Wolfgang Schwarz

Owned possibility and unowned ability

Superficially, modal auxiliaries such as 'must', 'may', 'might', or 'can' seem to be predicate operators. So it is tempting to interpret them as functions from properties to properties: just as 'Alice jumps' attributes to Alice the property of jumping, 'Alice can jump' attributes to her the property of being able to jump, 'Alice may jump' attributes the property of being allowed to jump, and so on.

Perhaps the biggest obstacle to this approach comes from quantified constructions. If 'Alice may jump' attributes to Alice the property of being allowed to jump, then 'one of us may jump' should say that one of us has the property of being allowed to jump. But while this is one possible reading of the sentence, 'one of us may jump' also has a reading on which it states that it is permissible that one of us jumps. There is a kind of de re/de dicto ambiguity here, which suggests that 'may' can not only apply to properties but also to propositions.

Not all modals seem to generate the de re/de dicto ambiguity. Consider epistemic 'must' or 'might'. 'Someone must/might be jumping' appears to only have a de dicto reading on which it says that it is must/might be the case that someone is jumping. At the other extreme, 'someone can jump' appears to have only a de re reading; it says that there is someone who has the ability (or opportunity) to jump.

One might conclude that epistemic 'must' and 'might' are sentence operators, circumstantial 'can' a predicate operator, and many other modals can occur in both forms. I'm more interested in the semantics than the syntax. The semantic analogue of the present proposal would be that epistemic modals express properties of propositions, circumstantial 'can' expresses a property of properties, while other modals can express either.

But I don't think that's true: epistemic modals can express properties of properties, and circumstantial modals can express properties of propositions.

First, the epistemic case. Imagine a murder investigation. There are ten suspects, and we know that exactly one of them is the murderer. You just found out that two of the suspects were not in town at the time of the murder. You say:

(1) Two of the suspects can't be the murderer because they weren't in town.

The intended reading on which (1) is non-trivial and true is de re. You are not attributing an epistemic status to the proposition that two of the suspects committed the murder. Rather, you are saying that two of the suspects don't have the property of possibly having committed the murder. Similarly, you could say:

(2) Eight of them might be the murderer.

By (2), you would mean that eight of the suspects have the property of possibly being the murderer.

Second, the case of circumstantial 'can'. Imagine a machine with ten arms. Normally, the arms can move simultaneously and independently, but now there's been a power outage and they all stand still. You just attached a solar panel to the machine that provides enough power to move one arm at a time. You say:

(3) One arm can now move.

The intended reading of (3) is de dicto: you don't mean that one of the arms has the property of being able to move. After all, each of the arms has that property, provided that the other arms stay still. What (3) expresses is that there is now a circumstantial possibility that verifies the proposition that one of the ten arms moves.

One might object that in some metaphysical sense, the ability attributed by (3) is "owned", namely by the machine. The machine can move one arm. Maybe. Still, (3) does not attribute an ability to the machine, since it doesn't even mention the machine. In fact, there needn't be a machine at all. Imagine a variant scenario in which there are ten independent, unconnected mechanical arms, but the solar panel only provides enough power for the movement of one.

So it looks like all modals can express both properties of properties and properties of propositions.