Abstract
A basic way of evaluating metaphysical theories is to ask whether they give satisfying (not necessarily truthful!) answers to the questions they set out to resolve. I propose an account of “third-order” virtue that tells us what it takes for certain kinds of metaphysical theories to do so. We should think of these theories as recipes. I identify three good-making features of recipes and show that they translate to third-order theoretical virtues. I apply the view to two theories—mereological universalism and plenitudinous platonism—and draw out their third-order virtues and vices. One lesson is that there is an important difference between essentially and non-essentially third-order vicious theories. I also argue that if a theory is essentially third-order vicious, it cannot be assessed for more standard “second-order” theoretical virtues and vices, like parsimony. This motivates the idea that third-order virtues are distinct from second-order ones. Finally, I suggest that the relationship between truth, progress, and third-order virtue is more complex than it seems.
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Notes
I find it problematic to think about theories in an ‘all-or-nothing’ way—which is why I frame things here as about virtue and vice. Policing the boundaries of theoryhood so that certain theories get ruled out doesn’t help us make progress.
For defenses of Plenitudinous Platonism, see eg. Balaguer (1995, 1998), Linsky and Zalta (1995), and possibly Hale (2013, ch. 9). Beall (1999) defends a view on which not just consistent, but also inconsistent mathematical objects exist. More recent applications and discussions of this kind of view or something in its ballpark can be seen in set theory (Hamkins 2011), as well as in responses to similar challenges in metaethics in Eklund (2017), Clarke-Doane (2017) and Balaguer (forthcoming) and in the metaphysics of color (see Kalderon 2007; Mizrahi 2006). The epistemic “reliability” challenge is due to Benacerraf (1973) and Field (1989).
My sense is that all versions will fail to be third-order virtuous, but the details make a difference. For example, Linsky and Zalta’s (1995) view is arguably guiding in a way that Balaguer’s is not, but still, I suspect, baseless and not sufficiently scaffolded. But that argument is for another day.
I’m using the non-reflexive notion of parthood.
I don’t pretend that this isn’t very messy; witness the ink that has been spilled about interpretation.
While barebones MU is guiding because of its formal axioms, we don’t need formalism to meet desiderata (b). Most metaphysical theories are written in (mostly) plain natural language. There is nothing superior about having a formal theory. Indeed, if a theory is guiding because of formal axioms, the theory will require more scaffolding (in explaining how to interpret the formalism).
For example (though not all of these are endorsements!), Beebee (2015), Hawthorne (2006, introduction), Korman (2010, 2015), Noonan (2014), Quine (1981: 13), Sidelle (2002), Sider (2001) and Van Cleve (1986, 2008). Also see Fairchild (ms) for worries about (a) clarifying arbitrariness arguments and (b) whether arbitrariness arguments can actually motivate views like MU.
Not all versions of PLP are committed to this; for example, if Hale (2013) counts as a proponent, he seems to be defending a tamer version.
Readers may start wondering about the relationship between primitive terms and fundamental entities: maybe there is some theory of mathematics that can ground or secure all of the non-fundamental facts/entities that the proponent of PLP believes in (though I’m pessimistic). If so, perhaps the only primitives we need are those in the fundamental theory. But first, given the epistemic challenge that PLP is supposed to be answering, I don’t see how any proponent of PLP could possibly endorse this kind of claim, given the epistemic leaps that are required to commit to it. Second, if a theory only provides us with fundamental terms, and then instructions, then in order to be third-order virtuous, it is going to have to end up with a lot of scaffolding. Given my framework, the grounding theorist must accept that claims about “what grounds what” just are scaffolding, and hence that they show up in the theory; but much more needs to be said about what this means for evaluating theories for second-order virtue, as well as for the question of whether grounding claims are themselves grounded in the fundamental. A proponent of my framework and grounding might use Dasgupta’s (2014) strategy (note, though, his use of ‘scaffolding’ is distinct from mine—though related).
See, e.g., Lewis (1986).
The claim that it is generally accepted that it is qualitative parsimony that matters often appears in general discussions of parsimony, for example, Baker (2016, §2). Lewis (1986) appeals to it to defend against the charge of a bloated ontology. However, there are dissenters: see Nolan (1997), Baker (2003) and Jansson and Tallant (2017).
See, e.g. Kant (1781/1787, B xxx). There is lots of contemporary analytic movement back to the inseparability claim (which non-analytic philosophers perhaps never lost sight of!). Among metaphysicians this is perhaps most prominent in ameliorist philosophers like Haslanger (e.g. 2012); in social and feminist metaphysics more generally; and in Chan’s account of “ethics first” metaphysics (ms).
See Balashov and Janssen (2003, §4).
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Acknowledgements
Thanks for helpful comments and discussion to Mark Balaguer, Foad Dizadji-Bahmani, Joshua Eisenthal, Maegan Fairchild, Cindy Holder, Colin Marshall, Colin McLear, Daniel Méndez, Ned Markosian, Elizabeth Miller, Sally Sedgwick, Elanor Taylor, Mallory Webber, Alastair Wilson, to audience members at the 2019 Pacific APA meeting in Vancouver, and especially to Rachael Molenaar, to the insightful participants in my 2019 ‘Third Realm’ graduate seminar at Boston University, and to Kerry McKenzie for believing in (an early stage of, at least!) this project.
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McSweeney, M.M. Theories as recipes: third-order virtue and vice. Philos Stud 177, 391–411 (2020). https://doi.org/10.1007/s11098-019-01398-7
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DOI: https://doi.org/10.1007/s11098-019-01398-7