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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 .
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 ...
In the philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities. [11] He was the main proponent of the view that philosophy is not conceptual analysis , but continuous with science; it is the abstract branch of the empirical ...
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]
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.
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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) .
Next, Quine reduces projectibility to the subjective notion of similarity. Two green emeralds are usually considered more similar than two grue ones if only one of them is green. Observing a green emerald makes us expect a similar observation (i.e., a green emerald) next time. Green emeralds are a natural kind, but grue emeralds are not.