1The impossibility of squaring the circle has been a longstanding problem in geometry, with many mathematicians attempting to find a solution.
2Does the impossibility of knowing certain truths with absolute certainty undermine the foundations of epistemology?
3The philosopher argued that the concept of free will is an impossibility in a deterministic universe.
4The team encountered an impossibility in their design, as the materials required to achieve the desired strength were too expensive to procure.
5There is a subtle distinction in logic between impossibility and improbability, with the former denoting a strict contradiction and the latter a high degree of unlikelihood.