{
  "aliases": [
    "paradox-of-entailment",
    "paradox-of-material-implication",
    "paradox-of-the-material-conditional",
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  "body": "\n## Summary\n\nThe **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:\n",
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