Definition & Meaning | English word INTUITIONISM

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Definitions of INTUITIONISM

1. (mathematics) An approach to mathematics/logic which avoids proof by contradiction, and which requires that, in order to prove that something exists, one must construct it.

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Examples of Using INTUITIONISM in a Sentence

• In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.
• In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism, strict formalism, actualism, predicativism, and strong finitism) is a form of finitism and intuitionism.
• As a foundationalist epistemological position, ethical intuitionism contrasts with coherentist positions in moral epistemology, such as those that depend on reflective equilibrium.
• With the benefit of hindsight, we can see that Couturat was in broad agreement with the logicism of Russell, while Poincaré anticipated Brouwer's intuitionism.
• Other mathematicians such as Hermann Weyl (who eventually became disenchanted with intuitionism, feeling that it places excessive strictures on mathematical progress) and Leopold Kronecker also played a role—though they are not cited by Brouwer in his definitive speech.
• Skolem's result applies only to what is now called first-order logic, but Zermelo argued against the finitary metamathematics that underlie first-order logic, as Zermelo was a mathematical Platonist who opposed intuitionism and finitism in mathematics.
• The two groups had contrasting beliefs about such divisive issues as scientific versus human values, determinism versus indeterminism, objectivism versus intuitionism, laboratory investigations versus field studies, nomothetic versus idiographic explanations, and elementism versus holism (Simonton, 2000).
• Moore's ethical intuitionism has been seen as opening the road for noncognitive views of morality, such as emotivism.
• Understanding and comprehension coming from addressing an object, as though part of the external world, something that joins the consciousness of the perceiving subject directly (noesis, insight), then becoming memory, intuitionism as the foundation of all noema or processes of consciousness.
• Tanabe disagreed with Nishida and Nishitani on the meaning of Absolute Nothingness, emphasizing the practical, historical aspect over what he termed the latter's intuitionism.
• According to Nikolay Lossky, the characteristic features of Russian philosophy are: cosmism, sophiology (teachings about Sophia), sobornost, metaphysics, religiosity, intuitionism, positivism, realism (ontologism).
• The formalistic school should therefore accord some recognition to intuitionism instead of polemicizing against it in sneering tones while not even observing proper mention of authorship.
• These include the program of intuitionism founded by Brouwer, the finitism of Hilbert and Bernays, the constructive recursive mathematics of mathematicians Shanin and Markov, and Bishop's program of constructive analysis.
• He was convinced the intuitionism of axiological ethics is not enough for a rigorous foundation, but aware as well of the very suggestions of Hartmann analysis on conflictive relations among values, ethical thinking of Maliandi develops as a pursuit of an ethical foundation non-intuitionist, that recognizes conflicts.

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