Blackwell Reference Online

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The boundaries of extended objects may be thought of in two ways: as limits or as thin parts. Limits of the object have fewer dimensions than it has itself: a three-dimensional brick has surfaces without thickness; the edge where two faces meet is a one-dimensional line; the corner where three faces meet is a point. An enduring event like a kiss has a beginning and an end without duration. There are also inner boundaries, like the half-way point in the flight of an arrow. Boundaries in this sense raise many ontological questions. Do they really exist or are they mathematical fictions? Are they parts of their objects, or of the surroundings, or neither? Alternatively, boundaries are simply ‘thin’ parts of the same dimensionality as their wholes. At stake is whether the highly successful mathematics of continuous structures, like the real numbers, which treat extents as composed of extension less points, truly depict reality. : Metaphysics ( Oxford : Clarendon Press , 1957 ) Bk 5, ch. 17, 1022; Bk 11, ch. 3, 1061 . : Surfaces ( Minneapolis : University of Minnesota Press , 1988 ). : An Enquiry Concerning the Principles of Natural Knowledge ( Cambridge : 1919 ); 2nd edn ( Cambridge : Cambridge University Press , 1925 ), esp. Part III , ‘ The method of extensive abstraction ’. ... log in or subscribe to read full text