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

1. Knowledge is justified true belief.

2. Humans cannot provide justification for their beliefs.

3. Humans possess knowledge.

Political philosophy

1. A just society maximizes individual liberty.

2. A just society maximizes material equality.

3. A just society cannot maximize both liberty and equality.

Ethics

1. Actions that maximize overall well-being are morally right.

2. Lying can sometimes maximize overall well-being.

3. 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)