When you have a memory (for instance, you remember walking down the street from your house to the office this morning) — it seems perfectly obvious that this must be your memory. If you remember it, then the remembered episode must also be one of your past experiences. Otherwise it would not be a memory, but a fantasy. (Or some other kind of imaginative project.)
Yet some philosophers have speculated about the idea of q-memories (or quasi-memories). A q-memory is like a memory; but if you have a q-memory, you don’t remember an episode from your own life, you remember one from another person’s life. (Perhaps we could profitably apply the notion in an interpretation of Poe’s “Tale of the Ragged Mountains”?)
1) Richard Wollheim has criticized the notion of q-memory as, first, “incompatible with the way […] in which persons, even as they live in the present, can be brought under the influence of the past” (TL 111-112); and secondly, as unintelligible (TL 112-117). The latter argument is more detailed, but the former is more interesting. Wollheim doesn’t pursue it in The Thread of Life, because in that book, he has used centered event-memory, the particular type of memory in question, to characterize what it means to live a human life. And assuming that characterization to fit, the argument would run into a circularity. But precisely why would that be?
2) The argument takes the form of modus tollens:
a) If q-memory were possible, then people could not lead their lives in the way they do.
b) People lead their lives in a way so that they can be brought under the influence of the past.
Premise b) expands the consequent of premise a) here, therefore
c) If q-memory were possible, then people could not be brought under the influence of the past.
The somewhat obscure phrase “brought under the influence of the past” means broadly this: when a person leads a life, he experiences it in the present — and thereby forms dispositions which then persist. Such dispositions can be beliefs, memories, dispositions to fantasize in a particular way, and so on. These dispositions exert some force over the person: memories come unbidden (sometimes); beliefs shape the way we perceive reality and act in the world; fantasies can inspire us or drain our energy away. We lead our lives, as Wollheim puts it, always “at a crossroads: at the point where a past that has affected him and a future that lies open meet in the present” (TL 31). And “that the past influences the person largely through mental states is responsible for much of how we live” (TL 32). This is the general claim of the book, and it is crystallized in premises a) to c) above.
d) We in fact lead our lives in the way we do.
e) Therefore, q-memory is not possible.
And e) follows from c) and d) by modus tollens.
3) So far, so good. The argument is valid, but its cogency would depend on the rather large claims about how we lead our lives. And evaluating those claims would mean to engage with the whole argument of The Thread of Life. But I’m not concerned with whether the argument is cogent; I’m concerned with the question why Wollheim thinks that it is circular.
To answer that question, it will be helpful to understand why Wollheim is interested in the idea of q-memory in the first place. The reason for that is that
“centered event-memory is best studied for the contribution it makes to the way in which persons lead their lives […] Specifically, it must be sufficient for the identity of a person’s life.” (TL 110)
In Wollheim’s picture, we can use centered event-memory as sufficient identity criterion for the life of a person (the totality of all events, actions, perceptions etc. in which that person is ever involved). If you have a centered event-memory of an episode (such as walking down the street from your house to the office this morning), this is sufficient for concluding that both the episode and your remembering pick out the same overall life.
Thus, the overall argument reads like this:
i) If q-memories were possible, centered event memory would not be a sufficient identity criterion for lives.
ii) If q-memories were possible, then people could not be brought under the influence of the past.
iii) People can in fact be brought under the influence of the past.
iv) Q-memories are not possible.
v) Therefore, centered event-memory is a sufficient identity criterion for lives.
Here, premises ii) to iv) are the equivalent of a) to e) above, and iv) follows from ii) and iii). As it stands, the argument is not valid, but it now fully reflects the line of thought which Wollheim presents. Supposing it could be made valid (which I think possible), it is now also quite clear where the circularity lies. For in order to state premise ii), one must assume something very close to v).
 Sydney Shoemaker (“Persons and Their Pasts”, in: American Philosophical Quarterly 7 (1970), 269-285), and following him, Derek Parfit, (“Personal Identity”, in: The Philosophical Review LXXX (1971), 3-27).
 Strictly speaking, the notion of q-memory is construed so that it contains memory as a special case, so when you’re having a q-memory, you are remembering something either from your own or from another person’s life. But the latter is of course the more intriguing possibility.
 Richard Wollheim, The Thread of Life. The William James Lectures 1982. New Haven: Yale UP 1984. Quoted directly with TL and page number.