Archive for February, 2009
Sorry – no presentation or write-up this week!
A lively discussion today of Tom Kelly’s ‘The epistemic significance of disagreement’. The presentation is here. Some thoughts follow.
It wasn’t entirely clear to us what kinds of disagreement was meant to be modelled by the proposal in the paper. Any disagreement, or only ones which persist over long periods and are resistant to resolution after lengthy discussion between peers? And are we to think of disagreement as stemming from differences in prior conditional credences (as Elga does), or from failures of logical omniscience, or from an arbitrary combination of the two? In what follows, I will assume the proposal is meant to apply to all disagreements, whatever their nature and their source, both for maximum generality, and because it will not always be clear from which source a particular disagreement stems.
We noted that the proposal didn’t generalize straightforwardly to a Williamsonian conception of one’s evidence as identical to one’s knowledge. That conception allows for an extra way in which two people could fail to be epistemic peers, in that they could have all the same credences but (due to environmental factors) have wildly different evidence. It seems that we won’t be able to rule out failures of peerhood due to this issue, so it will be even hard to identify epistemic peers if we make the identification E=K.
There was some discussion of Elga’s ‘bootstrapping’ argument in ‘Reflection and Disagreement‘ (p.15) against Kelly’s view, which Elga calls the ‘right-reasons’ view. Our consensus was that the argument simply doesn’t work – it’s not at all absurd that if you continue to stick to your ground in many cases of disagreement with a particular peer, and in fact in all those cases you had reasoned correctly and the peer had reasoned incorrectly, then you can legitimately come to consider that person no longer a peer. Of course, this depends on appealing to a sense of ‘legitimacy’ which lines up with the notion of rationality Kelly is interested in – more on this below.
We found it a bit mystifying why Kelly initially presents the asymmetry which refutes the symmetry argument as a perspectival asymmetry. The asymmetry which really matters is surely the non-perspectival asymmetry that one agent has reasoned correctly and one has not.
The assumption that in all relevant cases of disagreement one agent is correct and one is not is a deniable one. It seems to rely on a) objective bayesianism and b) the assumption that at least one agent has reasoned correctly. So Kelly’s view is silent on what we should think if we are inclined to subjective bayesianism, or on what should happen in cases where both agents have reasoned incorrectly and reached different conclusions.
It wasn’t obvious why the right-reasons view only applies to epistemic peers, rather than to anyone who shares my evidence. Surely, if I have in fact reasoned correctly and reached the correct conclusion, then in the relevant sense I shouldn’t defer to anyone, even people who have the same evidence but have much higher degrees of epistemic virtue than myself.
Now for the main issue. It seemed plausible to us that Kelly and Elga are simply talking past each other, because they are interested in different kinds of ‘epistemic norms’.
Kelly is interested in a kind of epistemic norm which is hard to follow (to follow it in all cases we would have to know which of us and our peer has in fact reasoned correctly), but if in fact followed correctly will always lead to the epistemically best results (that is, having our credences perfectly proportioned to the evidence). Elga, in contrast, is interested in a kind of epistemic norm which we can always know how to follow. However, it is quite possible that following Elga’s norm will in some unfortunate cases actually lead us to epistemically worse results.
Suppose that we have in fact reasoned correctly about something, but we defer to many peers all of whom agree with one another and all of whom have reasoned incorrectly. Then doing what Elga advises will in fact lead to an epistemically worse result, whereas doing what Kelly advises will in fact lead to the epistemically best result. However, we will not generally be in a position to know what precise credences Kelly’s view does advise, whereas Elga’s view always gives us a recipe for our new credences.
This line of thought leads us to think that Elga and Kelly have just been talking past each other, because they are referring to different norms when they ask what we should do in cases of disagreement. Elga’s norm obeys ought-implies-can, while Kelly’s does not. Elga’s norm will not always lead to the epistemically best result, while Kelly’s will. If this is right, then we can reconstruct the disagreement between Elga and Kelly as whether Elga’s norm counts as an epistemic norm. Perhaps Kelly’s view is that Elga’s norm should not count as an epistemic norm, but at most as a purely practical norm. And perhaps Elga’s view is that Kelly’s norm is unfollowable in some cases and therefore cannot be the most explanatory candidate for a ‘primary’ epistemic norm.
This week we discussed Cian Dorr’s ‘There are no abstract objects’, which isn’t currently available online, but is in ‘Contemporary Debates in Metaphysics’. Here’s the handout instead.
As we had Cian on the spot for this meeting, the discussion mostly took a question-and-answer format. So here are what I recorded of some questions and some answers, with a few that I didn’t get time to ask thrown in at the end.
Q: What about people who would resist the paraphrase strategy (p.37) because they think that counterpossibles are all vacuously true (Williamson takes this line in The Philosophy of Philosophy).
A: Nominalism/anti-nominalism are both contingent theses. But even if you think that nominalism is necessary if true, there will be certain kinds of truths like ‘there are possibly some things with a number-like structure’ which can be used to ground the relevant counterfactuals, along the lines of modal structuralism.
Q: Why require systematicity in our paraphrases?
A: Because we want to make straightforward sense of statements which mix different cases, such as ‘there are various different kinds of abstract objects’ – numbers, properties, sets, etc’
Q: Aren’t tables and numbers in the same boat according to the strategy applied here? What does this do for the nominalist intuition that tables are better known than numbers? How would the world look different if either existed
A: Bite the bullet – chairs do not differ from numbers in any interesting way. If they did exist, things would look just the same, but there’s still no good reason for us to suppose they do.
Q – Is the regress vicious (p.44)?
A – Yes, though it’s a little bit unclear why. One possible reason is that if denial of brute necessities is to get us anywhere, we’d better not have circular or regressive accounts of metaphysical primitives. For example, the following analysis does not get rid of brute necessities at any stage:
The necessity of ‘All fs are gs’ is explained by ‘to be an f is to be an f1 that is g.’ But why are all f1s gs? This is explained by ‘To be an f1 is to be an f2 that is g’… and so on.
Q: If we take property essences seriously, Kit Fine style, can we posit an essence of the instantiation relation that rules out pathological cases of instantiation?
A: The problematic cases can still be described in purely structural terms, so the problem has not completely gone away.
Q: Is this fictionalism?
A: Not if fictionalism is characterised by the literal falsity of claims about the domain one is fictionalist about.
Q: Why think that 6a or 7a in the fundamental sense do not analytically entail 6b and 7b in the fundamental sense? Isn’t it just the neo-Fregean project to defend these analytic entailments? What conception of analyticity makes it obvious that the entailment fails? Admittedly, a conception of analyticity which supports the entailment would have to have it analytically false that nothing exists.
Q: ‘Fundamental way’ – ‘ultimate furniture’ – ‘final analysis’ (p.34) – it seems like there are two ideas mixed up in the motivating metaphors. One is about the ideal science at the end of enquiry – but it’s not at all obvious (to me) that numbers won’t feature in this ideal science, if it’s formulated in the most natural way. Another involves ‘metaphysical explanatoriness’ – in this view, fundamental means something like ‘best trade off between simplicity and metaphysical explanatoriness’.
Q: Does it make a difference to the Alien Particulars Objection (p.49) whether we are committed to haecceitism? It looks like an anti-haecceitist can’t even express the objection.
[Note: I don't normally do the write up for the MLE seminar, so this is probably going to be a break from the normal format. In particular, I don't remember what people said and who said what, and all I have are my notes from when I read the paper, so I'm going to base it on that. -- Andrew]
Last week we read Gillies paper “On the truth conditions for ‘if’“. I had been meaning to work out what this view was about for a while so it was good to get an idea.
In the paper, Gillies argues that a dynamic view of conditionals can reconcile two apparently inconsistent claims. The first is that the English conditional does not have the truth conditions of material implication, and the second is the premises of Gibbards famous argument that the truth conditions of the English conditional must be that of the material conditional. Two notable premises are import-export, i.e., that the following two sentences are equivalent (where represents the English conditional.)
Since Gibbards argument is classically valid, either some classical laws must be rejected, or the step from mutual entailment to sameness of truth conditions must be bad. And, indeed, both of these lines are open – for example, Cian pointed out in the seminar the conjunction elimination fails on Gillies favoured account (see post below), and that the entailment relation displays some other rather odd behaviour (e.g., I don’t think it contraposes.) But also, it is not clear on the “information preservation” view of entailment, that you can infer sameness of truth conditions from mutual entailment. I expect this is how Gillies dodges the argument, but its not made clear.
But there were some things that still puzzled me about the paper, especially the stuff towards the end. The first was the central claim that the conditional could be given truth conditions. I wasn’t quite sure what the truth conditions were on the dynamic view; after all, all there is to the meaning of a sentence is its ‘context change potential’, or, the transformation it performs on information, and it’s not clear how one gets truth conditions out of this. You could, of course, define it in terms of idling on a singleton index, but that’s not a notion that plays any role in the entailment relation, which I thought was supposed to be a relation between the truth conditions of the relata.
On a related point, another issue I had with it was I couldn’t quite see how it engaged with the Gibbard argument. I guess you can consistently assign the conditional a non-extensional semantics, and retain import-export and other related inferences, but only at the cost of severing the tie between entailment and truth conditions.
That is, we seem to have two notions of entailment: entailment1, which is cashed out, roughly, in terms of preservation of truth, and entailment2 which is roughly preservation of information (if you assert the premises in the right order, then you’ll be in a context where the conclusion sounds good when you assert it.) Accepting the Gibbard premises, we get that and mutually entail1 each other. But entailment1 involves necessary preservation of truth, so we get that and have the same truth conditions. On the other hand, if we accep the Gibbard premises, and may mutually entail2 each other (perhaps, I haven’t checked.) But this notion of entailment, as it were, abandons truth conditions altogether. So I can see there’s a precisification of the ‘It’s a truth conditional account where the Gibbard entailments hold’ on which Gibbards entailments hold, and a precisification with a thoroughly truth-conditional account of ‘if’, but I can’t get both claims together?
Finally two minor things I didn’t get: (1) what IS the material conditional on the (second) dynamic view? Is it or (which aren’t equivalent) or something else? Because we need to know this if we’re to evaluate the claim that the English conditional is not a material conditional. (2) On the first view, if c is a context, there’s no guarantee that c+P is a context, (it won’t be well behaved if P is false for example), in fact, this situation will be very common, so what should the view be?
Cian pointed out that Conjunction Elimination fails to be valid on Gillies’ favoured account of entailment. On this notion of entailment (‘Entailment v.2.1′, p. 16), P entails Q just in case, for any context s, Q is true in the updated context s[P], that is, just in case:
s[P] = s[P][Q].
But on this account, when T is a tautology, and q an atom, ¬(if T)(q)&q doesn’t entail ¬(if T)(q) (although q&¬(if T)(q) does).
For consider a context s containing both q-worlds and not-q-worlds. The test (if T)(q) has us perform fails, returning the empty context, in s, but passes, yielding the whole updated context, in s[q]. Consequently:
= s[¬(if T)(q)][q]
= (s\s[(if T)(q))[q]
= s[q] (≠ Ø);
s[¬(if T)(q)&q][¬(if T)(q)]
= s[q][¬(if T)(q)]
= s[q]\s[q][(if T)(q)]
= s[q]\s[q] = Ø.
So the entailment fails.
This leaves some doubt about the intended interpretation of material implication on Gillies’ account. Given the semantics for ¬ and &, we cannot rely on the usual paraphrases, such as ¬(P&¬Q) or ¬(¬Q&P), to give us the semantics of material implication; for on this account, these need not be equivalent.
Hopefully, there will soon be a part 2 to this post with our other thoughts.