Necessary and sufficient conditions

A necessary condition must hold for something to be true; a sufficient condition guarantees that it is.

Also: necessary condition, sufficient condition, if and only if, iff

What it means

If P is sufficient for Q, then whenever P holds, Q does; and Q is then necessary for P. Encyclopaedia Britannica's example: a severed spinal column is sufficient but not necessary for death, while lack of consciousness is necessary but not sufficient. When each condition guarantees the other, they are necessary and sufficient, which is the standard form of a definition ('if and only if'). Twentieth-century philosophers used this format to analyse concepts such as knowledge and memory, and J. L. Mackie used it to analyse causes. The Stanford Encyclopedia notes, however, that ordinary speech uses 'if' and 'only if' in looser ways, so the simple logical textbook account is often misleading.

The questions it belongs to

• 4.1.1 Propositional LogicWhat follows from "if this, then that"?
• 2.1 Theories of KnowledgeWhat has to be added to a true belief to make it knowledge?

Thinkers

• J. L. Mackie
• Georg Henrik von Wright

Traditions

• Analytic

To read

• Ethics: Inventing Right and Wrong — J. L. Mackie
• The Miracle of Theism — J. L. Mackie

Sources and further reading

• Necessary and Sufficient Conditions (Stanford Encyclopedia of Philosophy)
• Condition (Britannica)

Written by the Coordinates of Thought editors and checked against the sources above on 29 October 2026. Not peer-reviewed. How we write and check.

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