Might, would, will

Stalnaker and Moss have given the following argument for the claim that ‘will’ and ‘might not’ are not contraries:

1.    ‘Arsenal might not win, but I believe that Arsenal will win’ is assertible.
2.    If ‘will’ and ‘might not’ are contraries then this is an instance of a Moorean paradox: p and I believe that not p.
3.    Moorean paradoxes are not assertible.
Therefore:
4.     ‘will’ and ‘might not’ are not contraries, and a fortiori ‘will’ and ‘might’ are not duals.

A similar argument appears to show that ‘might not have’ and ‘would have’ are not contraries:

5.    ‘If the game had been played, Arsenal might not have won; but I believe that if the game had been played, Arsenal would have won.’ is assertible.
6.    But if ‘will’ and ‘might not’ are contraries then this is an instance of a Moorean paradox: p and I believe that not p.
7.    Moorean paradoxes are not assertible.
Therefore:
8.    ‘would have’ and ‘might not have’ are not contraries, and a fortiori []→ and ◊→ are not duals.

These argument might lead us to reject the duality of ‘will’ and ‘might’, and of the []→ and ◊→ operators, which is enshrined in the Lewisian semantics for counterfactuals. But these dualities are motivated by the following sort of argument:

9.    ‘Arsenal might not win, but Arsenal will win’ is not assertible.
10.     ‘Arsenal might win, but Arsenal will not win’ is not assertible.
11.    There is no good explanation in pragmatic terms for the non-assertibility of 9 and 10.
Therefore
12.    The best explanation for their non-assertibility is that it derives from semantic inconsistency.
Therefore
13.    ‘might’ and ‘will’ are duals.

And for the counterfactual case:

14.     ‘If the game had been played, Arsenal would have won; but if the game had been played, Arsenal might not have won’ is not assertible.
15.    ‘If the game had been played, Arsenal would not have won; but if the game had been played, Arsenal might have won’ is not assertible.
16.    There is no good explanation in pragmatic terms for the non-assertibility of 14 and 15.
Therefore
17.    The best explanation for their non-assertibility is that it derives from semantic inconsistency.
Therefore
18.    []→ and ◊→ are duals.

We see that these two kinds of arguments lead to opposite conclusions. How should we respond to this state of affairs?

One common response in the non-counterfactual case is to reject 11). And although this response is less common in the counterfactual case, it seems equally open to us to reject premise 16).

How might rejecting these premises be motivated? One approach, suggested to me by John Hawthorne, goes as follows (take 9) as an example)

a) For ‘Arsenal might not win’ to be assertible at t, it must be the case that Arsenal not winning is compatible with my knowledge at t. (by the rules for deploying the epistemic modal ‘might’.)

b) For ‘Arsenal will win’ to be assertible at t, I must know at t that Arsenal will win. (by the knowledge norm of assertion.)

c) It cannot be the case at t both that I know that Arsenal will win, and that it be compatible with my knowledge that they not win. So the conjuncts are never simultaneously assertible, and the conjunct is never assertible.

This does provide a neat pragmatic explanation of the non-assertibility of 9), which obviously generalizes to 10). How do we generalize it to 14) and 15)?

The natural route is to interpret ”if the game had been played, Arsenal might have won’ as ‘it might be the case that, if the game had been played, Arsenal would have won’. Eagle here calls this the ‘epistemic’ reading of ‘might’ counterfactuals. No doubt this is the right reading for some ‘might’ counterfactuals – ‘if I were to look in the fridge, I might find some beer’ for example. It’s either the case that I would find some, or that I wouldn’t find some, I just don’t know which. But it doesn’t seem to be the right reading for ‘ontic’ readings of ‘might’ counterfactuals, which ascribe some genuine possibility of the consequent given the antecedent. We want to say that if the game had been played, it’s neither the case that Arsenal would have won nor that they wouldn’t have won. Either might have happened; ‘might’ here gets the same kind of reading as ‘could’.

A similar complaint can be made about the pragmatic explanation for the non-assertibility of 9) and 10). We might not want to accept that it’s either the  case that Arsenal will win, or that they won’t win, and we just don’t know which – we could insist that the ‘might’ and ‘will’ are given a ‘ontic’ or ‘objective’ readings whereby’might p’ requires a genuine possibility of p, and ‘will p’ requires no genuine possibility of ¬p. If this is so, how should we respond to the clash of arguments discussed above?

A different type of response to this clash would reject 2) and 6). Perhaps, despite appearances, ‘Arsenal might not win, but I believe that Arsenal will win’ and ‘if the match had been played, Arsenal might not have won; but I believe that if the match had been played, Arsenal would have won’ do not express propositions of the form ‘p, and I believe that not p’. If so, then which propositions do these sentences express?

An interesting point to note is that the following sentences do not seem assertible, unlike the original Stalnaker/Moss sentences:

19.    Arsenal will win, but I believe that Arsenal might not win.
20.    If the match had been played, Arsenal would have won; but I believe that if the match had been played, Arsenal might not have won.

These two sentences do seem like instances of Moorean paradoxes, as the duality theses would suggest. And the explanation of non-assertibility in terms of the knowledge norm of assertion does not seem to apply to them; it’s possible that I know Arsenal will win, but also that I know that I believe it to be compatible with my knowledge that Arsenal not win.

This suggests that there is something unusual about the way that ‘will’ and ‘would’ embed into propositional attitude contexts. Here is a proposal: perhaps we should read ‘I believe that Arsenal will win’ as expressing a high credence in Arsenal’s winning, and read ‘I believe that if the match had been played, Arsenal would have won’ as expressing a high conditional credence in Arsenal winning on the match played.

If this is right, then it predicts that the following two sentences should be inequivalent:

21.    I believe that Arsenal will win.
22.    I believe that ‘Arsenal will win’ is true.

And so should the following two sentences:

23.    I believe that if the match had been played, Arsenal would have won.
24.    I believe that ‘if the match had been played, Arsenal would have won’ is true.

We can test for this by reinserting 22) and 24) into the original Stalnaker/Moss sentences, as follows:

25.    Arsenal might not win, but I believe that ‘Arsenal will win’ is true.
26.    If the match had been played, Arsenal might not have won, but I believe that ‘if the match had been played, Arsenal would have won’ is true.

I submit that neither of these sentences are assertible. There is a tension between the two conjuncts, which is absent from the original Stalnaker/Moss sentences. If this is correct, then we have reason to reject 2) and 6), and with them the argument against the might/would and the []→ / ◊→ dualities. We can then adopt the simplest explanation for 9), 10), 14), and 15): the failure of assertibility derives from straightforward semantic inconsistency.

We can generalize the proposal to other epistemic propositional attitudes, such as suspecting. ‘I suspect that p will be the case’ plausibly also expresses a high credence in p, though probably not as high a credence as that expressed by ‘I believe that p’. We cannot, of course, generalize to the case of knowledge; ‘p might not be the case, but I know that p will be the case’ is not assertible. What about hoping and fearing? These are interesting cases, because they seem to have both epistemic and non-epistemic uses. To get a grip on the difference I have in mind, compare ‘I hope that p will happen’ to ‘I hope that p doesn’t happen’ – the former, but not the latter, appears to express optimism about p, while the latter remains neutral. I propose, then, that ‘I hope that p will be the case’ can be taken to express a credence in p which is satisfactorily high – similarly, ‘I fear that p will be the case’ can be taken to express a credence in p which is unsatisfactorily high.

Why should ‘will’, and ‘would have’ embed in this non-standard way into epistemic propositional attitude contexts? I suggest that it is because of the practical utility of being able to express our credences and conditional credences in a way which does not sound clumsy. But whether or not we have a genetic explanation for this non-standard behaviour, it seems to be the best explanation of our responses to the simple sentences involving ‘might’, ‘will’ and ‘would have’ which I have discussed.

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Might, would, will

2 thoughts on “Might, would, will

  1. Maggie Hamand says:

    Hmm. Interesting. A problem is in the use of the word ‘believe’. ‘Believe’ is often used in the sense of believing in an intellectual proposition. However, it is also often used to mean a commitment of faith or trust. This has considerable religious significnce; the Greek pisteo, to believe, actually means more to have faith in, trust in, than the Latin translation of it, credo. So ‘I believe Arsenal will win’ actually means: I have faith in Arsenal, I trust that they will win.’

  2. Trusting that and having faith that would be examples of alternative epistemic propositional attitudes, as discussed in the penultimate paragraph.

    One option I didn’t consider in this post was to have separate probabilistic frameworks for the various attitudes – so as well as credence (partial belief) we might also have partial trust, partial hope, partial suspicion, etc. Maybe I’ll write that up into a new post soon.

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