In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic...

ongoing rehabilitation of Frege's logicism. Boolos, George, 1998. Logic, Logic, and Logic. MIT Press. — 12 papers on Frege's theorem and the logicist approach...

known as Frege's theorem, which is the foundation for a philosophy of mathematics known as neo-logicism. Hume's principle appears in Frege's Foundations...

philosopher Gottlob Frege. Boolos proved a conjecture due to Crispin Wright (and also proved, independently, by others), that the system of Frege's Grundgesetze...

motivate Frege's later works in logicism. The book was also seminal in the philosophy of language. Michael Dummett traces the linguistic turn to Frege's Grundlagen...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf...

centuries saw the development of modern logic and formalized mathematics. Frege's Begriffsschrift (1879) introduced both a complete propositional calculus...

Foundations of mathematics Frege's theorem Goodstein's theorem Neo-logicism Non-standard model of arithmetic Paris–Harrington theorem Presburger arithmetic...

Dedekind–Peano axioms. Both results were proven informally by Gottlob Frege (Frege's Theorem), and would later be more rigorously proven by George Boolos and...

a specific value assigned to it within the context of the formula. Frege's theorem A result in logic and mathematics demonstrating that arithmetic can...

Press Freedom versus license Freethought Frege's Puzzle Frege's theorem Frege-Geach point Frege-Geach problem Frege–Church ontology Freie Arbeiter Stimme...

question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle...

X. Frege's propositional calculus is not a Frege system, since it used axioms instead of axiom schemes, although it can be modified to be a Frege system...

strongly recommended to examine Frege's argument on the point" (Russell 1903:522); The abbreviation Gg. stands for Frege's Grundgezetze der Arithmetik. Begriffsschriftlich...

of Frege's Begriffsschrift," Historia Mathematica 25(4): 412–422. Wikimedia Commons has media related to Begriffsschrift. Zalta, Edward N. "Frege's Logic...

paradox in 1901 by Bertrand Russell. This proved Frege's naive set theory led to a contradiction. Frege's theory contained the axiom that for any formal...

which lacks both excluded middle and the principle of explosion. Frege's theorem states ( B → ( C → D ) ) → ( ( B → C ) → ( B → D ) ) {\displaystyle...

term. Frege reduced properties and relations to functions and so these entities are not included among the objects. Some authors make use of Frege’s notion...

the Entscheidungsproblem ("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem. Alongside his doctoral student Alan Turing, Church...

"a formula language, modeled on that of arithmetic, of pure thought." Frege's motivation for developing his formal approach to logic resembled Leibniz's...

foundational systems, including ZFC and category theory, and from the system of Frege's Grundgesetze der Arithmetik using modern notation and natural deduction...

by Frege, Richard Dedekind, and Georg Cantor. Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929...

combination of Frege's Urteilsstrich, judgement stroke [ | ], and Inhaltsstrich, content stroke [—], came to be called the assertion sign." Frege's notation...

thereby qualifies as a Hilbert system dates back to Gottlob Frege's 1879 Begriffsschrift. Frege's system used only implication and negation as connectives...

Frege (1960) dismissed Schröder's work, and admiration for Frege's pioneering role has dominated subsequent historical discussion. Contrasting Frege with...

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...

incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and consistent. Gödel's theorem applies...

The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic...

to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization...