Epistemic Modals and Modality

24 06 2006

On Thursday and Friday this week there was a conference on epistemic modality here at ANU – though more of it ended up being about the semantics of epistemic modal words. Unfortunately, John MacFarlane and Brian Weatherson couldn’t be here, so the conference was trimmed slightly.

On the first day, Frank Jackson wondered about how we should assign probabilities to possible worlds so that we don’t end up with metaphysical omniscience – his answer was basically that our credence in a sentence should be the sum of the probabilities of the worlds contained in its A-intension, rather than its C-intension (I hope I’m getting the terminology right). That is, rather than finding out what proposition the sentence expresses and summing the probabilities over the (centered) worlds where that proposition is true, we should figure out in which centered worlds the sentence expresses a proposition that is also true in that centered world, and sum over those. So for instance, although “water is H2O” actually expresses a necessarily true proposition, there are worlds (ones like Putnam’s twin earth) in which “water” refers to a different substance, so the proposition expressed at that world ends up being false at that world. Since there might be worlds that we can’t tell apart from the actual one, it makes sense that those would play a role in our probability assignments. (My concern about the whole framework is a worry about why we should be assigning probabilities to sets of worlds in the first place, rather than to something more epistemically accessible – in which case the problem doesn’t arise.)

Andy Egan spoke about his version of relativist semantics for epistemic modals. Since I’ve mainly only been exposed to John MacFarlane’s version, I was quite interested in this. It does sound to me that the frameworks could be intertranslatable, if done carefully. John does this approximately by saying that the proposition expressed by uttering “might P” at CU is true when assessed at CA iff the proposition expressed by P (at CU?) is compatible with the knowledge of the agent at CA. Andy does it approximately by saying that the proposition expressed by uttering “might P” is a set of centered worlds including all centers whose knowledge is compatible with P. So roughly, John seems to view the proposition as a function, while Andy views it as a set. However, their main differences are in the norms for asserting and denying such statements, which I don’t think I understand fully enough for either – but they’ll have to give some convincing story in order to be able to say that propositions aren’t just true or false simpliciter.

Matt Weiner picked up where Andy Egan left off and gave an interesting argument for why we might have relativist semantics for epistemic modals, rather than contextualist semantics, like we do for “I”, “here”, and other similar terms. Basically, the idea is that we’ve got a conversational norm that one shouldn’t let a proposition one judges false remain unchallenged. Then relativist semantics makes it easy for people to assert modals to share their ignorance, and requires others to share their knowledge to fix this state. So this semantics makes them good tools for joint inquiry.

Seth Yalcin started the next morning by pointing out that epistemic modals lead to a certain type of Moore’s paradox. The ordinary paradox is approximately, “It’s raining, but I don’t know that it’s raining”, which is certainly a very bad thing for anyone to ever assert, but is perfectly reasonable to suppose or embed in the antecedent of a conditional. Depending on your account of epistemic modals, this should mean approximately the same as “It’s raining, but it might not be raining” – which is just as bad to assert, but is interestingly about equally bad to suppose or embed in a conditional. (Compare, “If it’s raining, but I don’t know that it’s raining, then I must be confused”, while “If it’s raining, but it might not be raining, then (I must be confused/it’s raining/etc.)”.) Then he attempted to explain this by giving a very interesting semantics involving sets of probability functions over sets of worlds, rather than just sets of worlds. I’m very interested in looking more at the details of that as he works it out.

Jonathan Schaffer then argued for the KGB account of modals over the CIA account. (That is, the contextualist view he called “Kratzer’s Graded Basis” over the relativists’ “Contexts and Indices of Assessment”.) He disputed the accuracy of a lot of the CIA data, showed that the KGB deals better with modals of all sorts (with epistemic modals just a special case), and showed that some of the propaganda pushed by CIA agents is predicted by the KGB, so it shouldn’t mislead us.

Finally, Dave Chalmers returned to the notion of epistemic modality, after four papers on semantics, and disputed Frank Jackson’s idea of doing epistemic modality in terms of worlds. Instead, he suggested that there should be some space of epistemic possibilities, which are effectively something like maximal consistent conjunctions (or perhaps sets, to deal with infinities?) of sentences. However, the sentences should be phrased in some basic vocabulary that is sufficient to deal with all concepts whatsoever, and “consistent” means “not knowable to be false by any a priori means”. Thus, he’s allowing much stronger reasoning principles than just first-order logic, because he thinks that all mathematical claims (for instance) can be settled by a priori reasoning (which I guess must therefore be much stronger than Turing complete). Also, he’d like to modify this view to deal with epistemically non-ideal agents.

Anyway, it was quite an interesting conference, I learned a lot, and I’m very interested in seeing how these projects continue to develop!

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One response

7 07 2006
Matt Weiner

Then relativist semantics makes it easy for people to assert modals to share their ignorance

Strictly speaking, this part of the point was made during discussion by some guy.

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