Must and Can

In “Modals and Conditionals Again” Angelica Kratzer treats natural language ‘must’ as the expression of a two-place relation between a premise set and a proposition. The trick is getting the relation straight. Consider the following 'must' claims:

Deontic: “One must not microwave kittens!”

Doxastic: “In light of what Jack mistakenly believes, Jill must be in love with him.

Epistemic: “Oh…, the gun must have been loaded.”

Dispositional: “If you must smoke, then please use an ashtray (and not my rhododendra)”

Bouletic: “You must wear that fabulous dress”

For Kratzer the two-place relation is 'must in view of', giving

Deontic: “In view of our duties, one must not incinerate kittens”

Doxastic: In view of what Jack mistakenly believes, Jill must be in love with him.

Epistemic: “In view of what we now know, the gun must have been loaded.”

Dispositional: “If, in view of what you are disposed to do, you must smoke, then use an ashtray”

Bouletic: “In view of what my preferences state, you must wear that fab dress”

The natural way to read these claims is as follows:

'In view of premise set A it must be that p' is true iff
p follows from A.
And the corresponding dual operator 'can' is read:

In view of A it can/might/may be that p iff
p is compatible with A.
Two well-known problems emerge for this sort of semantics. First it forces a vacuous reading of 'must' claims that relate a proposition to an inconsistent premise set. And second, it gives rise to all sorts of unwelcome modal collapses, and relatedly, forces a vacuous reading of 'must' claims that relate non-contingent propositions to premise sets. In my talk at Kioloa, I criticized a proposal by Kratzer for dealing with the first problem. I then argued that the two problems are related and sketched a unified solution.

Kratzer's proposal tells us that ‘musts’ and ‘cans’ follow from the appropriate consistent subsets of the given premise set. More specifically, let A be an inconsistent premise set of, say, legal judgments.
A = {p, ~p, q}And let X be the set of all A’s consistent subsets.
X = {ø, {p}, {~p}, {q}, {p, q}, {~p, q}}Kratzer’s proposal says:

"In view of A, it must be that p" is true iff
each set in X has a superset in X from which p follows.
The problem with inconsistent premise sets, of course, is that they entail everything. However, it is false that each set in X has a superset in X from which an arbitrary proposition follows. So, unlike the natural proposal with which we began, Kratzer's proposal doesn't predict the absurd claim that, in view of the law, we must commit murder.

However, the restriction not only blocks the application of 'must' to arbitrary propositions, but it blocks the application of 'must' to any contradicted premise. So claims like the following are predicted to be false:

"In view of what Graham believes, the Liar sentence must be true"
"In view of what Graham believes, the Liar sentence must not be true".

Moreover, Kratzer's proposal always blocks the application of 'must' to premises responsible for the inconsistency and it sometimes blocks the application of 'must' to important consequences that (at least partially) depend on at least one of the contradicted premises.

Here's an example of the latter type of case. White House chief of staff “Scooter” Libby was convicted of obstruction of justice and making false claims to federal investigators during the CIA leak investigation. Bush commuted his prison sentence from 33 months to 0 on the grounds that any term of imprisonment for such nonviolent first offenses by experienced government service employees is too harsh. This contradicts US federal sentencing guidelines and practice, which prescribe hard time for such offenders. In view of federal sentencing guidelines, what now must be prescribed for the sentencing of a like criminal c for like crimes? It would be irresponsible to let Bush’s incompetence and nepotism overly influence the federal justice system. Hence, in view of federal sentencing guidelines, c must do hard time.

But Kratzer’s view doesn’t predict this. For it depends on at least one contradicted legal judgment---viz., criminals of this sort are to do hard time. And when that is the case, it will be false that, for each consistent subset of the sentencing guidelines, there will be a superset among them from which it follows that c is to do hard time.

A second problem with the Kratzer proposal is that it says nothing about what to do when the proposition p fails to be a contingent matter. When p is necessarily true, then it follows from every set. Therefore, in every context, p must be the case. For instance, the view predicts that, in view of what Michael (the intuitionist) believes, excluded middle is correct. But Michael the intuitionist denies the unrestricted truth of excluded middle. To pick another example of this kind, we want to say that Obama might actually win in November. But suppose in fact Hillary wins. Then in view of what we know it must be that Hillary actually wins. That's because 'Hillary actually wins' is necessarily true (if true). So, in view of what we know, it must be that actually Hillary will win. But then, by the duality of the operators, it is false that in view of what we know Obama might actually win.

The problem of inconsistent premise sets and the problem of collapsed modals are at root the same problem. In each case we assume that the deontic/doxastic/epistemic/legal/bouletic "possibilities" are a subset of the logical possibilities. And that is not how it should be. After all, in view of what we know, it may be that Goldbach’s conjecture is false. Ex hypothesi, it’s true. And, for all we knew before the telescope, Hesperus might not have been Phosphorus. And, for all we know right now, Obama might actually be the next US president. Ex hypothesi, Clinton wins.

The view I proposed in Kioloa was this:

'In view of A, it must be that p' is true
iff
all the relevantly similar (possible or impossible) A-worlds are p-worlds.

'In view of A, it can be that p' is true
iff
some relevantly similar (possible or impossible)
A-worlds are p-worlds.
I treat 'musts' as counterfactuals because the corresponding strict conditional, which would quantify over all possible and impossible worlds, would be too strong and rarely (if ever) come out true. The corresponding 'can' claims would be too weak and would usually (if not always) come out true. The important insight is that, with the introduction of impossible worlds, we drop the assumption that the relevant accessibility relation is a subset of S4/S5 accessibility. In so doing, we block the familiar modal collapses and the special problems of inconsistent premise sets, and we get that much closer to the correct understanding of 'must and 'can'.