zompist wrote: ↑Thu Jul 09, 2020 8:35 pm
priscianic wrote: ↑Thu Jul 09, 2020 12:13 pm
Another puzzle about epistemic contradictions is that, as
Beddor and Goldstein (2018) point out, it's perfectly reasonable to personally hold a belief in
p, while also acknowledging that that belief might be mistaken and that it might be the case that not
p. But asserting both of these things at once, in the same breath, ends up sounding odd (to most people, I guess).
It's odd only if you view eliminating contradictions as possible in practice.
I assume you know Makinson's
paradox of the preface. Authors usually state that "remaining errors in the book are mine", and yet if asked, would maintain that they've fact-checked everything and are not
aware of any errors. This is hard to address with classical logic, but on a human level it's neither strange nor uncommon.
I'm not actually aware of the paradox of the preface—thanks for alerting me to it!
It's hard to address with classical logic, but that's why natural language semanticists don't use pure classical logic :p
It's very common to use tools from modal logic and multivalued logics, as I mentioned previously, and as well to embed the denotation of individual sentences within the an explicit theory of discourse context (i.e. to recognize that pragmatics exists, and should be explicitly theorized). (There's a whole subfamily of semantics called "dynamic semantics" which treats the meaning of sentences not as truth conditions but rather as functions from discourse contexts to discourse contexts, and as such takes very seriously the idea that utterances are made in a context in a very specific way).
zompist wrote: ↑Wed Jul 08, 2020 4:46 pm
priscianic wrote: ↑Thu Jul 09, 2020 12:13 pm
Yeah, this kind of data is one of the big arguments for the "
must is weak" camp—e.g.
Lassiter (2016), who argues for a probablistic semantics for
must. As you note, it's quite tricky to deal with this for the "
must is strong" camp, and you're forced to say something that perhaps isn't so satisfactory.
I'm glad we agree on this, though I'd note that
in form these sentences are identical to "It must be raining, but perhaps it's not." Classical logic at least doesn't let us peer into a proposition P to see if it's inherently difficult to test.
Yeah, exactly—this is precisely why von Fintel and Gillies have to appeal to pragmatics and the context-sensitivity of assertion in order to deal with this data.
zompist wrote: ↑Thu Jul 09, 2020 8:35 pm
priscianic wrote: ↑Thu Jul 09, 2020 12:13 pm
I'm not sure if I understand what the disagreement is then—neither I nor von Fintel and Gillies (nor Lassiter, nor Mandelkern, etc.) are challenging the idea that
must indicates deductive grounds/indirect evidence for our belief---I think everyone (now) acknowledges that this is probably true. But the question that people are arguing about in the literature is whether
must p entails
p, or if it doesn't.
It seems to me that you want to divide up "must" into two things, one of which we agree on.
I don't see that there's a pragmatic or deductive part that you can take away, leaving some sort of "essence of must" where must(p) -> p. To me the parts you want to set aside-- the things we both acknowledge weaken its meaning-- are key to its meaning. But perhaps I just don't understand you... what is the "other part" of "must"?
Ah, no, I think you're misunderstanding the position. The position is that
must has, at its core, the meaning of the necessity operator ☐ from modal logic—i.e. ☐p is true at a world
w iff for every world
v that is "accessible" from
w by some relation R (i.e.
wR
v), p is true in
v.
Now, what is R? What are these "accessible worlds"? Here, there's some freedom and context-sensitivity to play with. Making use of this context-sensitivity, von Fintel and Gillies formalize for us some ways to restrict R and these accessible worlds
v in order to capture the deductive character of
must (they don't characterize it in exactly this way, but this is essentially what they're doing). And of course, the set of worlds that are accessible via R is context-sensitive—intuitively, you'd only consider the relevant/salient possibilities. According to them, it's the combination of those two things that gets you the right characterization of the felt weakness of
must.
They also want the R you get with epistemic modals to be "reflexive"—i.e. for
wR
w to be true in all worlds in the model. This is supposed to be a characteristic of epistemic modals—they quantify over worlds that are open possibilities for what the actual world could be—so the "accessibility relation" R that you get with an epistemic modal needs to be reflexive, in order to capture this intuition. (Actually, strictly speaking, all you need is that the actual world
w* be accessible from itself. But general reflexivity is equivalent for our purposes here.) A consequence of the reflexivity of R is that if you universally quantify over all worlds
v such that
wR
v, then you'll also end up quantifying over
w as well. Thus, ☐p ends up entailing p (i.e. ☐p being true in a world
w entails that p is true in
w).
Von Fintel and Gillies think that this entailment is fine, and that we can capture the data by appealing the indirectness of
must to capture its felt weakness, plus some pragmatic principles. Lassiter, in contrast, thinks that this entailment is bad, and he weakens the meaning of
must to instead quantify over
almost all of the accessible worlds (a kind of probabilistic semantics), with the threshold of what counts as "enough" worlds being contextually variable. (And then he can also do some extra stuff to capture the deductive character of
must, just like von Fintel and Gillies).
So at its core, I think the disagreement can be boiled down to the following: von Fintel and Gillies (and others) think that the entailment from
must p to
p is fine, and that we can capture the weakness of
must with a combination of indirect evidentiality and the context-sensitivity of the relevant accessibility relation R. In contrast, Lassiter (and others) think that this entailment is terrible, and that we can't capture the weakness of
must with just indirect evidentiality and context-sensitivity of R, and that we have to instead weaken
must to quantifying over only
most of the relevant worlds, rather than
all of them (with the appropriate context-sensitivity for how many worlds count as "most" worlds, of course).
I hope that all makes sense...
zompist wrote: ↑Wed Jul 08, 2020 4:46 pm
When you say "emphasizes where language does not work like logic", I wonder what kind of logic you mean? I think most semanticists well understand that human language doesn't work on the principles of classical logic—this is why we make use of the tools of modal logic, or sometimes multivalued logics, etc.
It goes beyond "if", which he discusses. The words "and, or, each, every", and more, don't exactly match their logical counterparts.
This doesn't mean that there's something wrong with logic, just that we can't just say that e.g. "and" means AND and that's it. And conjunctions are relatively simple.
Tell me about it! You'd hope that conjunctions are simple, but then you see that people have written
1000-page books on the semantics of natural-language "and"...(though, funnily enough, Schein's argument is actually that "and" is
always Boolean conjunction, and he has to spend 1000 pages defending that thesis and addressing all the counterarguments...)