This chapter considers the metaphysics of geometric and non-geometric objects as they appear in physical theories such as general relativity, and the interactions between these considerations and the contemporary doctrines of perspectivalism and fragmentalism in the philosophy of science. Taking (following Quine) a kind’s being associated with a projectable predicate as a necessary condition for its being natural, there is a sense in which geometric objects can be assimilated to natural kinds but non-geometric objects cannot; this affords a rational reconstruction of philosophers’ and physicists’ suspicion of the latter (although this verdict can also be questioned). Even granting this, non-geometric objects can nevertheless represent real quantities in a perspectival sense-this is one way in which the perspectival realism doctrine can be endorsed. Moreover, recognising that non-geometric objects can represent real quantities in a perspectival sense affords support for fragmentalism: the view (at least in part) that frame-dependent effects are physically real. That said, one can argue that perspectivalism is superior to fragmentalism. In one sense, perspectivalism should be congenial to proponents of the ‘dynamical approach’ to spacetime theories-however, the pairing is imperfect. Endorsing perspectivalism/fragmentalism in this sense does not commit one to endorsing related-but arguably more opaque-‘structuralist’ views.