Abstract
Perhaps one of the biggest challenges to moral realism is the Benacerraf problem. Here Justin Clarke-Doane examines this problem by reconsidering mathematical truth, and our knowledge of it. This chapter has three parts. First, Clarke-Doane argues that the Benacerraf problem for realism about an area, F, is best understood as the problem of showing that our F-beliefs are reliable. Second, he argues that there is at least one version of mathematical realism, mathematical pluralism, that can arguably answer the Benacerraf problem for mathematical realism. However, in doing so pluralism gives up on the ‘objectivity’ of mathematical truths. Third, he argues that a pluralist response to the Benacerraf problem is strangely untenable when the domain in question, F, is normative. The reason for this is that even if there were a plurality of oughts, in practical situations we can only do one thing. The question of what to do remains open even assuming normative pluralism. This shows that getting it right in normative, as opposed to descriptive, domains is not just a matter of having true beliefs. Clarke-Doane concludes with the suggestion that the notions of realism and objectivity are independent, and in tension, contrary to what has been widely supposed.
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Notes
- 1.
The word ‘objective’ can mean a dizzying variety of things, including mind-and-language independent, intersubjective, or having objects. Again, I do not mean to suggest that pluralism is anti-objectivist in any of these senses. It is anti-objectivist in roughly the sense that the theory of relativity is anti-objectivist about simultaneity. There is an independent fact about what is simultaneous with what relative to a given reference frame, R. But there are myriad reference frames, and one gets different answers to the simultaneity question by plugging them in for R.
- 2.
The foundations of mathematical pluralism—and, indeed, pluralism about other areas (see below)—are more involved than I am letting on. The question of how inclusive the ‘pluriverse’ should be is vexed. It is natural to hold that any (first-order) consistent theory is witnessed somewhere in it. But, by Godel’s Second Incompleteness Theorem, such a position engenders pluralism about (classical) consistency itself (since this says that it is consistent to say false things about consistency, if weak theories of arithmetic are consistent). And this engenders pluralism about pluralism! Moreover, the pluralist must explain our knowledge of consistency, or the surrogate of consistency to which she appeals. Such knowledge will be tantamount to mathematical knowledge (e.g., of a Π1 arithmetic sentence). For pertinent discussion , see Clarke-Doane (2020, Chap. 6) and Field (1998).
- 3.
By ‘logic’ I mean the factual theory of what follows from what. I will come back to practical questions like what we ought to infer from what below.
- 4.
Similarly, Boyd writes of his realism, that, while it is pluralist in the present sense, it ‘is only in a relatively uninteresting sense non-realistic. The dependence of the truth of moral propositions upon moral beliefs envisioned [in a scenario where different properties causally regulate “good” in different communities] would be…an ordinary case of causal dependence and not the sort of logical dependence required by a constructivist conception of morals analogous to a Kuhnian neo-Kantian conception of the dependence of scientific truth on the adoption of theories or paradigms. The subject matter of moral inquiry in each of the relevant communities would be theory-and- belief-independent in the sense relevant to the dispute between realists and social constructionists’ (Boyd 1988, 225f). While Jackson and Boyd are ‘naturalists’, normative pluralists need not be (just as mathematical, modal, and logical pluralists need not be). For example, Scanlon , a non-naturalist, advocates a view according to which ‘as long as some way of talking [is] well defined, internally coherent, and [does] not have any presuppositions or implications that might conflict with those of other domains, such as science’ such talk is true (Scanlon 2014, 27, emphasis in original).
- 5.
See also Enoch’s objection to Scanlon in Enoch (2011, 121).
- 6.
A different formulation of the argument uses the logical law of weakening (Clarke-Doane 2020). Suppose that, for example, we ought to kill the one to save the five. Now stipulatively introduce to ought-like concept, ought*, according to which we ought* not kill the one to save the five. If knowledge that we ought to kill the one to save the five settles the question of whether to on its own, then it does so in tandem with knowledge that we ought* not. But it does not. So, knowledge that we ought to kill the one does not even settle the practical question on its own. (I borrow the star notation from Eklund (2017).)
- 7.
This is exactly the moral that Blackburn draws from Moore’s argument. He concludes, ‘evaluative discussion just is discussion of what to do about things’ (1998, 70).
- 8.
Thanks to Jennifer McDonald for suggesting this way of putting the point. This response is especially compelling if Gibbard (2003) is right that the resolving attitude is intention (assuming that we cannot intend to X and ~X, at the same time). (Note that if the New Open Question Argument works, it works however one construes the facts. For instance, if the normative facts are construed ‘constructivistically’ a la (Street 2006, Section 7) or (Korsgaard 1996), then the problem becomes Enoch’s ‘agent/shmegent’ problem. Just as we can wonder whether to do what we ought1 as opposed to ought2 to do, realistically construed, we can wonder whether to be an agent or a shmagent (Enoch 2006).)
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Clarke-Doane, J. (2020). Realism, Objectivity, and Evaluation. In: Kaspar, D. (eds) Explorations in Ethics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-48051-6_3
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