Abstract
W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism.
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Notes
See (1997, p. 4). Seven is the number of novels Jane Austen wrote if one includes her epistolary novel Lady Susan.
Burgess and Rosen raise some problems for a hard and fast distinction between abstract and concrete entities, but grant for the sake of argument that stereotypical examples of abstract entities such as numbers, sets, and novels are abstract. Quine also grants this: see (1960, p. 233).
See also (Burgess 2004, pp. 53–54), where Burgess clarifies this view. He says the phrase “without conscious mental reservation or purpose of evasion” is taken from legal contexts.
See (pp. 214–225).
Let me here make two points to clarify Burgess and Rosen’s views. First, Burgess and Rosen might say it is not “really” up to philosophers to assess nominalism’s merits in order to allow for exceptions to the Reliance View. Note, however, that their discussion strongly indicates that such exceptions would have to be rare; it indicates that they do not think the philosopher usually or mostly is not in a position to assess nominalistic theories even though she is in a good position in this or that kind of case. After raising the question “in what sense can philosophers proposing a revision of science claim to be judging by scientific standards, if they will not leave the merits of their proposal to be judged by practicing scientists?”, they do not specify how, in some exceptional cases, the philosopher is permitted not to “leave the merits of their proposal to be judged by practicing scientists.” But this would be what one would expect them to do if the exceptions were not rare. So, I will assume they allow for exceptions to the Reliance View at most only rarely. Second, notice that Burgess and Rosen do judge, as philosophers, that nominalism has demerit—they believe they are committed to its falsehood. The Reliance View is about who is best posed to assess changes to that commitment. In order to change that commitment and so endorse nominalistic theories, someone has to assess them. The Reliance View says that mathematicians and physicists, and not philosophers, are in a position to assess those proposed changes.
Daly and Liggins (2011) criticize Burgess, Rosen, and Lewis’ argument (what they call ‘the track record argument’) on different grounds. Paseau (2005) also criticizes their argument (what he calls the ‘Failure Argument’); however, he criticizes it as an argument for reinterpreting the content of mathematical theories by means of philosophical norms. I am arguing for something different: their argument does not support the claim that a philosopher who uses scientific standards could not assess the merits of revising mathematical theories themselves. In Sect. 6 of Paseau (2007), Paseau also criticizes Burgess and Rosen’s appeal to science journals as a test of the scientific merits of nominalism. As he reads it, Burgess and Rosen think that “whether scientific grounds vindicate nominalism can simply be determined by submitting a nominalist construal of some scientific theory (e.g. Hartry Field’s nominalization of Newtonian mechanics) to a scientific journal” (p. 138). Paseau argues against this, concluding that “[f]ailure of the publication test (or a fortiori of the publication-and-reception test) is no touchstone of scientific inferiority” (p. 139). While I agree with Paseau, I here assume that Burgess and Rosen’s “publication test” is not one of their reasons for the Reliance View. I instead think their test indicates that they hold the Reliance View, but I assume they hold it for different reasons.
See, for example, Quine (1960, pp. 12–13).
See (Quine 1960, pp. 176–186) for Quine’s motivations for eliminating proper names, one of which is to resolve problems arising from using proper names such as ‘Pegasus’ lacking a referent.
Note that Quine does not provide strict criteria for what counts as a good recipe for systematic replacement.
This explication of what it is to commit oneself to the existence of things is informal, since for Quine implication is defined over formulae on the basis of a definition of satisfaction within a meta-language mentioning those formulae. See (Quine 1980) for details.
Paraphrases such as these which systematically replace expressions within sentences such as ‘is 0’ and ‘is a natural number’ with other expressions within sentences are what Quine calls explications—see (Quine 1960, pp. 257–262).
As he explains in his intellectual autobiography: “We settled for a formalistic account of mathematics, but still had the problem of making do with an inscriptional proof theory in a presumably finite universe” (1986, p. 26).
Quine and Goodman’s nominalism does not require much knowledge of what mathematics is required in science, except for knowledge of proof theory. Since all platonistic theories are treated as meaningless marks described in nominalistic proof theory, it does not matter what platonistic theories are needed for science, as any platonistic theory is replaced by a nominalistic description of proofs of sentences in those theories. By contrast, Hartry Field’s nominalistic proposal in Science without Numbers to replace platonistic theories with theories of concrete geometrical objects requires detailed knowledge of physics. Interestingly, in the second edition to Science without Numbers (Field 2016), Field provides a letter from Quine in 1980 praising the first edition of the book, in which he says:
[Your book] is an impressive piece of work: reasonable, ingenious, learned and as central philosophically as can be. Moreover it appeals to my predilections, for, as you must know, I am a nominalist manqué from away back, and a reluctant Platonist only in honest recognition of what have seemed to be the demands of science. (p. 55).
Let me here note that Quine’s dispute with Burgess and Rosen’s Reliance View does not presuppose, as Quine sometimes seems to do in his work, that the empirical sciences take prevalence to some degree over the mathematical sciences. Whatever the relation between these two kinds of sciences, the philosopher for Quine is a participant in them who in some cases is best positioned to make revisions to them.
Thanks to two anonymous reviewers for motivating the second reading of Burgess and Rosen I give above and pressing me to state how that reading relates to Quine’s views.
See also (Paseau 2013), where he suggests that naturalism is an “anti-revisionist” doctrine.
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Acknowledgements
An early version of this paper was presented at the Society for Exact Philosophy conference in 2017 at the University of Calgary. Thanks for comments on various versions of this paper go to Daniel Buckley, Daniel Linsenbardt, Kirk Ludwig, Sean Murphy, Wade Munroe, Levi Tenen, and Ivan Verano. Special thanks go to Gary Ebbs for his invaluable feedback and constant support.
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Smith, J.A. Quine on naturalism, nominalism, and philosophy’s place within science. Synthese 198, 1549–1567 (2021). https://doi.org/10.1007/s11229-019-02143-7
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DOI: https://doi.org/10.1007/s11229-019-02143-7