Search results
Results From The WOW.Com Content Network
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]
This is a list of axioms as that term is understood in mathematics. In epistemology , the word axiom is understood differently; see axiom and self-evidence . Individual axioms are almost always part of a larger axiomatic system .
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)
Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...
Thus, in frequentist decision theory it is sufficient to consider only (generalized) Bayes rules. Conversely, while Bayes rules with respect to proper priors are virtually always admissible, generalized Bayes rules corresponding to improper priors need not yield admissible procedures. Stein's example is one such famous situation.
Arrow's theorem is not related to strategic voting, which does not appear in his framework, [3] [1] though the theorem does have important implications for strategic voting (being used as a lemma to prove Gibbard's theorem [15]). The Arrovian framework of social welfare assumes all voter preferences are known and the only issue is in ...
An abelian group with Ext 1 (A, Z) = 0 is called a Whitehead group; MA + ¬CH proves the existence of a non-free Whitehead group, while V = L proves that all Whitehead groups are free. In one of the earliest applications of proper forcing, Shelah constructed a model of ZFC + CH in which there is a non-free Whitehead group. [12] [13]
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".