- From: Christopher Menzel <chris.menzel@gmail.com>
- Date: Mon, 1 May 2006 10:52:36 -0500
- To: Pat Hayes <phayes@ihmc.us>
- Cc: Frank Manola <fmanola@acm.org>, "C. M. Sperberg-McQueen" <cmsmcq@acm.org>, public-swbp-wg@w3.org
>> Regarding the "bad philosophy", how bad is it? > > Not bad at all. Quine was an extreme nominalist: his entire > philosophical career can be characterized as a mission to reduce > ontological commitments to an absolute minimum. And since, using > one of his own slogans, to be is to be the value of a bound > [quantified] variable, this mission has the concomitant side-effect > of restricting what can be allowed into the domain of > quantification. At times this kind of purging can be cathartic, but > it can also be stultifying. Nicely put, Pat, though it might be a bit misleading to say Quine was a nominalist, as that view is commonly taken to deny the existence of abstract objects of any sort and, as you noted in your next paragraph, Quine unabashedly accepted the existence of sets. Quine (rightly) conceded that quantification over mathematical objects (notably, real numbers) is unavoidable in the natural sciences (our most trustworthy source of ontological commitment), and hence that commitment to mathematical objects is unavoidable. However, one needn't uncritically accept the entire mathematical zoo -- natural numbers, real numbers, complex numbers, functions on such -- that such quantification seems at first sight to entail. For one can identify all such objects as sets of one stripe or another and thereby reduce the "ontological commitments [of mathematics] to an absolute minimum." Chris Menzel
Received on Monday, 1 May 2006 16:25:50 UTC