Inconsistent triad

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'. ^[1]

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. ^[2]

Epistemology

Main article: Epistemology

1. Knowledge is justified true belief. ^[3]
2. Humans cannot provide justification for their beliefs. ^[4]
3. Humans possess knowledge. ^[5]

Political philosophy

Main article: Political philosophy

1. A just society maximizes individual liberty. ^[6]
2. A just society maximizes material equality. ^[7]
3. A just society cannot maximize both liberty and equality. ^[8]

Ethics

Main article: Ethics

1. Actions that maximize overall well-being are morally right. ^[9]
2. Lying can sometimes maximize overall well-being. ^[10]
3. Lying is always morally wrong. ^[11]

See also

• Classical logic
• Contradiction
• Dilemma
• Formal logic
• Reductio ad absurdum
• Trilemma

References

1. "The Oxford companion to philosophy". Choice Reviews Online. 33 (5): 33–2495–33-2495. 1996-01-01. doi:10.5860/CHOICE.33-2495 (inactive 22 February 2025). S2CID   142841293.
2. Sullivan, Scott M. (2005-10-26). An Introduction To Traditional Logic: Classical Reasoning For Contemporary. Booksurge Publishing. ISBN   978-1-4196-1671-6.
3. de Grefte, Job (2023-02-01). "Knowledge as Justified True Belief". Erkenntnis. 88 (2): 531–549. doi:10.1007/s10670-020-00365-7. ISSN   1572-8420.
4. Hume, David, An Enquiry concerning Human Understanding, Oxford University Press, doi:10.1093/owc/9780199549900.001.0001/isbn-9780199549900 (inactive 22 February 2025), ISBN   978-0-19-192173-5 , retrieved 2025-02-21
5. Descartes, René; Moriarty, Michael (2008). Meditations on first philosophy: with selections from the Objections and replies. Oxford: Oxford University Press. ISBN   978-0-19-280696-3.
6. Nozick, Robert (1974). Anarchy, State, and Utopia. New York: Basic Books.
7. Rawls, John (1971). A Theory of Justice: Original Edition. Harvard University Press. doi:10.2307/j.ctvjf9z6v. ISBN   978-0-674-88010-8. JSTOR   j.ctvjf9z6v.
8. Berlin, Isaiah (2002-03-07), Berlin, Isaiah; Hardy (eds.), "Two Concepts of Liberty", Liberty, Oxford University Press, pp. 166–217, doi:10.1093/019924989x.003.0004, ISBN   978-0-19-924989-3 , retrieved 2025-02-20
9. Bentham, Jeremy (1890). Utilitarianism. Progressive Publishing Company.
10. Greasley, Kate (2019). "The Morality of Lying and the Murderer at the Door". Law and Philosophy. 38 (5/6): 439–452. doi: 10.1007/s10982-018-09342-2 . ISSN   0167-5249. JSTOR   45284255.
11. Wood, Allen W. (2011). "Kant and the right to lie reviewed essay: On a supposed right to lie from philanthropy, by Inmanuel Kant (1797)". Eidos (15): 96–117. ISSN   1692-8857.

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) ISBN   978-0-07-340737-1