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Inconsistent triad

Three propositions that cannot all be true together

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated June 23, 2026

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.

01Epistemology

  1. Knowledge is justified true belief.
  2. Humans cannot provide justification for their beliefs.
  3. Humans possess knowledge.

02Political 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.

03Ethics

  1. Actions that maximize overall well-being are morally right.
  2. Lying can sometimes maximize overall well-being.
  3. Lying is always morally wrong.
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Sources and credits

This article is adapted from the Wikipedia article “Inconsistent triad”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Classical logic

Classical logic or Frege-Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy.

Contradiction

In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.

Dilemma

A dilemma 'double proposition') is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the horns of the dilemma, a clichéd usage, but distinguishing the dilemma from other kinds of predicament as a matter of usage.