We are pleased to present the next installment of Ethics at PEA Soup. Our featured article this time around is Justin Clarke-Doane’s “Morality and Mathematics: The Evolutionary Challenge,” which is available here. We are very grateful to Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong for kicking off the discussion with the following thought-provoking post (see below the fold). Questions and comments about either Clarke-Doane’s article or the post by Braddock et al. are most welcome.
“Comments on Justin Clarke-Doane’s ‘Morality and Mathematics: The Evolutionary Challenge’” by Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong (Duke University)
In “Morality and Mathematics: The Evolutionary Challenge” (Ethics 2012), Justin Clarke-Doane raises fascinating and important issues about evolutionary debunking arguments. He argues that insofar as our knowledge of the evolutionary origins of morality poses a challenge for moral realism, exactly similar difficulties will arise for mathematical realism. Clarke-Doane concentrates on the claim that we were not selected to have true moral beliefs, which he interprets to mean that we would have evolved the very same moral beliefs even if the moral facts were radically different from what we take them to be. He argues that an analogous claim holds with respect to our mathematical beliefs: we would have evolved the same mathematical beliefs even if the mathematical facts were radically different from what mathematical realists take them to be. However, even if Clarke-Doane is correct in this, we suspect that his points miss two other kinds of evolutionary debunking arguments, which look to pose a special problem for moral realism.
First, Clarke-Doane twice quotes this claim by Sharon Street: “to explain why human beings tend to make the normative judgments that we do, we do not need to suppose that these judgments are true” (Street, “Reply to Copp”, 208). We take Street’s point to be that one can give a complete explanation of why humans tend to make certain moral judgments rather than others without ever saying anything that implies that any moral beliefs are true. This claim is only about what needs to be said in a complete explanation. It does not assume that moral truths or facts could be different than they are now. Moreover, this claim has no parallel regarding mathematics, because arguably a complete explanation of why humans tend to make certain mathematical judgments (e.g. 1+1=2) rather than others (e.g. 1+1=0) would need to say or imply that 1+1=2 and 1+1≠0. Hence, an evolutionary debunking argument based on this claim by Street understood in this way is not affected by Clarke-Doane’s points.
Clarke-Doane could reply, “for any mathematical hypothesis that we were selected to believe, H, there is a nonmathematical truth corresponding to H that captures the intuitive reason that belief in H was advantageous is plausible. By nonmathematical truth I mean a truth … that does not imply the existence of a relevantly mind-and-language independent realm of mathematical objects” (332). This quotation seems to make what we call the ontological claim: that a complete explanation of why mathematical beliefs are advantageous does not need to imply a Platonic “realm of mathematical objects.” That ontological claim is weaker than what we call the semantic claim: that a complete explanation of why mathematical beliefs are advantageous does not need to include or entail any mathematical language. The ontological claim is compatible with the falsity of the semantic claim and hence with a crucial disanalogy between mathematics and morality, if a complete explanation of why moral beliefs are advantageous does not need to include or entail any moral language. Accordingly, we will assume that Clarke-Doane is making the stronger semantic claim, despite his reference to a “realm” of “objects”.
The non-mathematical truth that is supposed to explain why some mathematical beliefs are advantageous is stated in the text like this: “If there is exactly one lion behind bush A, and there is exactly one behind bush B, and no lion behind bush A is a lion behind bush B, then there are exactly two lions behind bush A or B.” (329-30) However, this formulation clearly uses mathematical language: the terms “one” and “two”. Hence, this formulation cannot establish the semantic claim. The real work is done by another formulation that occurs only in a footnote, where “there are exactly two lions behind bush A or B” is said to abbreviate “there is an x and a y such that x is a lion behind bush A or B and y is a lion behind bush A or B and, x ≠ y, and for all z, if z is a lion behind bush A or B, then z = x or z = y.” (330, note 41) Using this method, the whole conditional in the text can be restated without mathematical language. However, it is not clear what this conditional explains. It might explain why a particular person is not eaten by a lion (or two) on a particular occasion. However, what needs to be explained is a much more general truth: people who believe that 1+1=2 survive longer and reproduce more than people who believe that 1+1=0 (or do not believe that 1+1=2). This is not about lions or indeed any particular person or situation, so it is not at all clear how to explain this general truth without stating or implying that 1+1=2. In other words, even if mathematical truths are not needed to explain survival in the lions-behind-bushes case (or the geometrical case), why infer that this holds in general?
Moreover, here is a reason for doubting the strong semantic claim. If the mathematical facts are indispensable to our best physics—if the mathematical facts make an important empirical difference—then if the mathematical facts were very different, the laws of physics would be very different. But if the laws of physics were very different, then it is doubtful that we would arrive at the same mathematical beliefs. Hence the complete evolutionary explanation of our mathematical beliefs in general needs to cite or imply their truth. Since Clarke-Doane presumably does not want his argument to hinge on the denial of the indispensability of mathematics to physics, it is at least unclear how he would support his strong semantic claim.
Second, consider a different kind of premise:
Evolutionary Unreliability: our moral beliefs are products of unreliable evolutionary processes.
Evolutionary Unreliability, on a standard understanding of process reliability, implies the following: given different instantiations of the processes that have produced our moral beliefs (and holding fixed the actual process types and actual moral truths), we could easily have arrived at mostly false moral beliefs. Notice that, again, there is no reliance here on the tricky antecedent “if the moral truths were different.” Also notice that if Evolutionary Unreliability is plausible, then we have an undercutting defeater of our moral beliefs, since accessible unreliability qualifies as such a defeater. If plausible, then Evolutionary Unreliability packs a strong skeptical punch.
Is Evolutionary Unreliability plausible (on moral realism)? It seems to cohere with standard models of the cultural evolution of moral norms and the evolutionary biases that dispose us to accept particular moral norms over others. For instance, though today many of us accept harm norms that robustly forbid harm to most or all human beings, we might have easily accepted harm norms that by our current lights are morally detestable, as many of our ancestors did, such as harm norms that liberally permit or even obligate group members to harm out-group members, children, and nonhuman animals. We might recall detestable ancient moral norms that obligated men to kill enemy warriors and enslave their women and children. Far from threatening social stability, the acceptance of such norms could easily be quite beneficial to a group, as it plunders and eliminates its competition. Such discriminatory norms also resonate with various evolutionary biases (e.g. in-group biases) with which we have been endowed. History is littered with similarly detestable moral norms. Many still exist today. These empirical considerations suggest that given different instantiations of the processes behind our moral beliefs, we could have easily arrived at mostly false moral beliefs.
Would the unreliability claim apply with equal force to our mathematical beliefs (on mathematical realism)? It does not seem so. Given greater first-order cross-historical and cross-cultural mathematical agreement than moral agreement, it is less plausible to suppose that given different instantiations of the processes behind our mathematical beliefs, we could have easily arrived at mostly false mathematical beliefs. Though these are very early days for mathematical psychology, the greater extent of mathematical agreement suggests that the processes behind our mathematical beliefs are not as contingent with respect to the content of the mathematical beliefs at which we could have easily arrived.
Thus, even if Clarke-Doane does show that some evolutionary arguments fail to distinguish morality from mathematics, a lot more work is needed to show that there is “no epistemological ground on which to be a moral antirealist and a mathematical realist” (340).