"Peirce's law" meaning in All languages combined

{
  "etymology_text": "Named after the logician and philosopher Charles Sanders Peirce.",
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      "expansion": "Peirce's law",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
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          "kind": "other",
          "name": "English entries with incorrect language header",
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            "Entries with incorrect language header",
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          "kind": "topical",
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          "name": "Logic",
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      "examples": [
        {
          "text": "Consider Peirce's law, ((P→Q)→P)→P). If Q is true, then P→Q is also true so the law reads \"If truth implies P then deduce P\" which certainly makes sense. If Q is false, then (P→Q)→P≡(P→⊥)→P≡¬P→P≡¬P→P and ¬P≡¬P→⊥≡¬¬P so the law reads ¬¬P→P, which is intuitionistically false but equivalent to the classical axiom ¬P∨P."
        }
      ],
      "glosses": [
        "The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus."
      ],
      "id": "en-Peirce's_law-en-name-qObBZ7ws",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "propositional calculus",
          "propositional calculus"
        ],
        [
          "law of excluded middle",
          "law of excluded middle"
        ],
        [
          "implicational propositional calculus",
          "implicational propositional calculus"
        ]
      ],
      "raw_glosses": [
        "(logic) The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Charles Sanders Peirce",
        "Peirce's law"
      ]
    }
  ],
  "word": "Peirce's law"
}

{
  "etymology_text": "Named after the logician and philosopher Charles Sanders Peirce.",
  "head_templates": [
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      "args": {},
      "expansion": "Peirce's law",
      "name": "en-proper noun"
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  "lang_code": "en",
  "pos": "name",
  "senses": [
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        "English entries with language name categories using raw markup",
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        "English terms with non-redundant non-automated sortkeys",
        "English uncountable nouns",
        "en:Logic"
      ],
      "examples": [
        {
          "text": "Consider Peirce's law, ((P→Q)→P)→P). If Q is true, then P→Q is also true so the law reads \"If truth implies P then deduce P\" which certainly makes sense. If Q is false, then (P→Q)→P≡(P→⊥)→P≡¬P→P≡¬P→P and ¬P≡¬P→⊥≡¬¬P so the law reads ¬¬P→P, which is intuitionistically false but equivalent to the classical axiom ¬P∨P."
        }
      ],
      "glosses": [
        "The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "propositional calculus",
          "propositional calculus"
        ],
        [
          "law of excluded middle",
          "law of excluded middle"
        ],
        [
          "implicational propositional calculus",
          "implicational propositional calculus"
        ]
      ],
      "raw_glosses": [
        "(logic) The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Charles Sanders Peirce",
        "Peirce's law"
      ]
    }
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  "word": "Peirce's law"
}