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unprovable statement

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  • Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia

  • Curry's paradox — For Paul Curry s optical illusion and dissection puzzle, see Missing square puzzle. Curry s paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self referring sentence… …   Wikipedia

  • Proof procedure — In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements.There are several types of proof calculi. The most popular are natural… …   Wikipedia

  • Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …   Wikipedia

  • Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… …   Wikipedia

  • Zermelo–Fraenkel set theory — Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… …   Wikipedia

  • Existence of God — Part of a series on God General conceptions …   Wikipedia

  • Eastern epistemology — Jain EpistemologyAccording to Jain epistemology, reality is multifaceted ( anekanta , or non one sided ), such that no finite set of statements can capture the entire truth about the objects they describe. The Jain list of pramanas (valid sources …   Wikipedia

  • Johnston diagram — Johnston diagrams, which look similar to Euler or Venn diagrams, illustrate formal propositional logic in a visual manner. Logically they are equivalent to truth tables; some may find them easier to understand at a glance. By overlaying one… …   Wikipedia

  • Goodstein's theorem — In mathematical logic, Goodstein s theorem is a statement about the natural numbers made by Reuben Goodstein which states that every Goodstein sequence eventually terminates at 0. harvtxt|Kirby|Paris|1982 showed that it is unprovable in Peano… …   Wikipedia

  • Self-refuting idea — Self refuting ideas are ideas or statements whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are accused by their detractors of being self refuting, and such accusations are therefore almost… …   Wikipedia

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