---
tag: 3T7ZJFC9QF
kind: concept
name: Paradoxes of material implication
aliases: [paradox-of-entailment, paradox-of-material-implication, paradox-of-the-material-conditional, paradoxes-of-material-conditionals, paradoxes-of-the-material-conditional]
sources:
  - wikipedia: en:12857474@r1360716189
    locator: Paradoxes of material implication
    note: adopted
    mention: wikipedia://en/12857474
    sections: [Summary]
same_as:
  wikidata: Q1848046
  wikipedia: Paradoxes of material implication
inventory: [8DTQ4WW9HE]
---

## Summary

The **paradoxes of material implication** are a group of classically [[true formulae|05006AJ7DZ]] involving [[material conditionals|0NMG7W7Q11]] whose translations into natural language are intuitively false when the conditional is translated with English words such as "implies" or "if ... then ...". They are sometimes phrased as *arguments*, since they are easily turned into arguments with [[modus ponens|0Y0MQYST0M]]: if it is true that "if $P$ then $Q$" ($P \rightarrow Q$), then from that together with $P$, one may argue for $Q$. Among them are the following: