I’ve been thinking about Adam Elga’s recent version of the “equal weight view of disagreement”:http://philsci-archive.pitt.edu/archive/00003702/. This view endorses “giving ground in the face of disagreement about many matters, but not about disagreement itself”. I think this leads to some odd results when the disagreement about disagreement is sufficiently similar to the underlying first-order disagreement.

Suzy and Billy are doing there arithmetic homework. One of the questions is: What is the average of 0.87 and 0.59? Suzy says that she is quite confident that the answer is 0.73. In fact she is 87% confident that is the correct answer. Billy says that he is not that confident, he is only 59% confident that the correct answer is 0.73. Suzy regards (or at least prior to this question regarded) Billy as an epistemic peer when it comes to this kind of question.

Question: On the equal weight view of disagreement, what credence should Suzy have that the correct answer is 0.73?

The defenders of the equal weight view face a small puzzle here. On the one hand, if they say that Suzy’s credence in p should be the average of the credences of her peers, then the credence she should have is 0.73. After all, that is the average of the credences of her peers. On the other hand, if her credences should be directly responsive in this way to the _fact_ that the average of 0.87 and 0.59 is 0.73, then plausibly she should simply believe, with full credence, that the average of 0.87 and 0.59 is 0.73. That is, her credence that the correct answer is 0.73 should be 1.

This example is a little hackneyed, but I think there’s a general lesson here. Anyone who, like Adam, posits any mathematically defined rule for credences says that at some stage in evaluation, we simply have to say that credences must be sensitive to mathematical facts. But once we’ve said that, we have to wonder just which stage that is. I think, contra the equal weight view, that it’s typically very early in evaluation. One’s credences should be sensitive to mathematical facts directly (i.e., to the fact that the correct answer is 0.73), and not just to mathematical facts about credences of epistemic peers (e.g., the fact that the average of Suzy’s peers’ credences is 0.73). At risk of overlooking the obvious, I can’t see any reason to think otherwise, once the issue is stated in this form.

Related question: At which stage in the Achilles and the Tortoise dialogue should Achilles have refused the Tortoise’s recasting of his argument? I say – the very first time the Tortoise attempts to cast a rule of inference as a premise. Sometimes I think Adam’s version of the equal weight view is like a theory that accepts the Tortoise’s first alteration to Achilles’ argument, and rejects the second. There’s a regress that needs to be blocked, and he blocks it, but I can’t see why we would want to block it just _there_.

“Blome-Tillmann”:http://users.ox.ac.uk/~quee1101/papers/mbt_mate.pdf (PDF) also aims to counter an objection Jason Stanley raises to Lewisian contextualism. The objection turns on part of the picture of how so-called ‘quantifier domain restriction’ works that Jason worked out with Zoltán Szabó. Often when we say All Fs are Gs, we really mean All C Fs are Gs, where C is a contextually specified property. So when I say Every student passed, that utterance might express the proposition that Every student in my class passed.

Now there’s a question about what happens when sentences like All Fs are Gs are embedded in various contexts. Quantifier embeddings tend to allow for certain kinds of ambiguity. For instance, when we have a sentence like If p were true, all Fs would be G, that could express either of the following two propositions. (We’re ignoring context sensitivity for now, but we’ll return to it in a second.)

• If _p_ were true, then everything that would be _F_ would also be _G_.
• If _p_ were true, then everything that’s actually _F_ would be _G_.

We naturally interpret (1) the first way, and (2) the second way.

(1) If I had won the last Presidential election, everyone who voted for me would regret it by now.
(2) If Hilary Clinton had been the Democratic nominee, everyone who voted for Barack Obama would have voted for her.

Given this, you might expect that we could get a similar ambiguity with _C_. That is, when you have a quantifier that’s tacitly restricted by _C_, you might expect that you could interpret a sentence like If p were true, all Fs would be G in either of these two ways. (In each of these interpretations, I’ve left _F_ ambiguous; so these are just partial disambiguations.)

• If _p_ were true, then every _F_ that would be _C_ would also be _G_.
• If _p_ were true, then every _F_ that is actually _C_ would be _G_.

Surprisingly, you can’t get the second of these readings. That’s something Jason and Zoltán argue for, and that Jason also argues for in _Knowledge and Practical Interests_. He also argues that to complete a contextualist explanation of sceptical intuitions, you need the second of these readings.

Blome-Tillmann accepts the second of these premises, i.e. that the contextualist needs both kinds of readings, but thinks the first premise is false, i.e. he thinks both readings are available. He thinks he has examples that show you can get the kind of reading Jason denies is possible. But I don’t think his examples show any such thing. Here are the examples he gives.

(5) If there were no philosophers, then the philosophers doing research in the field of applied ethics would be missed most painfully by the public.
(6) If there were no beer, everybody drinking beer on a regular basis would be much healthier.
(7) If I suddenly were the only person alive, I would miss the Frege scholars most.

These are all sentences of (more or less) the form If p were true, all Fs would be G, and they should all be interpreted a la our disambiguation above. That is, they should be interpreted as quantifying over actual _F_s, not things that would be _F_ if _p_ were true. But the existence of such sentences is *completely irrelevant* to the issue Jason is raising. The question isn’t whether there is an ambiguity in _F_, it is whether there is an ambiguity in _C_. And nothing Blome-Tillmann raises suggests Jason’s claim that there is no ambiguity in that position is wrong. So I don’t think his defence of the contextualist account of embedded knowledge ascriptions works.

I suspect the situation for the contextualist is actually a little worse than the above discussion suggests. I think (though I’m not sure I’ve got the dialectic right at this point) that the contextualist needs a reading of If p were true, all Fs would be G where it means:

• If _p_ were true, every actual _C_ that would be _F_ would also be _G_.

The reason I think the contextualist needs that is that the contextualist, or at least the contextualist that Blome-Tillmann is defending analyses S knows that p as Every ~p possibility is ruled out by S’s evidence, and then insists that there is a contextual domain restriction on this, so it means something like Every ~p possibility (that I’m not properly ignoring) is ruled out by S’s evidence. They also want to accept that in a context where:

• I’m engaged in sceptical doubts;
• there is beer in the fridge
• I’ve forgotten what’s in the fridge; and
• I’ve got normal vision, so if I check the fridge I’ll see what’s in it

then (3) is still intutively false since we aren’t actually ignoring Cartesian doubts.

(3) If I were to look in the fridge and ignore Cartesian doubts, then I’d know there is beer in the fridge.

But the only way to get that to come out false, and false for the right reasons, is to fix on our actual quantifier domain restriction, but look at worlds that would be ruled out with the counterfactually available evidence. And I don’t see any reason to think that’s a possible disambiguation of embedded quantifiers.

George and Ringo both have $6000 in their bank accounts. They both are thinking about buying a new computer, which would cost $2000. Both of them also have rent due tomorrow, and they won’t get any more money before then. George lives in New York, so his rent is $5000. Ringo lives in Syracuse, so his rent is $1000. Clearly, (1) and (2) are true.

(1) Ringo has enough money to buy the computer.
(2) Ringo can afford the computer.

And I think (3) is true as well, though (4) is less clearly true.

(3) George has enough money to buy the computer.
(4) George can afford the computer.

But I want to focus for now on (3). It is a bad idea for George to buy the computer; he won’t be able to pay his rent. But he has enough money to do so; the computer costs $2000, and he has $6000 in the bank. So (3) is true. Admittedly there are things close to (3) that aren’t true. He hasn’t got enough money to buy the computer and pay his rent. You might say that he hasn’t got enough money to buy the computer given his other financial obligations. But none of this undermines (3).

The point of this little story is to respond to an argument Michael Blome-Tillmann makes in “a paper”:http://users.ox.ac.uk/~quee1101/papers/mbt_mate.pdf attacking interest-relative invariantism (IRI). (He calls IRI ‘SSI’, which I think is unfortunate, since everyone agrees that knowledge is subject-sensitive. No one thinks S knows that p entails T knows that p.) Here is one of the arguments he makes.

Suppose that John and Paul have exactly the same evidence, while John is in a low-stakes situation towards _p_ and Paul in a high-stakes situation towards _p_. Bearing in mind that SSI is the view that whether one knows _p_ depends on one’s practical situation, SSI entails that one can truly assert:

(11) John and Paul have exactly the same evidence for _p_, but only John has enough evidence to know p, Paul doesn’t.

And this is meant to be a problem, because (11) is intuitively false.

But SSI doesn’t entail any such thing. Paul does have enough evidence to know that _p_, just like George has enough money to buy the computer. Paul can’t know that _p_, just like George can’t buy the computer, because of their practical situations. But that doesn’t mean he doesn’t have enough evidence to know it. So there isn’t a problem for SSI here.

In a footnote attached to this, Blome-Tillmann tries to reformulate the argument.

I take it that having enough evidence to ‘know _p_’ in _C_ just means having evidence such that one is in a position to ‘know _p_’ in _C_, rather than having evidence such that one ‘knows p‘. Thus, another way to formulate (11) would be as follows: ‘John and Paul have exactly the same evidence for _p_, but only John is in a position to know _p_, Paul isn’t.’

The ‘reformulation’ is obviously bad, since having enough evidence to know _p_ isn’t the same as being in a position to know it, any more than having enough money to buy the computer puts George in a position to buy it. But might there be a different problem for SSI here?

No; the reformulated argument isn’t a problem because the conclusion is not unacceptable. Indeed, the conclusion is a kind of conjunction that is made true all the time, on relatively uncontentious theories of evidence. Consider this example.

Mick and Keith both have evidence _E_, which is strong inductive evidence for _p_. And _p_ in fact is true, just as _E_ would suggest. If Keith were to conclude _p_ on the basis of _E_, that would be knowledge. But Mick has been taking some philosophy classes. And as luck would have it, he has been taking classes from a smart Popperian, who has convinced him that induction is not a source of knowledge. Now if Mick concluded _p_ on the basis of _E_, this would not be knowledge, because his Popperian beliefs would constitute a doxastic defeater. So Mick and Keith have exactly the same evidence for _p_, but only Keith is in a position to know _p_, Mick isn’t.

I think it’s interesting to think about ‘afford’ in this context, since it seems very likely that some kind of IRI analysis of ‘afford’ will be true. We don’t want to have any kind of contextualism about ‘afford’, at least nothing like modern day epistemic contextualism. It would be crazy to say that if _my_ rent is $5000, and it is due tomorrow, then (2) is false, because after all, in my context someone with Ringo’s money couldn’t buy the computer and meet their financial obligations. If I’m right that ‘afford’ is interest-relative, then looking at the way ‘afford’ patterns should provide some useful evidence for or against IRI.

More details on the forthcoming Nottingham A Priori Workshop (9th October) are now available, including the programme and information on how to register.

Attendance is free (though we do require advance registration), lunch, tea and coffee are provided, and the speakers are Anthony Eagle (Oxford), Jessica Brown (St Andrews), myself (Nottingham) and Michael Devitt (CUNY/Nottingham Special Professor).

I converted the bibliography in my “SEP entry on David Lewis”:http://plato.stanford.edu/entries/david-lewis/ to BibTex format, and along the way fixed up some errors. I think this is the most complete and accurate Lewis bibliography in existence, but any suggestions for how to make it more accurate would be appreciated.

• David Lewis bibliography (BibTex)

I also made a printout of the bibliography. I couldn’t get it sorted by year as I wanted. (I tried the ‘plainyr’ package, but it messed up the location of books in the sort order.) So it’s sorted by first author, which is a little quirky. Anyway, in case it is helpful to anyone who wants to check it over, here it is.

• David Lewis bibliography (PDF)

The BibTex file is based on a download from the wonderful “PhilPapers”:http://philpapers.org website, though I’ve made a number of additions to it. But most of the issue numbers, for instance, are taken from the PhilPapers download, and many would have been unobtainable without that start.

UPDATE: Duncan Watson told me that there are some letters from David Lewis published in The Law of Non-Contradiction. I’ve included them (at his suggestion) as ”Letters to Priest and Beall” in the bibliography.

UPDATE 2 (Sept 2, 11am): I’ve updated the files to include the omissions pointed out by Wo in the comments. Thanks to Wo for spotting all those!