Any contradiction or paradox.
In the thought of the German philosopher Immanuel Kant (1724–1804): an apparent contradiction between valid conclusions; a paradox.
An incompatibility, as of two things that cannot be simultaneously fulfilled.
A clash or disagreement, often violent, between two or more opposing groups or individuals.
To overlap (with), as in a schedule.
To be at odds (with); to disagree or be incompatible