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February 06, 2011


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good work. I'm with you on many issues - especially the idea that the evidence Rossians have need not be limited to non-moral facts. I find Williamson on this kind of issues helpful.

I have to admit that I find the whole discussion very difficult because there are so many things going on at the same time. One thing that seems to me to be clear is that Bedke's argument, if it works, extends to all beliefs about things that are outside this world's causal order. This would include all modal facts - mathematical, logical, semantic, and so on. It might even perhaps include the knowledge of the causal order itself (surely modal), and also beliefs about the phenomenal might be included - there's an interesting discussion of this in Chalmers. Yet, there is equally a physical, historical explanation of our beliefs about these issues too so the cosmic coincidence should apply here too. But, if you think that there is some justified modal beliefs, then something must go wrong with the argument.

Hi Jussi,

Thanks for the comments. I think it's a fair worry that the argument that Bedke offers could overgeneralize. It's hard to say, however, because if it turns out that the argument rests on a luck intuition and that the luck at issue is benign, the argument might fail for the moral as well as the modal and the rest.

That's true. I guess I don't see how it could succeed for the moral and not for other modal domains. The argument doesn't seem to turn on anything special about morality. Of course there's been a lot of debate about similar problems elsewhere - it seems like it's just an application of Benacerraf's problem and I'm sure platonists in maths have had interesting things to say in response.

I also had another thought. I'm starting to play with the idea that there's no causal explanation of our intuitions. This might sound funny but I was thinking about something like Davidson's anomalous monism. On that view, the identity conditions of mental states are normative throughout (this is something like what Ralph thinks too). This would allow mental states to be multiply realisable on the physical level and thus prevent any mental state types to be physically explainable which would spell trouble for Bedke. Also, if mental states are ascribed on the basis of the principle of charity (loving the good and all that), it would not be surprise that such states reliably get it right.

Anyway, just wanted to say that liked your post and wished others would comment on it too. I'm sure Matt will have things to say

Hi Jussi,

that sounds like an interesting response to these kinds of arguments. Is the idea partly that events in our brains are part of the causal order, that they have mental states corresponding to them, but that these brain-events are not identical to these mental states? We attribute mental states to people (including intuitions) not because we have causal beliefs about them (so to speak), but because we think they are most charitably interpreted as being in certain mental states -- or am I misunderstanding your thought?

We'd end up with a way of answering the type of argument Bedke gives, but also with a kind of mind/body dualism -- not necessarily a Cartesian substance-dualism, but a kind of dualism nevertheless. Is that right? This may not necessarily be a bad thing, but it is interesting to think about what the further implications of this type of response to Bedke-style arguments would commit us to.

Also, nice post!

Hi Sven,

well, it's not really my thought but Davidson's. More here:

Should emphasize that the view is a version of monism as any token of a mental state is identical with some token brain-state.

OK, I think I misunderstood the idea. I thought, though, that mental states were part of the causal order on Davidson's view. If so, then why, I wonder, don't intuitions have causal explanations? However, I probably shouldn't try starting up a discussion about that here since this is a thread about the Bedke-article! I'll instead refresh my memory of what Davidson is claiming by looking at the SEP entry you sent me. Thanks, Jussi.

Quick answer: intuitions having causal explanations would require that there would be psychophysical laws from the physical to the mental and such laws are ruled out by holism and logical connections between the mental. But as token identical with the physical the mental is part of the causal order. There just is no causal explanations for the mental states. You are right though - let's not take over the thread.

I can't access the article now, but wonder whether the cosmic coincidence worry is grounded in following line of thought.

(1) A's moral beliefs amount to knowldge only if they result from sensitivity to the moral facts
(2) A's beliefs are the result of sensitivity to the moral facts only if the moral facts help (causally) explain the beliefs.
(3) Given the naturalisitc view sketched in your post, the moral facts do not help (causally) explain the beliefs.
So (4) A's blfs do not amount to knowledge.

I guess the idea would be that knowledge requires sensitivity to evidence and that that requires explanation, and that that requires causal influence. So the cosmic coincidence would be that the beliefs happen to track the facts even though the agent is not really sensitive to the facts.

Just trying to play devils advocate here.

Hey Brad,

I think that's basically right about how the argument is supposed to go, but my worry is (in part) about this notion of sensitivity. There's the technical notion and the non-technical notion, but in a perfectly good sense of "sensitive", it would seem that supervenience and the right wiring could give us the sensitivity we need to reliably attribute moral properties when the attributions are correct and refrain when the attributions aren't correct. Sensitivity, I don't think, requires responding to moral properties qua moral properties at the level of the cognitive mechanisms so long as we respond to the right subvening properties and things seem from the subject's point of view to be going right. If things are swell from the subject's point of view, that should be enough for justification. If things are going swell from the point of view of the mechanisms (too), I don't yet see why that's not yet enough for knowledge.

(I'm sort of devil's advocating, too. I think Bedke's argument is really interesting and I'm not entirely confident that the response I've offered is adequate.)


that's interesting as that's exactly how Chalmers formulates an objection to his theory of phenomenal properties in the Conscious Mind. So you could have that same argument like this:

1. A's beliefs about her experiences amount to knowledge only if they result from sensitivity to the phenomenal facts.
2. A's beliefs about her experiences are the result of sensitivity to the phenomenal facts only if the phenomenal facts help causally to explain the beliefs.
3. Given that the world is causally closed, phenomenal facts do not help causally explain the beliefs about experiences.
4. So, A's beliefs do not amount to knowledge.

It is interesting that Chalmers flat out denies the causal theory of knowledge in this context and I presume that the intuitionist will do the same. Recall that for the intuitionist being in the state of believing the true moral proposition itself is supposed to constitute the justification (given right kind of conceptual capabilities and the like). This is not far from what Chalmers says about having experiences.

Hi Guys,

Clayton wrote: "If things are swell from the subject's point of view, that should be enough for justification. If things are going swell from the point of view of the mechanisms (too), I don't yet see why that's not yet enough for knowledge."

Let's grant the first conditional. The worry about the second one is knowledge might require more than a mechanism that actually tracks the facts. The demand for sensitivity is a demand for the tracking to be non-accidental in some hard to specify sense. But I assume that it can be heard to demand at least this much: the (actual) mechanism is disposed to track the facts (and their absence) in some types of counter-factual circumstances. That is why actual tracking is not sufficient for sensitivity.

Now the thought is that knowledge obtains only if the mechanism is so disposed and that an account of knowledge would involve an explanation of this disposition. The causal account obviously represents one way of pushing this idea, perhaps building on the scientistic...I mean naturalistic ideas that all empirical explanations are causal and that the explanation of the mechanism's disposition must be empirical.

So, Clayton, I wonder where you get off this boat (assuming you do). Does the debate hinge on the correct specification of the "type of counterfactual circumstances" in terms of which sensitivity is understood? I am not all that familiar with epistemology, so perhaps I am making some novice mistakes in presenting this skeptical line of thought..

And, Jussi, I wonder whether this raises doubts about whether rejecting the causal theory of knowledge will make the problem go away for the intuitionist. It seems like she will need to reject that account of knowledge *and* give another account that explains (and thereby vindicates) the dispositional claim about the mechanism. I suspect that the cosmic coincidence worry is related to skepticism about the availability of an alternative explanation of that sort.


that's interesting. For Chalmers, zombies have identical beliefs about experiences formation mechanisms and they form the very same beliefs about experiences we have. Of course all their beliefs are false. Yet, this (that the mechanisms can badly misfire in other worlds) doesn't seem to threaten our knowledge of the experiences (and as Clayton notes, we also have justification not accessible to them in addition to the reliable in our world mechanisms). So, I guess in that context, people have claimed that you are setting too high criteria for knowledge.

Note that your line of reasoning might threaten our ordinary knowledge of zebras and barns given that our mechanisms would create the same beliefs in the painted-mule zoos and fake-barn country.


Is your idea that the mechanism's actually tracking the moral facts is sufficient for knowledge in the moral case (i.e. that we do not need any counterfactual reliability)?

Your points bring out that we should not ramp up the demands for counterfactual reliability too much. And that makes sense. We should not demand that the mechanism guarantee success. But one can admit that much while insisting that some degree of reliability is needed.


I think that was Clayton's idea and I think I am with him. It seems to correspond to Chalmers' idea that our experience tracking-mechanisms need to be sufficient only for this world and not for the zombie world.

But I agree that there is an interesting point here about in what counterfactual situations our mechanisms need to be able to work. Part of me wants to say that it's enough if they work in the actual world as we could never go to the other worlds any way - we are stuck here in this world.

Hi all,

Clayton, many thanks for the post. (I want to say my paper has been blogjectified or blobjectified, but only if that is clever.) And thanks to everyone for the feedback. I'd like to clarify a few things. First, the argument concerns intuitive justification for believing in non-natural ethical properties. Knowledge is above my pay grade, so maybe the Rossians described above have knowledge. Second, I don't make use of causal theories of justification or reliabilist theories of justification. Actually, I grant that ethical intuitions prima facie (pro tanto) justify, and I don't think intuitional justification is causalist or reliabilist. I do, however, make use of the premise that, holding the causal order fixed, we would have the same intuitions across the remaining conceptually possible worlds. Considering these remaining worlds, the likelihood that we are in a world where our intuitions are veridical is low even granting the evidence of intuition, for following those very intuitions we have landed in a metaphysical picture that separates evidence from fact (which contrasts with following the evidence of experiential seemings). Brad's comments along similar lines resonate with me. So there is a kind of unreliability (really, unlikelihood) the discovery of which is a defeater even if reliability (likelihood) isn't a condition on prima facie justification.

What would help me is to see how others respond to my parallel case. Andy has intuitions such that it seems that people have spirit animals, where having a spirit animal is a non-natural property. It seems that wise people have owl spirit animals, and on that basis he justifiably believes that they do, it seems that brave people have lion spirit animals, and on that basis he justifiably believes that they do, etc. He also justifiably thinks that the having of a spirit animal strongly supervenes on non-spirit animal facts, viz., character traits. That is, necessarily (conceptually), if X has character trait C and sprit animal A, then necessarily (metaphysically), anyone who has character trait C has spirit animal A. Andy then discovers some natural explanations for his particular intuitions/beliefs about who has what spirit animal. He realizes that, holding the causal order fixed, he would intuit that wise people have owl spirit animals, and would conclude that wisdom metaphysically necessitates an owl spirit animal, regardless of which spirit animals anyone has (if any) and so regardless of which spirit animals are actually metaphysically necessitated (if any) by which character traits. I say this: Though his spirit animal beliefs may have been initially justified by intuition, he now has a defeater for that justification.

What say others about this case? I'm not sure how far similar arguments extend. E.g., I'm not sure about modal skepticism simply because I'm not sure if we are talking about modal realism a la Lewis or something else, and because I don't know what the evidence is supposed to be. I can say that epistemic questions do present themselves (to me at least!) when Lewis posits his plurality of worlds. I won't confess my views on modality.

I should add that I would distinguish evidence from knowledge (and so part company with Williamson). I think people can have evidence that is not true, even not truth-apt (e.g., the way things appear - it is the way things appear and not propositions about the way they appear that is my evidence for how things are). More to the point, I think intuitionists should accept this. But I won't argue for that here.

Hey Jussi & Brad,

"Is your idea that the mechanism's actually tracking the moral facts is sufficient for knowledge in the moral case (i.e. that we do not need any counterfactual reliability)?"

I don't know about Jussi, but what I wanted to say was that the Rossians are reliable about moral properties insofar as they are reliable about the relevant non-moral subvenient properties. If Ns are Ms as a matter of metaphysical necessity and my moral judgments are made true by the Ms and prompted by the presence of Ns, I think I can satisfy the safety and sensitivity conditions on knowledge even if the Ms aren't what trigger my judgments.

Hey Matt,
I hope you can forgive me for hashing out my thoughts about your argument here. I'm torn between the sort of intuition that I think moves you to say there's a problem with non-naturalist intuitionism and another set of intuitions that suggests there's no problem at all. Just a couple of points. I tried to post this earlier and my comment was lost to the internets.

(i) I think what I want to say about the animal spirits case is that it's very different from the moral case because we don't have any reason to believe in animal spirits. When I put it that way, it doesn't sound all that impressive...

(ii) On K & J: I wanted to talk about K because I think that if you're the same on the inside as someone who knows p, you might not know p, but you are just as justified as they are in believing it. Given that K entails J, building the case for saying that the Rossians have moral knowledge is a way of building the case for the claim about justification.

(iii) On K & evidence: I don't think E = K is quite right, but I think it's close to being right. Here are two claims about evidence that I'd defend:

(IKSE) If you know p non-inferentially, p is part of your evidence.
(ET) If p is part of your evidence, p is true.

Now, combine that with the claim that the Rossians have non-inferential moral knowledge and we get to say that it's not terribly surprising that the Rossians' moral beliefs turn out to be correct given their evidence. They are lucky to have the evidence they have, but not lucky that their beliefs "turn out" to be correct given the bases for their beliefs.

To block this sort of response and to argue that the kind of epistemic luck at issue really is malignant, it seems there are three options: deny ET, deny IKSE, or deny that the Rossians have non-inferential moral knowledge.

For reasons mentioned above, I don't think the third option is well-motivated yet because it looks like the Rossians' beliefs meet all the standard conditions needed for knowledge (e.g., true, reasonable, reliably formed, sensitive, safe, based on strong evidence, etc...). Of course, the real issue is justification in light of some further facts. My claim is that these further facts don't defeat justification because you can know that your beliefs meet the conditions necessary for knowledge even if you acknowledge that these facts obtain.

So, I think to sort this out, we'll have to figure out whether we can say that the Rossians have the sort of evidence I've suggested. Instead, if I read you correctly, you prefer a view on which the Rossians' evidence is similar to the Randians' evidence (i.e., appearances or facts about appearances). I think that's not a good view for the intuitionists since they think we have non-inferential moral knowledge. Given this (and IKSE and ET) we should say that the Rossians' have facts about appearances as part of their evidence, but it doesn't exhaust their evidence.

I suspect that the stand off looks like this. If you were to concede to me that IKSE and ET were correct and were to concede that the Rossians had non-inferential knowledge, the epistemic luck at issue wouldn't be malignant. The Rossians could concede that there's a sense in which they are lucky but this wouldn't defeat justification.

If, however, I were to concede to you that the Rossians' evidence consisted only of appearances, I would also concede to you that it's just lucky that they have correct beliefs and I'd concede that if they were aware of this, their justification would be defeated.

So, does our dispute really just turn on competing accounts of evidence? That's my suspicion. As I said, I prefer my own account of evidence (naturally), but I can appreciate that this account is controversial and that without it, you've got a solid case against the non-naturalist intuitionist.


thanks. I'm not quite convinced about the analogy quite yet. The intuitionists like Sidgwick, Crisp, and many others give usually fairly demanding conditions for when an intuition are justified moral beliefs. Usually these include four conditions. One has to have clear understanding of the relevant concepts, one's intuition has to be stable under reflection, one's intuition has to cohere with one's other beliefs (wide reflective equilibrium), and there has to be amount of interpersonal agreement. I don't see how Andy's spirit intuitions could satisfy these conditions. It's hard to see how there could be a concept of animal spirits anyone could clearly understand, how the spirit intuitions could integrate to all other non-moral beliefs, and there certainly isn't interpersonal agreement.

This means that by intuitionists' lights the spirit case fails as illustration of the cosmic coincidence. And once you set the standards of relevant intuitions as high as Sidgwick and Crisp do, then it is harder to have cosmic coincidence intuitions without relying on a causal theory of justification which is fairly doubtful for necessary truths such as moral truths (oh yeah - that's another major difference to the spirit case).


I'm not sure that the base-property reliability is sufficient for moral property reliability. What does the work are the Rossians bridge-principles that may be implicit in their moral belief formation. If these are very fickle, then one might go with Brad to think that base-property reliability is not sufficient.

It seems to me that this argument has much the same structure as Kim's causal exclusion argument against mental causation. (i.e. all the causal work is done at the physical level, so there's no actual causal work being done by the putative supervening mental cause.) I wonder if there are not parallel strategies for response.

I'm not convinced that K entails J. But if it does, I think my argument entails ~K, naturally. I'm a little leery of your attempt to directly establish knowledge given a reliabilist theory, and then infer justification from that. A reliabilist theory of K might not have J as a condition. Anyway, if the target is knowledge and justification is a condition, shouldn't one look to see if the belief meets the justification condition?

I'm not sure that our disagreement turns on what the Rossian's evidence is. Suppose I grant that the Rossians have knowledge and are in some sense justified. Now I want to know if I'm one of the Rossians. Am I justified in taking myself to be in a situation like theirs? Maybe this highlights a sense of justification I'm interested in, an internalist (not necessarily accessibilist) one connected with the question What should I believe?, rather than a second or third personal evaluation of beliefs. Huemer seems to work with this notion of justification. Some intuitionists, like Audi, characterize self evidence propositions as true, but that is usually in the context of discussing knowledge, and even he has lately placed more emphasis on seeming states and their ability to justify. In any event, I don't want to go robustly externalist with justification. I would say that my intuition on the fatman trolley case, e.g., pro tanto justifies my belief that it's impermissible to push him off the bridge. Its status as a justifier is not beholden to the falsity of consequentialism.

That said, I guess I'd worry that externalist theories of justification might require more by way of reliability or objective probability than is secured by the intuitive non-naturalist, as intimated by Brad.

I worry about appeal to intuitionists, as the epistemic commitments of the view are often not clearly separated from the other, non-epistemic, commitments. But I also don't see why Andy *cannot* meet the conditions you spell out. Can I stipulate it?

As for the necessary truth disanalogy, Andy is meant to have the same justification for believing in the necessary truth of spirit animal propositions that we have for believing in the necessary truth of moral propositions. Our evidence is 1) evidence of the actual moral facts plus 2) evidence for some kind of supervenience, which entails, 3) the necessary truth of moral propositions. After all, we don't think moral truths are conceptually necessary. Do you think we have more evidence than this for the necessary truth of moral propositions? (On a similar point, I think Audi distinguishes the self evidence of a truth that is necessary from the self evidence of the necessity of the truth.)

I'm not a fan of Kim's causal exclusion argument, and I'm thinking that the parallels don't run too deep. Isn't his argument one against non-reductive physicalism, forcing reductive (type-type) views or non-reductive views? (This last option is also fishy in light of his causal exclusion argument if we take the mental to be causal.) I don't use any causal criteria for being, or argue against the existence of irreducible moral properties. I simply say that we are not intuitively justified in believing them.

Hi Matt,

There's a lot of ground to cover, but I'll give it a shot.

(i) Here's why I think K entails J: If you know p, it cannot be that you oughtn't believe p for purely epistemic reasons. If it's not the case that you oughtn't believe p for purely epistemic reasons, your belief that p is true is permissibly held. So, it's justified. Justified beliefs are just those you can hold while meeting your epistemic duties. You can't have an epistemic duty to refrain from believing what you know is true.

(ii) I didn't intend to establish that the Rossians knew on reliabilist grounds. I wanted to show that the Rossians satisfy the standards for knowledge on the standard accounts of knowledge. The processes are reliable, their beliefs are sensitive and safe, they are reasonably held, etc... It might be that the example shows that there's more to knowledge than the standard accounts suggest, but the standard accounts don't imply the Rossians don't know. I wanted to offer this as a challenge--if the Rossians don't have knowledge, what are they missing?

(iii) You said that the sense of justification that interests you connects to the question, "What should I believe?" That's the notion that interests me, too. It seems you should be able to settle the question whether p is true and come to justifiably believe p or believe ~p without knowing or justifiably believing that you are in the Rossians position (under that description) because "the Rossians" picks out a group that has moral beliefs that constitute knowledge as a rule. If I can't justifiably believe some moral proposition p unless I can justifiably judge that I'm in the Rossian's position, I can't justifiably judge that p is true unless I can also justifiably judge that I know that p is true. It's not obvious that whenever you can justifiably believe p you can also justifiably judge that you know p.

You remarked, "In any event, I don't want to go robustly externalist with justification. I would say that my intuition on the fatman trolley case, e.g., pro tanto justifies my belief that it's impermissible to push him off the bridge. Its status as a justifier is not beholden to the falsity of consequentialism."

I'm not sure how "externalist" my remarks on justification are. I suggested that someone the same on the inside as someone who knows is justified in her beliefs. (Technically, I think a person being justified and a belief being justified are different, but that's for another time.) That's sort of internalist, it allows that external differences between those who know and those who are mental duplicates of those who know don't matter to justification even if they matter to knowledge.

I don't know what I've said so far would commit me to denying what you just said about your intuition and its ability to justify. Above, I said two things about evidence. First, that it consists of true propositions or facts. Second, that your evidence will include anything you know non-inferentially. If you take your evidence to be that it seems to you that it's wrong to push, that's evidence on my view. (It's true and you know that it seems to you that this is so non-inferentially.) I don't think that exhausts your evidence. I also think that your evidence would include moral facts (e.g., that it would harm him counts against pushing). Everything you seem to want to treat as evidence, I think I can agree is part of your evidence. Everything you think is evidence that supports your moral beliefs I think I can say stands in the same support relations. The difference seems to be that I think we have evidence for our beliefs that you seem to think we lack--evidence that doesn't just consist of seemings/facts about seemings.

I took the intuitionist view to be that we can have non-inferential moral knowledge and this knowledge of seemings/appearances is non-moral knowledge. So, I think the intuitionist should say that while we have both sorts of knowledge it would be a mistake to say that only the non-moral propositions constitute evidence. So do the moral ones. And, if the moral propositions that, say, it's prima facie wrong to do something that harms the guy is part of my evidence and I come to believe that it's permissible to push only if there are very good reasons to do so, I don't think you can say that I'm lucky that this belief is correct. It's very unlikely that this belief would be false given what my evidence is.


I guess I have hard time understanding what Andy is believing. What are animal spirits? What is it to believe in them? What does it mean to call something an animal spirit? Given that I have no idea of how to answer these questions, I have no idea what would be evidence for them and no way of having intuitions about whether Andy is justified in having the beliefs he has. I don't think you can just stipulate here - stipulating senseless things makes no sense...

In contrast, I do grasp mathematical sentences, moral sentences, and the like and I can explain their meaning to other people usually by giving platitudes that connect these claims to other mathematical and moral claims. This is why there's a sense in which I can assess justification for these claims.

So, Andy believes that there are animal spirits in all possible worlds? That there could not be human being without animal spirits in any world?

Thanks. This is helpful. I'd still resist discussion of knowledge because I think knowledge is a funny concept, I suspect it might not be a concept that carves nature at its joints (primarily serving non-referential purposes), and I don't have a theoretically independent sense of whether the agents you describe have it. In short, I don't understand it. But that's just me.

In any event, I think we can just ask about justification and settle that question without appeal to knowledge (and a showing of improbability defeats justification). I don't know what you think about this proposal. Am I right that you think this is a mistake in part because if you know something, that's part of your evidence? I would say: that conditional can be true without knowledge being an evidence maker. That is, if the things you know are part of your evidence, it is not *because* you know them. So we can still settle questions of evidence and justification without appeal to knowledge. Is this one place where we part ways?

On internalism-externalism, I think that your belief that p is justified iff p is supported by a preponderance of your evidence (this is too rough, but it'll do). You say: "If p is part of your evidence, p is true." So it looks like justification would not supervene on internals unless the only evidence you have are truths that strongly supervene on internals (which you seem to reject). So sounds like an externalist theory of justification to me. We might ultimately part ways with the truth condition on evidence.

I might be confused here. You say "I suggested that someone the same on the inside as someone who knows is justified in her beliefs." So you think justification strongly supervenes on internal states, but evidence and knowledge do not (for they must be truths, and the truth of some of your evidence does not supervene on internals)? You must reject my proposed connection between evidence and justification, then. Another place where we part ways?

You also say "I also think that your evidence would include moral facts (e.g., that it would harm him counts against pushing)." In the trolly case, I want to say that the intuition is evidence, but the fact that it's impermissible to push the guy (if that is a fact - consequentialism anyone?) is not. In any event, if the facts are evidence for you, they wouldn't be intuitive evidence, and so this supplemented evidential base might escape my argument. Fair enough?

Last, I'm confused when you say:
"I took the intuitionist view to be that we can have non-inferential moral knowledge and this knowledge of seemings/appearances is non-moral knowledge. So, I think the intuitionist should say that while we have both sorts of knowledge it would be a mistake to say that only the non-moral propositions constitute evidence."
The intuitionist is not saying that what is non-inferentially known/justifiedly believed is a proposition about your seemings/appearances, and from this you infer moral knowledge. They'd say your seemings/appearances with moral contents (for you, propositions about having these seemings with moral contents) non-inferentially justify your moral beliefs. It's seeming to you that p pro tanto justifies believing that p. Right?

Nonsense? Ouch. Well, now you know how some error theorists feel about morality :) (I can hear some of them replacing "animal spirit(s)" in your questions with "moral facts.") Maybe I tricked myself into thinking I imagined a case where people believe such things (indeed, had a rich set of platitudes about them), and had seeming states that supported such things. Would ghosts be better? I don't want the case to unduly distract us. I was just trying to get a parallel case that wouldn't be clouded by our extant strong commitments (e.g., to math, morality). Also, I wanted a case that stipulates beliefs about non-natural facts, since my argument only applies to the moral non-naturalist, and I don't think I can make such a stipulation with mathematical beliefs. But maybe we should just stick to the moral case.

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