{
  "aliases": [
    "excluded-middle",
    "tertium-non-datur"
  ],
  "backlinks": null,
  "body": "\n## Statement\n\nIn classical logic, for each [[proposition|0ZGC7ZESYN]] $p$, the proposition $p \\lor \\neg p$ is true.\n\n## Remarks\n\nThe formula $p \\lor \\neg p$ is a [[tautology|0D1AHYPM8N]].\nSome systems take the law as an axiom.\nIntuitionistic logic does not accept the law in general.\nThe law is the basis of [[proof by cases|0WCP0PVET6]] on $p$ and $\\neg p$.\n\n## Explanations\n\n### L1 human\n\nThe law says that there is no third option: a statement is true, or its negation is true.\nFor example, each natural number $n$ is even or not even.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "aliases": [
      "excluded-middle",
      "tertium-non-datur"
    ],
    "kind": "statement",
    "msc": [
      "03B05"
    ],
    "name": "Law of excluded middle",
    "role": "theorem",
    "same_as": {
      "wikidata": "Q468422",
      "wikipedia": "Law of excluded middle"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Law_of_excluded_middle"
      }
    ],
    "tag": "0RYYK8PG4S",
    "uses": [
      "0H5GKDTB01",
      "0XR7A7RSXB"
    ]
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/0RYYK8PG4S/",
  "links": [
    {
      "field": "uses",
      "target": "0H5GKDTB01"
    },
    {
      "field": "uses",
      "target": "0XR7A7RSXB"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0RYYK8PG4S.md",
  "msc": [
    "03B05"
  ],
  "name": "Law of excluded middle",
  "prov": null,
  "role": "theorem",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0RY/0RYYK8PG4S.md",
  "status": null,
  "tag": "0RYYK8PG4S",
  "uri": "m2://0RYYK8PG4S",
  "url": "https://math2.tamnd.com/wiki/law-of-excluded-middle/",
  "writing": {
    "tag": "0RYYK8PG4S",
    "kind": "statement",
    "level": "W1",
    "next": [
      {
        "what": "edge about out",
        "note": "the concepts that the statement is about",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge proves in",
        "note": "at least one proof node",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of or illustrates in",
        "note": "one example that shows the statement at work",
        "have": 0,
        "want": 1
      },
      {
        "what": "explanation L2",
        "have": 0,
        "want": 1
      }
    ]
  }
}