"intuitionistic" meaning in All languages combined

See intuitionistic on Wiktionary

Adjective [English]

Etymology: intuition + -istic Etymology templates: {{suffix|en|intuition|istic}} intuition + -istic Head templates: {{en-adj|-}} intuitionistic (not comparable)
  1. (mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction Tags: not-comparable Categories (topical): Logic, Mathematics Derived forms: intuitionistically, intuitionistic logic Related terms: intuitionism, intuition Translations (Translations): intuitionistinen (Finnish), intuitionistisch (German), intuizionistico (Italian), intuicjonistyczny (Polish), intuiționist (Romanian)

Download JSON data for intuitionistic meaning in All languages combined (3.2kB)

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        "2": "intuition",
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  "etymology_text": "intuition + -istic",
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          "name": "English entries with incorrect language header",
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          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
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            "Philosophy",
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      "derived": [
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          "word": "intuitionistically"
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      "examples": [
        {
          "text": "Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus. Type Theory extends this identification to predicate logic by introducing dependent types, that is types which contain values. Type Theory internalizes the interpretation of intuitionistic logic proposed by Brouwer, Heyting and Kolmogorov, the so called BHK interpretation. The types of Type Theory play a similar role to sets in set theory but functions definable in Type Theory are always computable.ᵂᴾ"
        },
        {
          "text": "The system, which has come to be known as IZF, or Intuitionistic Zermelo–Fraenkel (ZF refers to ZFC without the axiom of choice), has the usual axioms of extensionality, pairing, union, infinity, separation and power set. The axiom of regularity is stated in the form of an axiom schema of set induction. Also, while Myhill used the axiom schema of replacement in his system, IZF usually stands for the version with collection.ᵂᴾ"
        }
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        [
          "proof by contradiction",
          "proof by contradiction"
        ]
      ],
      "raw_glosses": [
        "(mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction"
      ],
      "related": [
        {
          "word": "intuitionism"
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        {
          "word": "intuition"
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      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "intuitionistinen"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "word": "intuitionistisch"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "Translations",
          "word": "intuizionistico"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "word": "intuicjonistyczny"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "Translations",
          "word": "intuiționist"
        }
      ]
    }
  ],
  "word": "intuitionistic"
}
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      "word": "intuitionistic logic"
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      "word": "intuitionism"
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        "English uncomparable adjectives",
        "Translation table header lacks gloss",
        "en:Logic",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus. Type Theory extends this identification to predicate logic by introducing dependent types, that is types which contain values. Type Theory internalizes the interpretation of intuitionistic logic proposed by Brouwer, Heyting and Kolmogorov, the so called BHK interpretation. The types of Type Theory play a similar role to sets in set theory but functions definable in Type Theory are always computable.ᵂᴾ"
        },
        {
          "text": "The system, which has come to be known as IZF, or Intuitionistic Zermelo–Fraenkel (ZF refers to ZFC without the axiom of choice), has the usual axioms of extensionality, pairing, union, infinity, separation and power set. The axiom of regularity is stated in the form of an axiom schema of set induction. Also, while Myhill used the axiom schema of replacement in his system, IZF usually stands for the version with collection.ᵂᴾ"
        }
      ],
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      ],
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          "logic"
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        ]
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        "(mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction"
      ],
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  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "intuitionistinen"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "word": "intuitionistisch"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "Translations",
      "word": "intuizionistico"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "word": "intuicjonistyczny"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "Translations",
      "word": "intuiționist"
    }
  ],
  "word": "intuitionistic"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-04 from the enwiktionary dump dated 2024-05-02 using wiktextract (e9e0a99 and db5a844). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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