"Contradictory ideas" refers to a situation where two or more thoughts or beliefs cannot exist or be true at the same time because they directly oppose or contradict each other. Full definition
It's like each party is now increasingly a supermarket of contradictory ideas, which you can pick from at will. (politics.co.uk)
What things in her life have prepared her to accept two seemingly contradictory ideas? (bookbrowse.com)
For most of the artists, their experience of everyday life is the filter through which they focus their paintings, entertaining multiple contradictory ideas at once. (brooklynrail.org)