<logic, philosophy of science, moral philosophy> reliance on unmediated awareness as a criterion of truth. In logic and mathematics, intuitionism denies the independent reality of mathematical objects and the principle of excluded middle. In moral philosophy, intuitionism is the metaethical theory that moral judgments are made by reference to a direct, non-inferential awareness of moral value. Ethical intuitionists usually hold that we recognize our duties in the specific features of particular moral decisions. Recommended Reading: Gisele Fischer Servi, Intuitionism and Models of Cognition (Giro, 1996); Michael Dummett, Elements of Intuitionism (Oxford, 2000); Grant C. Sterling, Ethical Intuitionism and Its Critics (Peter Lang, 1994); and James Q. Wilson, Moral Intuitions (Transaction, 2000).
[A Dictionary of Philosophical Terms and Names]
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<ethics, philosophy of mathematics> 1. in ethics the term refers to the doctrine (popular in Britain around the turn of the century) that all of our moral judgments are made through an appeal to our moral intuitions or "moral sense". This ethical doctrine is derived from a more general idea in epistemology dating back to Plato: namely, a radical intrinsicism which holds that all of our knowledge is gained through intuition, immediate insight, or spiritual vision of a transcendent higher reality. In addition, the movement of ethical intuitionism picked up on the ideas of the earlier "moral sense theorists" such as David Hume (1711-1776) and Adam Smith (1723-1790). Even though intuitionism is a form of intrinsicism, it ends up being a kind of subjectivism, in which the justification for ethical values is the fact that a certain person or philosopher thinks they are true. Historically, intuitionism has tended to be a kind of deontologism, although the cause may have been simply the beliefs of the intuitionists themselves and not anything about intuitionism in general. (References from emotionalism and mysticism.)
2. in philosophy of mathematics see intuitionistic logic
Edited by Giovanni Benzi
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<logic, mathematics> Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B.
In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking proofs by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic).
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