This question reminds if God is almighty can he create a stone large enough he cannot lift. As people have mention earlier our rules of logic only allow for one to exist. However if you insist on having them both why not expand our logic. Just like the square root of (-1) is no longer a real value and we created imaginary values. Why not expand the state of an object. So now you'll have 3 states: moving, not moving, new state(something that is moving and not moving at the same time).
I know it looks contradictory but is basically saying when an immovable object and the irresistible force colide the state of the object is no longer moving or resting is some state that satisfies both.
Light has properties of both particles and waves which is it :).