This post is subject to an important correction.
I think the origin of talking about actions “under a description” is Donald Davidson’s 1963 “Actions, Reasons and Causes”. If I am right, Davidson does not so much provide an argument for his thesis, but rather, simply puts it forward:
“I flip the switch, turn on the light, and illuminate the room. Unbeknownst to me I also alert a prowler to the fact that I am at home. Here I need not have done four things, but only one, of which four descriptions have been given.[…]Since reasons may rationalize what someone does when it is described in one way and not when it is described in another, we cannot treat what was done simply as a term in sentences like ‘My reason for flipping the switch was that I wanted to turn on the light’; otherwise we would be forced to conclude from the fact that flipping the switch was identical with alerting the prowler, that my reason for alerting the prowler was that I wanted to turn on the light.”
It seems that Davidson’s view here has two components:
A) My flipping the switch = my turning on the light = my illuminating the room = my alerting the burglar.
B) My flipping the switch was intentional, though my alerting the burglar was not.
Here is a reason to think that if my φing = my ψing, it is not possible that one was intentional and the other not:
1) If my φing = my ψing, then for any property P, if my φing has property P, so does my ψing.
2) Suppose that my φing was intentional but my ψing was not.
3) Then, there is a property P (namely: being intentional) such that my φing has P, but my ψing does not.
4) Then, it is not the case that my φing = my ψing.
5) So, if my φing = my ψing, it is not the case that my φing was intentional while my ψing was not.
Granted, Davidson, it seems, would either deny (1) or the inference to (3) under the supposition of (2). I would have thought that (1) is an uncontroversial instance of Leibniz’s law, so I assume it is more likely for one to deny (3). But, at the same time, being intentional seems like a perfectly nice property.
Since I think we should concede component (B) of Davidson’s position, I can only assume the motivation to reject (1) or (3) in my argument comes from some good reasons to accept component (A) of Davidson’s position, however, it seems like we also have good reason to abandon (A):
1) My flipping the switch could have occurred without the light being turned on.
2) My turning on the light could not have occurred without the light being turned on.
3) So, my flipping the switch is not the same thing as my turning on the light.
(repeat with the necessary alterations for each of the items being identified).
Here’s a naive conclusion to draw from my two arguments: My flipping the switch is not the same thing as my alerting the burglar, and thus, we need not appeal to the notion of an action’s being “intentional under some description” to explain how my flipping the switch is intentional when my alerting the burglar is not.
But perhaps I am being insufficiently charitable to the Davidsonian position.
It is harder to make the case for non-identity if we consider, for example, my opening the door and my opening the door clumsily. Supposing there is only one door that gets opened, and that I opened it clumsily, we might want to maintain:
A’) My opening the door = my opening the door clumsily.
B’) My opening the door was intentional, but my opening the door clumsily was not intentional.
Now, my Leibniz law argument should work just as well here, so we still have a problem with reconciling the two theses. On the other hand, I am less confident about my modal argument for the distinctness of the actions in this case. I know there is a decent sized literature on modal-fragility of events, and maybe something from that would help illuminate what to say about this case. Just to consider it briefly, the new version of the modal argument is:
1′) My opening the door could have occurred without the door being opened clumsily.
2′) My opening the door clumsily could not have occurred without the door being opened clumsily.
3′) So, my opening the door is not the same thing as my opening the door clumsily.
(1′) still sounds good, just not as good as (1) did earlier. (2′) on the other hand sounds at least as good as (2), I think. Suppose we abandon (1′), then. Assuming we are not prepared to give up the claim that my opening the door was intentional, is it possible to say that my opening the door clumsily was intentional? This seems completely unacceptable.
I guess I’ll have to look at the literature on the modal profiles of events and at Davidson’s “The Logical Form of Action Sentences” to really sort this all out.