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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory , proof theory , set theory , and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
In 2006, Oxford University Press published his book, Plural Predicates a, in which he gives an account of a semantics for a plural logic. In particular he develops a Russellian account of plural definite descriptions. He is also the author of the following textbooks: Modern Formal Logic (Macmillan, 1989; second edition, Thomson, 2006),
From Frege to Gödel: A Source Book on Mathematical Logic 1879–1931. Harvard University Press. Bernard Meltzer (1962). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translation of the German original by Kurt Gödel, 1931. Basic Books, 1962. Reprinted, Dover, 1992. ISBN 0-486-66980-7. Raymond Smullyan (1966).
This last condition, likewise, enables us to give the most explicit enunciation of the object-matter of Logic, in saying that Logic is the science of the Laws of Thought as Thought, or the science of the Formal Laws of Thought, or the science of the Laws of the Form of Thought; for all these are merely various expressions of the same thing."
Moreover, the syntax of the primary algebra can be extended to formal systems other than 2 and sentential logic, resulting in boundary mathematics (see § Related work below). LoF has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken. Some of these authors have ...
Begriffsschrift (German for, roughly, "concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.. Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, for pure thought."
Perhaps De Morgan's best known work, Formal Logic, or the Calculus of Inference, Necessary and Probable [71] was published in 1847 in the same week (by arrangement) as George Boole's Mathematical Analysis of Logic. The book is primarily a reissue of his paper "On the structure of the syllogism" (1846) [45] but also includes his earlier book ...
Organon Roman copy in marble of a Greek bronze bust of Aristotle by Lysippos, c. 330 BC, with modern alabaster mantle. The Organon (Ancient Greek: Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic.