Debunking, supervenience, and Hume’s Principle

ABSTRACT

Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents a difficulty for the debunker’s claim that, had the moral facts been otherwise, our evolved moral beliefs would have remained the same.

KEYWORDS:

• Mathematics
• metaethics
• evolutionary debunking
• Hume’s principle
• supervenience

Acknowledgments

I am grateful to members of the White Rose Early Career Ethics Researchers (WRECERS) group (including Richard Yetter Chappell, Daniel Elstein, Johan Gustafsson, and Jack Woods) and of the Practical Philosophy group at York (including Rebecca Davis, Christopher Jay, and Christian Piller) for discussions of earlier versions of this paper. I am grateful also to Debbie Roberts and Alan Thomas for comments on earlier drafts. I received insightful and challenging comments from two anonymous referees and an editor for Canadian Journal of Philosophy and I thank them for their time and efforts in helping bring this paper to its published form. This research was originally carried out during a period of leave that was made possible by the Leverhulme Trust under their Research Fellowship scheme (award number RF-2016-245). I am extremely grateful to the Leverhulme Trust for supporting this research.

Notes

1. In the mathematical case, this dialectic is borne out in debates over so-called ‘makes no difference’ arguments for nominalism. Nominalists argue that, given the supposed acausal nature of mathematical objects, their existence or otherwise would make no difference to spatiotemporal going on, so that ‘if all the objects in the mathematical realm suddenly disappeared, nothing would change in the physical world’ (Balaguer, 1998, 132). On the other hand, Platonists question the intelligibility of such thought experiments (e.g. Baker 2003), holding that on their picture of the relation of mathematical to physical objects, a world with no mathematical objects (even if we can conceive of such a thing) would have to be very different indeed from our world, so much so that it may not even be intelligible to imagine our world being maths-free.

2. Compare with Arend Heyting’s character of the intuitionist (a constructivist, though admittedly not a strict finitist) in his Disputation: ‘We have no objection against a mathematician privately admitting any metaphysical theory he likes, but Brouwer’s program entails that we study mathematics as something simpler, more immediate than metaphysics. In the study of mental mathematical constructions “to exist” must be synonymous with “to be constructed”.’ (Heyting 1956, 2).

3. I am grateful to anonymous referees for this journal for drawing my attention to some examples.

4. It is worth noting that, while the supervenience of the moral on the natural is certainly widely accepted in some form or other, assent is not universal. Aside from the challenge raised by Rosen (2014), other challenges to ethical supervenience are found in, e.g. Raz (2000), Sturgeon (2009), and Roberts (2017).

5. I should note that the sensitivity of our D-beliefs to the D-facts involves more than the simple variation of D-beliefs with variation in the D-facts, since our beliefs could vary with variations in the facts while still failing to get things right about those facts. However, as the debunking argument that we are concerned with here involves the claim that, had the moral facts been different our evolved beliefs would still have been the same (and thus a claim concerning a lack of variation), we can set aside this additional complexity. I am grateful though, to an anonymous referee for raising this possibility, which could potentially be used to launch a further debunking argument even if it is accepted that changes in D-facts are likely to lead to a change in the evolutionary environment and thus a corresponding change in our evolved D-beliefs.

6. It’s perhaps worth noting that, although Clarke-Doane (2012) is aimed at arguing that, to the extent that there is a sensitivity challenge to moral realism there is an analogous challenge to mathematical realism, the paper from which this quote is taken, Clarke-Doane (2016), aims to show that we cannot in fact launch a compelling sensitivity challenge to moral realism.

7. Thus, for example, Bedke (2014, 119) argues that our belief that water is H₂O is not oblivious to the facts since if we consider the allodoxic possibility that water is not H₂O, ‘we would have a lot of explaining to do for why we have the false belief and the misleading evidence we have’. On the other hand, considering the moral claim that pain is bad, Bedke suggests that if we consider the allodoxic possibility that pain is not bad, we are not similarly at a loss for an explanation of why we have the belief that it is bad, since the badness of pain does not feature in the explanation of our belief that pain is bad.

8. I am grateful to an anonymous referee for pushing me to clarify this point, and to an editor for CJP for suggesting this example of an apparently evolutionarily irrelevant change in the supervenience base.

9. What I haven’t here argued is that the debunking challenge is best understood as taking this form. I have followed Clarke-Doane’s (2012) reconstruction of Street’s challenge in order to consider whether, if the challenge takes this form, it is a genuine one, either for moral or mathematical realists. As noted above though, there are alternative construals of the debunking argument in metaethics (including Enoch (2010), which presents the challenge as a metaethical analogue of Benacerraf’s original epistemological challenge to Platonism) that do not require that we make sense of the conceptual possibility of the moral facts being otherwise while the evolutionary environment remains the same. This paper in no way speaks to those alternative formulations of the debunking considerations.

10. The formulation of the account of number presented here is borrowed from Edward Zalta’s (2017) and (2018) presentation of Frege’s Theorem in the Stanford Encyclopedia of Philosophy.

11. These conditions are notational variants of those presented in Zalta (2018).

12. See Zalta (2018) for details.

Additional information

Funding

This research was funded by the Leverhulme Trust under their Research Fellowship scheme (grant number RF-2016-245).

Notes on contributors

Mary Leng

Mary Leng completed her PhD at the University of Toronto in 2002 before holding a Research Fellowship at St John’s College, Cambridge. She lectured at the University of Liverpool (2006–2011) before moving to the University of York in 2012, where she remains. Her research interests are in the philosophy of mathematics and science, and in particular, realism/anti-realism debates. She is currently working on analogies between debates over realism/anti-realism in the philosophy of mathematics and in metaethics.