Antinomy
|
|
Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction.
Immanuel Kant believed that when the categories of understanding are carried above possible experience, they often fall into various antinomies, or equally rational but contradictory views. 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 example, Kant thought that one could reason from the assumption that the world had a beginning in time to the conclusion that it did not, and vice versa. This was part of Kant's critical program of determining limits to science and philosophical inquiry.
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).
See also
- See antimony for the chemical element having a name that is an anagram of "antinomy".
- interesting number paradox
- Richard's paradox
- Ship of Theseus
- Sorites paradox
- Logic of antinomies (http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?first=1&maxdocs=3&type=html&an=0724.03003&format=complete)
- This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.