an anepistemic modality in English

Epistemic modalities are modalities of knowledge. Anepistemic (don’t bother to look it up, I coined it just for this) modality is a subspecies of knowledge modality — it’s a modality of the lack of knowledge, a modality of ignorance or uncertainty. It essentially involves knowledge, because one can’t assert one’s uncertainty without knowing that one is uncertain. One can assert all kinds of statements without knowledge — “Hermitage is in Petrograd.” Do I know it? Well, I’ve never actually been there. I believe it and that’s why I assert it. But assertions of uncertainty reflect on one’s own state of knowledge and it seems that one can’t sincerely assert uncertainty without actually knowing — in a meta-epistemic way — that one knows that one is uncertain. Wittgenstein had some objections to this kind of knowledge, but I’ll deal with those philosophical issues in another article soon. For the moment, I’m going to assume that when one asserts one’s own uncertainty, one knows that one is uncertain. So it’s a kind of recursive epistemic modality. It’s possible to have such recursiveness of knowledge in simple epistemic modalities as well if you are willing to grant that the assertion that one knows something entails that one knows (that one knows that one knows etc.) that one knows it. It all depends on how you set up the system entailments.

This entry is about “might” and why it doesn’t follow the pattern of modal auxilliaries of possibility under negation. The conclusion is that “might” is not a modality of possibility, but an anepistemic modal. This article gets a little dense, and I’m not sure I wrote it as smoothly as I should have, so if you’re looking for fun linguistics, skip to the next entry.

The basic data will be familiar to anyone who has read Larry Horn’s Natural History of Negation, a superb book that gave me a lot of recipes for this spread.

The modal auxilliary “must” means something like “necessarily.” The negation of “must” is “must not” or “mustn’t” and they mean
necessarily not.
The modal auxiliary “can” means something like “possibly.” The negation of “can” is “can not” or “can’t” and it means
not possible.
The scope of negation is the reverse of “mustn’t.” This is peculiar. Looking just at the sense of possibility and necessity, “can” and “must” mean very different things, but “can’t” and “mustn’t” mean pretty much the same, at least as far as their action consequences. Both ‘necessarily not’ and ‘not possible’ entail ‘impossible.’ And the interpretation of ‘possibly not’ doesn’t seem to have an available contraction in English.

Most of the other modal auxiliaries can be categorized as either having a sense of necessity or possibility, and, what do you know, the ones that have the sense of possibility act just like “can” under negation, and the ones that have the sense of necessity act like “must.”

could = possible
couldn’t = not possible
should = (morally) necessary
shouldn’t = (morally) necessarily not
may (permissive) = possible
may not = not possible (not permitted)

except when we come to “might”:
might = possible
might not = possibly not

In my 1999 dissertation I used conjoined sentences to tease out the meanings of all these modals. The first conjunct is modal and the second is apodictic — it predicts a real consequence:
She can but she won’t
She can but she will*
She can and she won’t
She can and she will

You see right away that ‘can’ and ‘will’ are so completely consistent with each other that they are infelicitous to the intervention of “but” between them.

She can’t but she won’t*
She can’t but she will*
She can’t and she won’t
She can’t and she will*

Here the absence of possibility leaves only one assertion coherent. The modals of necessity pattern according to the kind of necessity, deontic (moral) or epistemic (necessary conclusion from evidence):

She should but she won’t
She should but she will*
She should and she won’t
She should and she will

It must be raining outside, but it isn’t*
It must be raining outside, but it is*
It must be raining outside, and it is
It must be raining outside, and it isn’t*

A great deal can be observed in these, but moving on to “might”:
She might leave but she won’t*
She might leave but she will*
She might leave and she won’t*
She might leave and she will*

None of the conjoined sentences is coherent. “Might” precludes any prediction of fact. Why?

It’s not exactly a modal of possibility. Or, more accurately, it isn’t just a modal of possibility. To say something might happen is equivalent to saying that you don’t know whether it will happen or not. That implies that you believe it’s possible, because if you believed it impossible, then you’d know that it wouldn’t happen. And since you assert with “might” that you don’t know whether it’ll happen, you can’t also know that it’s impossible.

If “it might be” means you don’t know whether it’ll happen, what about “it might not be”? Does that mean: it is not the case that you don’t know whether it’ll happen? Or does that mean: you don’t know whether it won’t happen?

To put it notationally:

~(~K(p) & ~K(~p)) = K(p) v K(~p)
or
~K(~p) & ~K(~~p) = ~K(p) & ~K(~p)

The conjoined sentences tell us that it’s the second, not the first.

She might not leave, but she won’t*
She might not leave, but she will*
She might not leave, and she won’t*
She might not leave, and she will*

Negation of “might” does not entail knowledge. So the scope of negation is narrow, just like the modals of necessity. In fact, “she might not” and “she might” don’t seem to show any difference in meaning. The conditions of their use depend on whether the context is biased towards the positive or the negative and whether the speaker is in an agreeable or disagreeable frame of mind. It’s just a matter of whether the speaker wants to express her uncertainty with or without “not.”

Well, I wrote a dissertation on this, so there’s a bit more to say, but not today.

Some more

Can’t resist a few more observations:

In case you’re skeptical about the difference in pattern between modals of possibility and modals of necessity under negation, here’s the compelling fact: when English speakers use may in the permissive sense

your witness may testify (said by the judge)

the negation follows the pattern of modals of possibility

your witness may not testify (the judge means: not permitted to testify; he doesn’t mean: permitted to not testify)

But when English speakers use may to mean might,

She may testify — the judge might let her (said by a court observer)

the negation takes narrow scope, just like might

She may not testify. The judge is excluding all the important evidence and might not let her.

That’s the kicker. It means that the difference in pattern is not a fact about the word-forms, it’s a fact about the meanings. It’s about the underlying logical form.

What’s particularly interesting about the logical form I’m suggesting for might is that it’s a conjunction

~Kp & Pp (speaker doesn’t know whether p and p is possible)

The negation of a conjunction is true if either of the conjuncts is false:

~(~Kp & Pp) is true if ~Pp or if Kp:

i.e.,

~(~Kp & Pp) is true I know that p or if p is impossible.

So, if might took wide scope negation, an assertion like

She might not testify

would be ambiguous between

She cannot testify (p is impossible)

and

I know she will testify (I know that p),

But if might not takes narrow scope, then there’s no ambiguity. The logical form would be

~K~p & P~p (I don’t know that ~p and it’s possible that ~p)

which is just what might not means: I don’t know that she won’t testify (which implies that I believe it’s possible she will) and I assert that it is possible she won’t.

All right. Enough. I have to do the laundry.

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