Ethics Discussions at PEA Soup: Justin Clarke-Doane’s “Morality and Mathematics: The Evolutionary Challenge” with commentary by Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong

24 Replies to “Ethics Discussions at PEA Soup: Justin Clarke-Doane’s “Morality and Mathematics: The Evolutionary Challenge” with commentary by Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong”

1. Thanks to Justin for a very interesting paper, and to Matthew, Andreas and Walter for their illuminating commentary.
   Justin argues that the evolutionary challenge for moral realism doesn’t depend on the claim that:
   (1) our moral beliefs are actually the products of evolutionary forces.
   All it requires, he says, is the weaker conditional claim that:
   (2) if our moral beliefs were indeed the products of evolutionary forces, then those forces would have been non-truth tracking and we would not have been selected to have true moral beliefs,
   along with the claim that:
   (3) it is intelligible to imagine the basic moral truths being very different.
   But this puzzles me in a couple of different ways. First, let’s grant Justin’s point that 2 by itself is sufficient to establish:
   (4) we were not selected to have true moral beliefs.
   This is clearly right, since 4 is true whether the antecedent in 2 is true or false. But all 4 tells us is that realists cannot explain our having largely true moral beliefs by claiming that we were selected to have true moral beliefs; they’ll obviously need some other explanation. But that doesn’t yet amount to an “evolutionary challenge to realism” in the usual sense. The realist can just hold that our moral beliefs are not in fact products of evolution (thus denying 1), and seek to explain our coming to hold largely true moral beliefs by instead telling some other story about our current employment of truth-tracking methodologies (shaped not by evolutionary forces, but by cultural development and intelligent reflection) to arrive at moral truths (much as we think we do with respect to metaphysical truths, say, through engaging in sound, culturally developed reasoning to arrive at the belief that water is necessarily H20, etc.). Nor does the addition of 3 turn 4 into an evolutionary challenge (more on 3 in a minute).
   Without 1, we have no evolutionary challenge to realism per se: all we have is a blocking of one possible (bad) way a realist might have tried to explain our having true moral beliefs. As a realist, that doesn’t bother me in the least, since I was never inclined to look to evolution to explain why we have largely accurate moral beliefs (or beliefs about metaphysics, etc.). But it would bother me very much if 1 were indeed true, as Street claims, because given 2 this would then give rise to just the epistemological problems Street raises for realists. So 1 does seem crucial to the real evolutionary challenge to realism.
   Second, I am puzzled by the claims about the importance of 3. I see 3 as having very little significance to this debate. It comes in peripherally insofar as its falsity would preclude a certain way of arguing for claims like:
   (5) Even if the basic moral truths had been very different, we would still have had the same basic moral beliefs we actually have, or
   (6) If the basic moral truths had been very different, we would have had correspondingly different moral beliefs.
   That is, if 3 is false, then it will be hard to understand and evaluate claims like 5 or 6. But that shouldn’t worry either the evolutionary debunker or the realist because they don’t need 5 or 6 to make their central claims and arguments. (Here I am agreeing with one of the points in the commentary.) Suppose I reject 3. While I’ll then balk at a claim like 5, I can still understand and appreciate the implications of Street’s claim that the actual etiology of our moral beliefs was insensitive to moral truths as such: they were caused simply by evolutionary forces having to do with genetic propagation, which has no general connection with the realist’s moral truths. This etiological claim is sufficient to entail that the forces that gave rise to our moral beliefs were not truth-tracking and that our beliefs are thus unreliable (though of course I reject that etiological claim to begin with).
   So Street’s argument doesn’t depend on a counterfactual like 5 for its intelligibility or force: the claim about insensitivity to moral truths in the actual etiology of the beliefs, together with the claim about the lack of alignment between what’s relevant to natural selection and what’s relevant to the real values I believe in, is enough to generate Street’s challenge. Similarly, if I want to propose my own account of how our moral beliefs are the products of (non-evolutionary) truth-tracking processes, I needn’t rely on 6 (and therefore 3), contrary to the claim on 324. All I have to do is to provide an account of how the moral truths figure into the actual etiology of our moral beliefs via whatever truth-tracking processes we’ve developed, pace Street: it’s no strike against me that I can’t go on to assert 6 simply because I think the truths are metaphysically necessary and can’t intelligibly be imagined to be otherwise. At most it might be argued that I’m committed to a weaker claim like:
   (6’) Insofar as it’s intelligible to imagine the basic moral truths having been very different, had they been very different we would have had correspondingly different moral beliefs.
   That’s okay, but it doesn’t commit one to 3, and it really just amounts to a heuristic—a way of highlighting the real point about the sensitivity (or insensitivity in the case of the corresponding 5’ for the evolutionary debunker) of the belief-forming processes to the moral truths.

2. Response to Braddock, Mogensen, and Sinnott-Armstrong – Part I
   I am grateful to Matthew Braddock, Andreas Mogesen, and Walter Sinnott-Armstrong (henceforth, “BMS”) for their thoughtful and incisive comments on my paper. They conclude:
   “[E]ven if Clarke-Doane is correct [that we would have evolved the same mathematical beliefs even if the mathematical facts were radically different from what mathematical realists take them to be] we suspect that his points miss two other kinds of evolutionary debunking arguments, which look to pose a special problem for moral realism.”
   In what follows, I try to respond to all of BMS’s arguments. I begin with a discussion of the first kind of evolutionary debunking argument which my points are supposed to miss. I then turn to the second such argument and conclude with a suggestion that BMS make along the way.
   The first kind of evolutionary debunking argument which my points are supposed to miss says that we “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.” The key difference between this “evolutionary debunking argument” and the one that I discuss is that, unlike the latter, “[t]his…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.”
   I tried to address this suggestion by distinguishing Harman’s argument from the evolutionary argument (see 324, fn. 31, 328-9, 334, and 339-40 of my paper). The argument outlined above is just an application of Harman’s from _The Nature of Morality_. Harman argues there that, unlike our scientific beliefs, our moral beliefs cannot be justified “by their role in explaining observations [including “moral observations”] (p. 10).” This argument is widely taken to imply that we “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.”
   Neither Joyce nor Street can be sympathetically interpreted as merely applying Harman’s argument (no matter how often they may appear to be doing this). Both Joyce and Street explicitly take as their primary targets what are sometimes called “non-naturalist” moral realists — such as Dworkin, Enoch, Nagel, or Parfit — who *grant* Harman’s argument (see Street [2006] or Joyce 2006, Ch. 6). Indeed, Joyce explicitly takes such moral realists as his *only* targets.
   But set aside how we ought to read Joyce and Street. Could the above argument “debunk” our moral beliefs? In answering this, recall that debunking arguments are supposed to *grant* that our moral beliefs are defeasibly justified. Such arguments do not merely purport to show that our moral beliefs lack justification that even an antirealist would accept (notoriously, even our *perceptual* beliefs seem to lack this kind of justification). Such arguments purport to *undermine* whatever (defeasible) justification our moral beliefs are assumed to already enjoy. Joyce writes,
   “My contention…is that moral nativism…might…render [our moral beliefs] unjustified….In particular, any epistemological benefit-of-the-doubt that might have been extended to moral beliefs…will be neutralized by the availability of an empirically confirmed moral genealogy that nowhere…presupposes their truth (2008, 216).”
   How might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs *undermine* those beliefs? One way is by showing that our moral beliefs are not *sensitive* to the moral truths in the sense that had the moral truths been different, our moral beliefs would have been the same. But the above evolutionary argument is meant to avoid the assumption “that moral truths or facts could be different than they are now”. Another way that the relevant genealogical claim might undermine our moral beliefs is by showing that our moral beliefs are not *safe* in the sense that, holding the moral truths fixed, our moral beliefs might have easily been different (and thereby false). But this is the foundation of the second evolutionary argument that BMS claim that I miss (to be discussed below). Unless the first argument presupposes the second, the first must allow that our moral beliefs are safe.
   Could “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs undermine those beliefs *even under the assumption that our moral beliefs are both sensitive and safe?* I do not see how. If we can show that our moral beliefs are both sensitive and safe then we could show that they were *bound* to be true.
   (What if one could go on to argue that it would be a “massive coincidence” that our moral beliefs were true? How could a “massive coincidence” *which in no way calls into question the reliability (sensitivity or safety) of our moral beliefs* undermine those beliefs? I cannot see.)
   I do not mean to suggest that Harman’s argument has no epistemological significance. On the contrary, if sound, it plausibly shows that *whatever (defeasible) justification our moral beliefs enjoy is not empirical justification.* This conclusion is dialectically significant. As Field writes of our mathematical beliefs, “[t]he only non-question-begging argument for the view that mathematics is a body of truths…rests ultimately on the [role of mathematics in explaining observable phenomena] (1980, viii).” But, as Field also recognizes (1989, p. 26), this dialectical point is insufficient to *undermine* any a priori justification our mathematical beliefs might enjoy. In order to do that, he thinks, one must argue that “we would have had exactly the same mathematical…beliefs even if the mathematical…truths were different…[T]his undermines those beliefs (2005, 81).” This argument is just the argument on which BMS claim not to rely.
   Note that, if I am right in the above, then I need not deflect the worry that “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.” Even if this were true, it would at most show that our mathematical beliefs enjoy (defeasible) empirical justification (see p. 328-9 of my paper). It would not show that whatever (defeasible) justification our moral beliefs enjoy is undermined in a way in which the defeasible justification that our mathematical beliefs is not. Nor would it threaten my argument that it would have benefitted our ancestors to have the same mathematical beliefs even if the mathematical truths were radically different (or even if there were no atomic or existentially quantified such truths at all).
   Nevertheless, the relevant worry is doubtful, and it might be useful to say why. As BMS note, I give a recipe in my paper for explaining the advantage of believing mathematical truths without assuming any mathematics (see p. 330 – 332). In the case of arithmetic, the strategy is to cite corresponding (first-order) logical truths about objects in our environments, rather than citing arithmetic truths. In the case of geometry, the strategy is to cite corresponding truths about spacetime, rather than citing geometric truths. But BMS suspect that such truths are not sufficiently general. They illustrate their concern in the case of arithmetic. First-order logical truths of the relevant sort are invariably about concrete objects of a given kind, such as lions or cliffs. But in order to explain the general fact that people who believe that 1 + 1 = 2 do better than those who do not, it is insufficient to cite a given corresponding (first-order) logical truth about lions, say. The fact that if there is “exactly one” lion to the right, and there is “exactly one” lion to the left, and no lion to the left is a lion to the right, then there are “exactly two” lions to the left or to the right (where “exactly one” and “exactly two” here are abbreviations for constructions out of ordinary quantifiers plus identity) does not explain the general fact at issue.
   The suspicion is fair so far as it goes, but it does not point to an objection to the basic approach. First, it does not even arise prima facie in the case of geometry. One can explain the general fact that people who believe that the shortest distance between two points is a straight line do better than those who believe some alternative to it on the general grounds that the shortest distance between two points of spacetime approximates a straight line. Second, as I suggest on pages 332 and 338, any arithmetic explananda which are not covered by the first-order logical truths mentioned can obviously be covered by corresponding mereological or impure set-theoretic truths. Perhaps they can even be covered by other logical truths. We might ascend to second order logic. Believers in 1 + 1 = 2 did better than believers in its alternatives because, for any properties F, G, and H, if there is “exactly one” F that is G, and there is “exactly one” H that is G, and no F is an H, then and there are “exactly two” Fs or Hs that are G (I prefer mereological or impure set-theoretic truths to such truths for reasons alluded to in fn. 41). Alternatively, if we are content with schemas, rather than truths per se, then we might make do with first-order logical explanans alone (take the second-order truths just mentioned and remove the second-order quantifiers). No matter how we proceed, we will not need to invoke mathematical truths.
   To sum up: the first kind of evolutionary debunking argument which my points are supposed to miss is really no “debunking” argument at all. It is a simple application of Harman’s argument. But no matter what kind of argument it is, it works equally against mathematical realism.

3. Response to Braddock, Mogensen, and Sinnott-Armstrong – Part II
   What of the second argument which my points are supposed to miss? According to that argument, “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.” The key difference between this argument and the one that I discuss is that “again, there is no reliance here on the tricky antecedent “if the moral truths were different.” What exactly is this argument claiming? In personal correspondence, BMS clarify:
   “[D]ifferent instantiations of the process of cultural group selection [for example] have produced divergent normative systems, which nonetheless solve the same design-problem: namely, that of getting human societies to function as adaptive corporate units. In this way, one and the same process type may, through its various instantiations, easily result in divergent moral systems.”
   (In a follow up, BMS clarify that “the…argument…in our post need not focus exclusively on distal processes, nor need it be committed to empirical claims regarding group selection.)
   The importance of this argument is apparently that, if sound, it shows that our moral beliefs are not *safe* in the aforementioned sense. We might have easily had false moral beliefs, not because the moral truths might have easily been different, but because our moral *beliefs* might have easily been different. Knowledge of this contingency, in turn, arguably undermines those beliefs.
   I discuss the argument that our moral beliefs might have easily been different on p. 319 – 320 of my paper. As I observe there, Darwin’s own “debunking argument” seems closer to this one. But, as I also observe, there is an obvious problem with the argument. Prima facie our *core* moral beliefs could *not* have easily been different. As I put it, “[p]rima facie creatures who believed that pain is good and that pleasure is bad would be less successful at passing on their genes than creatures that believed the opposite (p. 320).” Indeed it is just this line of thinking that Sharon Street takes to help show that our moral beliefs are the products of evolutionary forces in the first place. Street writes, “among our most deeply and widely held judgments, we observe many…with exactly the sort of content one would expect if the content of our evaluative judgments had been heavily influenced by selective pressures (2006, 116).” To the extent that selective pressures, or other evolutionary forces, fail to constrain the contents of our moral judgments, it is hard to see how the fact that our moral judgments have the contents that they do would confirm that they are products of evolutionary – rather than any number of other — forces.
   BMS may not have intended to make the doubtful suggestion that our core moral beliefs could have easily been different. They conclude that “we could easily have arrived at *mostly* false moral beliefs”. Might the above argument still undermine our *non-core* moral beliefs? There is a natural argument for the negative answer. In the present context, the reliability of our abductive methodology is not in doubt. But given the safety of our core moral beliefs, and given the safety of our abductive methodology, there is a “bootstrapping” argument for the safety of our moral theories. Here it is: our core moral beliefs are safe; our moral theories “follow” from those via principles of abduction; our belief in the principles of abduction is safe; so, our belief in our moral theories is safe (obviously, one would need some closure principle — which I will not attempt to formulate here, but assume is relevantly benign — in order to complete this argument).
   It might be responded that something must be wrong with this argument. The existence of pervasive disagreement over non-core moral matters shows that our non-core moral beliefs could have easily been different – that they are *not* safe. What it actually shows is that, contrary to the above assumption, our *abductive methodology* – which takes us from our “core” beliefs about a subject to a corresponding theory – is not safe. But if *this* conclusion undermines our moral theories, then it undermines our theories generally. In particular, it undermines our mathematical theories (while mathematical “axioms” are logically primary, they are epistemically secondary, arrived at by something like an inference to the best explanation).
   To sum up: the second kind of evolutionary debunking argument which my arguments are supposed to miss either fails against moral realism or works against mathematical realism too.
   In closing, let me mention a brief remark of BMS which suggests that not even the antecedent of the conditional for which they argue is true. They offer the remark in defence of the view that (what I have argued is) Harman’s argument does not work equally against mathematical realism. But the remark is actually relevant to the argument that I discuss. They write,
   “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.”
   Note that this argument is conditional on the assumption that mathematics is indispensable to our best physics. Whether that is true is comparably contentious as whether Harman’s argument is sound. But suppose that mathematics is so indispensable. In order to be at odds with the upshot of my paper, BMS’s conclusion must be that had the mathematical truths been very different, it would have benefitted our ancestors to have correspondingly different mathematical beliefs. In order to derive this conclusion from the assumption that mathematics is indispensable to our best physics, however, BMS must assume a hypothesis like the following. It would have benefitted our ancestors to believe mathematical hypotheses which are indispensable to our best physics.
   I will resist any sweeping claims about the relevance of indispensability considerations to debunking arguments. But I assume that few if any indispensabilists would be comfortable with the hypothesis at issue (for critical discussion, see Field [2005], p. 78-81; Field [1989], p. 28-30).
   Works Cited
   Field, Hartry. [1980] Science without Numbers. Princeton: Princeton University Press.
   —–. [1989] Realism, Mathematics, and Modality. Oxford: Blackwell.
   —–. [2005] “Recent Debates about the A Priori.” in Gendler, Tamar and John Hawthorne (eds.) Oxford Studies in Epistemology, Vol. 1. Oxford: Clarendon Press. 69 – 88.
   Harman, Gilbert. [1977] The Nature of Morality: An Introduction to Ethics. New York: Oxford.
   Joyce, Richard. [2006] The Evolution of Morality. Cambridge: MIT Press.
   —–. [2008] “Precis of Evolution of Morality and Reply to Critics.” Philosophy and Phenomenogical Research. Vol. 77. 213 – 67.
   Street, Sharon. [2006] “A Darwinian Dilemma for Realist Theories of Value.” Philosophical Studies. Vol. 127. 109 – 166.

4. Quick correction: In my earlier post I said, just before proposition 5, that “I see 3 as having very little significance to this debate. It comes in peripherally insofar as its falsity would preclude a certain way of arguing for claims like 5 and 6…” What I meant to say was that 3 comes in peripherally insofar as its falsity would preclude using claims like 5 or 6 in mounting the evolutionary challenge or responses to it, respectively. And then the claim is that while this is interesting, it doesn’t ultimately matter much, because the real arguments on each side don’t have to rely on claims like 5 or 6.

5. First off, I’d like to thank Justin for his detailed response. I hope to be able to reply to a number of the points he makes. I’ll start off by discussing an issue raised in part I of his reply.
   We suggested that evolutionary accounts of morality pose a challenge for morality which has no analogue in the mathematical case, because it seems that when it comes to evolution and morality “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,” whereas it seems that mathematical claims will have to be presupposed in any scientific account of our mathematical beliefs. Absent doubts about the indispensability of mathematics to science, this sets up an important disanalogy between morality and mathematics.
   In reply, Justin asks:
   “How might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs undermine those beliefs?”
   Justin suggests that there are two ways in which it might be thought to do so. The availability of such an explanation might give us reason to deny that our beliefs are sensitive. On the other hand, it might give us reason to deny that they are safe. He suggests that this exhausts the possibilities. I am not sure about this.
   Let’s consider the following case. I am told by someone whose testimony I am ordinarily entitled to trust that chemical substance C has composition XYZ. So I believe this. I later learn that this person told me this for the following reason: the day before, she was hit on the head, causing a pattern of neurological damage which, for some reason, causes everyone with such damage to believe that C is XYZ. (It just strikes them as obviously true, the way ‘Nothing is both red all over and green all over’ strikes me as obviously true.) Thus, I get evidence that if C is XYZ this is (most likely) explanatorily irrelevant as to my believing it. This, intuitively, is defeating.
   Now, it cannot be defeating because it provides a reason to believe that my belief is unsafe. A belief formed via method M is unsafe if forming a belief on the matter using M in nearby possible worlds leads to a false belief. I can’t have reason to believe that this is the case in the example describe. Why not? Well, if C is XYZ, then this is necessary true. So the only way in which relying on the kind of testimony involved in the above example could lead to a false belief in a nearby possible world is if C is not XYZ in the actual world. (If it is in the actual world, it will be in all nearby possible worlds, and so I can’t go wrong in relying on the testimony in question.) Hence, if I had reason to believe that my belief was formed via an unsafe method, I would have reason to deny that C is XYZ. But I don’t.
   What about sensitivity? Do I have reason to deny that If C were not XYZ, I would not believe it. Note that if I have reason to deny this, then I have reason to deny the following principle, which many philosophers (e.g. David Lewis) have thought correct: A subjunctive conditional with a necessarily false antecedent is trivially true. But plausibly I am given no reason to deny this by my discovery in the above scenario. This has the air of trickery about it, so let me add the following point. I think that having reason to deny that your belief is sensitive is not defeating at all. If it were, then I would not be justified in believing that I am not a brain in a vat, and so I would not be justified in believing that I have hands, am seated at a computer, etc. So even if you did have reason to deny that your belief was safe, this couldn’t be the source of defeat.
   So there must be something that is defeating in my discovery that is not to do with safety or sensitivity. Now, a lot more could be said about this, but I would propose that something like the following principle is likely to be true and explains the case:
   S’s belief that p is subject to an undercutting defeater to the extent that S has reason to believe that the explanation of why she believes p provides no reason to believe p.
   This principle seems to explain the case we have been considering: what explains my belief is that my friend got a knock on the head which made C is XYZ intuitively attractive to her, and that is no reason to believe that C is XYZ! And I think this principle answers Justin’s question. It seems to me that if we have a sufficiently complete explanation of our believing some moral proposition and no moral claims are cited in that explanation, then the explanation provides no reason to believe the proposition in question, since it provides no reason to believe any moral proposition: no moral claim could be inferred from the explanation by deduction, by abduction, or by any other form of inductive inference. So, by the principle proposed, the availability of an empirically confirmed moral genealogy that nowhere presupposes the truth of any moral beliefs undermine those beliefs.
   That is my longwinded and rather tentative suggestion. I expect that some may raise doubts about the claim that if we have a sufficiently complete explanation of our believing some moral proposition and no moral claims are cited in that explanation, then the explanation provides no reason to believe the proposition in question. However, I’ve gone on at some length now, so I’ll draw this post to a close.

6. Braddock – Post Re: Debunking Arguments and the Intelligibility of Moral Truths Being Very Different
   William Fitzpatrick is puzzled by the alleged importance of the following claim:
   Intelligibility: “It is intelligible to imagine the basic moral truths being very different.”
   With Clarke-Doane, I can see how the Intelligibility claim, if true, precludes the realist from invoking certain “trivial explanations” of our having many true moral beliefs, i.e. explanations of “our having many true moral beliefs in terms of the hypothesis that it is unintelligible to imagine the moral truths being very different” (324). But Fitzpatrick rightly points out that debunking arguments don’t need to rule out trivial explanations and thus don’t need to rely on the Intelligibility claim.
   That said, *some* debunking arguments may rely on the claim that we no plausible explanation of our having many true moral beliefs (e.g. Consider Field-style Argument and IBE Argument sketched in my previous post). Moreover, Street’s argument, as an interpretive matter, may rely on this claim, even if it is not essential to the *force* of her argument.
   So it is worthwhile to ask why we should accept the Intelligibility claim. Clarke-Doane thinks that it follows from a crucial premise of the Evolutionary Challenge that he ascribes to Sharon Street and others, namely
   Non-Truth-Tracking: if we were selected to have certain moral beliefs at all, then we would not be selected to have true moral beliefs.
   A central conclusion of Clarke-Doane’s article is that the truth of Non-Truth-Tracking “establishes that there is no evolutionary or trivial explanation of our having many true moral beliefs” (326). I want to question that conclusion in what follows.
   Why does Clarke-Doane think that Non-Truth-Tracking “establishes” that there is no trivial explanation of our having many true moral beliefs? The argument is located on pp. 325-26. He reasons that Non-Truth-Tracking “carries with it the conclusion that it is intelligible to imagine the moral truths being very different because it intuitively implies the counterfactual that if we were selected to have certain moral beliefs at all, and if the moral truths were very different, we still would have had the same moral beliefs” (325-26).
   But I do not see how Non-Truth-Tracking “carries with it” the Intelligibility claim.
   Clarke-Doane’s explicitly articulated inference in the passage is this:
   FROM:
   P1: Non-Truth-Tracking: if we were selected to have certain moral beliefs at all, then we were not selected to have true moral beliefs.
   AND
   P2: If we were selected to have certain moral beliefs at all and if the moral truths were very different, we would still have the same moral beliefs.
   TO:
   C: It is intelligible to imagine the moral truths being very different.
   An implicit premise between P1 and P2 appears to be this claim that Doane-Clark accepts (see pp. 319-320):
   P1.5: IF we were not selected to have true moral beliefs, THEN if the moral truths were very different, we would still have the same moral beliefs.
   Together P1 and P1.5 imply P2. But how to get to C? How to get to the Intelligibility claim? My attempts to work it out myself have failed. So my (defeasible) hunch is that we can’t plausibly get from Non-Truth-Tracking to Intelligibility. If so, then the Non-truth-tracking premise does not rule out trivial explanations of our having many true moral beliefs. If it does not do this, one begins to wonder whether Non-Truth-Tracking does interesting work.
   To be sure, Clarke-Doane importantly shows that at best Non-Truth-Tracking rules out evolutionary and trivial explanations of our having mostly true moral beliefs, not *all* explanations—-and this only if the mathematical realist is similarly denied access to evolutionary and trivial explanations. But it is at least unclear to me how Non-Truth-Tracking plausibly rules out trivial explanations.

7. Braddock’s Response to Clarke-Doane, Part I
   Kind thanks to Justin Clarke-Doane for his stimulating and insightful comments, and for his excellent article. Let me offer a response here to Part I of his response.
   Clarke-Doane asks:
   “How might ‘the availability of an empirically confirmed moral genealogy that nowhere… presupposes’ the truth of our moral beliefs *undermine* those beliefs?….. Could “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs undermine those beliefs *even under the assumption that our moral beliefs are both sensitive and safe?* I do not see how.”
   Clarke-Doane concludes:
   “To sum up: the first kind of evolutionary debunking argument which my points are supposed to miss is really no ‘debunking’ argument at all. It is a simple application of Harman’s argument. But no matter what kind of argument it is, it works equally against mathematical realism.”
   A response:
   A variety of debunking arguments could deploy the Harman premise—-i.e. that we can completely explain our moral judgments without presupposing their truth-—to undermine our moral judgments, and might do so without assuming that the moral truths could have been different, even under the de facto (unknown) assumption that our moral beliefs are both sensitive and safe.
   Here are three arguments that come to mind:
   (1) Field-style Argument: The Harman premise says that moral facts do not explain our moral judgments. Moral realism says that moral judgments do not explain the moral facts. If the moral facts and our moral judgments bear no explanatory relation to each other, then since no plausible “third-factor” explanation comes to mind, it seems the claim that our moral judgments coincide with the moral facts is inexplicable. If apparently inexplicable, that’s reason to think the coincidence does not obtain—-i.e., that our moral judgments are unreliable. Accessible unreliability counts as a defeater of whatever initial justification our moral judgments may have had.
   (2) IBE Argument: If the moral facts and our moral judgments bear no explanatory relation to each other-—as conveyed by the Harman premise and response-independence condition of moral realism-—then since we have no plausible “third-factor” explanation of the reliability of our moral belief-forming processes, it seems we have no plausible explanation of the reliability of our moral belief-forming processes. The best explanation of why we have no plausible explanation of moral reliability is that there is no such reliability. Accessible unreliability, again, counts as a defeater.
   (3) Explanatory Independence Argument: One might appeal to a “because” constraint: for our moral judgments (or intuitions) to be evidence for the moral facts, they must bear some explanatory relation to the moral facts. Since our moral judgments bear no such explanatory relation—-as suggested by the combination of the Harman premise and the response-independence condition of moral realism-—our moral judgments are not evidence of the moral facts. In the language of epistemic defeat: the accessible explanatory independence between our moral intuitions and the moral facts counts as a defeater of whatever initial justification our moral intuitions might have enjoyed.
   All this is to say: debunking arguments running from the Harman premise can still undermine our moral judgments, without assuming the moral truths could have been different. The Harman premise can do more than just show that the (defeasible) justification of our moral judgment is not empirical justification. Given this dialectical situation, it appears Clarke-Doane *does* need to deflect our contention that a complete explanation of our mathematical judgment would need to imply mathematical truths. For if our contention is true, then Harman-premise-based debunking arguments may very well undermine our moral judgments without undermining our mathematical judgments (on realism).
   Here is one way we motivated the claim that a complete explanation of our mathematical judgment would need to imply mathematical truths:
   Argument from Indispensability
   (1) Math facts are indispensable to our best physics.
   (2) IF: math facts are indispensable, THEN: if the math facts were very different, the laws of physics would be very different.
   (3) If the laws of physics were very different, we would not arrive at the same mathematical beliefs.
   (4) So, if the mathematical facts were very different, we would not arrive at the same mathematical beliefs. (From 1-3)
   (5) Hence, the complete explanation of our mathematical beliefs needs to cite or imply their truth. (From 4)
   In Part II of his response, Clarke-Doane suggests that in order to reach (4), we must assume a hypothesis like “It would have benefitted our ancestors to believe mathematical hypotheses which are indispensable to our best physics.” I do not see why we must make this assumption. Premise (3) does the job of helping us reach (4) and seems highly plausible to me.
   Clarke-Doane also suggests that the argument’s assumption of the indispensability of math to physics is contentious. The point we wanted to make, however, is that Clarke-Doane presumably wanted the success of his argument not to hinge on the question of the indispensability of math to physics. If it does so hinge, as our argument suggests, then to make his argument work, Clarke-Doane has a lot more work to do.

8. Braddock’s Response to Clarke-Doane, Part II
   In response to the second debunking argument in our post–the argument from the unreliability of the processes producing our moral judgments–Clarke-Doane writes:
   “I discuss the argument that our moral beliefs might have easily been different on p. 319 – 320 of my paper. As I observe there, Darwin’s own “debunking argument” seems closer to this one. But, as I also observe, there is an obvious problem with the argument. Prima facie our *core* moral beliefs could *not* have easily been different. As I put it, “[p]rima facie creatures who believed that pain is good and that pleasure is bad would be less successful at passing on their genes than creatures that believed the opposite (p. 320).”
   A response:
   Whether core moral beliefs could have easily been different depends on how we delineate the category of “core” beliefs. It may be that we could not have easily believed that “pain is good”, but could we have easily believed that liberally causing pain to out-group members is permissible? It seems so, and the many nasty norms we find in the ethnographic and anthropological record suggest so. This suggests, disturbingly, that the belief that we should *not* liberally harm out-group members is unreliably produced (on moral realism). Even if this belief is not “core”, it is fairly morally basic and would plausibly influence other moral norms and beliefs we form. If so, then if the belief is unreliably produced, it would function as a distorting influence on other moral beliefs.
   Doane-Clark continues:
   “BMS may not have intended to make the doubtful suggestion that our core moral beliefs could have easily been different. They conclude that “we could easily have arrived at *mostly* false moral beliefs”. Might the above argument still undermine our *non-core* moral beliefs? There is a natural argument for the negative answer. In the present context, the reliability of our abductive methodology is not in doubt. But given the safety of our core moral beliefs, and given the safety of our abductive methodology, there is a “bootstrapping” argument for the safety of our moral theories. Here it is: our core moral beliefs are safe; our moral theories “follow” from those via principles of abduction; our belief in the principles of abduction is safe; so, our belief in our moral theories is safe.”
   It is not obvious to me that we arrive at our moral theories and commonsensical moral beliefs on the basis of the latter being best explanations of our “core” moral beliefs. It seems many of us, when we reason to our moral beliefs, adopt something like the coherentist method of reflective equilibrium and shift back and forth between “core” and “non-core”—-general and particular—-moral beliefs. The problem with this, as many have pointed out, is that if the input moral judgments are unreliably produced, then we cannot expect the operation of coherentist reasoning mechanisms to get us closer to true moral beliefs. Garbage in, garbage out. So if a debunking argument can show that many of our input moral judgments-—regardless of the degree to which they are “core” or basic—-are unreliably produced, this can present a real skeptical threat, one that isn’t alleviated by invoking the safety of “core” moral judgments and abductive reasoning.
   Would the skeptical threat from unreliability apply to our mathematical judgments as well? I don’t see why. Even if mathematicians reason to mathematical judgments in a similar fashion—-through the coherentist method of reflective equilibrium—-IF their starting points are sufficiently reliable, then no garbage in/garbage out skeptical threat arises for mathematical realism. And we have no reason to suppose that the processes producing our mathematical judgments are unreliable, for they could not have easily led to very different mathematical judgments, given (for one thing) the apparently greater convergence we find in mathematics as opposed to morality.
   Clarke-Doane concludes:
   “To sum up: the second kind of evolutionary debunking argument which my arguments are supposed to miss either fails against moral realism or works against mathematical realism too.”
   I have sketched reasons for thinking that the evolutionary debunking argument from unreliability neither misses moral realism nor works against mathematical realism. But much more work, of course, is necessary to fill out and adequately motivate the argument.
   Kind thanks again to Justin for his comments.

9. In response to the second half of Justin’s reply, I just want to add the following points to what Matthew has noted.
   We suggested that evolutionary processes could have led to moral beliefs which disagree with our own. It seems that the process of cultural group selection which has shaped our moral beliefs has in fact led to a wide variety of contrary moral beliefs. Once we consider the kinds of moral beliefs that might have been produced in other species, as in Darwin’s thought experiment of intelligent social beings raised under the conditions of hive bees (discussed in Justin’s article on p.319-320), it seems plausible that evolutionary processes are capable of yielding radically divergent moral systems.
   Justin suggests that the evolutionary processes responsible for our moral beliefs could not easily have led to moral systems in which the core beliefs were different, thus limiting the force of this argument. Quoting his own paper he says: “As I put it, “[p]rima facie creatures who believed that pain is good and that pleasure is bad would be less successful at passing on their genes than creatures that believed the opposite (p. 320).”” As this may be expected to hold under any realistic scenario, evolution by natural selection could not easily have led to creatures believing that pain is good and pleasure bad.
   I find this example difficult to evaluate. I take it that Justin supposes that one of our core moral beliefs is that pain is bad and pleasure good. But what is exactly is meant by the claim that “pain is bad”, so understood? It is doubtful that every human being who has moral beliefs believes that pain as such is morally bad, no matter who is in pain, or why they suffer. For example, Brandt’s description of Hopi attitudes towards animal pain in his “Hopi Ethics” suggests that the Hopi do not (or at least did not) regard chicken pain as morally bad. I grant that almost everyone believes that the fact that an action would cause oneself pain is a reason for one not to perform that action. However, the reason here is prudential, not moral. It is not clear that there is a moral belief which can be summarized as “pain is bad” and which is such that there are no conditions under which evolution by natural selection could favour moral systems that are agnostic with respect to the believed proposition. It may be that there are certain moral beliefs which any evolved moral system would have to incorporate. However, I feel that Justin needs to say more if he is to show that this holds for sufficiently many of our core moral beliefs to salvage a workable morality.

10. I just got free to join the conversation. I see that my coauthors have already responded ably, so I will not repeat their points but just wait for Justin to respond. However, I do want to build on one important point made by Matthew.
    Justin wrote, “there is an obvious problem with the argument. Prima facie our *core* moral beliefs could *not* have easily been different” (his emphasis). However, as Matthew responds, “Whether core moral beliefs could have easily been different depends on how we delineate the category of ‘core’ beliefs.” Let me expand.
    Justin’s only example of a “core” moral belief is the belief that pain is good and that pleasure is bad. I doubt that this belief by itself counts as moral, since I think my own pain is bad, but that belief concerns prudence instead of morality. Maybe the supposed core moral belief is that pain in others is bad, but the badness of the pain people feel during earthquakes is also not a sign that the earthquake is immoral. Maybe the core moral belief is that an agent causing pain to a victim is bad. But even if that act is bad to some extent, it need not be immoral if the agent has an excuse or justification, such as self-defense. So maybe the core moral belief is that an agent causing pain to a victim without an adequate justification or excuse is morally wrong. But then we get many disagreements about what counts as an agent (children? adolescents? mentally ill?), which victims (fetuses? cows?) are morally protected, what counts as pain (disappointment? anger?), what counts as causing (do omissions cause harm?), and which excuses and justifications are adequate for which harms. Moral beliefs on all of these issues “could … have easily been different”, contrary to Justin’s claim.
    The basic mistake is to think that the only alternatives to “pain is bad” is “pain is good” (320) or perhaps “pain is never bad”. Maybe we could not have evolved to believe that pain is good, as Justin says. Nonetheless, we could have evolved with very different beliefs about WHEN pain is bad or when it is immoral to cause pain. The evidence for this claim is that we DO have different beliefs about THAT. Maybe we had to have some belief that sometimes it is immoral to cause some kinds of pain in some ways in some circumstances, but that “core” moral belief cannot be used to help us decide what to do in real cases.
    SO, any so-called “core” moral belief that is any use to our evolutionary ancestors or to us does seem to be one that we could have evolved not to believe.

11. Andreas posted his most recent comment while I was composing mine and then interrupted. Sorry for the repetition.
    Also, I hope it is clear that I meant to say “Justin’s only example of a “core” moral belief is the belief that pain is bad and that pleasure is good” instead of what I did write: “Justin’s only example of a “core” moral belief is the belief that pain is good and that pleasure is bad”. Oops!
    Please excuse my inexperience with blogging,
    Walter

12. William, thanks a lot for the thoughtful comments. I take it that my Response to BMS — Part I is relevant. But let me add to that.
    You note that in Section II of my paper, I argue “that the evolutionary challenge for moral realism doesn’t depend on the claim that (1) our moral beliefs are actually the products of evolutionary forces.” I argue that it merely depends on “the weaker conditional claim that (2) if our moral beliefs were indeed the products of evolutionary forces, then those forces would have been non-truth tracking and we would not have been selected to have true moral beliefs, along with the claim that (3) it is intelligible to imagine the basic moral truths being very different.” This puzzles you, first, because “all [2 shows] is that realists cannot explain our having largely true moral beliefs by claiming that we were selected to have true moral beliefs…[T]hat doesn’t yet amount to an “evolutionary challenge to realism” in the usual sense.” This is correct. I sought to argue that the “evolutionary challenge” in the usual sense does not get off the ground.
    But you think it does get off the ground so long as (1) and (2) can be established. Indeed, you suggest that (1) and (2) are sufficient to generate the challenge in the usual sense, and that, contrary to what I argue in Section II, (2) does not presuppose (3). If so, then we can “debunk” the moral realist’s moral beliefs even under the assumption that the moral truths could not have been different (in whatever sense is relevant). We grant that the realist’s first-order moral beliefs are (defeasibly) justified. We then argue that those beliefs are the products of “non-truth-tracking” forces (where we do *not* take this to imply that had the moral truths been different, our moral beliefs would have failed to be correspondingly so). How would this argument undermine the realist’s moral beliefs? Presumably, it could only do this by somehow calling into question the reliability of those beliefs. But we are assuming that the argument does *not* call into question the reliability of the realist’s moral beliefs by showing that the moral truths might have been different (while her moral beliefs failed to be correspondingly different). Could the argument undermine the realist’s moral beliefs by showing that her moral *beliefs* might have easily been different (while the moral truths remained the same)? It would certainly seem not. The whole point of evolutionary arguments like Street’s is that at least our “core” moral beliefs were all but inevitable.
    This brings me to second source of your puzzlement, “the importance of 3”. If debunking arguments do not threaten the realist’s moral beliefs by showing that her moral beliefs might have easily been different (while the moral truths remained the same), then – given that information cannot threaten our beliefs without somehow calling into question their reliability – such arguments must threaten the realist’s moral beliefs by showing that the moral truths might have been different (while our moral beliefs failed to be correspondingly so). But then (3) is important to the evolutionary challenge after all. (1) and (2) do not generate a threat – let alone the evolutionary challenge in the usual sense — unless (3) is also assumed.
    Let me conclude with a comment on your remark that “if I want to propose my own account of how our moral beliefs are the products of (non-evolutionary) truth-tracking processes…[a]ll I have to do is to provide an account of how the moral truths figure into the actual etiology of our moral beliefs via whatever truth-tracking processes we’ve developed.” I’m not sure what you’re suggesting here, but you might be suggesting that in order to explain the reliability of our beliefs of a kind, F, it suffices to show that the contents of our F-beliefs figure into the best explanation of our coming to have those beliefs. If so, then I disagree (see p. 328-329 of my paper). Consider our elementary first-order logical beliefs. Surely we must assume their contents in the best explanation of our having them, at least at the level of inference. But no one thinks that this resolves the mystery of how we are reliable with respect to first-order logic.
    Of course, I believe that besides not being sufficient, it is also not necessary to show that the contents of our beliefs of a kind, F, figure into the best explanation of our having those beliefs in order to explain the reliability of our F-beliefs in the relevant sense. For reasons alluded to above, I think that it suffices to show that F-truths could not have been different, and that we could not have easily had different F-beliefs. In this sense, explanatory challenges like Harman’s and reliability challenges like Street’s are independent.

13. Andreas, thanks for the response. You write:
    “S’s belief that p is subject to an undercutting defeater to the extent that S has reason to believe that the explanation of why she believes p provides no reason to believe p.”
    Clarificatory Question: Do you think that non-naturalist moral realism is trivially incoherent?

14. Hi, Matthew. Thanks a lot for the comments. Regarding your response to my response, Part I:
    1. Field-style argument: Let’s assume that there is some hyperintensional sense of “explain” in which there might fail to be an explanation of the reliability of our beliefs of a kind, F, despite the fact that the F-truths could not have been different and our F-beliefs could not have easily been different. How would the apparent impossibility of offering such an explanation undermine our F-beliefs — *given* that those beliefs are both sensitive and safe? You seem to suggest that it would do so by way of a principle like the following. We ought not believe in (hyperintensionally) inexplicable coincidences. But that seems crazy. Do you have a different principle in mind?
    2. IBE Argument: I don’t see the relevant difference between this argument and the Field-style argument. Do you think that we should not believe that anything is (hyperintensionally) inexplicable? Alternatively, why, in this case in particular, is the best explanation of the fact that we have no explanation for a purported correlation that there is none?
    3. Explanatory Independence Argument: I can see how this argument would undermine one’s justification if one were antecedently committed to the Quine-Harman view that our “observations” are only evidence for what best explains them. But how would this undermine the moral beliefs of a moral non-naturalist who rejected that view?

15. Hi again, Matthew. Regarding the other part of your response to my response to you, part I:
    How do you get
    (3) If the laws of physics were very different, we would not arrive at the same mathematical beliefs.
    if not via something like the hypothesis that it would have benefitted our ancestors to believe mathematical hypotheses which are indispensable to our best physics?
    Also, how exactly do you take (5) to follow from (4)?

16. Thanks very much for Matthew’s and Andreas’s second round of comments, and for Walter’s helpful expansion on them. I take their principal upshot to be that there is no “common core” of moral beliefs which is both safe and such that a non-trivial moral theory “follows” from it. I will comment on this now.
    In Street’s “Darwinian Dilemma” she writes:
    “Consider, as a brief sampling, the following judgements about reasons:
    (1) The fact that something would promote one’s survival is a reason in favor of it.
    (2) The fact that something would promote the interests of a family member is a reason to do it.
    (3) We have greater obligations to help our own children than we do to help complete strangers.
    (4) The fact that someone has treated one well is a reason to treat that person well in return.
    (5) The fact that someone is altruistic is a reason to admire, praise, and reward him or her.
    (6) The fact that someone has done one deliberate harm is a reason to shun that person or seek his or her punishment.
    ….Why do we think that altruism with no hope of personal reward is the highest form of virtue…? …[V]ery roughly…these sorts of judgements about reasons tended to promote survival and reproduction much more effectively than the alternative judgements.“
    BMS do not say whether they accept that the beliefs to which Street alludes are safe. If they do accept this, then I am not sure why the “bootstrapping” argument which I sketched would be less successful in the moral case than in the mathematical. In neither case can we claim that our theory is safe in its entirety. In the mathematical case, there is obviously much disagreement about theoretical matters, such as the size of the continuum or the “height” of the large cardinal hierarchy. Any of us with views on these matters could have easily had conflicting ones – by, say, attending a different graduate school. So, our theoretical mathematical beliefs do not seem to be safe. But arguably there is a non-trivial mathematical theory which we can abduct from safe starting points. (I say, arguably, because there is case to be made that when the question of what axioms are true is cleanly distinguished from the question of what follows from them, almost no axioms of interest are safe.) The question is whether there is similarly a non-trivial moral theory which we can abduct from safe starting points. If the beliefs to which Street alludes are safe, then it seems to me that there is such a theory.
    If beliefs like the ones to which Street alludes are *not* safe, then there may be a “debunking” argument against moral realism which fails to apply to mathematical realism. But now the question arises: what does this argument have to do with evolution? Suppose that we knew nothing of the origins of our moral beliefs, but still bore witness to pervasive and apparently rationally irresolvable moral disagreement. Would not this show equally that our moral beliefs were unsafe? I take it that the picture that has traditionally moved debunkers is one of *inevitability*. We were *bound* to have moral beliefs like we do have, so, no matter what the moral facts were, we would have believed as we do. If the idea is instead that, far from showing that our moral beliefs are inevitable, evolutionary considerations show that they are all but random, then such considerations would seem to be superfluous. The reality of pervasive and apparently rationally irresolvable disagreement – which is supposed by BMS to be evidence for the randomness of the relevant evolutionary forces anyway — suffices.

17. Based on my earlier comments, Justin asks:
    “Do you think that non-naturalist moral realism is trivially incoherent?”
    I am tempted to say ‘no’, but it all depends, of course, on how we understand ‘non-naturalist moral realism’ (and ‘trivially’).
    I do think that any theory which implies that moral facts and properties cannot enter into the explanation of our moral beliefs leads ultimately to moral skepticism. I wouldn’t want to say that this entailment is at all ‘trivial’, however. It is not an analytic truth or anything like that – if I am correct, it’s merely a synthetic, unobvious epistemological truth. On some understandings, denying the explanatory potency of moral facts is an entailment of non-naturalism; and on that understanding I do think that non-naturalism leads to moral skepticism.
    But not everyone understands the term in that way. If to be a non-naturalist is merely to believe that moral facts are irreducible or sui generis, then non-naturalism does not entail moral skepticism by the kind of principle I have proposed. One could believe, like Ralph Wedgwood, that evaluative facts are both irreducible and capable of entering into explanations of psychological phenomena. Indeed, by my own lights, this seems to be the most plausible metaethical view.

18. Hi all. I was preparing a short paper in response to Justin Clarke-Doane’s thought-provoking article, and I thought I might as well float some thoughts from that paper here.
    In order to assess the validity of an evolutionary debunking argument against mathematical realism, we need to take a closer look at the evidence for evolved numerical competence and its origin. This has been lacking in the debate on mathematical realism and evolutionary debunking, which I find surprising given the rich body of empirical evidence on numerical cognition in animals and infants. Evidence for exact discrimination of small numbers and approximate discrimination of large numbers is very strong, including in mammals, reptiles, amphibians, birds, and even insects (e.g., honey bees and ants). It suggests that animals use numerical cues in a variety of ecologically relevant conditions, e.g., choosing the larger number of items in foraging, picking the larger shoal, clutch size assessment etc.
    To see if the EDA against mathematical truths work, we need to examine whether these evolved capacities that we actually see in animals evolved without tracking some relevant mathematical truths. Now, Clark-Doane proposes that what is being tracked is not relationships between numbers, but first-order logical relationships. He argues that if mathematical truths (which he conceives of as Platonic entities that are entirely removed from the environment) were changed (e.g., 1 + 1 = 0 instead of 2), but first-order logic was kept constant, an agent who would now (correctly) believe something like 1 + 1 = 0 would still not have higher fitness, because the real-world live events (i.e., there is a lion hiding behind bush A, and another lion behind bush B) would not change.
    Interestingly, there is a model that explains elementary arithmetical capacities in infants and animals by reference to first-order logical properties: the object-file system proposed by Susan Carey and colleagues. According to this view, an object-file of two entities is represented as follows: there is an entity, and there is another entity numerically distinct from it, and each entity is an object, and there is no other object:
    (∃x)(∃y){(object[x] & object[y]) & x ̸= y & ∀z(object[z] → [z = x] ∨ [z = y])}
    As there are severe limitations on working memory, the object-file system explains why small number discrimination is limited to 3, or at most 4.
    However, these is a lot of evidence that animals and infants possess the capacity to perform arithmetical operations over larger numbers as well. This approximate arithmetic is characterized by the Weber-Fechner signature (i.e., decreasing precision with increasing size). For instance, humans without precise number words and nonhuman animals are able to distinguish between larger collections, e.g., they can judge that 20 < 80, and that 15 + 15 < 60 (Pica et al., 2004). Representing these collections as object files would not be feasible within the constraints of working memory. The empirical evidence rules out this interpretation, since it would, for instance, predict that we are able to subitize (i.e., see at a glance) the difference between, say, 50 and 51 objects, which we cannot. Even under the assumption that the small number system is not sensitive to numerosity, but to first-order logical relationships, as Carey has suggested, we still need to explain the larger, approximate system. Proponents of the object-file system are typically committed to the view that there are two evolved systems for detecting numerosity: object-files that track first-order logical relationships, and fuzzy, approximate representations of larger numerosities that track discrete magnitudes. I will not go into the specifics of the models that explain approximate larger numbers (i.e., linear scalar variability and logarithmic models with fixed variability), but all these models propose that what animals and infants are sensitive to are *numerical* properties of the environment. Experimental psychologists have in their studies attempted to carefully control for non-numerical properties like surface area and density of the display, and they are pretty confident that although animals also use these cues, they can also rely on the cardinality of a collection of items to guide their responses. For example, take the neural network model by Changeux and Dehaene, which has been confirmed in studies on actual firing rates of neurons in humans and monkeys, According to this model, numerical information is extracted from perceptual input (visual, auditory or haptic), and recoded in terms of the firing rate of number-sensitive neurons. Since neural resources are limited, this model predicts a logarithmic spacing of neural thresholds, such that a decreasing number of neurons is allocated to increasingly larger numerosities, which explains the growing imprecision of numerosity detection with increasing cardinality. Thus, number-sensitive neurons adapt to the range of quantities the animal is dealing with. So, I'm using something like the paraphrasing challenges in debates on abstract objects: psychologists invoke numerical properties of the environment to explain how animals evolved their number sense. First-order logical properties simply don't do the job. I think this opens prospects for some forms of mathematical realism, e.g., structuralism as Shapiro conceives of it. We need not think of mathematical truths as present in an causal Platonic realm to accept some form of mathematical realism. There is still a wide variety of positions between straightforward mathematical error theory and Platonism.

19. FitzPatrick: Reply to Justin’s Response to my First Post:
    Thanks, Justin, for the lucid reply, which helps to bring out more clearly where the real disagreement lies. Here are my thoughts in response, which I think will clarify my own take on the evolutionary challenge and the best response to it:
    As I see it, the evolutionary challenger (who seeks to debunk realism) needs to begin with the claim that (1) our moral beliefs are actually the products of evolutionary forces, together with the claim that (2) those forces were not truth-tracking. This pair of claims, I’ve argued, would be enough to raise a problem for the realist, and this is so even if the basic moral truths could not have been otherwise (and indeed even if it’s not even intelligible to imagine their having been otherwise); I also claim that without 1 there is no real challenge to the realist (which means that the debunker really does need to engage in evolutionary speculation to try to get her challenge off the ground). Now you suggest that if 1 and 2 raised a problem for the realist then this could only be “by somehow calling into question the reliability of those beliefs,” but you doubt that the reliability of those beliefs could be called into question by 1 and 2 without the further assumption that the basic moral truths could have been different. Your claim, if I understand you correctly, is then that the only two ways to call into question the reliability of those beliefs is either (i) by showing that the moral truths could have been different while our moral beliefs failed to be correspondingly different, or (ii) by showing that our moral beliefs might easily have been very different even while the moral truths remained the same. And then your argument here is that the first option won’t be available to those who don’t think it makes any sense to imagine the moral truths having been different; and as for the second, the debunker herself (e.g., Street) insists that our basic moral beliefs had to be more or less what they are, given their shaping by natural selection, so the second option won’t be available either. So, you wonder, how could 1 and 2 themselves raise a problem for the realist? I hope that’s an accurate summary of your position.
    My response is that I think the above characterization misses the real heart of the evolutionary challenge. As I see it, the challenge, at least in Street’s case, goes something like this: “Look, you have all these moral beliefs, but you have them all for reasons having nothing to do with their being true: you have them simply because (to oversimplify) your early ancestors’ having them improved their reproductive success. You realists yourselves don’t think your objective values align particularly well with the genetically-oriented concerns of natural selection (i.e., the realist moral truths are not generally concerned with what maximizes reproductive output, etc.), so you should recognize that your moral beliefs were formed in ways that should give you no confidence at all that you arrived at moral beliefs that tend to align well with the objective moral truths you posit. Yet you seem quite confident that your moral beliefs are generally true. How can you possibly explain that? It’s of course possible that your moral beliefs are mostly true in the sense you think they are, i.e., that they generally align with independent moral truths (which have nothing to do with the causal principles that gave rise to your beliefs), but that would require a massive and very ‘convenient’ coincidence, which we have no reason at all to think has occurred. So in the absence of a good story to tell to explain this astonishing alignment, your confidence is unfounded and you should instead be worried that your moral beliefs are massively off track.”
    Now it will not help the realist at all here to say: “But wait, the moral truths are necessary: they couldn’t have been otherwise.” Even if the evolutionary challenger granted this, she could still press her above challenge, saying: “fine, they couldn’t have been otherwise. Still, you have absolutely no reason to think that your beliefs, arrived at through processes utterly insensitive to them, would have tended to align with these eternal, changeless, necessary truths. So the problem remains.” Nor will it help for the realist to say to the challenger (in the case of Street, though not Joyce): “But you yourself grant that our moral beliefs are mostly justified, since you yourself want to avoid moral skepticism, claiming that it’s deeply implausible!” That’s true, but all that means is that someone like Street will insist that realism must therefore be false, since realism cannot make sense of how our moral beliefs could be justified (as they plausibly are). In other words, she’ll say: “Yes, our basic moral beliefs are surely justified, but they _couldn’t_ be if moral truth were what the realist says it is (i.e., a matter of moral beliefs representing independent moral facts), so moral truth isn’t what the realist says it is: it’s just something to be understood on a subjectivist constructivist model” (e.g., Street’s own).
    Finally, it won’t help the realist to say: “But wait, on my view the moral truths are necessary, and you yourself, Street, admit that our basic moral beliefs had to be pretty much what they are, given that we’re evolved creatures. Therefore, if our moral beliefs are mostly correct, then they _had_ to be mostly correct, and so are totally reliable!” That, I think, just misses the point of the challenge. Yes, it’s true that IF our moral beliefs are in fact true, and couldn’t have been otherwise, and the truths couldn’t have otherwise, then our beliefs were ‘destined to be true’. But the whole question is whether we have any grounds in the first place for confidence that our moral beliefs _are_ true _according to the realist model_, accurately representing independent moral facts; and the evolutionary challenger purports already to have undermined any reasonable confidence in that (though again, she herself agrees that our moral beliefs are justified and true—but only because and insofar as moral truth is _not_ understood on the realist model!). And moreover, even if it turns out somehow that our moral beliefs were destined to be true, because the moral truths are necessary and our beliefs had to be what they because of evolution, this itself would be a pure cosmic coincidence: it would be a matter of pure luck that principles of natural selection that simply reward genetic propagation just happen to give us beliefs that match independent moral truths grounded in objective values having nothing to do in particular with genetic propagation! So there would be a kind of ‘reliability’ (though again, not one we have any reason to believe is actually the case), but it would be purely accidental in any case. And I don’t think any realist should rest happy with that sort of picture of how he wound up with largely true moral beliefs. I myself would give up my realism if I thought it all came down to something like a massive happy accident of that sort (which I certainly don’t).
    So this is all by way of explaining how I think the evolutionary challenger could raise a real problem for realism with just 1 and 2, even without any claims about the contingency of moral truths or even any claims about how our moral beliefs could easily have been different: neither of the latter two claims is very central to the real challenge, I think; but 1 is crucial, and it’s because I don’t think anyone has given realists any good reason to accept 1 (in the relevant strong sense in which it would need to be understood to generate a real challenge here—mere claims of some plausible evolutionary influence are obviously not enough) that I think realists can escape these debunking arguments simply by denying their starting points. In the end, I think the evolutionary challenge never gets off the ground, but that’s because its crucial starting premise—i.e., 1 above—is never established in a non-question-begging way. Realists still have important work to do in providing a positive epistemology, of course, but that’s nothing new, and it’s far from clear to me that anything from respectable evolutionary science presents the realist with any new, serious challenge along these lines.

20. William, thanks so much for this helpful response. You write:
    “[I]t’s true that IF our moral beliefs are in fact true, and couldn’t have been otherwise, and the truths couldn’t have otherwise, then our beliefs were ‘destined to be true’. But the whole question is whether we have any grounds in the first place for confidence that our moral beliefs _are_ true _according to the realist model_.”
    Debunking arguments *grant* that the realist’s moral beliefs are defeasibly justified, realistically conceived. So, those beliefs *are* justified, at least before realists are exposed to (1) our moral beliefs are actually the products of evolutionary forces and (2) those forces were not truth-tracking. I take you to also be allowing realists access to the assumptions that the moral truths would have whatever truth-values they have of necessity, and that our moral beliefs could not have easily been different. *Given these assumptions*, your view, I take it, is that, upon learning (1) and (2), the realist’s moral beliefs are undermined. But how? Let’s first get clear on what you could mean by (2), given that you do not take it to imply that had the moral truths been different, our moral beliefs would have been the same (as your talk of “insensitivity” and “non-truth-tracking” seems to imply). Presumably, you mean that the contents of our moral beliefs, realistically conceived, do not figure into the evolutionary explanation of our having them. On this reading, our elementary logical beliefs are trivially truth-tracking, because we must trivially assume their contents at the level of inference in any explanation whatever (contrary to the common view – e.g., Schechter, “The Reliability Challenge and the Epistemology of Logic” — that it is a very open question how we could manage to be reliable about elementary logic). Moreover, given this reading of “truth-tracking”, (2) implies Harman’s thesis in the context of (1) – it says that the best explanation of our having the moral beliefs that we have does not assume their contents. We’re, therefore, back to the question of the epistemic significance of Harman’s thesis. As I said in response to BMS, my view is that that thesis shows that whatever defeasible justification the realist’s moral beliefs might enjoy is not thanks to the fact that the contents of those beliefs figure into the best explanation of our having those beliefs. But, of course, Joyce’s and Street’s primary targets – “non-naturalist” moral realists — *grant* that much (their view is *defined* in terms of this concession). Does Harman’s thesis *undermine* non-naturalist’s moral beliefs as well? Obviously, non-naturalists do not think so! Nor do I. Given the defeasible justification of our moral beliefs, realistically conceived, and given that those beliefs were bound to be true, why should the fact that their contents fail to explain our having them register as more than an interesting theoretical observation? Presumably, you allow that we have reason right and left to believe of coincidences that they obtain and are coincidental. What is different about the “coincidence” at issue?

21. Helen, thanks so much for the thoughtful comment. I think that I’ll need to read your paper in order to properly consider your suggestion. But here are two brief thoughts. You write,
    “I’m using something like the paraphrasing challenges in debates on abstract objects: psychologists invoke numerical properties of the environment to explain how animals evolved their number sense. First-order logical properties simply don’t do the job. I think this opens prospects for some forms of mathematical realism, e.g., structuralism as Shapiro conceives of it. We need not think of mathematical truths as present in an causal Platonic realm to accept some form of mathematical realism. There is still a wide variety of positions between straightforward mathematical error theory and Platonism. “
    First, which of the following two claims are you making?
    1. The best explanation of our having the mathematical beliefs that we have assumes their truth.
    2. Had the mathematical truths been different, but the first-order logical and spatiotemporal truths been the same, our mathematical beliefs would have been correspondingly different?
    I find it very hard to imagine how an experiment could establish 2 (presumably the psychologists haven’t figured out how to vary the numerical properties while holding fixed the first-order logical ones on which they supervene!). Moreover, your claim that “psychologists invoke numerical properties of the environment to explain how animals evolved their number sense” is directly relevant only to 1.
    Second, I did not actually assume that mathematical entities would be “Platonic entities that are entirely removed from the environment”. What I said is that, if mathematical realism is going to be understood on analogy with moral realism, then it must be committed to a face-value interpretation of mathematical language. Thus, if “There are prime numbers” is true, then there are prime numbers. I explicitly left it open what the likes of prime numbers would be (see Section I of my paper). But there is a tempting argument to the conclusion that they’d be Platonic entities indeed. Presumably if “There are prime numbers” is true, it is true of necessity. But if “There are prime numbers” is true of necessity, then it would seem that prime number must exist of necessity. And, yet, nothing in our environment exists of necessity. So, prime numbers would be objects that exist of necessity, removed from our environment. I’m not endorsing this argument. I’m just pointing out that it is not easy to hold that there are numbers while denying that they would be Platonic entities. In my view, Shapiro’s structuralism does not resolve the tension. He takes mathematics at face-value, and so believes that there are literally prime numbers. He also believes that prime numbers exist of necessity. The mystery about our knowledge of them is supposed to be partly resolved because numbers are universals whose instances are concreta, like collections of things or people in a line. But now all the work is being done by a Platonic theory of universals, and he does not offer a substantive such theory.

22. Andreas, thanks a lot for the reply. I plan to follow up. But, first, back to your example.
    You write,
    “A belief formed via method M is unsafe if forming a belief on the matter using M in nearby possible worlds leads to a false belief. I can’t have reason to believe that this is the case in the example describe.”
    I defined beliefs of a kind, F, as safe if, holding the F-truths fixed, our F-beliefs could not have easily been different. I don’t see anything in your example which suggests that I couldn’t have easily had a different belief about the chemical composition of XYZ. (Perhaps I couldn’t if I only investigated the chemical composition of things by asking people with that peculiar kind of brain damage. But that seems irrelevant.) Nevertheless, let’s suppose that I could not have easily had a different belief about the chemical composition of XYZ. Then *if I could not reason to this fact* perhaps my belief would be undermined (because I could not block the worry that my belief on the matter might have easily been different). But in the moral case I argued that we *can* reason to the analogous fact. So, the case strikes me as irrelevant.

23. Just a reply to Justin’s last post:
    Justin, as I took it, your suggestion was that in cases where it seems worrying that one’s belief that p can be explained without reference to the truth of p, this worry arises either because this genealogical discovery provides evidence that one’s belief is unsafe or evidence that one’s belief is insensitive. I offered an example in which this seemed doubtful: one relies on someone’s testimony as to whether or not C is XYZ, but then discovers that they say that C is XYZ only because of a certain pattern of brain-damage. Here, one gets no reason to think that your belief is unsafe, since that would require one to have reason to deny that C is XYZ, which one doesn’t.
    Justin suggests that in the example, there is nothing to suggest that I couldn’t have easily had a different belief about the composition of XYZ. He offers a slightly different account of safety to the one I proposed: beliefs of a kind, F, are safe if, holding the F-truths fixed, our F-beliefs could not have easily been different. (My account of safety was: A belief formed via method M is unsafe if forming a belief on the matter using M in nearby possible worlds leads to a false belief.) Now, Justin grants that in all nearby worlds in which I rely on the testimony of the person that I asked, I get the belief that C is XYZ. Justin suggestion, if I understand him, is that I could easily have had a different belief, since I could easily have used a different method.
    One problem with this rejoinder is that it’s not clear why I should expect that a different method would yield a different belief. After all, if my informant told the truth, we should expect other methods to concur, and I have no reason to think that he did not tell the truth.
    Secondly, I think that my account of safety, with its relativization to methods, is preferable. At least, I think that finding out that one’s belief is ‘unsafe’ in Justin’s sense doesn’t seem disturbing and so cannot account for why the discovery in the example is debunking. Most obviously, there may be cases in which we are lucky to receive evidence that overturns some prior false belief. Those will be cases in which we know that we could very easily have had a different belief, and a false belief to boot. Knowing this doesn’t defeat the evidentiary value of evidence that we are lucky to receive. (Otherwise investigative journalism would be a difficult business!) So knowing that our beliefs could have been different if we had formed them in a different way just doesn’t seem to be intrinsically debunking. We need the relativization to methods. However, with this in place, the example that I discuss is clearly one in which one has no reason to deny that one’s belief is safe.
    Justin also suggests that there is an important disanalogy between the case that I discuss and the moral case, because in the moral case, we do have reason to think that our beliefs are safe. Now, if we had reasons to think this that were suitably independent of our evolved beliefs/intuitions, then I grant that that would provide a remedy for the challenge posed by evolutionary considerations to our ethical beliefs. However, if the considerations which are supposed to certify our beliefs as safe are themselves derived from evolution, then my objection would be that those considerations are undermined in just the way that the evidentiary value of testimony is undermined in the hypothetical scenario that I have been discussing. Justin, I wasn’t entirely clear as to whether you had in mind the first possibility or the second.

24. Justin, I’m sorry it took a while to get back to you (I had a workshop to organize). I’m wondering if you could clarify the following reading of my suggestion:
    “Had the mathematical truths been different, but the first-order logical and spatiotemporal truths been the same, our mathematical beliefs would have been correspondingly different”
    In your paper, you say several times that mathematical truths supervene on first-order logical and spatiotemporal truths. But I do not seem to remember you giving a positive case for this. Why should one accept that, say, numerical truths supervene on first-order logical truths? (I can send you my paper as soon as I’ve fine-tuned it in the course of the next weeks)