Lockean theories of personal identity maintain that we per-sist by virtue of psychological continuity, and most Lockeans say that we are material things coinciding with animals. Some animalists ar-gue that if persons and animals coincide, they must have the same intrinsic properties, including thinking, and, as a result, there are ‘too many thinkers’ associated with each human being. Further, Lockeans have trouble explaining how animals and persons can be numerically different and have different persistence conditions. For these reasons, the idea of a person being numerically distinct but coincident with an animal is rejected and animalists conclude that we simply are animals. However, animalists face a similar problem when confronted with the vagueness of composition. Animals are entities with vague boundaries. According to the linguistic account of vagueness, the vagueness of a term consists in there being a number of candidates for the denotatum of the vague term. It seems to imply that where we see an animal, there are, in fact, a lot of distinct but overlapping entities with basically the same intrinsic properties, including think-ing. As a result, the animalist must also posit ‘too many thinkers’ where we thought there was only one. This seems to imply that the animalist cannot accept the linguistic account of vagueness. In this paper the author argues that the animalist can accept the linguistic account of vagueness and retain her argument against Lockeanism.
The paper is devoted to convergence of double sequences and its application to products. In a convergence space we recognize three types of double convergences and points, respectively. We give examples and describe their structure and properties. We investigate the relationship between the topological and convergence closure product of two Fréchet spaces. In particular, we give a necessary and sufficient condition for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet space.