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Hartry Hamlin Field was born on November 30, 1946, in Boston, Massachusetts, to Adelaide ( née Anderson) and Donald Field. [2] Field earned a B.A. in mathematics from the University of Wisconsin–Madison in 1967 and an M.A. in philosophy from Harvard University in 1968. [3] He earned his Ph.D. in philosophy from Harvard in 1972 under the ...
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 ...
Mathematical fictionalism was brought to fame in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine's indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about ...
According to Putnam, Quine's version of the argument was an argument for the existence of abstract mathematical objects, while Putnam's own argument was simply for a realist interpretation of mathematics, which he believed could be provided by a "mathematics as modal logic" interpretation that need not imply the existence of abstract objects.
Putnam gave Quine's argument its first detailed formulation, although he later expressed disagreement with some of the central aspects of the argument. Many counterarguments have been raised against the idea. An influential argument by Hartry Field claims that mathematical entities are
Willard Van Orman Quine. Willard Van Orman Quine ( / kwaɪn /; known to his friends as "Van"; [9] June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". [10] He served as the Edgar Pierce Chair of Philosophy at ...
Overview. An Introduction to the Philosophy of Mathematics is a textbook on the philosophy of mathematics focusing on the issue of mathematical realism, i.e. the question of whether or not there are mathematical objects, and mathematical explanation. [1] [2] Colyvan described his intention for the book as being a textbook that " [gets] beyond ...
Inscrutability of reference. The inscrutability or indeterminacy of reference (also referential inscrutability) is a thesis by 20th century analytic philosopher Willard Van Orman Quine in his book Word and Object. [1] The main claim of this theory is that any given sentence can be changed into a variety of other sentences where the parts of the ...