Objection 1. It would seem that fear cannot be feared. For whatever is feared, is prevented from being lost, through fear thereof: thus a man who fears to lose his health, keeps it, through fearing its loss. If therefore a man be afraid of fear, he will keep himself from fear by being afraid: which seems absurd.
Objection 2. Further, fear is a kind of flight. But nothing flies from itself. Therefore fear cannot be the object of fear.
Objection 3. Further, fear is about the future. But fear is present to him that fears. Therefore it cannot be the object of his fear.
On the contrary, A man can love his own love, and can grieve at his own sorrow. Therefore, in like manner, he can fear his own fear.
I answer that, As stated above (Article 3), nothing can be an object of fear, save what is due to an extrinsic cause; but not that which ensues from our own will. Now fear partly arises from an extrinsic cause, and is partly subject to the will. It is due to an extrinsic cause, in so far as it is a passion resulting from the imagination of an imminent evil. In this sense it is possible for fear to be the object of fear, i.e. a man may fear lest he should be threatened by the necessity of fearing, through being assailed by some great evil. It is subject to the will, in so far as the lower appetite obeys reason; wherefore man is able to drive fear away. In this sense fear cannot be the object of fear, as Augustine says (QQ. 83, qu. 33). Lest, however, anyone make use of his arguments, in order to prove that fear cannot be at all be the object of fear, we must add a solution to the same.
Reply to Objection 1. Not every fear is identically the same; there are various fears according to the various objects of fear. Nothing, then, prevents a man from keeping himself from fearing one thing, by fearing another, so that the fear which he has preserves him from the fear which he has not.
Reply to Objection 2. Since fear of an imminent evil is not identical with the fear of the fear of imminent evil; it does not follow that a thing flies from itself, or that it is the same flight in both cases.
Reply to Objection 3. On account of the various kinds of fear already alluded to (ad 2) a man's present fear may have a future fear for its object.
Source: Summa Theologica (New Advent)