truth lemma
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Diagonal lemma — In mathematical logic, the diagonal lemma or fixed point theorem establishes the existence of self referential sentences in certain formal theories of the natural numbers specifically those theories that are strong enough to represent all… … Wikipedia
Spinoza: metaphysics and knowledge — G.H.R.Parkinson The philosophical writings of Spinoza are notoriously obscure, and they have been interpreted in many ways. Some interpreters see Spinoza as (in the words of a contemporary)1 ‘the reformer of the new [sc. Cartesian] philosophy’.… … History of philosophy
Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… … Wikipedia
Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements … Wikipedia
Implicational propositional calculus — In mathematical logic, the implicational propositional calculus is a version of classical (two valued) propositional calculus which uses only one connective, called implication or conditional. In formulas, this binary operation is indicated by… … Wikipedia
Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… … Wikipedia
Tarski's undefinability theorem — Tarski s undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth… … Wikipedia
metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… … Universalium
Exact sciences (The) in Hellenistic times: texts and issues — The exact sciences in Hellenistic times: Texts and issues1 Alan C.Bowen Modern scholars often rely on the history of Greco Latin science2 as a backdrop and support for interpreting past philosophical thought. Their warrant is the practice… … History of philosophy
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
The Hardest Logic Puzzle Ever — is a title coined by George Boolos in La Repubblica 1992 under the title L indovinello più difficile del mondo for the following Raymond Smullyan inspired logic puzzle:Boolos provides the following clarifications:George Boolos, The Hardest Logic… … Wikipedia
