'Perhaps' and 'Surely'
Isidora Stojanovic
Institut Jean-Nicod / CNRS
(abstract)
In this paper, we propose a non-truth-conditional (albeit model-theoretic) approach to the meaning of words like 'perhaps', 'surely', 'definitely', etc., and to epistemic modals more generally. That words such as 'perhaps' are truth-conditionally inert has been argued by others (e.g. Edgington (1995)), and it will not be properly our goal to argue that it is impossible to provide a truth-conditional semantics for such words. In fact, some recent truth-conditional accounts of epistemic modals, as in Egan et al. (2005), von Fintel and Gillies (2006), or MacFarlane (2006), are easily applicable to words like 'perhaps', and though those accounts might be problematic in various respects, they are certainly not hopeless. Our position is, rather, that, given the apparent difficulties that the truth-conditional approach faces, there is no compelling reason to pursue it. As Barwise and Perry pointed out with what they called the "fallacy of misplaced information" (1983), it is a mistake to think that all the information that one can correctly derive from some utterance ought to be traced to the semantic (or truth-conditional) content of the sentence uttered. Words such as 'perhaps' are, we believe, precisely such: they provide information on the speaker's epistemic evidence, and on her justification for saying what she says, without reaching into the truth conditions of the asserted content. Our goal in this paper is to propose a non-truth-conditional analysis of this lexically encoded function of 'perhaps', viz. that it serves to inform the hearer that the speaker's evidence does not exclude the falsity of the claim qualified with 'perhaps'. Since the proposed analysis is nevertheless model-theoretic, it will be easy to compare it with the above mentioned truth-conditional accounts, and we will point out certain aspects in which ours appears to be superior to those. 
1. The Data
Suppose that Jorge asks Carmen if she knows where Professor Villalobos might be, and consider three replies that she might make:
(1) Perhaps he is in his office.
(2) He is in his office.
(3) He is surely in his office.
Our claim is that (1), (2) and (3) do not differ in their truth conditions. In other words, (1) is true iff (2) is true, and either is true iff (3) is true. Now, the proposed truth conditions, which make 'perhaps' truth-conditionally equivalent to 'surely', are not intuitively obvious. For, intuitively, even if Prof. Villalobos is not in his office (at the time of (1)), the intuition is that Carmen was not really wrong to say (1) – provided that she did not know that he was not in his office. On the other hand, it is problematic to say that (1) may be true in circumstances in which it is also true that Prof. Villalobos is not in his office, given that the following conjunction simply sounds incoherent:
(4) Prof. Villalobos is not in his office and perhaps he is.
Of course, one might try to argue that (4) is coherent, even if it can never be truly uttered. One would then say that there are circumstances relative to which (4) is true, though there is no context in which an utterance of (4) is true. What is more interesting for us, though, is that examples such as (1)-(3) clearly show that the primary job of words like 'perhaps' and 'surely' is to provide information on what is known, or at least believed, in the context of utterance. And this is, too, what epistemic modals do:  
(1) He might be in his office.
(2) He is in his office.
(3) He must be in his office.
2. The Theory
The gist of our proposal is that, in addition to the notion of truth (in a model) we also have a notion of truthfulness, which will also be a model-theoretic notion. The idea is that, on the assumption that Prof. Villalobos is not in his office but that Carmen's evidence does not exclude his being in his office, her utterance of (1) is false, yet it is a truthful utterance. On the other hand, if Carmen knows that Villalobos is not in his office, then typically, her utterance of (1) is not just false, but also untruthful. We say "typically" because our account does not commit us to saying the truthfulness of an utterance is necessarily linked to the speaker's evidence. Our account is more flexible. Thus suppose that Jorge already checked into Villalobos's office before asking Carmen where he was. Then her utterance of (1), though truthful from her own perspective, is untruthful from Jorge's perspective. (In this sense, our account bears some similarities to MacFarlane's.) 
So let us outline the formal account. Truthfulness will be a relation between models and sentences (very much in the way in which, in formal semantics, truth is a relation between models and sentences), and we will use the notation M ||– F to mean "sentence F is truthful with respect to model M", and, as usual, M |= F will mean that F is true with respect to M.
The definition of truth is the usual one, except that we need to provide truth clauses for the epistemic modal operators 'perhaps' and 'surely'. However, those operators are idle with respect to truth conditions, so the clauses are:
S,w,t,f |= Perhaps (F) iff_def S,w,t,f |= Surely (F) iff_def S,w,t,f |= F
Turning now to the definition of truthfulness, if F is a sentence that contains no epistemic expressions, then, by definition:
M ||– F iff_def M|=F.   
Otherwise, the truthfulness of sentences containing 'perhaps' or 'surely' is recursively defined upon the truthfulness of the embedded sentence. The model M will be a quadruple (S, w, t, f), with S a structure of interpretation, w a possible world, t a time and f an assignment of values to variables. The clauses are:
S,w,t,f ||– Perhaps_x(F) iff_def there is w' such that wR_f(x),tw', and S,w',t,f ||– F     
S,w,t,f ||– Surely_y(F) iff_def for every w' such that wR_f(y),tw', S,w',t,f ||– F
The structure of interpretation S will provide a bunch of accessibility relations (R_A,t1, R_B,t2, etc.). Intuitively, w is accessible from w' via relation R_A,t when the information available to agent A at time t does not enable A to tell w' from w: "for all A knows or believes at t in w, w' might turn out to be the actual world." (The use of such accessibility relations is not novel – it comes from epistemic logic and is used in providing the semantics of doxastic expressions such as “A believes that”; cf. Hintikka (1962).)
Two things deserve emphasizing. First, both 'perhaps' and 'surely' are indexed with a variable, and the value assigned to the variable specifies the relevant agent and ipso facto the relevant accessibility relation. That is how we can account for the fact that (1) is truthful from Carmen's perspective, while untruthful from Jorge's perspective. We may say that by default, the value that indexes 'perhaps' and 'surely' takes the speaker as its value. However, that is not mandatory, and this flexibility proves to be a great advantage when it comes to the phenomenon of the "third party assessment" (cf. MacFarlane (2006)). Secondly, the relevant accessibility relation also depends on the time at which a sentence is evaluated for its appropriateness. This will similarly help to account for the data regarding the phenomenon that came to be called "retrospective assessment".   
The remainder of our paper consists in applying this account to the data under consideration.
References
Barwise, J. and J. Perry (1983), Situations and Attitudes, MIT Press
Edgington, D. (1995). “On Conditionals,” Mind 104: 235–329.
Egan, A. (2006). “Epistemic modals, relativism and assertion,” Philosophical Studies, forthcoming.
Egan, A., J. Hawthorne, and B. Weatherson (2005). “Epistemic modals in context,” in: G. Preyer and G. Peter (eds.), Contextualism in Philosophy (New York: Oxford University Press).
von Fintel, K. and A. Gillies. (2006) "CIA Leaks," (ms.)
 Gibbard, A. (1981). “Two recent theories of conditionals,” in W. L. Harper, R. Stalnaker, and G. Pearce (eds.), Ifs(Dordrecht: Reidel).
Hintikka, J. (1962). Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell: Cornell University Press
MacFarlane, J. (2006). “Epistemic modals are assessment-sensitive,” (ms.)
Swanson, E. (2005). “Something ‘might’ might mean,” (ms.)