Perhaps, perhaps, perhaps

Epistemic modals give rise to many puzzles. Here is one pointed out by Seth Yalcin in his paper ‘Epistemic Modals’ in Mind:
Sentences of the form “p but perhaps not p” (call them Yalcin-sentences) are generally not assertable (you may substitute ‘perhaps’ with other modal phrases expressing epistemic possibility here.) For instance, any utterance of

(1) It’s raining but perhaps it is not raining.

is rejectable.

This observation may seem reminiscent of Moore-paradoxical sentences such as:

(2) It’s raining but I don’t believe it’s raining.

The problematic character of (2) does not seem to be a semantic phenomenon. After all, the proposition expressed by sentence (2) is not contradictory but can indeed be true. The non-assertability of (2) then clearly seems to be a pragmatic phenomenon. Can the defect of Yalcin-sentences such as (1) be assimilated to that of Moore-paradoxical sentences?

Yalcin argues it cannot. He draws attention to the fact that Moore-paradoxical sentences behave well in suppostional contexts. That is, the embedding of such a sentence in a suppostional phrase it not defective any more. By way of illustration, the following sentences may have a proper use in certain conversations:

(3.1) Suppose it’s raining but I don’t believe it’s raining.
(3.2) If it is raining but I don’t believe it’s raining, then I am wrong.

However, the case is different with Yalcin-sentences. They resist even being embedded in suppositional contexts, as the following examples show:

(4.1) Suppose it’s raining but perhaps it is not raining.
(4.2) If it’s raining but perhaps it is not raining, then …

So, Yalcin develops a logic for epistemic modals on which (1) comes out contradictory.

However, both the motivation for his logic as well as his specific proposal leave us unconvinced. Let us comment on both points.

1. The motivation of Yalcin’s proposal. One should notice that simple sentences with epistemic modals already resist embedding in the contexts mentioned by Yalcin. By way of illustration, take the following examples:

(5.1) Suppose it is perhaps raining.
(5.2) If it’s perhaps raining then …

Unless the modals are understood in a non-epistemic sense here, it seems hard to make any sense of such contexts.
But then it seems that the deficiency of the complex (4.1) and (4.2) is inherited from the deficiency of the simpler (5.1) and (5.2). The latter are, however, clearly not contradictory. So, we need an alternative explanation of their deficiency. In his ‘Expressivism Concerning Epistemic Modals’ (forthcoming in Philosophical Quarterly), Benjamin proposes an expressivist account of epistemic modals and uses it to explain what is wrong with (5.1) and (5.2).

2. Yalcin’s logic of epistemic modals. Moritz examines Yalcin’s notion of informational consequence in his ‘Epistemic Modals and Informational Consequence’ (forthcoming in Synthese). He argues that it is inadequate as an account of the logic of epistemic modals. Informally put, his main argument is as follows:
On Yalcin’s account,

(6) They must be at home.

follows from

(7) They are at home.

However, in many situations you can have evidence which gives you a high credence in (7) while it leaves some amount of uncertainty. (You pass by their home and see that their lights are on; since they usually turn their lights off, you think that they are at home, but you are not 100% certain). In such a situation, then, you assign a high credence to (7), while you should assign a low credence to (6) (after all, you are not certain that they are at home). So, on Yalcin’s account, there are cases in which it is rational to take a statement to be probable without taking an immediate logical consequence of it to be probable as well. Thereby, the account violates a reasonable constraint on logical consequence.

Are we right with our criticisms? As an answer, we’d like to quote Cake: Perhaps, perhaps, perhaps!



  1. I agree that the deficiency of (4.1) and (4.2) should be explained in terms of the deficiency of (5.1) and (5.2), but an obvious problem for the expressivist solution is that it drives a wedge between epistemic and objective uses of ‘might’. The standard linguistic theory of ‘might’ says that it expresses existential quantification over possible worlds, while the different uses (i.e. epistemic, objective) correspond to different choices of the set of possible worlds that constitutes the domain of quantification. On the expressivist account, that picture doesn’t apply anymore, which raises the question why we use the same word for both uses?

    Despite the fact that “perhaps” and “may” do not scope under negation, what about “John can’t be home” or “John need not be home” (with emphasis on the modal)?

  2. Uuh, tough questions … Here is what we think about them:

    1. Different uses of modals.

    What has to be accounted for is the following observation:

    There are different readings (in a wide and liberal sense of ‘reading’ ) of modal expressions in natural languages. At least some of them allow a reading on which they bring some sort of epistemic dimension into play, and another reading in which they bring some non-epistemic dimension into play.

    What you suggest is that

    (i) the quantificational story about (both epistemic and objective) modals, on which the different readings correspond to different domains of worlds, can easily account for the datum
    (ii) the expressivist account of epistemic modals cannot (easily) account for it.

    Concerning (i), we partly agree (though only partly):

    The proponent of the quantificational story can say that the different readings of modals result from different domains of quantification. So, basically they result from shifting a certain parameter to which ‘might’s are sensitive. So far, this sounds like a nice and neat explanation of why we use the same expression in different readings.
    However, we think that this cannot be quite the whole story, since there are severe restrictions on what the domain of quantification can consist in. The relevant domain of quantification will never be, say, the set of tables or the set of tablets. Simplifying a bit, it can consist either in a certain set of epistemically possible worlds or in a set of metaphysically possible worlds (ignoring the deontic case).
    The problem is that epistemically possible worlds and metaphysically possible worlds are very different in kind. That Goldbach’s conjecture is false may be epistemically possible but it is not possible in any objective sense. Instances of the contingent a priori provide examples that the converse does not hold either. So, we think that the proponent of the quantificational story still has to explain why it is exactly these two domains (with optional restrictions on each) that are admissible.

    Concerning (ii), we think that one should distinguish two elements of the expressivist account:

    – first, such an account says that an epistemic modal does not modify the truth-conditions of sentences but rather conditions of the speech-act performed (and/or, perhaps, its acceptance conditions).
    – second, such an account still has to specify what the specific contribution of the modal to the relevant conditions is (e.g., in the case of ‘mit might be that p’, that the speaker is not certain that not p).

    The quantificational account you seem to have in mind also has two components:

    – first, it says that an epistemic modal modify the truth-conditions of sentences.
    – second, it says that they introduce a quantification over different kinds of worlds.

    Because of that, we do not think that one can simply contrast the quantificational and the expressivist account. For, one can combine the second element of the quantificational story with the first element of the expressivist account. The resulting expressivist position would be that an epistemic modal affects the conditions under which an utterance is acceptable, while the way it does that is spelled out in terms of quantification over epistemically possible worlds.

    Anyway, we think that the important thing to explain is why modals have the epistemic and the objective dimension (whether those dimensions affect truth-conditions or conditions of the speech-act performed). And that is not explained by saying that two kinds of worlds are in play, because the two kinds of worlds are yet so different that we should explain why a single expression is used with those specific domains.
    How could the explanation look like. Here is our current hunch of an evolutionary explanation: people are not very good in distinguishing between things they cannot exclude on the basis of their knowledge and things that are objectively possible. They tend to infer objective possibility from ignorance (epistemic possibility) alone. So it may be that the epistemic reading is somehow parasitic on the objective reading: it became an option because uncertainty was the typical ground for statements of objective possibility.

    2. Scope and negation.

    Indeed, the data on what scope epistemic modals can take are not as uniform as we would like them to be. (By the way, this seems to be a difficulty for any theory about them.) In the cases you mention, one possibility (which you seemed to favour yourself once) would be to say that, for some reason or the other, those constructions form a single linguistic unit, rather than following some straightforward compositional rules. But we admit that this is a difficulty that one should think about more.

    Benjamin & Moritz

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