"material implication" meaning in English

{
  "antonyms": [
    {
      "word": "strict implication"
    }
  ],
  "forms": [
    {
      "form": "material implications",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "material implication (plural material implications)",
      "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": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "In the truth table in Figure 1, the first row corresponds to modus ponens, the last row corresponds to modus tollens, the second row could be taken to represent an invalid argument (where P→Q is the argument and P is a premise or conjunction of premises), and the third row helps ensure that an argument of the form P→Q,¬P⊢¬Q is invalid."
        },
        {
          "text": "The following paradox (and also axiom) of material implication: P→(Q→P) could be taken to mean the monotonicity of entailment, that is, if 'P' is true then no other or new fact 'Q' should be able to arise which would imply the nullification of P's truth, i.e., it could not be the case, for any 'Q', that Q → ¬P."
        }
      ],
      "glosses": [
        "An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as \"any proposition whatsoever is a sufficient condition for a true proposition\"."
      ],
      "hypernyms": [
        {
          "word": "logical connective"
        }
      ],
      "id": "en-material_implication-en-noun-7ysIPiVz",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "implication",
          "implication"
        ],
        [
          "propositional logic",
          "propositional logic"
        ]
      ],
      "raw_glosses": [
        "(logic) An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as \"any proposition whatsoever is a sufficient condition for a true proposition\"."
      ],
      "related": [
        {
          "word": "entailment"
        }
      ],
      "synonyms": [
        {
          "word": "material conditional"
        }
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "material implication"
      ]
    }
  ],
  "word": "material implication"
}

{
  "antonyms": [
    {
      "word": "strict implication"
    }
  ],
  "forms": [
    {
      "form": "material implications",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "material implication (plural material implications)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "logical connective"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "entailment"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Logic"
      ],
      "examples": [
        {
          "text": "In the truth table in Figure 1, the first row corresponds to modus ponens, the last row corresponds to modus tollens, the second row could be taken to represent an invalid argument (where P→Q is the argument and P is a premise or conjunction of premises), and the third row helps ensure that an argument of the form P→Q,¬P⊢¬Q is invalid."
        },
        {
          "text": "The following paradox (and also axiom) of material implication: P→(Q→P) could be taken to mean the monotonicity of entailment, that is, if 'P' is true then no other or new fact 'Q' should be able to arise which would imply the nullification of P's truth, i.e., it could not be the case, for any 'Q', that Q → ¬P."
        }
      ],
      "glosses": [
        "An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as \"any proposition whatsoever is a sufficient condition for a true proposition\"."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "implication",
          "implication"
        ],
        [
          "propositional logic",
          "propositional logic"
        ]
      ],
      "raw_glosses": [
        "(logic) An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as \"any proposition whatsoever is a sufficient condition for a true proposition\"."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "material implication"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "material conditional"
    }
  ],
  "word": "material implication"
}