Objection 1. It would seem that hope belongs to the cognitive power. Because hope, seemingly, is a kind of awaiting; for the Apostle says (Romans 8:25): "If we hope for that which we see not; we wait for it with patience." But awaiting seems to belong to the cognitive power, which we exercise by "looking out." Therefore hope belongs to the cognitive power.
Objection 2. Further, apparently hope is the same as confidence; hence when a man hopes he is said to be confident, as though to hope and to be confident were the same thing. But confidence, like faith, seems to belong to the cognitive power. Therefore hope does too.
Objection 3. Further, certainty is a property of the cognitive power. But certainty is ascribed to hope. Therefore hope belongs to the cognitive power.
On the contrary, Hope regards good, as stated above (Article 1). Now good, as such, is not the object of the cognitive, but of the appetitive power. Therefore hope belongs, not to the cognitive, but to the appetitive power.
I answer that, Since hope denotes a certain stretching out of the appetite towards good, it evidently belongs to the appetitive power; since movement towards things belongs properly to the appetite: whereas the action of the cognitive power is accomplished not by the movement of the knower towards things, but rather according as the things known are in the knower. But since the cognitive power moves the appetite, by presenting its object to it; there arise in the appetite various movements according to various aspects of the apprehended object. For the apprehension of good gives rise to one kind of movement in the appetite, while the apprehension of evil gives rise to another: in like manner various movements arise from the apprehension of something present and of something future; of something considered absolutely, and of something considered as arduous; of something possible, and of something impossible. And accordingly hope is a movement of the appetitive power ensuing from the apprehension of a future good, difficult but possible to obtain; namely, a stretching forth of the appetite to such a good.
Reply to Objection 1. Since hope regards a possible good, there arises in man a twofold movement of hope; for a thing may be possible to him in two ways, viz. by his own power, or by another's. Accordingly when a man hopes to obtain something by his own power, he is not said to wait for it, but simply to hope for it. But, properly speaking, he is said to await that which he hopes to get by another's help as though to await [exspectare] implied keeping one's eyes on another [ex alio spectare], in so far as the apprehensive power, by going ahead, not only keeps its eye on the good which man intends to get, but also on the thing by whose power he hopes to get it; according to Sirach 51:10, "I looked for the succor of men." Wherefore the movement of hope is sometimes called expectation, on account of the preceding inspection of the cognitive power.
Reply to Objection 2. When a man desires a thing and reckons that he can get it, he believes that he can get it, he believes that he will get it; and from this belief which precedes in the cognitive power, the ensuing movement in the appetite is called confidence. Because the movement of the appetite takes its name from the knowledge that precedes it, as an effect from a cause which is better known; for the apprehensive power knows its own act better than that of the appetite.
Reply to Objection 3. Certainty is ascribed to the movement, not only of the sensitive, but also of the natural appetite; thus we say that a stone is certain to tend downwards. This is owing to the inerrancy which the movement of the sensitive or even natural appetite derives from the certainty of the knowledge that precedes it.
Source: Summa Theologica (New Advent)