1 We may subvert their doctrine as to transmigration from body to body by this fact, that souls remember nothing whatever of the events which took place in their previous states of existence. For if they were sent forth with this object, that they should have experience of every kind of action, they must of necessity retain a remembrance of those things which have been previously accomplished, that they might fill up those in which they were still deficient, and not by always hovering, without intermission, round the same pursuits, spend their labour wretchedly in vain (for the mere union of a body [with a soul] could not altogether extinguish the memory and contemplation of those things which had formerly been experienced), and especially as they came [into the world] for this very purpose.
For as, when the body is asleep and at rest, whatever things the soul sees by herself, and does in a vision, recollecting many of these, she also communicates them to the body; and as it happens that, when one awakes, perhaps after a long time, he relates what he saw in a dream, so also would he undoubtedly remember those things which he did before he came into this particular body. For if that which is seen only for a very brief space of time, or has been conceived of simply in a phantasm, and by the soul alone, through means of a dream, is remembered after she has mingled again with the body, and been dispersed through all the members, much more would she remember those things in connection with which she stayed during so long a time, even throughout the whole period of a bypast life.
Source: Adversus haereses (New Advent)