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The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
Free-will libertarianism is the view that the free-will thesis (that we, ordinary humans, have free will) is true and that determinism is false; in first-order language, it is the view that we (ordinary humans) have free will and the world does not behave in the way described by determinism.
Kempe's proof did, however, suffice to show the weaker five color theorem. The four-color theorem was eventually proved by Kenneth Appel and Wolfgang Haken in 1976. [2] Schröder–Bernstein theorem. In 1896 Schröder published a proof sketch [3] which, however, was shown to be faulty by Alwin Reinhold Korselt in 1911 [4] (confirmed by ...
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Nielsen–Schreier theorem (free groups) Orbit-stabilizer theorem (group theory) Schreier refinement theorem (group theory) Schur's lemma (representation theory) Schur–Zassenhaus theorem (group theory) Sela's theorem (hyperbolic groups) Stallings theorem about ends of groups (group theory) Superrigidity theorem (algebraic groups)
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The problem of free will has been identified in ancient Greek philosophical literature. The notion of compatibilist free will has been attributed to both Aristotle (4th century BCE) and Epictetus (1st century CE): "it was the fact that nothing hindered us from doing or choosing something that made us have control over them".
Other approaches do not require free will to be a fundamental constituent of the universe; ordinary randomness is appealed to as supplying the "elbow room" believed to be necessary by libertarians. Free volition is regarded as a particular kind of complex, high-level process with an element of indeterminism.