(a) How does Kant construct antinomies to illustrate the illusory tendencies of pure reason ? Explain and examine the antinomies…

(a) Kant’s antinomies of pure reason

Construction: in the Transcendental Dialectic of the Critique of Pure Reason, Kant shows that reason, by its nature, seeks the unconditioned for every conditioned. For the series of conditions in the world (the cosmological idea), it treats the totality of appearances as if it were a thing in itself. The result is an antinomy: a thesis and an antithesis, each proved apagogically (by refuting the opposite), so that reason is in conflict with itself. This is a natural and unavoidable transcendental illusion, not a mere logical slip, and the antinomy is placed alongside the paralogisms (soul) and the ideal (God).

The four antinomies, following the four classes of categories:

1. Quantity: the world has a beginning in time and limits in space, versus the world is infinite in time and space.
2. Quality: every composite substance consists of simple parts, versus nothing in the world is simple.
3. Relation: besides natural causality there is causality through freedom, versus everything happens by laws of nature alone.
4. Modality: an absolutely necessary being belongs to the world (as part or cause), versus no necessary being exists in or outside the world.

Examination and resolution through transcendental idealism:

• Mathematical antinomies (1 and 2): both sides are false, since the world as a whole is never given in experience. The series of conditions is only given in a regress that is indefinite, so the world is neither finite nor infinite in itself.
• Dynamical antinomies (3 and 4): both sides may be true, the antithesis of phenomena and the thesis of noumena. Human actions are causally determined as appearances yet may be free as things in themselves. This makes room for morality and faith.
• Significance: the antinomies are the strongest indirect proof of transcendental idealism and expose the limits of speculative metaphysics.
• Criticism: Hegel argued that contradiction is not confined to four cases but belongs to every concept, and that Kant showed “too much tenderness for things” by putting contradiction in reason rather than reality. Later critics also note that some proofs (the first thesis) rest on questionable assumptions about infinity.

(b) Hegel’s dialectical method and the Absolute

Dialectic, for Hegel, is the self-movement of the concept. Every logical idea has three moments (Encyclopaedia, paragraphs 79-82):

1. The abstract or understanding moment: a concept is fixed in its one-sidedness (Being).
2. The dialectical or negatively rational moment: the concept passes into its opposite (Being turns out to be indistinguishable from Nothing).
3. The speculative or positively rational moment: the unity of the opposites (Becoming). The usual formula thesis-antithesis-synthesis comes from Fichte and is not Hegel’s own.

Key notions:

• Determinate negation: negation yields a specific, richer result, not empty nothing.
• Aufhebung (sublation): the earlier stage is cancelled, preserved and raised up.
• Mediation: nothing is merely immediate.

Realising the Absolute:

• The Absolute is not a fixed substance but subject, “the true is the whole” (Phenomenology of Spirit, Preface). It exists only as the result of its own development.
• In the Phenomenology, consciousness rises through sense-certainty, perception, understanding, self-consciousness, reason and spirit to absolute knowing.
• In the system: Logic (the Idea in itself), Nature (the Idea outside itself) and Spirit (the Idea returning to itself) culminate in Absolute Spirit as art, religion and philosophy.
• Dialectic is thus both the method of knowing and the structure of reality, since “the real is rational”.

(c) Wittgenstein: pictorial form and logical form

In the Tractatus, a proposition is a logical picture of a fact. The elements of the picture (names) stand for objects, and their arrangement shows that objects are so arranged (2.15).

Difference:

• Pictorial form (form of representation) is what a picture must share with reality to depict it in its own way, for example spatial form for a spatial picture or colour for a coloured one. It differs from one kind of picture to another (2.17, 2.171).
• Logical form is what every picture, of whatever form, must have in common with reality to depict it at all, rightly or falsely (2.18). Every picture is also a logical picture, but not every picture is spatial (2.182).
• So logical form is the minimum common form, and pictorial forms are particular kinds of it. A proposition is a picture whose pictorial form is purely logical.

Logical form and the language-reality relation:

• Isomorphism: the logical multiplicity of the proposition matches that of the state of affairs. Elementary propositions are combinations of names as atomic facts are combinations of objects.
• It fixes sense: a proposition has sense independently of whether it is true, since it shows a possible state of affairs.
• It cannot be pictured or said: a picture cannot depict its own form, it shows it (2.172, 4.12). Logical form is shown in language, not stated, which sets the limits of language and the unsayable.