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What is an antilogy?

What is an antilogy? Here are some definitions.

Noun
  1. (rhetoric) A contradiction in related terms or ideas. Usually an inconsistency in syllogisms, of a person or group supposedly of one set of ideals.
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More generally, antilogy names the basic rhetorical theory that two contrary arguments may be given about everything.
Were I to refuse to come at the problem by way of moral self-acceptance, I could easily reduce the cogito to either tautology or antilogy.
Very little use of antilogy is made by his contemporary Neapolitan chroniclers of the Conspiracy of Macchia.
The rigor of antilogy tends to transform all the elements of argumentation into comparable givens, subject to addition or subtraction, and thus interchangeable.
On this account of Isocrates' understanding of antilogy and his uses of the speeches, Isocrates' students would learn that reality is what rhetoric presents it to be.
The practice of antilogy involved new intellectual tools, including the argument based on probability.

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