Objection 1. It would seem that choice in not only of possible things. For choice is an act of the will, as stated above (Article 1). Now there is "a willing of impossibilities" (Ethic. iii, 2). Therefore there is also a choice of impossibilities.
Objection 2. Further, choice is of things done by us, as stated above (Article 4). Therefore it matters not, as far as the act of choosing is concerned, whether one choose that which is impossible in itself, or that which is impossible to the chooser. Now it often happens that we are unable to accomplish what we choose: so that this proves to be impossible to us. Therefore choice is of the impossible.
Objection 3. Further, to try to do a thing is to choose to do it. But the Blessed Benedict says (Regula lxviii) that if the superior command what is impossible, it should be attempted. Therefore choice can be of the impossible.
On the contrary, The Philosopher says (Ethic. iii, 2) that "there is no choice of impossibilities."
I answer that, As stated above (Article 4), our choice is always concerned with our actions. Now whatever is done by us, is possible to us. Therefore we must needs say that choice is only of possible things.
Moreover, the reason for choosing a thing is that it conduces to an end. But what is impossible cannot conduce to an end. A sign of this is that when men in taking counsel together come to something that is impossible to them, they depart, as being unable to proceed with the business.
Again, this is evident if we examine the previous process of the reason. For the means, which are the object of choice, are to the end, as the conclusion is to the principle. Now it is clear that an impossible conclusion does not follow from a possible principle. Wherefore an end cannot be possible, unless the means be possible. Now no one is moved to the impossible. Consequently no one would tend to the end, save for the fact that the means appear to be possible. Therefore the impossible is not the object of choice.
Reply to Objection 1. The will stands between the intellect and the external action: for the intellect proposes to the will its object, and the will causes the external action. Hence the principle of the movement in the will is to be found in the intellect, which apprehends something under the universal notion of good: but the term or perfection of the will's act is to be observed in its relation to the action whereby a man tends to the attainment of a thing; for the movement of the will is from the soul to the thing. Consequently the perfect act of the will is in respect of something that is good for one to do. Now this cannot be something impossible. Wherefore the complete act of the will is only in respect of what is possible and good for him that wills. But the incomplete act of the will is in respect of the impossible; and by some is called "velleity," because, to wit, one would will [vellet] such a thing, were it possible. But choice is an act of the will, fixed on something to be done by the chooser. And therefore it is by no means of anything but what is possible.
Reply to Objection 2. Since the object of the will is the apprehended good, we must judge of the object of the will according as it is apprehended. And so, just as sometimes the will tends to something which is apprehended as good, and yet is not really good; so is choice sometimes made of something apprehended as possible to the chooser, and yet impossible to him.
Reply to Objection 3. The reason for this is that the subject should not rely on his own judgment to decide whether a certain thing is possible; but in each case should stand by his superior's judgment.
Source: Summa Theologica (New Advent)