General terms:
* Contradiction: This is the most straightforward term, emphasizing the conflicting ideas within the phrase.
* Oxymoron: This specifically refers to a phrase combining two seemingly contradictory terms (e.g., "living dead," "deafening silence").
* Aphorism: A short, pithy statement that expresses a general truth or observation, often containing a paradoxical element.
* Proverb: Similar to an aphorism, but often with a longer history and cultural significance.
Terms emphasizing the thought-provoking nature:
* Irony: This highlights the contrast between the literal meaning of the phrase and the intended meaning.
* Satire: This emphasizes the use of irony to criticize or mock something.
* Double entendre: This refers to a phrase with two or more possible meanings, often with one being humorous or suggestive.
* Witticism: A clever, often paradoxical remark that is intended to be humorous.
Terms for specific types of paradoxes:
* Zeno's paradox: A specific type of paradox that deals with the nature of motion and space.
* Russell's paradox: A paradox in set theory that raises questions about the nature of sets.
* The liar paradox: A paradox that arises from self-referential statements that seem to contradict themselves.
Ultimately, the best term to use for a paradoxical phrase depends on the specific context and the type of paradox it embodies.