This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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adj. Having self-contradictory properties.

adj. Of the nature of a paradox.

adj. Inclined to paradoxes, or to tenets or notions contrary to received opinions.

Of the nature of a paradox; characterized by paradoxes; apparently absurd, yet true.

Inclined to paradox or to tenets or notions contrary to received opinions: applied to persons.

adj. seemingly contradictory but nonetheless possibly true

"I think the term paradoxical is more appropriate than impossible for obvious reasons, but intriguing stuff no less."

inexplicable    incomprehensible   

paradoxical contraction    paradoxical reaction   

paradoxicality    paradox    paradoxically   

contradictory    illogical    ambiguous    incomprehensible    sophistical    incongruous    mislead    improbable    perverse    bizarre