different between intuitionistic vs intuition

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

Alternative forms

• intuïtion (pedantic)

Etymology

From Middle French intuition, from Medieval Latin intuitio (“a looking at, immediate cognition”), from Latin intueri (“to look at, consider”), from in (“in, on”) + tueri (“to look, watch, guard, see, observe”).

Pronunciation

• (UK) IPA^(key): /??ntj?????n/
• (US) IPA^(key): /?ntuw????n/

Noun

intuition (countable and uncountable, plural intuitions)

1. Immediate cognition without the use of conscious rational processes.
2. A perceptive insight gained by the use of this faculty.

Derived terms

Translations

References

• intuition in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• intuition in The Century Dictionary, New York, N.Y.: The Century Co., 1911.

Danish

Noun

intuition c (singular definite intuitionen, plural indefinite intuitioner)

1. intuition

Declension

Related terms

• intuere
• intuitiv

References

• “intuition” in Den Danske Ordbog

Finnish

Noun

intuition

1. Genitive singular form of intuitio.

Anagrams

• innoittui

French

Etymology

Borrowed from Medieval Latin intu?ti?.

Pronunciation

• IPA^(key): /??.t?i.sj??/

Noun

intuition f (plural intuitions)

1. (uncountable, philosophy) intuition (cognitive faculty)
2. (countable) intuition, hunch
3. premonition

Derived terms

• intuitionner
• intuitionnel

Related terms

• intuitif

Further reading

• “intuition” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).