Incongruous vs. Paradoxical — What's the Difference?

Lacking in harmony; incompatible

A statement that seems to contradict itself but may nonetheless be true

Not in agreement, as with principles; inconsistent

A person, thing, or situation that exhibits inexplicable or contradictory aspects

Not in keeping with what is correct, proper, or logical; inappropriate

A statement that is self-contradictory or logically untenable, though based on a valid deduction from acceptable premises.

Not similar or congruent; not matching or fitting in.

Having self-contradictory properties.

(math) Of two numbers, with respect to a third, such that their difference can not be divided by it without a remainder.

Of the nature of a paradox.

Not congruous; reciprocally disagreeing; not capable of harmonizing or readily assimilating; inharmonious; inappropriate; unsuitable; not fitting; inconsistent; improper; as, an incongruous remark; incongruous behavior, action, dress, etc.

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

Lacking in harmony or compatibility or appropriateness;

Seemingly contradictory but nonetheless possibly true;