material implication

蕴涵

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: implication

Translation evidence: Literature usage

Meaning in context

The classical connective P→QP\to Q, false exactly when PP is true and QQ is false.

经典命题联结词 P→Q；它恰在 P 真且 Q 假时为假。

Example

(2=3)→(5=7)(2=3)\to(5=7) is true as a material implication.

Usage and distinctions

A true implication with false antecedent is not evidence of a causal connection.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§2.4 The Language of Propositional Logic · Checked 2026-10-14

Translation sources

  1. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§2.4 蕴涵（名称证据，非正文定义证据） · Checked 2026-10-14
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