different between intuitionistic vs intuitive

English

Etymology

intuition +? -istic

Adjective

intuitionistic (not comparable)

1. (mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction

        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

        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

Derived terms

• intuitionistically
• intuitionistic logic

Related terms

• intuition

Translations

• Italian: intuizionistico (it)

English

Etymology

Borrowed from Middle French intuitif, from Medieval Latin intuitivus, from Latin intueri.

Pronunciation

• IPA^(key): /?n?tju??t?v/

Adjective

intuitive (comparative more intuitive, superlative most intuitive)

1. Spontaneous, without requiring conscious thought.
   • 2013 February 16, Laurie Goodstein, “Cardinals Size Up Potential Candidates for New Pope”, NYTimes.com:

     These impressions [of potential papal candidates], collected from interviews with a variety of church officials and experts, may influence the very intuitive, often unpredictable process the cardinals will use to decide who should lead the world’s largest church.

   The intuitive response turned out to be correct.

2. Easily understood or grasped by intuition.

   Designing software with an intuitive interface can be difficult.

3. Having a marked degree of intuition.

Antonyms

• unintuitive
• nonintuitive
• counterintuitive

Related terms

• intuition
• intuit

Translations

Noun

intuitive (plural intuitives)

1. One who has (especially parapsychological) intuition.

French

Adjective

intuitive

1. feminine singular of intuitif

German

Pronunciation

Adjective

intuitive

1. inflection of intuitiv:
   1. strong/mixed nominative/accusative feminine singular
   2. strong nominative/accusative plural
   3. weak nominative all-gender singular
   4. weak accusative feminine/neuter singular

Italian

Adjective

intuitive

1. feminine plural of intuitivo

Norwegian Bokmål

Adjective

intuitive

1. definite singular of intuitiv
2. plural of intuitiv

Norwegian Nynorsk

Adjective

intuitive

1. definite singular of intuitiv
2. plural of intuitiv