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[non-primary source needed] Since there is no limit to the number of such expressions to be considered, Putnam embraced a form of semantic holism. Despite the many changes in his other positions, Putnam consistently adhered to semantic holism. Michael Dummett, Jerry Fodor, Ernest Lepore, and others have identified problems with this position ...
The Quine–Putnam indispensability argument [a] is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. It was named after the philosophers Willard Quine and Hilary Putnam, and is one of the most important arguments in the ...
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to ...
In a narrow sense, foundations of mathematics is the logical and mathematical framework that allows developing mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This includes also the philosophical study of the relation of this framework with the reality.
Twin Earth thought experiment. Twin Earth is a thought experiment proposed by philosopher Hilary Putnam in his papers "Meaning and Reference" (1973) and "The Meaning of 'Meaning ' " (1975). It is meant to serve as an illustration of his argument for semantic externalism, or the view that the meanings of words are not purely psychological.
Putnam strongly rejected the term "Platonist" as implying an over-specific ontology that was not necessary to mathematical practice in any real sense. He advocated a form of "pure realism" that rejected mystical notions of truth and accepted much quasi-empiricism in mathematics.
The result. Theorem (Fuglede) Let T and N be bounded operators on a complex Hilbert space with N being normal. If TN = NT, then TN* = N*T, where N* denotes the adjoint of N . Normality of N is necessary, as is seen by taking T = N. When T is self-adjoint, the claim is trivial regardless of whether N is normal: Tentative Proof: If the underlying ...
The Davis–Putnam–Logemann–Loveland algorithm is a 1962 refinement of the propositional satisfiability step of the Davis–Putnam procedure which requires only a linear amount of memory in the worst case. It eschews the resolution for the splitting rule: a backtracking algorithm that chooses a literal l, and then recursively checks if a ...
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