What can I know?

Kant's first great question — and the question that split the philosophy of his age. His answer is the “Critique of Pure Reason”, the book that divides the history of philosophy into a before and an after.

Where does our knowledge come from — and how far does it reach? Over this core question of epistemology, two camps faced each other in the eighteenth century. The rationalists in the tradition of Descartes and Leibniz trusted reason: secure knowledge is reached by logical inference from clear concepts, on the model of mathematics. The empiricists around Locke, Berkeley and Hume objected: all knowledge comes from experience — whatever does not enter through the senses is empty speculation.

It was David Hume who delivered the decisive blow to both camps. He showed that no amount of experience can ever prove that an effect must follow its cause — we only ever observe events succeeding one another, never the necessity itself. The objection struck Kant to the core. The remembrance of Hume, he later wrote in the “Prolegomena” (1783, Ak. 4:260), “first interrupted my dogmatic slumber” and gave his investigations “a completely different direction”. He worked on his answer for more than a decade; in 1781 the “Critique of Pure Reason” appeared with the publisher Johann Friedrich Hartknoch, followed in 1787 by the heavily revised second edition.

Sources: Wikipedia: Critique of Pure Reason · Wikipedia: Epistemology · Kant, Prolegomena (1783), Ak. 4:260 (quotations in own translation)

Analytic

The predicate is already contained in the concept of the subject — the judgment merely unpacks what was thought all along. Kant's example: “All bodies are extended.” Such judgments are always true, but they teach us nothing new.

Synthetic

The predicate adds something to the concept that was not contained in it — the judgment extends our knowledge. “All bodies are heavy” joins two ideas that are not wrapped up in one another.

A priori

Valid independently of all experience — recognisable by necessity and strict universality: no exception is possible.

A posteriori

Drawn from experience — useful, but never necessary: the next observation might turn out differently.

The interesting part is where the two pairs cross. Analytic a priori judgments are trivial, synthetic a posteriori ones are everyday fare. But are there synthetic a priori judgments — statements that extend our knowledge and hold necessarily? Kant says yes, right in the middle of mathematics. In “7 + 5 = 12”, no analysis of seven, five or the concept of a sum will ever yield the twelve — and yet the proposition admits of no exception.

Source: Wikipedia: Critique of Pure Reason (analytic–synthetic distinction, 7 + 5 = 12)

The first stem is examined in the Transcendental Aesthetic. Its result: space and time are neither properties of things themselves nor concepts abstracted from experience. They are pure a priori forms of intuition — the glasses we can never take off. We can think everything out of space, but never space itself; there is only ever one space and one time; their parts are merely limitations of this one whole. This is exactly why geometry is possible: it spells out with necessity what lies in the pure intuition of space — and even “7 + 5 = 12” rests on the succession given in time.

The second stem is the understanding. While sensibility merely receives impressions, the understanding combines them spontaneously — concepts, Kant says, rest on the spontaneity of thought as intuitions rest on the receptivity of impressions. This ordering follows twelve root concepts, the categories, which Kant arranges in four groups of three:

Quantity

Unity, plurality, totality — we grasp every object as one, as many, or as all.

Quality

Reality, negation, limitation — something is, is not, or is bounded.

Relation

Substance and accident, cause and effect, reciprocity — here sits the reply to Hume: causality is a form of the understanding.

Modality

Possibility, existence, necessity — together with their counterparts impossibility, non-existence, contingency.

With that, Kant takes Hume's problem to be solved — in a surprising way. Causality is not a feature we would have to coax out of the world; it is a condition without which we would have no ordered experience at all. It holds necessarily for everything we can experience — because it belongs to the equipment of the experiencer.

Source: Wikipedia: Critique of Pure Reason (Transcendental Aesthetic and Analytic, table of categories)

David Hume chose an example from the billiard table: one ball rolls towards another, touches it, and the second starts to move. All you see is that one thing follows the other; a necessary connection, a causing, is nowhere to be seen. That we are nevertheless sure about the next shot, Hume explained by custom.

Kant took the objection seriously but drew a different conclusion. Precisely because the concept of cause demands strict necessity, it cannot come from mere repetition. It belongs to the categories that the understanding brings along, and so it holds for everything we can experience at all. Which cause has which effect, however, we learn even according to Kant only from experience.

Sources: Hume, An Enquiry Concerning Human Understanding (1748), IV § 25, V § 36 · Kant, Critique of Pure Reason, Ak. 3:29 (in German) · Wikipedia: An Enquiry Concerning Human Understanding

In the Transcendental Dialectic, Kant sets out four conflicts in which reason seems to have equally good proofs for a claim and for its opposite. The first concerns the beginning and limits of the world. The thesis says: the world has a beginning in time. The antithesis says: it has none. Kant writes down both proofs himself, side by side.

His resolution: both parties silently assume that the world as a whole is a ready-made thing in itself. But the world we experience is appearance and is never given as a completed whole; that is why it exists neither as a finite nor as an infinite whole. That reason contradicts itself here shows, for Kant, that it has overstepped the limit of possible experience.

Sources: Kant, Critique of Pure Reason, Ak. 3:294 f. (in German) · Ak. 3:346 f. (in German) · Wikipedia: Kant's antinomies

At first the difficult work met with silence. But through the “Prolegomena” (1783), Reinhold's “Letters on the Kantian Philosophy” (1786/87) and the second edition of 1787, Kant became the leading and most debated philosopher of his time. Moses Mendelssohn called him the “all-crushing” Kant — for his critique of traditional metaphysics, which includes the proofs of God; the Catholic Church placed the book on its Index of Forbidden Books in 1827. At the same time it became the founding text of German idealism — Fichte, Schelling, Hegel — and later the reference point of Neo-Kantianism.

Sources: Wikipedia: Critique of Pure Reason (reception and influence) · Wikipedia: Immanuel Kant · Mendelssohn, Morgenstunden (1785), preface (in German)

Next comes the second question — “What should I do?” — in Chapter III · Ethics.