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.
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.
(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!