Full Idea
If we say (in opposition to a physical view of identity) that when Jones dies 'Jones ceases to exist' but 'Jones' body does not cease to exist', this shouldn't be pressed too hard, because it would make 'dead person' a contradiction.
Gist of Idea
'Dead person' isn't a contradiction, so 'person' is somewhat vague
Source
Bernard Williams (Are Persons Bodies? [1970], p.74)
Book Reference
Williams,Bernard: 'Problems of the Self: Papers 1956-1972' [CUP 1979], p.74
A Reaction
A good point, which nicely challenges the distinction between a 'human' and a 'person', but the problem case is much more the one where Jones gets advanced Alzheimer's, rather than dies. A dead body ceases as a mechanism, as well as as a personality.