I’ve been thinking about Hartry Field’s nominalist programme recently. In connection with this (and a draft of a paper I’ve been preparing for the Nottingham metaphysics conference) I’ve been thinking about parallels between the error theories that threaten if ontology is sparse (e.g. nominalistic, or van Inwagenian); and scientific revolutions.
One (Moorean) thought is that we are better justified in our commonsense beliefs (e.g. `I have hands’) than we could be in any philosophical premises incompatible with them. So we should always regard “arguments against the existence of hands” as reductios of the premises that entail that one has no hands. This thought, I take it, extends to commonsense claims about the number of hands I possess. Something similar might be formulated in terms of the comparative strength of justification for (mathematicized) science as against the philosophical premises that motivate its replacement.
So presented, Field (for one) has a response: he argues in several places that we exactly lack good justification for the existence of numbers. He simply rejects the premise of this argument.
A better way presentation of the worry focuses, not on the relative justification for one’s beliefs, but on conditions under which it is rational to change one’s beliefs. I presently have a vast array of beliefs that, according to Field, are simply false.
Forget issues of relative justification. It’s simply that the belief state I would have to be in to consistently accept Field’s view is very distant from my own—it’s not clear whether I’m even psychologically capable of genuinely disbelieving that if there are exactly two things in front of me, then the number of things in front of me is two. (If you don’t feel the pressure in this particular case, consider the suggestion that no macroscopic objects exist—then pretty much all of your existing substantive beliefs are false). Given my starting set of beliefs, it’s hard to see how speculative philosophical considerations could make it rational to change my views so much.
Here’s one way of trying to put some flesh on this general worry. In order to assess an empirical theory, we need to measure it against relevant phenomena to establish theory’s predictive and explanatory power. But what do we take these phenomena to be? A very natural thought is that they include platitudinous statements about the positions of pointers on readers, statements about how experiments were conducted, and whatever is described by records of careful observation. But Field’s theory says that the content of numerical records of experimental data will be false; as will be claims such as “the data points approximate an exponential function”. On a van Inwagenian ontology, there are no pointers, and experimental reports will be pretty much universally false (at least on an error-theoretic reading of his position). Sure, each theorist has a view on how to reinterpret what’s going on. But why should we allow them to skew the evidence to suit their theory? Surely, given what we reasonably take the evidence to be, we should count their theories as disastrously unsuccessful?
But this criticism is based on certain epistemological presuppositions, and these can be disputed. Indeed Field in the introduction to Realism Mathematics and Modality (preemptively) argues that the specific worries just outlined are misguided. He points to cases he thinks analogous, where scientific evidence has forced a radical change in view. He argues that when a serious alternative to our existing system of beliefs (and rules for belief-formation) is suggested to us, it is rational to (a) bracket relevant existing beliefs and (b) consider the two rival theories on their individual merits, adopting whichever one regards as the better theory. The revolutionary theory is not necessarily measured against we believe the data to be, but against what the revolutionary theory says the data is. Field thinks, for example, that in the grip of a geocentric model of the universe, we should treat `the sun moves in absolute upward motion in the morning’ as data. However, even for those within the grip of that model, when the heliocentric model is proposed, it’s rational to measure its success against the heliocentric take on what the proper data is (which, of course, will not describe sunrises in terms of absolute upward motion). Notice that on this model, there’s is effectively no `conservative influence’ constraining belief-change—since when evaluating new theories, one’s prior opinions on relevant matters are bracketed.
If this is the right account of (one form of) belief change, then the version of the Moorean challenge sketched above falls flat (maybe others would do better). Note that for this strategy to work, it doesn’t matter that philosophical evidence is more shaky than scientific evidence which induces revolutionary changes in view—Field can agree that the cases are disanalogous in terms of the weight of evidence supporting revolution. The case of scientific revolutions is meant to motivate the adoption of a certain epistemology of belief revision. This general epistemology, in application to the philosophy of mathematics, tells us we need not worry about the massive conflicts with existing beliefs that so concerned the Mooreans.
On the other hand, the epistemology that Field sketches is contentious. It’s certainly not obvious that the responsible thing to do is to measure revisionary theory T against T’s take on the data, rather than against one’s best judgement about what the data is. Why bracket what one takes to be true, when assessing new theories? Even if we do want to make room for such bracketing, it is questionable whether it is responsible to pitch us into such a contest whenever someone suggests some prima facie coherent revolutionary alternative. A moderated form of the proposal would require there to be extant reasons for dissatisfaction with current theory (a “crisis in normal science”) in order to make the kind of radical reappraisal appropriate. If that’s right, it’s certainly not clear whether distinctively philosophical worries of the kind Field raises should count as creating crisis conditions in the relevant sense. Scientific revolutions and philosophical error theories might reasonably be thought to be epistemically disanalogous in a way unhelpful to Field.
Two final notes. It is important to note what kind of objection a Moorean would put forward. It doesn’t engage in any way with the first-order case that the Field constructs for his error-theoretic conclusion. If substantiated, the result will be that it would not be rational for me (and people like me) to come to believe the error-theoretic position.
The second note is that we might save the Fieldian ontology without having to say contentious stuff in epistemology, by pursuing reconciliation strategies. Hermeneutic fictionalism—for example in Steve Yablo’s figuralist version—is one such. If we never really believed that the number of peeps was twelve, but only pretended this to be so, then there’s no prima facie barrier from “belief revision” considerations that prevents us from explicitly adopting a nominalist ontology. Another reconciliation strategy is to do some work in the philosophy of language to make the case that “there are numbers” can be literally true, even if Field is right about the constituents of reality. (There are a number of ways of cashing out that thought, from traditional Quinean strategies, to the sort of stuff on varying ontological commitments I’ve been working on recently).
In any case, I’d be really interested in people’s take on the initial tension here—and particularly on how to think about rational belief change when confronted with radically revisionary theories—pointers to the literature/state of the art on this stuff would be gratefully received!