Quine's Weak and Strong Indispensability Argument |
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Authors: | Lieven Decock |
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Institution: | (1) Centre of Logic, University of Leuven, Kardinaal Mercierplein 2, B-3000 Leuvent, Belgium (Lieven.Decock@hiw.kuleuven.ac.be) |
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Abstract: | Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished
from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism
and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider
all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even
clearer if one takes into account Maddy's critique of Quine's strong indispensability thesis. Maddy's critique does not refute
Quine's weak indispensability argument. We are left with a weak and almost unassailable indispensability argument.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | Maddy Quine epistemic virtues indispensability argument mathematical ontology |
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