Cuconato on Quinean Indispensability and Commitment

Cuconato, S. (2022). Impegno ontologico e l’argomento di indispensabilità in filosofia della matematica. : Il Sileno Edizioni.

I read this booklet (main text is 63 pages) because it’s in a current area of interest, was freely downloadable, and gave me a chance to practice my Italian. As the title suggests, it’s about the relationship between ontological commitment and indispensability arguments in mathematics. The goal of the booklet doesn’t seem to be to break any new ground on these subjects, but rather to explicate and clarify. With a few qualifications that I’ll get to, it would make a nice introduction to the subject for readers of Italian.

Start with indispensability: If we wish to inventory the universe in the broadest sense, it’s natural to begin with a notably successful human endeavor, science. Our best scientific theories explain by positing entities and relationships between them, and we might think that if the theories themselves are justified, then so too are the entities they posit.

But scientific theories happen to be stated using quite a bit of mathematics, and mathematics is filled with claims that are also stated in existential language (“There is exactly one prime number”). Well, if existential language then perhaps . . . existents? But mathematical objects, if they exist, are even stranger than quarks: non-spatio-temporal and acausal, yet somehow supposedly accessible to and discoverable by the wet gunk in your skull. But if we can’t state a scientific theory without all that math, isn’t the math part of the theory itself and so tangled up with its overall commitments? The Quine-Putnam Indispensability Thesis is just the argument that we’re justified in believing what our best scientific theories say exist, our best scientific theories include mathematics as an indispensable part, so taking our best scientific theories of the world seriously requires us to recognize mathematical objects, however strange, among the things that exist.

This quick and inadequate sketch of the position has flown by a number of critical choicepoints and doesn’t really convey how much work it is to develop this view into something respectable. The relation between mathematics and the scientific theories that draw on it has been an area of fierce controversy in analytic metaphysics, especially over the last 75 years. Quine himself held a strong version of confirmational holism, which makes mathematics and science (and philosophy, etc.) out to be parts of one continuous whole, standing or falling together, but this view (which helps to motivate Quine-Putnam indispensability) has largely fallen out of favour.

More enduring (though still endlessly disputed) is Quine’s attempt to give a more rigorous way of understanding ordinary language existential claims, to clarify which ones are genuinely ontologically committing and which ones are not. The role this plays in Quine-Putnam indispensability arguments is to provide a particular, precise way of understanding exactly when ordinary language claims are and are not committing. In a nutshell, Quine’s strategy is to regiment ordinary language discourse into classical first-order predicate logic and then read off the ontological commitments of the discourse from the domain. The existential quantifier that we meet in first year logic classes becomes the star of the show here, capturing no more or less than what philosophy can hope to say about existence.

Cuconato begins with indispensability and various ways of formulating the view, pans out to situate it in broader historical context, and then looks at Quine’s specific criterion of ontological commitment and later neo-Quinean approaches like van Inwagen’s. It’s a lot to cover in 63 pages, but the basics are pretty well covered. Usually, they’re covered in a way friendly to relative beginners, though there are a few places that made me wonder about the intended audience. E.g., the quick definition of completeness on p. 50, or the amount of detail in Cuconato’s exposition of Field’s attempt to nominalize a fragment of Newtonian physics. There were also a few places where the book had the feel of something condensed from a much longer text in ways that hurt clarity. One example: I thought the page devoted to Church’s alternative approach to Quinean commitment was a bit tricky to follow and not well integrated with the rest of the text.

Perhaps the biggest reservation I had is that in giving a nice survey of Quinean metaontology the booklet risks leaving an unsuspecting reader with a distorted sense of the full range of live metaontological alternatives to Quine. Quinean metaontology was without question the dominant approach for the second half of the twentieth century. But by the mid 90s, it all started to fall apart. There’s no mention in Cuconato’s survey of Thomasson or easy ontology, of Yablo, of Hirsh’s quantifier variance or any of the other broadly neo-Carnapian alternatives to Quine that have flourished since Quine’s dominance started to recede (indeed, no mention anywhere of Carnap, an important foil and influence for Quine as he developed his own views). A single paper of Azzouni’s made it into the bibliography but is not actually cited in the main text. Cuconato’s historical survey mentions the Aristotelian tradition and its view of categories of being as a significant alternative to Quine’s approach to existence, but he does not mention McDaniel’s and Turner’s 21st century revival of ontological pluralism. As the book closes, Cuconato mentions the flatness of Quine’s ontology, guesting at the now-vast 21st century literature on grounding and dependence. But a beginner could easily miss a) how many alternatives to Quinean metaontology have emerged in the last 30 years; and b) how far out of favour Quine’s metaontology has fallen, in spite of (inevitably) some hold outs.

It would be churlish and unfair to complain that a booklet fails to cover all these topics outside of its main theme (especially when it succeeds in being so wide-ranging). So let me clarify that this is not what I’m trying to do! My suggestion is just that it would have been good to briefly situate Quinean metaontology in this broader context in order to give readers a fuller sense of the options in the space, and to underline that, especially as this century has unfolded, Quinean metaontology has gone from being the “standard view” to being something more like the underdog.

Two minor points: First, shouldn’t “o che il vocabolario di 𝑆 è indispensabile per 𝑆” on p. 53 be “o che il vocabolario di 𝑇 è indispensabile per 𝑆”? Second, (not of course in any way a criticism of Cuconato) Cuconato mentions Malament’s point against Field that quantum mechanics makes indispensable reference to complex numbers. By coincidence, while reading Cuconato I happened to notice this development from 2025. I’m not currently qualified to judge the dispute, but it made me wonder if Malament’s influential line of argument might need to be updated.