Tradition
Intuitionism
Overview
In 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. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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But to determine à priori an intuition in space (its figure), to divide time into periods, or merely to cognize the quantity of an intuition in space and time, and to determine it by number—all this is an operation of reason by means of the construction of conceptions, and is called mathematical.
Immanuel Kant, The Critique of Pure Reason
States what Intuitionism is; the author is tied to Intuitionism in the knowledge graph.
I have shewn with regard to judgments of what is _good in itself_, that this is the case; no reason can be given for them. But it is the essence of Intuitionism to suppose that rules of action--statements not of what ought to _be_, but of what we ought to do--are in the same sense intuitively certain. Plausibility has been lent to this view by the fact that we do undoubtedly make immediate judgments that certain…
G. E. Moore, Principia Ethica
Names Intuitionism.
Any quality, therefore, by which our actual world is distinguished from other abstractly possible worlds, must be ignored by mathematics and philosophy alike. Mathematics and philosophy differ, however, in their manner of treating the general properties in which all possible worlds agree; for while mathematics, starting from comparatively simple propositions, seeks to build up more and more complex results by…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
The author is tied to Intuitionism in the knowledge graph.
Philosophers who discussed Intuitionism
- Henri Bergson
- Immanuel Kant
- John Finnis
- Willard Van Orman Quine
- Arthur Schopenhauer
- Louis Couturat
- Gerrit Mannoury
- John Penn Mayberry
Related ideas
- Alan Turing
- Georg Cantor
- Zermelo–Fraenkel set theory
- Finitism
- Negation
- Kurt Gödel
- Intuitionistic logic
- Foundations of mathematics
- Law of excluded middle
- Mathematics
- Quantum indeterminacy
- Mind
- Model theory
- Constructivism (philosophy of mathematics)
- Natural number
- Anti-realism
- Stephen Cole Kleene
- Truth
- Michael Dummett
- Intuitionistic type theory
- Actual and potential infinity
- Bertrand Russell
- Russell's paradox
- Philosophy of mathematics
Place in the tradition
Part of Analytic philosophy.