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Surely the great cultural antinomy of ancient times was not between Rome and Jerusalem, but between Hellenism and Judaism?
Although the use of "paradox" is widespread within deontic logic and it does conform to a technical use in philosophical logic, namely the distinction between "paradox" and "antinomy " stemming from Quine's seminal "The Ways of Paradox" (Quine 1976 [1962]), I will also use "puzzle", "problem" and "dilemma" below.
The same strategy is deployed in the second antinomy , where the proponent of the thesis position argues for the necessity of some ultimately simple substance by showing the impossibility of infinite divisibility of substance, etc. Obviously, the success of the proofs depends on the legitimacy of the exclusive disjunction agreed to by both parties.
Finally, in the fourth antinomy , the requirement for a necessary being is pitted against its opposite.
Left unresolved, then, this antinomy leaves us wit the following dilemma: on the assumption of transcendental realism, both nature and freedom seem to be undermined.
As George Boolos points out, the antinomy can be pressed all the way to paradigm cases of logical constants: "it might be said that logic is not so 'topic-neutral' as it is often made out to be: it can easily be said to be about the notions of negation, conjunction, identity, and the notions expressed by 'all' and 'some', among others …" (1975, 517).
In its imprecise form, the objection is that Zermelo is less than explicit about the principles he uses in 1904, and that he employs procedures which are reminiscent of those used crucially in the generation of the Burali-Forti antinomy , e.g., in showing that if the set Lγ ≠ M, then it can be extended.
However, whatever Zermelo's intention, there is no explicit attempt to exclude the possibility that Lγ = W and thus the suggestion that antinomy might threaten.
Kant's important discussions of freedom include not only the texts cited here from the Critique of Practical Reason, but also the third antinomy and its resolution in the Critique of Pure Reason and section III of the Groundwork.
The antinomy is dissolved, Kant now maintains, by recognizing that causal relations must structure outward phenomena.
For the sake of historical accuracy, we should remark that Beppo Levi, the author of the 1902 paper "Intorno alla teoria degli aggregati" where the axiom of choice is first formulated as an independent principle of proof, outlined an antinomy which is essentially a variant of Berry's paradox in the context of discussing Richard's paradox (see Levi 1908).
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The primary grammatical function of "antinomy" is that of a noun . Ludwig and other examples show it referring to a contradiction, paradox, or conflict of principles. It acts as a subject, object, or complement within a sentence.
Expression frequency: Very common
