antilogy vs antithesis

antilogy

noun
  • A contradiction in related terms or ideas. Usually an inconsistency in syllogisms, of a person or group supposedly of one set of ideals. 

antithesis

noun
  • A proposition that is the diametric opposite of some other proposition. 

  • A device by which two contrasting ideas are juxtaposed in parallel form; a figure of speech arranged in this manner 

How often have the words antilogy and antithesis occurred in a corpus of books? (source: Google Ngram Viewer )