Search results

...ompleteness of [https://en.wikipedia.org/wiki/Predicate_calculus predicate calculus] was proved by [https://en.wikipedia.org/wiki/Kurt_G%C3%B6del Kurt Gödel] ...theorems incompleteness theorems], which showed that sufficiently strong [[proof]] theories cannot prove their own consistency (provided that they are in fa

...nterpretations, depending on the [[meanings]] of the derivation rules. The proof of a mathematical theorem is a [[logical]] [[argument]] demonstrating that ...l]]. On the other hand, a deep theorem may be simply [[stated]], but its [[proof]] may involve [[surprising]] and [[subtle]] connections between disparate a

...on, or principle) is the study of valid [[inference]] and [[demonstration (proof)|demonstration]]. ...logic into other areas, in particular to the study of [[model theory]], [[proof theory]], [[set theory]], and [[recursion theory]].

...bolize and evaluate arguments; the characteristic topic is [[propositional calculus|propositional logic]], the logic of simple indicative statements. ([[Classi [[Mathematics]] uses very specific, rigorous methods of proof that philosophers sometimes (only rarely) try to emulate. Most philosophy

...leene recursive functions of 1930, 1934 and 1935, Alonzo Church's [[lambda calculus]] of 1936, Emil Post's "Formulation 1" of 1936, and [[Alan Turing]]'s [[Tur ...osition". The problem of wrong answers must be solved with an independent "proof" of the algorithm e.g., using induction:

...Rosenblueth, Norbert Wiener, and Julian Bigelow; and the paper "A Logical Calculus of the Ideas Immanent in Nervous Activity" by Warren McCulloch and Walter P ...ed to social [[memes]], living cells, and even computer viruses is further proof of the somewhat surprising [[universal]]ity of cybernetic study.

...the behavior of the subject of the field of study. Unlike a mathematical proof, a scientific theory is [[empirical]], and is always open to [[falsifiabili ...ot in seeking for their verification (such as claiming certain or probable proof or disproof; both the proposal and falsification of a theory are only of me

...the behavior of the subject of the field of study. Unlike a mathematical proof, a scientific theory is [[empirical]], and is always open to [[falsifiabili ...ot in seeking for their verification (such as claiming certain or probable proof or disproof; both the proposal and falsification of a theory are only of me