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By Richard Swinburne

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This is to say that every region of space is of logical necessity surrounded on all sides by other regions of space. The denial of this is the assertion that it is logically possible that there be a boundary to space. A boundary to space would be, as it were, a wall barring further progress. Yet it must be that behind this wall either there is some object, in which case that object would occupy space; or there is no object, that is there is unoccupied space. It does not seem possible to give a coherent description of any third possibility.

For us on Earth this is always the E-group. But it is possible to identify material objects relative to another group, and there might be people whose surroundings had the sort of stability which made it natural for them to make their judgements relative to a different MO-invariant group. They would make provisional judgements to identity on the basis of the criterion of similarity. There would be enough such judgements to yield a stable frame of reference (which was not an E-frame), by means of which they could check individual such judgements to see ifthey satisfied the conditions of spatio-temporal continuity relative to their frame.

BIBLIOGRAPHY [l] Kant, Critique of Pure Reason (trans. N. Kemp-Smith), London, 1929, Transcendental Aesthetic, section J, 'Space'. (In references to this work in this and other chapters, where a passage appears in both editions I give a reference to the second edition only. ) [2] Anthony Quinton, 'Spaces and Times', Philosophy, 1962, 37, 130-46. Spaces 41 For definitions of discreteness, density, and continuity see: [3] E. V. , 1917. For discussion of the point that empirical tests could not decide between the theory that space is continuous and the theory that it is merely dense, See: [4] W.

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