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  2. Free will theorem - Wikipedia

    en.wikipedia.org/wiki/Free_will_theorem

    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:

  3. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    No free lunch theorem (philosophy of mathematics) No-hair theorem ; No-trade theorem ; No wandering domain theorem (ergodic theory) Noether's theorem (Lie groups, calculus of variations, differential invariants, physics) Noether's second theorem (calculus of variations, physics) Noether's theorem on rationality for surfaces (algebraic surfaces)

  4. Free will - Wikipedia

    en.wikipedia.org/wiki/Free_will

    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".

  5. Theory of everything - Wikipedia

    en.wikipedia.org/wiki/Theory_of_everything

    Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [48] Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not ...

  6. Rule of replacement - Wikipedia

    en.wikipedia.org/wiki/Rule_of_replacement

    In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression.A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system.

  7. Completeness (logic) - Wikipedia

    en.wikipedia.org/wiki/Completeness_(logic)

    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 ...

  8. Decidability (logic) - Wikipedia

    en.wikipedia.org/wiki/Decidability_(logic)

    A theory is a set of formulas, often assumed to be closed under logical consequence.Decidability for a theory concerns whether there is an effective procedure that decides whether the formula is a member of the theory or not, given an arbitrary formula in the signature of the theory.

  9. History of the Church–Turing thesis - Wikipedia

    en.wikipedia.org/wiki/History_of_the_Church...

    J. B. Rosser's paper An Informal Exposition of Proofs of Gödel's Theorem and Church's Theorem [44] states the following: "'Effective method' is here used in the rather special sense of a method each step of which is precisely predetermined and which is certain to produce the answer in a finite number of steps.