Friday, December 11, 2009

2 questions

Here are two questions I’d appreciate any thoughts on. Firstly, I’ve recently detected an apparent tension in my beliefs. In my paper for Phil Compass on the grounds of necessity, I argue that the Lewisian realist needn’t be worried about the epistemological objection. The objection goes: how could we know what’s (merely) possible if what’s possible is what’s true at a spatially-temporally isolated concrete world – such worlds do not interact with us causally, so how can we come to know what they’re like? Lewis responds by saying that causal interaction is necessary only when the subject matter is a contingent truth – when the claim to be known is a non-contingent matter, causal acquaintance with what the claim is about is not necessary even when the claim is about the realm of concreta. It’s not obvious to me that this is a good reply, but I thought Lewis had a simpler reply available: metaphysical priority is not conceptual priority. To say that what it is for it to be possible that p is for p to be true at some world does not commit us to saying that our epistemic access to the fact that p is possible must go via epistemic access to there being a world at which p. The Lewisian realist needn’t claim we have any way of discovering what’s true at a world independently of discovering what’s possible. Why can’t the Lewisian simply say she knows there’s a world where there’s a talking donkey because she knows that there could be talking donkeys (here appealing to whatever story about modal epistemology that any realist appeals to), and she knows that everything that could be the case is the case at some world (and here she cites the familiar Lewisian reasons for believing that claim)? What’s the problem?

That still seems convincing to me. Here’s my problem. I also find convincing an epistemological objection to consequentialism: were consequentialism true we couldn’t know what’s right or wrong because we can’t know what the full consequences of our actions would be. And it doesn’t seem to me in the least bit satisfying for the consequentialist to say: I know that murdering X will have the worst consequences because I know that murder is wrong – metaphysical priority isn’t epistemic priority, so my knowledge that it is wrong can ground my knowledge about the consequences even though what it is for it to be wrong is for it to have the worst consequences.

What I’d like is for the two cases to be disanalogous so I can consistently do what seems to me intuitive: hold the epistemological objection to consequentialism and reject the epistemological objection to Lewisian modal realism. I haven’t been able to convince myself that they’re analogous yet, so any thoughts on this are welcome (even if they’re of the form: they’re obviously analogous, and you’re wrong about the epistemological objection to ____). (Incidentally, I barely know the literature on consequentialism, so if anyone knows what consequentialists say about the epistemological objection, please enlighten me!)

Question 2. I was reminded by Brian’s post about the autonomy in logic issue. There’s a thought that every logical truth should be provable using only the rules governing the connectives in that truth. This is meant to be bad for classical logic because there are classical tautologies like Pierce’s law where the only connective is the conditional but one can’t prove Pierce’s law using only the rules for the conditional. I was thinking about this briefly, and I couldn’t see how the objection could possibly be right. We can do classical logic with just one logical connective: the Sheffer stroke, e.g. Every wff of classical logic – a fortiori every theorem – has a translation into a sentence statable using only the Sheffer stroke, and the translations of the theorems will be provable using only the rules governing the Sheffer stroke, as those are the only rules you have. But it can’t be the case that the acceptability of a logic depends on what connectives you allow yourself to use to state its theorems. The defenders of the objection are obviously going to be unimpressed with such a simplistic response, so my question to those who know more about this than me (= those who know than is written in this paragraph!) is: why not?

23 comments:

Jason said...

Hi Ross,

I don't know the answer to your question 2. But the first place I'd check is for a failure of completeness when you translate the axioms and inference rules of propositional logic into Sheffer-stroke notation. E.g., modus ponens becomes

p
p|(q|q)
-----
q

Suppose you've got a system with axioms and just modus ponens as an inference rule. It's not obvious you'll be able to always get what you need into the form p|(q|q) to use modus ponens when needed. Of course, if you would have been able to do the proof in standard notation, you'll be guaranteed a truth-functionally equivalent to p|(q|q) that you can get; but you might not have the resources to make the transition between the truth-functional equivalencies within the proof theory.

(Or maybe you can, and you have a devastating objection to the non-classicist's worries. I'm just saying I'd look here first.)

Aaron Boyden said...

On question 1, when we want to know about a specific possible world, we generally want to know about one that's similar to the actual world, and presumably the features of the actual world to which that possible world are similar are the source of our knowledge of what the possible world is like (the only thing not given by knowledge of actual world features the possible world is similar to is the fact that such a world exists as all, and that's an especially blatantly non-contingent fact). Of course, I think a consequentialist can know what's right because he knows an action is similar to other actions and has enough experience to know what consequences actions like that have (this doesn't give him certainty, but surely one needn't refute skepticism to be a consequentialist), so I don't myself think you should accept that epistemological argument any more than you accept the other.

Richard said...

re: Q1, one significant difference is that the plausibility of Lewisian realism (but not consequentialism) seems to depend on the facts being a certain way.

That is, if an oracle tells us that ours is the only concrete spatiotemporal region, Lewisians will (presumably) abandon their view rather than conclude that talking donkeys etc. are impossible. Lewisian realism requires a plenitude of concrete regions in order to achieve its theoretical ambitions.

Not so for consequentialism. If we learnt that various acts of terrorism or murder actually had good long-term consequences, then consequentialists wouldn't blink. They'd just conclude that those particular actions were objectively right (though perhaps not rational or 'subjectively right' given the antecedently available info) after all. The theoretical motivation for consequentialism does not at all depend on how the non-moral facts turn out. It's compatible with the whole variety of conceivable outcomes.

This difference would seem to explain the noted epistemic asymmetry. Consequentialists must give some credence to the possibility that a given murder will be beneficial (compatibly with their theory being true), whereas Lewisian realists should not give any credence to there being few concrete regions (compatibly with Lewisian realism) -- if they accepted the view about concrete regions, they would reject a Lewisian account of their modal significance.

P.S. I suspect many consequentialists would appeal to a distinction between 'objective' and 'subjective' (i.e. rational, evidence-relative) oughts. Objective oughts may be unknowable, but it doesn't much matter because it's the rational oughts that are action-guiding anyway (as we see in mineshaft cases and the like).

Ross Cameron said...

Jason: I might be missing some of the import of what you said, so correct me if I'm off on the wrong track here, but I wasn't thinking about translating the inference rules, only translating the wffs and using new inference rules governing the connectives used to state the translations - but those new rules needn't be obtainable via the translation from the old rules. Since those rules govern all the connectives of this logic, and since this logic proves all the theorems of classical logic, classical logic is conservative in the required sense.

I was thinking the point of resistance would be to say: this system doesn't prove the theorems of classical logic, only their translations: that's not Pierce's law you just proved, it's something else - Pierce's law is not provable in a conservative manner. But I was thinking this move was implausible: this just *is* classical logic, and that is Pierce's law, just stated in a different language.

I feel I may not be taking on your point here though - let me know.

Ross Cameron said...

Aaron: I'm not sure why similarity is coming into the discussion. I was interested in knowledge just of what's possible, not knowledge of the truth of counterfactuals or anything like that. Also, the objection to consequentialism is precisely that we *don't* know what the consequences of any action are, even past ones, because the consequences of every event are still unfolding. Of course, the consequentialist could choose an arbitrary cut-off for when the consequences no longer matter - and then, I agree, they could use induction to have some warrant about the likely consequences of similar actions - but that would be . . . arbitrary.

Richard: that's an excellent point, thanks! Unless anyone comes along and convinces me otherwise, I'm happy to take that a relevant disanalogy, and go on believing what I've been believing.

(For the record, I'm worried about knowability of subjective oughts given consequentialism as well - and I also don't like the move that objective oughts are unknowable but it's okay because they're not what we need for decision making, either - I don't like a theory of the good that makes the good not very interesting. But that's another issue.)

Rich_c90 said...

I'm not sure if Richard's disanalogy is perfectly fair.

It's true that Lewisian might abandon GMR if the oracle tells her that there is only one space-time region. But the Lewisian won't *always* abandon GMR if the oracle tells her certain things --- say that there aren't duplicate regions of space-time. In those cases, she'll alter her modal beliefs (or in this case, move from agnosticism to belief).

Similarly, there are things that the oracle could tell the consequentialist that wouldn't bother her. In such cases, she'll alter her moral beliefs (or acquire some new ones). But surely there are things that the oracle could tell the consequentialist which would force her to reject her view (say that killing the everything apart from the happiness monster (who gets intense happiness from the deaths of others would maximize overall happiness.)

Jason said...

Hi Ross,

I guess I was worried that there might not be a complete (finintely specifiable) proof procedure for propositional logic using the Sheffer stroke. (Maybe it's well known that there is --- I've never looked into it!) If there isn't, then there will be some theorem statable using only "|" not provable using just the inference rules governing it.

On the bus home, I was wondering whether the worry was something else --- something in the neighborhood of your "That's not Pierce's law" move, but more plausible. The thought might be that the inference rules that govern each truth-function suffice to prove every theorem "statable" using only that truth-function. Then Pierce's law is a theorem that can be thought of as being statable using just the Sheffer truth-function, or just the material-conditional truth-function. And even if it can be proven using the Sheffer rules, it still can't be proven using the material conditional rules and so there is a truth-function F and a theorem S statable using just F where the inference rules for F don't suffice for provability of S.

(One thing I don't know is whether the non-classical logics supposed to be motivated by this sort of argument meet the strong constraint I just outlined. "Truth-functions" might be too narrow --- not clear the intuitionist can even make sense of the constraint, we'd need to find a way to widen it --- but suppose we just consider Kleene logics or something, there are still a lot of truth functions, and it'd be surprising if they all had inference rules sufficient to proving all theorems statable using just them.)

Ross Cameron said...

Hi Jason, I'm pretty sure there is a complete finitely specifiable proof procedure for classical logic with the Sheffer stroke, although I could be wrong.

Really interesting question whether, say, intuitionist logic meets that stronger constraint. I have no idea. Anyone? Bueller?

Rich_c90 said...

I'll ask one of the intuitionist-fanciers at Cambridge and get back to you...

Richard said...

Rich - I don't see what non-moral things an oracle could tell a consequentialist that would essentially undermine the view. Anyone troubled by the possibility of "happiness monsters" will not be a utilitarian in the first place (but perhaps a consequentialist with a different axiology -- one on which such an outcome would be classified as impartially bad despite the increase in net happiness). Learning that the situation is actual doesn't make it any more or less of a problem than the mere possibility.

As for the cases where some non-modal fact p is compatible with (or wouldn't essentially undermine) Lewisian realism, my diagnosis of the issue implies that those are precisely the cases where the agent couldn't dismiss the possibility of p on the basis of their prior modal knowledge. And doesn't that seem exactly right?

Brian said...

Can you even state distinctively classical results using the Sheffer-stroke? The law of excluded middle becomes (A|A)|((A|A)|(A|A)). But on a literal interpretation of that, i.e. an interpretation of X|Y as ¬(X ∧ Y), then (A|A)|((A|A)|(A|A)) will be an intuitionist theorem as well.

Rich_c90 said...

Thanks Richard --- I guess I struggle to see what's different between these two cases:

Suppose I'm a utilitarian in that i think that X-ing is good iff X-ing maximizes happiness. And I also think that I know that wearing red socks isn't morally wrong. But now the Orcale tells me that it maximizes happiness. So I can either: reject utilitarianism, or reject my prior moral opinion. Neither is enforced.

Suppose I'm a Lewisian in that i think that p is possible iff p is true at some world. And suppose I also think that I know that it's possible for there to be talking donkeys. But now the Orcale tells me that there is no world at which donkey's talk. So I can either reject Lewisianism, or reject my prior modal opinion. Neither is enforced.

I see this two cases as being on a par, whereas I was hearing you as suggesting they were disanalogous.

Jason said...

Brian: What if we stipulated that we were understanding the Sheffer stroke as meaning ~p v ~q? Or (if that's cheating somehow), suppose we introduce an operator ":" where "p:q" is explicitly defined as ~p v ~q. We think of it as "classical" by saying it obeys the same inference rules as "|", and deny it by saying that it obeys some other rules. Then Ross's point will go through using ":", no?

Ross Cameron said...

Brian: I'm not sure that the *classical* logician should be worried, even if the intuitionist should think the classicist should be. Whether or not two wffs are equivalent is depends, of course, on what the correct logic is. So the classical logician should be happy to say that the formula using the Sheffer stroke *is* Pierce's law, and hence that Pierce's law is provable conservatively. Maybe by the intuitionists own lights, that isn't Pierce's law, but rather is some distinct intuitionistically acceptable theorem - but since the point about conservativeness is meant to move us away from classical logic, they'd better be able to worry the classicist by their own lights, and I'm not sure they can do this.

Richard said...

Hi Rich,

If you're a utilitarian, you think that the moral status of red socks is contingent on its consequences. In particular, you already think that in the possible world w42 where wearing red socks (somehow) causes great unhappiness, wearing red socks there is wrong. You acknowledge this as a real possibility (though an unlikely one) -- you don't think that that is a possible world in which utilitarianism is falsified. So while your credence Cr(w42) is low, you conditional credence Cr(Utilitarianism | w42) is equal to Cr(Utilitarianism).

Now suppose an oracle tells you that possibility w42 is actual after all. It would be bizarre -- the height of diachronic irrationality -- to update on this information by concluding that utilitarianism must be false.

By contrast, Cr(Lewisianism | no concrete talking donkeys) is less than Cr(Lewisianism). The absence of talking donkeys at least partly undermines the view. You're right that it might not decisively undermine the view; I discuss this more in a postscript here.

Mike Almeida said...

Not so for consequentialism. If we learnt that various acts of terrorism or murder actually had good long-term consequences, then consequentialists wouldn't blink.

They wouldn't? Why wouldn't they wonder whether it's the consequences that are relevant to the moral status of actions? I would. But suppose they're just stubbornly utilitarian, and won't consider the moral intuition that such actions are wrong despite their favorable consequences. The stubborn Lewisian can do the same thing. If there are no worlds in which there are talking donkeys, they can insist that it's the modal intuition has to go, and not genuine modal realism (GMR).

One other point. Your comparison between GMR's and utilitarians doesn't seem esp. apt. The Lewisian is considering there being exactly one world and reasonably abandoning GMR on that basis. That's a situation in which the cost of being stubborn is that most of his modal intuitions are mistaken. The utilitarian ought to be in an analogously extreme situation. Imagine the oracle tells the utilitarian that almost all of the actions that we ordinarily take to be right have bad consquences and similarly for wrong actions. The cost to utilitarians in this analogous extreme situation would also be too high to remain a utilitarian. To remain utilitarian you have ot abandon more or less every moral intuition.

So in the less extreme situations both can be stubborn. In the extreme situation, both should abandon their positions.

Richard said...

Mike - my previous point about conditional probabilities stands. Just let w42 be the world where almost all our actions have unexpected consequences. Our prior credence in the conjunction (w42 and utilitarianism) is low, but only because our credence is w42 simpliciter is low. Our conditional credence in utilitarianism given w42 should not be any different from our unconditional credence in utilitarianism.

(And even in the less extreme case, one's credence in GMR should be at least somewhat reduced. One's credence in moral theories should not be reduced at all.)

"Why wouldn't they wonder whether it's the consequences that are relevant to the moral status of actions?"

One should already have taken all such considerations into account in forming one's original credence in utilitarianism. Maybe it's only 0.75 for just this reason. Whatever. The point is that learning that some particular possible world is actual shouldn't change our fundamental moral beliefs in the slightest. If w42 undermines utilitarian principles, it does so whether w42 is actual or merely possible.

Mike Almeida said...

If you're a utilitarian, you think that the moral status of red socks is contingent on its consequences. In particular, you already think that in the possible world w42 where wearing red socks (somehow) causes great unhappiness, wearing red socks there is wrong. You acknowledge this as a real possibility (though an unlikely one) -- you don't think that that is a possible world in which utilitarianism is falsified.

I don't deny that, on the extreme assumption, an irrational utilitarian might refuse to take the countless, actual counterexamples seriously, and might abandon moral intuition altogether. But giving up on moral intuition altogether amounts to abandoning moral theorizing altogether.

But the irrational Lewisian can also take this route. He can abandon modal intuition altogether and conclude that all modal distinctions collapse. After all, it is not beyond all epistemic possibility that we live in a Segerberg dead end world. Dead end worlds have access to no world but themselves: modal distinctions collapse there. An irrational Lewisian might prefer that to giving up GMR. He too realizes going in that this is an epistemic possibility. He knew going in that this is something he might discover to be true. So, on your reasoning, it should not affect his posterior probability for GMR.

Of course, this reasoning treats the evidential weight of knowing that such things are possible with the evidential weight with knowing such things are actual. So, the inference from priors to posteriors is pretty dubious.

Richard said...

To avoid taking over Ross's thread, I've continued my part in this discussion in a new post: 'The Normative Irrelevance of the Actual'. (Anyone interested is welcome to join in there.)

Mike Almeida said...

My point is pretty simple. If the posterior probability for utilitarianism is unaffected by the oracle's revelation because the thoughtful utilitarian would have already taken into account the epistemic possibility revealed, then the posterior probability for GMR is unaffected by the oracle's revelation because the thoughtful GMR's would have taken into account the epistemic possibility that ours is a dead end world.

Richard said...

Mike - my post explains that there's a difference between the two kinds of theories, which explains why one, but not the other, has P(theory | epistemic possibility Ci) = P(theory).

If you are unconvinced by my post, it would help if you left a comment there explaining exactly why. In particular, do you not agree that this formula (representing "the irrelevance of the actual") holds of utilitarianism but not modal realism? Or are you just not clear on what my proposed explanation for the difference is?

Alastair said...

on Q1:

I'm with Rich_c90. The analogy between the objections to consequentialism and to utilitarianism looks a be a good one, because in both cases variations in the concrete facts (about what worlds there are, and about what consequences x-ing has) may or may not undermine the theory, depending on how extensive they are.

An impression to the contrary might be generated by taking Lewis' views about what worlds there are to be an integral part of the modal realist analysis of modality. But the two parts of his view are distinct: you can be a modal realist without buying into Lewis' particular modal beliefs. That is, someone who accepts the modal realist analysis of possibility and necessity need not accept the principle of recombination, which expresses Lewis's Humean modal beliefs.

I like that sort of view - a modal-realist style analysis of modality is correct, but what's possible and what's not is right up for grabs. Maybe the laws of nature are necessary - maybe they aren't. Whether they are depends on what worlds there are.

Does this undermine the motivation for accepting the modal realist analysis of modality? Not if what you're impressed by in it is the reduction of the modal to the non-modal rather than by the ability of recombination to capture our modal intuitions. Since I think primitive modality would make it inexplicable why we use modal talk, or how we know modal truths, and because I think modal realism is the only way of avoiding primitive modality, I'd hold onto it except in extreme cases, like learning there was only one possible world.

But even if, somehow, we discovered that there was only one spatio-temporally isolated collection of stuff, we might still try to hold on to the modal realist analysis of modality and change what sorts of things are identified with possible worlds. Lewis' invocation of spatio-temporal isolation as the demarcation criterion isn't sacrosanct. Maybe some other fundamental external relation could do the job - quantum entanglement relations are an interesting candidate.

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