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Quine's and Putnam's arguments have also been influential outside philosophy of mathematics, inspiring indispensability arguments in other areas of philosophy. For example, David Lewis , who was a student of Quine, used an indispensability argument to argue for modal realism in his 1986 book On the Plurality of Worlds .
Putnam considers the argument in the two last sections as independent of the first four, and at the same time as Putnam criticizes Quine, he also emphasizes his historical importance as the first top rank philosopher to both reject the notion of apriority and sketch a methodology without it.
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 considers the argument in the two last sections as independent of the first four, and at the same time as Putnam criticizes Quine, he also emphasizes his historical importance as the first top-rank philosopher to both reject the notion of a-priority and sketch a methodology without it. [21]
The explanatory indispensability argument is an altered form of the Quine–Putnam indispensability argument [3] first raised by W. V. Quine and Hilary Putnam in the 1960s and 1970s. [4] The Quine–Putnam indispensability argument supports the conclusion that mathematical objects exist with the idea that mathematics is indispensable to the ...
Both Putnam and Quine invoke naturalism to justify the exclusion of all non-scientific entities, and hence to defend the "only" part of "all and only". The assertion that "all" entities postulated in scientific theories, including numbers, should be accepted as real is justified by confirmation holism .
The Quine–Putnam indispensability argument claims that we should believe in abstract mathematical objects such as numbers and sets because mathematics is indispensable to science. One of the most important ideas in the philosophy of mathematics , it is credited to W. V. Quine and Hilary Putnam (pictured) .
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