This will be a rather dogmatic post, summarizing a bunch of my thinking about intention and action.
I think the fundamental concept in regard to intention isn't the binary relation of x's intending that p (or x's intending to G), but the ternary relation of x's Aing with the intention that p. In other words, intentions qualify actions: "The surgeon is cutting the heart with the intention of healing, while the assassin is cutting the heart with the intention of killing."
But isn't it possible just to intend? Maybe, but that's a defective case. Moreover, when you just intend that p, you are still acting—you are trying with the intention that p. Intending in the sense I am after—the sense that occurs in the Principle of Double Effect and that Anscombe is elucidating in Intention—is not the same as wishing, hoping, resolving or planning. We do use the word "intend" in cases of resolve or plan, and I think I can explain that. Start with resolve. When I resolve to A, I am trying to produce a future action. My resolving is an action done with the intention to A later. And so I can be literally said to intend to A. However, sometimes we have something weaker, like a plan. In those cases, I think we are simply extending the word "intend" from the stronger sense to the weaker.
This dovetails with Nietzsche's remark that making promises is tied to the great power of controlling our future actions. Plausibly, when I promise to A, I ought to be intending that I will A—a sincere promise, then, is also an attempt to bring about, or at least probabilify, a future action of one's own.
But isn't an action caused by its intention? Yes and no. The problem with a simply affirmative answer is that as soon as the intention has occurred, one has already begun to try. Since to begin to try is already to act, on pain of vicious regress it cannot be that every action is caused by an intention. Moreover, when the action goes on to successful fruition, there aren't two actions, a beginning-to-try and the full action. There is just one action which began when one began to try and went on to fruition. But we can temporally subdivide the action, and the temporally later parts of it are caused by the beginning of it. We can, if we like, use "intending" as a stage term, akin to "embryo", for that first part of the action—the beginning-to-try. But just as we should not say that the embryo causes the organism—the embryo, after all, is the organism.[note 1] But of course we can say that the embryo is a cause of the later stages of development, and likewise we can say that the intention is a cause of the later stages of the action. So while the action is not caused by its intention, much of the action is caused by its intention. The intention is an essential part of the action—the rest of the action is not necessary for the action's occurrence though usually necessary for the action's success. This is just as the embryo stage of life is essential to the organism's existence (any horse that came into existence fully-formed, skipping the embryonic stage, would not be Bucephalus), and later stages of life are unnecessary for the organism to have existed, but are necessary for the organism to have successfully matured.
This matters ethically. For it lets one hold on to the intuitions that (a) primary moral evaluation is of the intention, (b) the subject matter of moral evaluation is the action, and (c) the success or failure of an action can be morally relevant features. The intention is the essential core of the action, and the primary question whether a person has acted rightly is a question of the evaluation of the intention. But at the same time the success or failure matters morally. One is no better as a person if one's attempt to commit a crime fails, but one is better off morally speaking (for instance, one typically owes less to the prospective victim if one has completely failed).
Finally consider Knobe cases. We have the case of the CEO who is told of a possible new programme which will make the company oodles of money. There is one catch—the programme will also harm the environment. The CEO says he doesn't care about the environment, but will go for the program. Most people say that the CEO intentionally harms the environment.
Consider, however, this variant question which is tied more closely to what I think is the fundamental ternary nature of intention: Did the CEO go for the programme with the intention of harming the environment? Surely the answer is negative. We can, after all, paraphrase as: Did the CEO go for the programme in order to harm the environment? This suggests (but see also this paper by Wasserman) that we want to distinguish between intentionally Aing and doing something with the intention to A. The concept I am after is that of doing with the intention to A.