John MacFarlane, UC Berkeley
July 1, 2011 @ Sydney
Any account of the meaning of “it is possible + INDICATIVE” must allow us to explain what is wrong with asserting or believing an epistemic contradiction.
This is a strong constraint. For example, it rules out interpreting “it is possible + INDICATIVE” as expressing logical possibility.
It’s bad to believe that p and it’s possible that not-p because this belief can be true only if it does not amount to knowledge.
It’s bad to assert that p and it’s possible that not-p because in doing so one represents oneself as knowing that p, while saying (in effect) that one does not know that p.
Wrong subject matter
Agreement/disagreement
Retraction
When I say, ‘Bob might be in his office,’ I am talking about Bob and his office, not myself or the extent of my information. Suppose the building is on fire and everyone has been told to leave. I am afraid that Bob might still be in his office. I am not afraid that I don’t know he’s elsewhere. (Yablo 2011, 230–1)
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
A: It’s possible that the letter will arrive tomorrow.
B: #I agree, but it can’t arrive tomorrow; they told me yesterday that they hadn’t even mailed it yet.
If I disagree with your claim that it is probably going to snow, I am not disagreeing that given your evidence it is likely that this is so; but indicating what follows from my evidence. Indeed, I might agree that it is probably going to snow and yet think it false that this follows from your evidence. (Price 1983, 403)
Does it help to interpret the modal relative to all the evidence that is available in principle?
…consider the surgeon who says, ‘Your operation has probably been successful. We could find out for sure, but since the tests are painful and expensive, it is best to avoid them.’ The accessibility, in principle, of evidence which would override that on which the [single-case probability] judgment is based, is here explicitly acknowledged. (Price 1983, 405)
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
A: Ah, then I stand corrected/I take that back.
It is possible that p is not used to make assertions, but to express an attitude of leaving-it-open-that p. The phrase that it is possible that p does not express an assertible content; possible modifies force, not content.
It is possible that p expresses a possible content of judgment and assertion, but the truth of this content is relative not just to a possible state of the world but to an information state. The correctness of an assertion with this content varies with the context of assessment, and depends on the information of the assesser, not that of the speaker.
It is possible that p expresses a state of regarding p as an open possibility
Its communicative purpose is not to convey information, but to effect coordination on what questions are open and relevant.
Epistemic contradiction is bad because it expresses the impossible mental state of believing that p while not believing that p (regarding not-p as an open possibility).
It’s possible that Bob is in his office expresses an attitude towards the proposition that Bob is in his office, which is the real subject matter.
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
A: Ah, then I stand corrected/I take that back.
What to say about embedded uses, which do not modify force?
It is not possible that the letter will arrive tomorrow.
If it is possible that the letter will arrive tomorrow, then we should leave today.
If the letter was mailed on Tuesday, then it is possible that it will arrive tomorrow.
Joe thinks it is possible that the letter will arrive tomorrow.
There are at least two students who might fail the exam.
Hare suggested that an understanding of “If that is a good movie, then…” and “If …, then that is a good movie” could be derived from a generic understanding of “If…then” (as a modus ponens license) and an understanding of the unembedded “that is a good movie.”
a thought echoed by many expressivists since, including Horwich and Price.
But it is possible that φ behaves differently than non-modalized sentences in conditionals, in ways that can’t be predicted from facts about their standalone behavior:
Modus tollens
If it is raining, then the streets are not dry.
The streets are dry.
So, it isn’t raining.
If it is raining, then it is not possible that the streets are dry.
It is possible that the streets are dry.
So, it isn’t raining. (!)
But it is possible that φ behaves differently than non-modalized sentences in conditionals, in ways that can’t be predicted from facts about their standalone behavior:
Yalcin’s observation
If it is raining and none of us know this, then we’re deluded.
#If it is raining and it it is possible that it isn’t raining, then we’re deluded.
But it is possible that φ behaves differently than non-modalized sentences in conditionals, in ways that can’t be predicted from facts about their standalone behavior:
Interaction with subjunctives
We know that the gun wasn’t his. But if we hadn’t checked the state records, we wouldn’t know this.
#It’s not possible that the gun was his. But if we hadn’t checked the state records, it would have been possible that the gun was his.
But this is too quick.
Indices will include a world and an information state, which we’ll represent as a set of possible worlds.
Terminology: A sentence φ is accepted at c, i iff ∀ w ∈ i, φ is true at c, i, w.
It rained in Seattle on December 3, 1967 is true at c, i, w iff it rained in Seattle on December 3, 1967 in w.
Poss φ is true at c, i, w iff
∃ wʹ ∈ i, φ is true at c, i, wʹ
Nec φ is true at c, i, w iff
∀ wʹ ∈ i, φ is true at c, i, wʹ
If φ , ψ is true at c, i, w iff
for every maximal φ-accepting subset iʹ of i, ψ is accepted at c, iʹ.
A sentence φ is true as used at c and assessed from cʹ
iff φ is true at c, icʹ, tc, wc.
A content p is true as used at c and assessed form cʹ
iff p is true at icʹ, wc.
Constitutive norms governing assertion:
Norm governing belief:
Yalcin’s observation:
If p but I don’t know that p, then I’m deluded.
#If p but it is possible that not-p, then I’m deluded.
This cuts against ordinary subjectivism, but not the relativist view, which predicts the difference.
There is no nonempty set of worlds at which
p but it is possible that not-p
is accepted, so the second conditional crashes.
Predicted to be invalid:
If it is raining, then it is not possible that the streets are dry.
It is possible that the streets are dry.
So, it isn’t raining. (!)
#It’s not possible that the gun was his. But if we hadn’t checked the state records, it would have been possible that the gun was his.
This semantics allows us to shift the world independently of the information state.
The content expressed by
It is possible that Bob is in his office
is not about the subject or any particular body of information; it is “informationally neutral,” in the sense that its truth varies with the information state.
Moreover, the correctness of an assertion of this content does not hang on any particular information state; it, too, is relative.
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
According to subjectivism, B should agree that what A said is true. Relativism does not make this prediction.
A: It’s possible that the letter will arrive tomorrow.
B: No, it’s not possible. They told me yesterday that they hadn’t even mailed it yet.
A: Ah, then I stand corrected/I take that back.
Retraction is called for by the norm governing retraction.
The relativist view retains what is appealing about subjectivism while avoiding its problems. And it solves the compositionality problem where expressivism cannot.
Coopt the techniques of truth-conditional semantics to give a systematic representation of incompatibility and implication relations between descriptive, normative, and mixed sentences.
Sentences “hold” or “do not hold” relative to a world and complete normative system.
We can recursively define “holds at w, N”.
S implies T if T holds at every pair where S holds.
S is incompatible with T if there is no pair at which both hold.
Uses the same compositional semantics as the relativist.
Semantic values of sentences are information-state relative, but nothing follows from this about the contents of assertions or mental states.
Epistemic possibility claims and beliefs are not “factual,” in the sense that they don’t rule out possible worlds. (Instead, they rule in possible worlds.)
They do not have “information content,” the sort of thing that can be modeled by a set of possible worlds.
Their communicative purpose is to engender coordination on which possibilities are open.
These features are all shared with the relativist view.
Yalcin denies that questions of truth arise for epistemic possibility claims (e.g. 326).
Care is needed here. It’s part of ordinary talk to say:
It’s true that it might be raining.
He said it might be raining, and what he said is true.
Our semantics should explain this. The expressivist can coopt the relativist semantics for monadic “true,” which gives it disquotational properties.
In what sense, then, do questions of truth not arise?
Yalcin denies that these information-relative semantic values correspond to a distinctive class of belief contents.
One might think of this as an ‘adverbialist’ model of epistemic possibility belief. Such beliefs do not correspond to a distinctive class of believed contents; rather, they correspond to a distinctive way of being doxastically related to a proposition. (309)
In the simplest version: “it might be raining” expresses the absence of belief that it is not raining; believing that it might be raining just is not-believing that it is not raining. In the more sophisticated version:
To believe that a proposition is possible, or might be, is for the proposition to be compatible with one’s view, and moreover for it to be an answer to a question one is sensitive to. (319)
There are good compositional semantic reasons to give a relational semantics for “believes,” on which it expresses a relation between a person and a content.
Sam doubts everything that Joe believes.
Joe believes that John Lennon lives.
So, Sam doubts that John Lennon lives.
But if the expressivist does this, the contents must be informationally neutral.
Surely the relation expressed by “believes” is the relation of believing. So it follows that epistemic possibility beliefs do have distinctive contents.
For Yalcin, believing that it is possible that p just is leaving p open [= being sensitive to the question whether p, while not believing not-p.]
For me, these are distinct state types, and it is possible to be in one without being in the other, though this is normatively bad.
Similarly, for Yalcin, believing that it is more likely than not that p just is having a credence > 0.5 that p.
For me, these are distinct state types. But if you are trying to believe what is true (as assessed from your current context), and trying to conform your credence to your evidence, then you’ll try to make sure that you believe that it’s more likely than not that p just when you have a credence > 0.5 that p.
Yalcin’s view makes a certain kind of epistemic akrasia impossible:
believing that it is possible that it is raining while believing that it is not raining.
believing that it more likely than not that the card is a spade while having a credence of 0.4 that the card is a spade.
In the same way, Gibbard’s view makes a certain kind of normative akrasia impossible:
The choice between expressivism and relativism hangs on whether you think this is a bug or a feature.
Yalcin’s view implies that any creature with the conceptual resources to entertain the question whether p and believe that p is also capable of believing that it is possible that p.
Fido believes that I might give him a bone.
On the relativist view, extra conceptual resources are needed, beyond what is needed to believe that p, to believe that it is possible that p.
Again: bug or feature?