Hi, Nice question. A paradox is the final word about some assumption. Since it is the final word, we say it is a theorem. Here is what I what I wrote in "The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us": "In a way, the paradox is a test to see if an assumption is a legitimate addition to reason. If one can use valid reason and the assumption to derive a falsehood, then the assumption is wrong. The paradox shows that we have stepped beyond the boundaries of reason. A paradox in this sense is a pointer to an incorrect view. It points to the fact that the assumption is wrong. Since the assumption is wrong, it cannot be added to reason. This is a limitation of reason." For more, on paradoxes, please see Resolving Paradoxes (Philosophy Now 2015) http://www.sci.brooklyn.cuny.edu/~noson/PARADOXES.pdf and Paradoxes, Contradictions, and the Limits of Science (American Scientist 2016) http://www.sci.brooklyn.cuny.edu/~noson/2016-05Yanofsky.pdf All the best, Noson -----Original Message----- From: Patrik Eklund [mailto:peklund@cs.umu.se] Sent: Sunday, January 8, 2017 7:40 AM To: Categories Subject: categories: Theorem or Paradox Since the Incompleteness Theorem uses the Liar Paradox, why is it called the Incompleteness Theorem and not the Incompleteness Paradox? A Theorem closes a development or debate, and calls for admiration (because the inventor did something supposedly good), whereas a Paradox opens up development and debate (since the detector has pointed at something being wrong), and delays the call for admiration of the disruptively innovative solution until it is really deserved. Best, Patrik -- Prof. Patrik Eklund Ume?? University Department of Computing Science SE-90187 Ume?? Sweden ------------------------- mobile +46 70 586 4414 website www8.cs.umu.se/~peklund [For admin and other information see: http://www.mta.ca/~cat-dist/ ]