Memory, animals and personhood

Consider the following plausible theses:

1. Some non-human animals that are not persons (maybe dogs and maybe even rats) have experiential memories, i.e., memories in which they remember having lived through past events.
2. Human intellectual development is continuous and relatively slow.
3. It is an essential property of me that I am a person. In particular, if personhood begins at some point t after conception, then t is when I come to exist.

Interestingly, we cannot hold on to (1)-(3) as well as this thesis:

4. Personhood requires developed capacities for distinctively personal functioning.

For suppose for a reductio ad absurdum that (4) is true. Then at some point a year or two after conception, just when I developed capacities for distinctively personal functioning, I came into existence. Now imagine me on that first day of personhood and of existence. Because of the continuity of human intellectual development, a day earlier I was also a very sophisticated animal, presumably sophisticated enough to have formed experiential memories. After all, it seems very plausible given (2) that I've gone through all intermediate levels of intellectual development, and those stages, by (1) and (4) (we need (4) here to guarantee for the sake of argument what I ultimately deny, namely that personhood is a level of intellectual development), include a level where there are experiences but no personhood. These memories surely carry over.

So let's suppose that on my first day of personhood I remember myself as playing blocks with my dad a day earlier. But according to (3), I did not exist before personhood, and if I did not exist, I did not play blocks with my dad, either. And hence this experiential memory, inherited from the non-person human animal that preceded me, is incorrect and unveridical. This is absurd enough.

And here is a further, more serious, oddity. That experiential memory was veridical in the human animal a day before personhood came to be. It presumably still is correct in the human animal. So both the human animal and the human person have the same memory, or apparent memory, but it's only correct in the human animal and not in the human person. So the two memories have different content. This is very weird indeed. Furthermore, such formation of animal memories surely continues during personhood. So I have memories of having eaten breakfast and my animal has memories of having eaten breakfast, and these two memories have different content—for one can be correct (if, say, one remembers a breakfast prior to the advent of one's personhood) while the other is not. All this is very weird. (Of course, there is a non-coincidental resemblance here to Olson's arguments for animalism, but I find these versions add something, though maybe not.)

This is all too odd. So we really can't hold on to all of (1)-(4). I think one should deny (4). Some (e.g., Jeff McMahan) will deny (3) instead.