Intuitionistic logic

Intuitionism referred to different philosophical, mathematical and partly psychological positions that give the intuition of a priority. Often it is assumed here that certain facts be directly detected or proven. A distinction is made mainly uses of words in epistemology, ethics and meta-ethics of intuitionistic as well as a mathematical and logical intuitionism.

Epistemological intuitionism

In the classification of epistemological positions designated intuitionism ' the view that epistemic, cognitive and possibly metaphysical facts are immediately apparent and can serve as axioms the basis for further philosophical argument. Intuition ' can be epistemologically based on a knowledge of pure reason ( a priori knowledge ), non-specific include general to states that sensory experience and introspection on the appearance of the existence of a fact or.

Early modern period - 17th and 18th century

The epistemological position is usually associated with René Descartes and Claude Buffier. The so-called Scottish School ( Thomas Reid, Dugald Stewart, Sir William Hamilton, Pierre Paul Royer - Collard ) continues to evolve, initially to the skepticism of David Hume and later by Etienne Bonnot de sensualism of Condillac to be contradicted. Since the 19th century this direction is called " intuitionism ," by which their successors of the so-called French eclecticism are called. Similar ideas are also well received in " Scottish school " track Shaftesbury and Francis Hutcheson, with sensation and feeling are emphasized as direct evidence and contrary to the empiricism of John Locke.

19th and early 20th century

Since the 19th century created a flow of ethical theory which uses " intuitionism " as a self-designation.

The theorists of the so-called French eclecticism concepts of the Scottish school with ideas from the German idealism are connected. The representatives include Victor Cousin, Adolphe Garnier (1801-1864), Théodore Simon Jouffroy and Pierre Janet. Wilhelm Traugott Krug also referred to ideas of Friedrich Heinrich Jacobi as " intuitionism ." The latter is influenced by Shaftesbury and Hutcheson and their sense of orientation and also attempts against Locke, Hume, George Berkeley, and now also Immanuel Kant, to establish a direct access to metaphysical truths and objects. In this line also moves the speculative idealism of Friedrich Wilhelm Joseph Schelling, who - holds on to an intellectual intuition - against Kant and the aforementioned.

Henri Bergson builds on the ideas of intuitionism and works the approach further. He provides scientific discursive and philosophical "intuition" face to face.

In the wake of Bergson turn Edmund Husserl developed his phenomenological method of ideation or essences, which assumes an immediate, independent of scientific theory epistemic access to things or values ​​in themselves. Max Scheler closes because of his value philosophy.

Late 20th and early 21st century

Different positions is a " intuitionistic " orientation attributed to contain or defend about with respect to Vladimir Lossky (1903-1958), Martin Heidegger and Theodor W. Adorno, who also emphasized the element of direct access to reality over argumentative or rationally mediated positions.

Even in disciplines today's theoretical philosophy is " intuitionism " is used as a classification term, but which generally represent no explicit continuity with the aforementioned positions.

Ethical intuitionism and metaethischer

After Robert Audi in today's epistemology of morality " moral intuitionism " is a collective term for positions, which - unlike utilitarianism and deontological ethics as that of Kant - agree in the following theoretical commitments:

• There are several irreducible principles of morality. ( In common elaborations contrast, utilitarian and deontological ethics, especially adopted in the Kantian ethics only one or a few moral principles from which other moral truths or derivable on which they are to be retaliatory logically reducible. )
• Each of the moral principles refers to a natural reason which implies a prima facie duty.
• These moral principles are intuitively knowable, so be not just by inference ( inferential ) were recognized.

Because of the third hypothesis is postulated to a variant of epistemological fundamentalism, ie a theory that last foundations of knowledge reasoning. Counter-positions of the empiricism of utilitarianism, the rationalism of the Kantian deontological ethics, and also the Nonkognitivismus.

Some authors distinguish naturalistic and " metaphysical " intuitionism. The latter is in this case, for example, understood as committed to the thesis that expressions such as "good" lecture on " ethical objects" that detects human consciousness when it acquires ethical knowledge.

The moral intuitionism has precursors in Henry Sidgwick, George Edward Moore, Max Scheler, William David Ross, Hastings Rashdall (1858-1924), but are deferred, such as Moore. Current Representatives include Robert Audi, Noah Lemos ( b. 1956 ), Grant C. Sterling, Russ Shafer -Landau ( b. 1963 ) and William Donald Hudson.

Gerd Gigerenzer understands " intuitionist ethics " as a heuristic easier and evolvierter rules of thumb for the intelligent complexity reduction.

Intuitionistic mathematics and logic

The mathematical intuitionism represents that mathematics is an active constructive activity. All mathematical objects are constructs produced by ideal mathematicians who nevertheless remain finite and therefore aktual infinite mathematical objects can not really construct. To exclude nichtkonstruktive evidence, the laws of double negation elimination (non -non -A = A) and the exclusion of a third alternative in logical opposites (A or non-A ) must be suspended from classical logic. That is why classical mathematical theories like Peano arithmetic have to be revised. While in the area of ​​arithmetic syntactic translations are easily accomplished in intuitionistic statements, the intuitionist approach in calculus and other higher mathematics theories increases the complexity enormously. Opposite positions in the philosophy of mathematics are logicism ( Frege: mathematics is reducible to logic), formalism (David Hilbert ), Prädikativismus ( Bertrand Russell).

LEJ Brouwer is the founder of mathematical intuitionism. The starting point for this intuitionism ( to radicalize the Frege's logicism to revise the classical mathematics and discard various logical principles ), the concept of infinity, because infinity never as a complete whole (as " Current - infinite ", for example, as there is an infinite many numbers ), but regarded as a mere possibility of unlimited progression was ( as " potentially infinite ", for example, so far as one may state any natural number is a number following it, see also finitism ); so that the generality of the principle of the excluded middle must be denied because it could not apply without reservation as applied to infinite subject areas ( the negation of the statement " there is a natural number with the property F " results in unnecessary one in terms of infinite populations logical contradiction, because then the situation that you can not specify F still derive a contradiction is possible). Today's representatives are for example Anne Troelstra and Dirk van Dalen. For the aforementioned reasons, the constructivist mathematics requires a revised logic. This base represents the intuitionistic logic. Besides Brouwer intuitionistic logic systems were involved in the drafting, among other Errett Bishop, Arend Heyting, Gerhard Gentzen, Stephen Cole Kleene, Kurt Godel, Saul A. Kripke and Michael Dummett.

Other uses of words

Retrieved from " intuitionistic " positions has also spoken with respect to Pavel Alexandrovich Florensky and Nikolai Lossky and Martin Heidegger, the latter with respect to its rationality criticism and the acceptance of an immediate " demand [s ] of being," each " reification " of single beings precedes.

Evidence

• Epistemology