The paper presents an approach to constructing an ontology of physical objects founded on a theory of the spatio-temporal distribution of matter types. The starting point for this construction is the formal theory D of 'space, time, matter and things' given in (Bennett 2001c), in which physical objects are modelled as maximal self-connected portions of some matter type. However, that theory is not compatible with the common-sense view of 'physical objects' according to which it is normal to regard an object as persisting (i.e. retaining its identity) despite the loss (or possibly gain) of small parts, which are deemed 'insignificant'. The current paper gives a more elaborate theory of the nature of physical objects and specifies their identity criteria in a way that allows for possible loss of small particles. This is achieved by explicitly taking account of an intrinsic vagueness in the identity criteria for commonsense physical objects. The paper also uses this theory to characterise various degrees of physical damage which an object can undergo.
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