An inconsistent triad is a set of three propositions that cannot all be true together. For example, 'She was an orphan; Tim outlived her; Tim was her father'.
All inconsistent triads lead to trilemmas:
If A and B are true, C must be false. If A and C are true, B must be false. If B and C are true, A must be false.
Epistemology
Knowledge is justified true belief. Humans cannot provide justification for their beliefs. Humans possess knowledge.
Political philosophy
A just society maximizes individual liberty. A just society maximizes material equality. A just society cannot maximize both liberty and equality.
Ethics
Actions that maximize overall well-being are morally right. Lying can sometimes maximize overall well-being. Lying is always morally wrong.
See also Classical logic Contradiction Dilemma Formal logic Reductio ad absurdum Trilemma
References
Further reading Brewer, B. (2011). The Inconsistent Triad. Perception, Causation, and Objectivity, 68. Howard-Snyder, F., Howard-Snyder, D., & Wasserman, R. (2009). The Power of Logic (4th Edition). New York: McGraw-Hill. (p. 336)