Full Idea
According to 'animalism', I existed before I was a person and I may well go one existing for some time after I cease to be a person; hence, I am not essentially a person, but a human organism.
Gist of Idea
For 'animalism', I exist before I became a person, and can continue after it, so I am not a person
Source
report of Eric T. Olson (The Human Animal [1997]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10
Book Reference
Lowe,E.J.: 'Introduction to the Philosophy of Mind' [CUP 2000], p.284
A Reaction
There is a very real sense in which an extremely senile person has 'ceased to exist' (e.g. as the person I used to love). On the whole, though, I think that Olson is right, and yet 'person' is an important concept. Neither concept is all-or-nothing.