"law of excluded middle" meaning in English

{
  "head_templates": [
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      "args": {
        "1": "?"
      },
      "expansion": "law of excluded middle",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Mandarin terms with redundant transliterations",
          "parents": [
            "Terms with redundant transliterations",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "glosses": [
        "A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P."
      ],
      "id": "en-law_of_excluded_middle-en-noun-YPaibYyC",
      "links": [
        [
          "logic",
          "logic"
        ]
      ],
      "raw_glosses": [
        "(logic) A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P."
      ],
      "related": [
        {
          "word": "tertium non datur"
        }
      ],
      "synonyms": [
        {
          "word": "LEM"
        },
        {
          "word": "law of the excluded middle"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "páizhōnglǜ",
          "sense": "Translations",
          "word": "排中律"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "kolmannen poissuljetun laki"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "Translations",
          "tags": [
            "masculine"
          ],
          "word": "principe du tiers exclu"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "lögmál um annað tveggja"
        },
        {
          "alt": "はいちゅうりつ",
          "code": "ja",
          "lang": "Japanese",
          "roman": "haichūritsu",
          "sense": "Translations",
          "word": "排中律"
        },
        {
          "code": "la",
          "lang": "Latin",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "principium tertii exclusi"
        },
        {
          "code": "la",
          "lang": "Latin",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "tertium non datur"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "zasada wyłączonego środka"
        }
      ],
      "wikipedia": [
        "law of excluded middle"
      ]
    }
  ],
  "word": "law of excluded middle"
}

{
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      "args": {
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      "expansion": "law of excluded middle",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "tertium non datur"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English nouns with unknown or uncertain plurals",
        "Mandarin terms with redundant transliterations",
        "Translation table header lacks gloss",
        "en:Logic"
      ],
      "glosses": [
        "A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P."
      ],
      "links": [
        [
          "logic",
          "logic"
        ]
      ],
      "raw_glosses": [
        "(logic) A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P."
      ],
      "synonyms": [
        {
          "word": "LEM"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "law of excluded middle"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "law of the excluded middle"
    }
  ],
  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "páizhōnglǜ",
      "sense": "Translations",
      "word": "排中律"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "kolmannen poissuljetun laki"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "Translations",
      "tags": [
        "masculine"
      ],
      "word": "principe du tiers exclu"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "lögmál um annað tveggja"
    },
    {
      "alt": "はいちゅうりつ",
      "code": "ja",
      "lang": "Japanese",
      "roman": "haichūritsu",
      "sense": "Translations",
      "word": "排中律"
    },
    {
      "code": "la",
      "lang": "Latin",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "principium tertii exclusi"
    },
    {
      "code": "la",
      "lang": "Latin",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "tertium non datur"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "zasada wyłączonego środka"
    }
  ],
  "word": "law of excluded middle"
}