> [!definition]
> **Entailment** · *Definition*
>
> One claim guarantees another: *P entails Q* means there is no way for P to be true while Q is false.

Two readings should be distinguished at the outset: the *metalogical* reading (no interpretation or model in which P holds and Q fails, a formal-semantic relation) and the *modal-metaphysical* reading (no possible world in which P obtains and Q fails, an alethic relation). Throughout this book *entails* carries the modal-metaphysical reading unless the context is explicitly formal-logical; the Quinean concern that the slide between the two is illicit is addressed at §[§4.1.6](<4.1.6 Quinean Modal Skepticism.md>)–4.1.8. The textbook case: *Socrates is a bachelor* entails *Socrates is unmarried*. There is no possibility of the first holding while the second fails. *P implies Q* and *Q follows from P* name the same relation in most uses. *P necessitates Q* is the strong modal version: P's holding requires Q's holding in the alethic/metaphysical sense fixed at [§1.1](<1.1 Reality.md>), not logical necessity (truth across all interpretations) and not nomological necessity (consistency with natural law). The operators are read formally as truth carrying over: in any case where P holds, Q holds too. The relation among the kinds of modality is the subject of [§2.6](<2.6 Triconditionality of Nature.md>).


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← [1.5.2 Constitution](<1.5.2 Constitution.md>) | [1.5.4 Supervenience](<1.5.4 Supervenience.md>) →
