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Friedrich Ludwig Gottlob Frege

Gottlob Frege (b. 1848, d. 1925) was a German mathematician, logician, and philosopher who worked at the University of Jena. He wrote philosophical works about logic, mathematics, and language.

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Frege virtually founded the modern discipline of mathematical logic. He developed a system of conceptual notation (inspired by Leibniz's conception of a rational calculus), and though we no longer use his notation, his system constituted the first predicate calculus. Frege's second-order predicate calculus was based on the `function-argument' analysis of propositions and it freed logicians from the limitations of the `subject-predicate' analysis of Aristotelian logic. Frege's formal system made it possible for logicians to develop a strict definition of a proof. Unfortunately, Frege employed a principle (Basic Law V) in his later system (Grundgesetze) which turned out to be inconsistent. Despite the fact that a contradiction invalidated his system, Frege validly derived the Peano Axioms governing the natural numbers from a powerful and consistent principle now known as Hume's Principle (some philosophers have proposed that the derivation of the Peano Axioms from Hume's Principle should be called `Frege's Theorem'). Frege is most well-known among philosophers, however, for suggesting that the expressions of language have both a sense and a denotation (i.e., that at least two semantic relations are required to explain the significance of linguistic expressions). This seminal idea in the philosophy of language has inspired research in the field for over a century.

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