Antinomy

Not to be confused with antimony, a chemical element.

Antinomy (Greek αντι-, against, plus νομος, law) literally means the mutual incompatibility, real or apparent, of two laws. It is a term often used in logic and epistemology, when describing a paradox or unresolvable contradiction.

Historical background

The term antinomy is found in Plutarch (46 – 127), but it became a key philosophical term with Kant. The term was used as a legal term since seventeenth century and it meant a contradiction among laws. Kant adopted the term in legal field into philosophy as he did with other terms and concepts. With the term antinomy, Kant tried to present contradictory claims reason can equally make. Kant attempted to show the limit of how reason can be used.

Kant carried out the critique of reason in his three critical works, Critique of Pure Reason, Critique of Practical Reason, and Critique of Judgment. He tried to present the limit of use of reason by presenting contradictions reason can fall into. These critical works dealt with issues on epistemology or theory of knowledge, Ethics, and Aesthetics respectively. In the Critique of Pure Reason, he examined reason as a faculty of knowledge or cognition. In the Critique of Practical Reason, he dealt with reason as a faculty of moral judgment and actions, and in the Critique of Judgment, he examined reason as a faculty of aesthetic judgment. For Kant, critique meant a critical examination of reason as a faculty of judgment. Kant discussed elements of antinomy in all these critical works. Antinomy discussed in the Critique of Pure Reason, is however best known.

The faculty of reason naturally pursues the unconditioned from the conditioned or the premise from the conclusion. Kant called the unconditioned “Ideas” (in German, “Idee”). There are three Ideas, soul, world, and God.

When we have internal experiences, we try to think the totality of internal experiences and led to the Idea of “soul.” Likewise, from experiences we have with external things, we tend to think the totality of the external experiences and led to the Idea of “world.” From experiences we have with particular beings, we are led to think the totality of all beings and think the Idea of God.

Kant argued that we tend to think of these Ideas (soul, world, and God), as the objects of cognition. These Ideas are, however, not the objects of cognition since they lack any sensible contents such as colors, shapes, sound, smells, and textures. We cannot see, smell, and touch them unlike other tangible objects. The problem arises, Kant argued, when we take these Ideas as real existence in the same sense a tangible thing exists. Kant called these mistakenly understood Ideas “transcendental illusion” or “transcendental semblance” (in German, “transzendentaler Schein”).

These Ideas such as God, soul, and the world, had traditionally been thought to exist by themselves. Kant opposed the position that took Ideas as objects of cognition and assumed their existence without consideration of conditions of human knowledge. For Kant, cognitive knowledge is the result of constitution of sensible contents, such as colors and shapes, supplied by things and the form which mind is equipped with such as space, time, quality, quantity, relation, and modality. We impose these categories or forms of mind onto sensible contents we acquire form things outside of us. Human experience is the result of constitution of these forms of mind and sensible contents from outside. Since these Ideas lack sensible contents, they cannot be an object of cognition. In the Critique of Pure Reason, Kant examined the process of how and the limit of what we can know.

Kant refused to take Ideas as the “constitutive principle” (“konstitutives Prinzip”) of knowledge and accepted them as the “regulative principle” (“regulatives Prinzip”) or “heuristic principle” (“heuristisches Prinzip”) that guide our reasoning. Kant, however, revealed a different way to approach these Ideas in his moral philosophy. For Kant, these Ideas are properly approachable within the sphere of morality. Kant argued that these Ideas are postulated for morality. Kant refused traditional speculative metaphysics which posited these Ideas as existence behind and above phenomena we can experience. Kant was accused of being a “destroyer” of metaphysics for his rejection of these Ideas. Kant denied metaphysicians’ approaches to Ideas but opened a practical approach to them in the sphere of morality.

In the section, “Transcendental Dialectic” in the Critique of Pure Reason, Kant presented four types antinomy. They arise when we take the Idea of the world as if it exists as the object of cognition.

Transcendental Semblance or Transcendental Illusion

1. First Antinomy

• • Thesis: The world is finite in time and space.
  • Antithesis: The world is infinite in time and space.

The first antinomy arises for the question of whether the world has the beginning in time or not, and whether it is specially finite or not. Reason can argue for each position but cannot reach any conclusive position. Reason cannot decide and resolve the antinomy.

1. Second Antinomy

• • Thesis: The world is consisted of indivisible elements.
  • Antithesis: The world is not consisted of indivisible elements.

The question is about the divisibility of components of the world. Can we divide the component of the world into such elements as atoms, particles or waves, and further divide into finer components indefinitely? Or do we reach the final component whose further division is impossible?

1. Third Antinomy

• • Thesis:
  • Antithesis:

There are four antinomies — two mathematical, two dynamical — connected with

1. the limitation of the universe in respect of space and time,
2. the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist),
3. the problem of freedom in relation to universal causality,
4. the existence of a universal being

about each of which pure reason contradicts the empirical, as thesis and antithesis. This was part of Kant's critical program of determining limits to science and philosophical inquiry. Kant claimed to solve these contradictions by saying, that in no case is the contradiction real, however really it has been intended by the opposing partisans, or must appear to the mind without critical enlightenment. It is wrong, therefore, to impute to Kant, as is often done, the view that human reason is, on ultimate subjects, at war with itself, in the sense of being impelled by equally strong arguments towards alternatives contradictory of each other. The difficulty arises from a confusion between the spheres of phenomena and noumena. In fact no rational cosmology is possible.

It can also be argued that antinomies do not highlight limitations in the power of logical reasoning. This is because the conclusion that there is a limitation is (supposedly) derived from the antinomy by logical reasoning; therefore any limitation in the validity of logical reasoning imposes a limitation on the conclusion that there is a limitation on logical reasoning. (This is an argument by self-reference.) In short, in terms of the validity of logical reasoning as a whole, antinomies are self-isolating: they are like scattered discontinuities within the field of logic, incapable of casting doubt on anything else but themselves.

This carefree position is incompatible with the principle of explosion. In mathematical logic, antinomies are patently not self-isolating, and are usually seen as disasters for the formal system in which they arise (as Russell's paradox in Frege's work).

References

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• John Watson, Selections from Kant (trans. Glasgow, 1897), pp. 155 foll.
• W. Windelband, History of Philosophy (Eng. trans. 1893)
• H. Sidgwick, Philos. of Kant, lectures x. and xi. (Lond., 1905)
• F. Paulsen, I. Kant (Eng. trans. 1902), pp. 216 foll.
• This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.

External links

• Logic of antinomies

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