Lots of definitions of irony but I don't see the problem as posed. A paradox is completely different:
par·a·dox   
n.
A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking.
One exhibiting inexplicable or contradictory aspects: "The silence of midnight, to speak truly, though apparently a paradox, rung in my ears" (Mary Shelley).
An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.
A statement contrary to received opinion.


[Latin paradoxum, from Greek paradoxon, from neuter sing. of paradoxos, conflicting with expectation : para-, beyond; see para-1 + doxa, opinion (from dokein, to think. See dek- in Indo-European Roots).]
para·doxi·cal adj.
para·doxi·cal·ly adv.
para·doxi·cal·ness n.

Source: The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2000 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.

My favourite quote on the word is:
A pig is a paradox; it must be killed before it can be cured

Nigel