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Infinite Divisibility, Ontology, and Spatial Relations1

Published online by Cambridge University Press:  09 June 2010

Eike-Henner W. Kluge
Eike-Henner W. Kluge
Affiliation:
University of California, Irvine
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Extract

Consider the paradox of Achilles and the tortoise. Both Zeno and the philosophic tradition after him have accorded it the status of a legitimate problem. It is my aim to show, that both Zeno and the tradition have been mistaken; that the basis of the alleged paradox is a none too clear analysis of the nature of spatial relations; and that the appearance of the paradox itself rests on a confusion of two types of analysis: an ontological analysis on the one hand, and a qualitative one on the other. I shall therefore suggest a solution to the paradox that in effect amounts to a denial of its legitimacy.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 9 , Issue 3 , December 1970 , pp. 356 - 365
Copyright
Copyright © Canadian Philosophical Association 1970

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References

2 This merely amounts to an acceptance of the metaphysical enterprise.

3 The first assumption itself carries with it no small amount of doctrine. The point of my distinction lies in the fact that mere acceptance of the metaphysical enterprise does not constitute acceptance of the particular metaphysics that I shall sketch shortly.

4 Criteria of ontological basicness are here in order, as are examples of entities satisfying them. A fairly safe generalization seems to be that what is physically complex or analysable cannot be ontologically basic. This is by no means a complete answer; but I must defer further considerations to another occasion.

5 Or space-time. I am not concerned to argue the one locution over the other; and hence shall take this qualifier as understood.

6 Newton, I., Mathematical Principles (trans., Motte, A., edit. Cajori, F.) Berkeley, 1934, pp. 6–10Google Scholaret passim.

7 I disregard the notion of unanalysable yet extended quanta, since this ultimately can be shown to be contradictory.

8 Indeed, the frame may simply lack the notion of an object. How would the present problem be posed here?