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Antinomy (Greek ἀντί, antí, "against, in opposition to," and νόμος, nómos, "law") literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology, particularly in the philosophy of Kant and Roberto Unger.

Kant's use

The term acquired a special significance in the philosophy of Immanuel Kant (1724–1804), who used it to describe the equally rational but contradictory results of applying to the universe of pure thought the categories or criteria of reason that are proper to the universe of sensible perception or experience (phenomena). Empirical reason cannot here play the role of establishing rational truths because it goes beyond possible experience and is applied to the sphere of that which transcends it.

For Kant there are four antinomies,^[1]^[2]^[3]^[4] connected with:

the limitation of the universe in respect of space and time,
the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist),
the problem of free will in relation to universal causality
the existence of a necessary being

In each antinomy, a thesis is contradicted by an antithesis. For example: in the First Antinomy, Kant proves the thesis that time must have a beginning by showing that if time had no beginning, then an infinity would have elapsed up until the present moment. This is a manifest contradiction because infinity cannot, by definition, be completed by "successive synthesis"—yet just such a finalizing synthesis would be required by the view that time is infinite; so the thesis is proven. Then he proves the antithesis, that time has no beginning, by showing that if time had a beginning, then there must have been "empty time" out of which time arose. This is incoherent (for Kant) for the following reason: Since, necessarily, no time elapses in this pretemporal void, then there could be no alteration, and therefore nothing (including time) would ever come to be: so the antithesis is proven. Reason makes equal claim to each proof, since they are both correct, so the question of the limits of time must be regarded as meaningless.

This was part of Kant's critical program of determining limits to science and philosophical inquiry. These contradictions are inherent in reason when it is applied to the world as it is in itself, independently of our perceptions of it (this has to do with the distinction between phenomena and noumena). Kant's goal in his critical philosophy was to identify what claims we are and are not justified in making, and the antinomies are a particularly illustrative example of his larger project.

However, there are many other examples of antinomy besides these four. A self-contradictory phrase such as "There is no absolute truth" can be considered an antinomy because this statement is suggesting in itself to be an absolute truth, and therefore denies itself any truth in its statement. A paradox such as "this sentence is false" can also be considered to be an antinomy; for the sentence to be true, it must be false, and vice versa.

References

^ Chisholm, Hugh, ed. (1911). "Antinomy" . Encyclopædia Britannica (11th ed.). Cambridge University Press.
^ S. Al-Azm, The Origins of Kant's Argument in the Antinomies, Oxford University Press 1972.
^ M. Grier, Kant's Doctrine of Transcendental Illusion, Cambridge University Press 2001.
^ M. Grier, "The Logic of Illusion and the Antinomies," in Bird (ed.), Blackwell, Oxford 2006, pp. 192-207.

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 incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Antinomy". Encyclopædia Britannica (11th ed.). Cambridge University Press.
This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

External links

"Antinomy", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Antinomy at PhilPapers

[1] Chisholm, Hugh, ed. (1911). "Antinomy" . Encyclopædia Britannica (11th ed.). Cambridge University Press.

[2] S. Al-Azm, The Origins of Kant's Argument in the Antinomies, Oxford University Press 1972.

[3] M. Grier, Kant's Doctrine of Transcendental Illusion, Cambridge University Press 2001.

[4] M. Grier, "The Logic of Illusion and the Antinomies," in Bird (ed.), Blackwell, Oxford 2006, pp. 192-207.

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 This was part of Kant's critical program of determining limits to [[science]] and philosophical inquiry. These contradictions are inherent in reason when it is applied to the world as it is in itself, independently of our perceptions of it (this has to do with the distinction between [[phenomena]] and [[noumena]]). Kant's goal in his critical philosophy was to identify what claims we are and are not justified in making, and the antinomies are a particularly illustrative example of his larger project.
-However, there are many other examples of antinomy besides these four. Contradictory phrases, such as "This sentence is false" can be considered an antinomy. If this sentence is true, then it cannot be false, and therefore it contradicts itself. If this sentence is false, then it must be true, again contradicting itself. Either the sentence itself in meaningless, or it reveals a limitation of semantics. Other phrases can appear to be an antinomy, but fail upon examination of the antithesis. For example, the phrase "There is no absolute truth" yields a contradiction if it is true. Since this statement itself is an absolute truth, if it is true, it contradicts itself. However, if the statement is false, then there is absolute truth. Stating that there is absolute truth does not contradict the phrase; it demonstrates that the phrase is false. The phrase "There is no absolute truth" provides in itself proof that it is false. Even if there is no other absolute truth, this phrase can not be true. The antithesis fails to contradict.
+However, there are many other examples of antinomy besides these four. A self-contradictory phrase such as "There is no absolute truth" can be considered an antinomy because this statement is suggesting in itself to be an absolute truth, and therefore denies itself any truth in its statement. A [[paradox]] such as "[[this sentence is false]]" can also be considered to be an antinomy; for the sentence to be true, it must be false, and vice versa.
 ==See also==