If two contradictory statements both seem reasonable and true, you can call this conundrum an antinomy. The noun comes from the Latin and Greek word antinomia, which meant a contradiction in the law.

The philosopher Immanuel Kant famously suggested four antinomies. One of them stated that the world had a definite beginning and will have a definite end. On the other hand, Kant added, the world is infinite in terms of time and space. Both statements at first blush appear reasonable, but since it's impossible that the world could be both finite and infinite, the two ideas together form an antinomy.

Definitions of antinomy
  1. noun
    a contradiction between two statements that seem equally reasonable
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    type of:
    contradiction, contradiction in terms
    (logic) a statement that is necessarily false
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