antilogy vs cross-purpose

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. 

cross-purpose

noun
  • A contrary or conflicting purpose or understanding, especially an unintentional or misconceived one. 

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