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The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. [1]
Stone's theorem on one-parameter unitary groups (functional analysis) Stone–Tukey theorem ; Stone–von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics) Stone–Weierstrass theorem (functional analysis) Strassmann's theorem (field theory) Strong perfect graph theorem (graph theory)
In 2004, Conway and Simon B. Kochen, another Princeton mathematician, proved the free will theorem, a version of the "no hidden variables" principle of quantum mechanics. It states that given certain conditions, if an experimenter can freely decide what quantities to measure in a particular experiment, then elementary particles must be free to ...
Metaphysical libertarianism is the form of incompatibilism which posits that determinism is false and free will is possible (at least some people have free will). [27] This view is associated with non-materialist constructions, [ 15 ] including both traditional dualism , as well as models supporting more minimal criteria; such as the ability to ...
The free will theorem says that if we have free will, then particles must have free will. This presumably is counterintuitive. It makes no claim about a world in which we don't have free will (a deterministic world). There's no way to argue for free will on the basis of this theorem - and yet, this is what the section claims, without any ...
Tarski's undefinability theorem (general form): Let (,) be any interpreted formal language which includes negation and has a Gödel numbering () satisfying the diagonal lemma, i.e. for every -formula () (with one free variable ) there is a sentence such that (()) holds in .
The neuroscience of free will encompasses two main fields of study: volition and agency. Volition, the study of voluntary actions, is difficult to define. [citation needed] If human actions are considered as lying along a spectrum based on conscious involvement in initiating the actions, then reflexes would be on one end, and fully voluntary actions would be on the other. [17]
"Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original?" The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different ...