[represents appearances] in the empirical consciousness of the identity of these reproductive representations with the appearances through which they were given, and therefore in recognition." "The original and transcendental condition...that unity of consciousness which precedes all data of intuitions, and by reference to which all representation of objects is alone possible." "...the condition under which alone [representations] can stand together in one universal self-consciousness, because otherwise they would not one and all belong to me." 

 

◦ Understanding: The faculty which brings synthesis to concepts. "The faculty...which allows us to think the object of sensible intuition." "...our faculty of producing representations by ourselves." "...the spontaneity of knowledge (as opposed to the receptivity of sensibility), or the faculty of thought, or the faulty of concepts or of judgements..." "...the faculty of rules." 

 

◦ Imagination: The faculty responsible for synthesis in general. "...a blind but indispensable function of the soul without which we should have no knowledge whatsoever." "...[represents appearances] in association (and reproduction)." "...the faculty of representing an object in intuition even without its presence." 

 

◦ Synthesis: "...the act of putting different representations together, and of comprehending their manifoldness in one item of knowledge." "...the mere result of the faculty of imagination."

◦ Transcendental logic: "...a logic in which we do not abstract from all content of knowledge [as we do in general logic]...[it treats] of the origin of our knowledge of objects, as far as that origin cannot be attributed to the objects..." "It deals...only with that form of the understanding which can be imparted to the representations, whatever their origin may be." 

Confused? Yeah, me too.

• One of Kant's main goals in the Critique is to prove that synthetic a priori knowledge is possible. The book took him ten years to write, so I'm guessing he had at least as hard a time solving the problem for himself as I've had following his solution.

◦ To the best of my knowledge, logicians don't make these sort of distinctions anymore, but they were seen as useful in the eighteenth century.

∙ Epistemologically, a proposition can be either a priori or a posteriori: known independently of experience, or known through experience. The classic example of an a priori statement is "all bachelors are unmarried." An a posteriori statement would be something like "all bachelors have trouble getting laid." According to Kant, a priori knowledge is that knowledge which is necessary. A posteriori knowledge is contingent.

∙ Semantically or logically, a proposition can either be analytic or synthetic. An analytic statement "adds" nothing to the subject; again, "all bachelors are unmarried." It states nothing but what the word already means. A synthetic statement does more than just "unpack" the term: "Patrick is a bachelor." The criterion of an analytic judgement's truth is the principle of contradiction. For a synthetic judgement, non-contradiction merely indicates the possibility of its truth.

∙ Analytic knowledge is usually also a priori knowledge, and synthetic knowledge is usually also a posteriori knowledge. Synthetic a priori knowledge would have to somehow consist of the addition of something not contained in the object concerned to the object concerned, and the addition must not only be justified, but necessary. 

Vasily Kandinsky, Inner Alliance (1929)

• Kant saw synthetic a priori knowledge as the solution to David Hume's riddle about causal connection. Hume argued that we have no logical grounds for the ascription of a causal relationship between the cue ball's impact and the billiard balls scattering; all we can say is that one event comes after the other. Kant conceded the point, but was convinced that Hume had overlooked something. We can't know a posteriori that one event is necessarily contingent upon another—all we can claim is that we're habituated to witnessing an object in our hand falling when we relax our fingers. But what if we can know causal connection a priori?

◦ I'm not remotely qualified to make any but the most superficial comments regarding the continental rationalist tradition, but Kant felt that its toolkit wasn't up to the task of satisfactorily demonstrating the a priori veracity of cause and effect.

◦ Kant posits mathematics as indirect evidence of the existence and necessity of synthetic a priori knowledge. As mathematical knowledge is not empirical (so Kant maintains; others differ), nor its operations strictly analytic, Kant imagines Hume would find himself backed into a corner if asked to confirm that the statement 2+2=4 expresses only a mental habit, and its veracity subject to uncertainty.

• General logic cannot account for causal connection, but Kant believes it does contain a clue towards the solution. From Kant's posthumously published Introduction to Logic (1800):

If, however, we set aside all knowledge that we can only borrow from objects, and reflect simply on the exercise of the understanding in general, then we discover those rules which are absolutely necessary, independently of any particular objects of thought, because without them we cannot think at all. These rules, accordingly, can be discerned a priori, that is, independently of all experience, because they contain merely the conditions of the use of the understanding in general, whether pure or empirical, without any distinction of its objects.

• In the Critique, Kant bifurcates all things into appearances and things-in-themselves. Appearances consists of sense-objects: what we see, feel, hear, etc. All we experience, all we can know, are appearances. Things-in-themselves are what's really outside of our skin, as they exist independently of our sense perceptions. Kant brackets off things-in-themselves and sweeps them off the table. We don't deal with them. They exist, but that's just about all we can say about them. We cannot experience them without the mediation of our intuitive and conceptual faculties, so they're epistemologically out of bounds.

◦ If empiricism refers only to our experience, and not to things-in-themselves, then the manner in which we experience things (or can potentially experience them) is what we need to examine in our search for synthetic a priori knowledge.

Vasily Kandinsky, Three Elements (1925)

• Synthetic a priori judgements are possible if the following three things...

1: "...the formal conditions of a priori intuition..."

2: "...the synthesis of imagination..."

3: "...and the necessary unity of this synthesis in a transcendental apperception..."

...are referred to the possibility of knowledge/experience in general.

◦ Consulting some secondary sources, I found a lucid synopsis of the transcendental method Kant employs in substantiating his claims that's too helpful not to reproduce here: 

...one proves the truth of a synthetic a priori principle (for instance, the causal principle) by proving two things: (1) that the conditions of possibility of our experience of an object are also the conditions of possibility of this object itself...(2) that presupposing the truth of the synthetic principle under consideration (for instance, the causal principle)...is a condition of possibility of our experience of any object, and therefore (by virtue of (l)), of this object itself. 

∙ You'll notice this stacks up with Kant's insistence on a strict distinction between appearances/objects of experience and things-in-themselves. Remember, if everything we can know or experience is in some way a "mental construct," an examination of "objective reality" must necessarily entail an examination of our faculties of sense perception, cognition, and conceptual sorting.

Let's peer at each of Kant's three criteria in order.

• (1) With regard to sense perception, we need to winnow out the most fundamental and absolutely general forms of intuition. As soon as any specific object or quality of perception enters into our inquiry, it's over: we can't call our knowledge a priori because we've introduced empirical data into it. We can only include the requisites for possible sensory experience, because they are its necessary preconditions.

◦ The Transcendental Aesthetic, the first chunk of the Critique, explicates the fundamental forms of sense perception: space and time. We cannot experience objects or events outside our skin (or relate one part of our body to another part, for that matter) without the "pure intuition" of three-dimensional space. We cannot experience anything in ourselves (and therefore neither can we experience anything external to us) except in terms of a temporal continuum. Kant (controversially) maintains that space and time are only real as forms of sense perception; we cannot ascribe noumenal reality to them. 

∙ Steeped as we are in the empirical tradition, we're probably inclined to object to the idea that space and time are not things-in-themselves that exist independently of our experience of the world—but if it makes us feel better, we can believe that space and time, as we experience them, precisely correspond to how they actually operate as things-in-themselves. Kant would wag his finger and say "but we can't know that," sure. But Kant still agrees with us that space and time are real—as real as they possibly can be, in that it is impossible to conceive of an existence without space and time, or of an existence in which they behaved any differently than they do in ours.

◦ Since all concepts refer to intuitions, the pure forms of intuition (space and time) are implicated in every concept. It stands to reason that the a priori concepts of understanding must refer to the pure forms of intuition.

Vasily Kandinsky, Development (1926)

• (2) As was implied way up in the definitions, Kant considers imagination the faculty responsible for the spontaneous association and reproduction of representations. In everyday parlance, it connects ideas. Any mental act wherein one object relates to another is the province of the imagination. Remember, what we're after is synthetic knowledge—a relation of A to B in which B is not contained in A by mere tautology—so the imagination must be examined.

• But we also need to discern the pure concepts of the understanding which the spontaneity of the imagination junctions to the pure forms of sensibility.

• Famous quote: "Thoughts without content are empty, intuitions without concepts are blind." (Also translated as: "Concepts without percepts are empty, percepts without concepts are blind.") In other words, all experience must not only be sensory, but someways...what? Rational? Discursive? Let's say organized. Since we're granting that all we can discuss are appearances, this entails that our sensory and conceptual equipment contribute to the construction of what we know as reality.

◦ This does not mean that one person's belief in a flat Earth creates a personal universe in which the Earth is flat. The organizing concepts Kant is getting at—the ones that do have a role in constructing reality (and remember, we're just talking about reality in terms of phenomena, because appearances are all we're capable of experiencing)—are fundamental, pure concepts of the understanding. It's the "knowledge" that remains after we scrub away every particular item of empirical information and are left with the a priori forms by which we organize sense data so as to make, well, sense of it.

∙ Somebody could believe that the Earth is flat. Somebody else could believe the Earth is round. Both are items of empirical knowledge. ("Knowledge," in the Kantian sense, does not have to be correct. We mean that Salviati and Simplicio each have an a posteriori conception of the world that informs how they operate in it.) But Kant holds that there must exist absolutely non-negotiable, self-evident, necessary concepts without which neither person could conceivably operate within the world, even if they do not recognize or cannot articulate these concepts (which is probably the case).

• Let's return to logic. The imagination's function (or one of them) is to arrange representations under a common representation, ie., a concept. According to Kant, what the understanding does with concepts is judge by means of them. The forms of understanding can be enumerated in full if we draw up a list of the forms of judgement—which we discover by consulting general logic. Kant draws up a table of the function of thought in judgements: twelve "moments," three of each under the four headings of Quality, Quantity, Relation, and Modality.³

◦ Corresponding to these twelve kinds of logical judgements are twelve categories of pure understanding.⁴ These are the a priori forms of thought that make possible the coherence of sense data given in the pure forms of intuition. Kant provides receipts for their validity (via the transcendental method summarized above), but I wouldn't trust a layman like me to audit them.

∙ To clarify a point made earlier: general logic cannot account for causal connection, but transcendental logic can and does.

◦ Kant expounds a series of schemata which serve as the "third terms" mediating between the pure forms of intuition and the pure concepts of understanding (the categories). We won't get explore them here, but we mention them to convey that the intercourse between intuition and conception that produces synthetic a priori propositions is governed by rules.

Vasily Kandinsky, Catacombae. Sepulcrum romanum (1928)

• (3) Finally, transcendental apperception is...oh god. I'm already dreading opening up the book to the infamous "A" and "B" Deductions and reviewing my notes. Getting your head around this section is like trying to pass a kidney stone—a kidney stone that excites fascination and astonishment during those moments where it's squeezed further down the plumbing, but a damn kidney stone nonetheless.⁵

• Both versions of the Transcendental Deduction emphasize the centrality of transcendental apperception to Kant's scheme. "Apperception," as Kant means it, is very, very roughly synonymous with "self-consciousness."

◦ Kant differentiates transcendental apperception from empirical consciousness, which is merely the awareness of internal and external events, considered in an atomistic, moment-to-moment basis.

◦ The substratum of empirical consciousness is transcendental apperception: the consistency of the self' across time, and our awareness of that consistent self. To use an analogy out of materialism (which Kant would almost certainly object to), all of our actions follow from our coherence and unity as organisms. In a similar sense, organized cognitive behavior of any kind (the synthesis of intuitions with concepts on any level) presupposes a transcendentally stable identity that retains its integrity as Moment A elapses into Moment B.

 ◦ I am just going to go ahead and type this as a block quote while I ponder how to paraphrase it.

...the original and necessary consciousness of the identity of oneself is at the same time a consciousness of an equally necessary unity of the synthesis of all appearances according to concepts, that is, according to rules which render these appearances not only necessarily reproducible, but which thereby determine an object for their intuition, that is, a concept of something in which they are necessarily connected. The mind could never think its own identity in the manifoldness of its representations, and indeed think this identity a priori, if it did not have before its eyes the identity of its act, by which it subjects all synthesis of apprehension (which is empirical) to a transcendental unity, and thus renders possible their connection according to a priori rules.

Let me give it a shot: one's experiential complex falls into the stable, rational organization of "objective" reality, if, and only if, one is conscious of the unity of one's own consciousness.

∙ One of the fun things about reading Kant (one that will inspire you to take liquor with your espresso as you leaf through his fucking book into the night) is arriving at the end of a dense paragraph and, after a moment of reflection, condensing it into somewhat succinct statement like the one above. When you test your own understanding of Kant's argument for leaks (for instance, looking at the syncopated point above and asking "but why, though?") you often have no recourse but to turn back to Kant, who lays it out for you thus:

The first pure knowledge of the understanding, therefore, on which all the rest of its use is founded, and which at the same time is entirely independent of all conditions of sensible intuition, is this very principle of the original synthetic unity of apperception. Space, the mere form of outer sensible intuition, is not yet knowledge; it supplies only the manifold of a priori intuition for a possible knowledge. In order to know anything in space (for instance, a line), I must draw it, and so synthetically produce a determinate combination of the given manifold, so that the unity of this act is at the same time the unity of consciousness (in the concept of a line), and so that an object (a determinate space) is thereby first known. The synthetic unity of consciousness is, therefore, an objective condition of all knowledge. It is not a condition that I only require for myself in order to know an object, but a condition to which each intuition must be subject in order to become an object for me. For otherwise, and without such a synthesis, the manifold could not unite in one consciousness.

What, you still don't get it?

• That's all three! In Kant's words, "the representation of space and time is a mere schema that always refers to the reproductive imagination which calls up and summons the objects of experience, without which they would be meaningless...it is therefore the possibility of experience which gives objective reality to all our a priori knowledge." These operations are mutually interdependent with the "transcendental and necessary unity of apperception" which makes possible "the synthetic unity of appearances," without which our "rhapsody of perceptions...would never grow into a context according to the rules of an altogether connected (possible) consciousness." 

• The short version: synthetic a priori propositions are not only possible, but necessary, because we construct what we experience through the spontaneous combination of raw sense data with conceptual framing. The rules governing our assemblage of appearances are also the rules by which we make sense of appearances. In his proof of the a priori validity of cause and effect, Kant basically asserts that it it must be valid because we cannot possibly experience state changes across time except by way of the "mental construct" of causal connection.

◦ Yes: an implication of the Kantian scheme is that these principles of experience are no different from the laws of nature we scrutinize in the physical sciences. Kant makes a subtle but important distinction between his own doctrine and that of idealism (the belief that the external world is someways illusionary), which he articulates in an elegant section called "The Refutation of Idealism" by demonstrating the dependency of inner experience on outer experience.

 
So—what do we make of all this? I have some ideas.

1. In the edition of the Critique which I've been reading, translator/editor Marcus Weigelt describes at some length the challenge of translating the German Erkenntis and erkennen into English. Weigelt and Müller (the Critique's original English translator) both translate them as "knowledge" and "know," while other translators use "cognition" and "cognize" instead. In a text as wonky as the Critique, the distinction between "[t]he two aspects of knowledge, as possessive and dynamic, as comprehension and apprehension" (Wiegelt) is a crucial one, and I sometimes struggled to understand what "knowledge" signified when it appeared multiple times on any given page. According to Wiegelt, the same ambiguity laces the German text's usage of Erkenntis and erkennen. I don't know whether to feel relieved or uneasy about this.

2. This is neither here nor there, but I have a hard time typing "judgment" instead of "judgement." It just doesn't look right to me.

3. In case you're interested, these "movements" are: Universal, Particular, Singular (Quantity), Affirmative, Negative, Infinite [Indefinite] (Quality), Categorical, Hypothetical, Disjunctive (Relation), Problematic, Assertoric, Apodictic (Modality).

4. Again, in case you're curious: Unity, Plurality, Totality (Quantity), Reality, Negation, Limitation (Quality), Inherence & Subsistence, Causality & Dependence, Community (Relation), Possibility/Impossibility, Existence/Nonexistence, Necessity/Contingency (Modality).

5. Translator/editor Marcus Weigelt on the Transcendental Deduction:

...it is...strange that in relation to the autocratic bulk of the text, to which Kant affords a meticulous scheme of internal support and substantiation, this all-important sections [sic] scarcely pulls its own weight and is only made productive when reconstructive commentaries of a highly sophisticated nature are brought to bear. In consequence, many readers feel that, rather than being able to establish the validity of the categories, it has the frustrating feature of proving in the end to have been about nothing in particular, as it seems to get the clues for its inferences from off the printed page.

Oh, good. So it wasn't just me.