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(1992) Synthese 92 (3).
An epistemological use of nonstandard analysis to answer Zeno's objections against motion
William I McLaughlin, Sylvia L. Miller
pp. 371-384
Three of Zeno's objections to motion are answered by utilizing a version of nonstandard analysis, internal set theory, interpreted within an empirical context. Two of the objections are without force because they rely upon infinite sets, which always contain nonstandard real numbers. These numbers are devoid of ‘numerical meaning’, and thus one cannot render the judgment that an object is, in fact, located at a point in spacetime for which they would serve as coordinates. The third objection, ‘an arrow never appears to be moving’, is answered by showing that it only applies to a finite number of instants of time. A theory of motion is also advanced; it consists of a finite series of contiguous infinitesimal steps. The theory is immune to Zeno's first two objections because the number of steps is finite and each lies outside the domain of observation. ‘Present motion’ is hypothesized to be an unobservable process taking place within each step. The fact of motion is apparent through a summing (Riemann integration) of the steps.
Publication details
DOI: 10.1007/BF00414288
Full citation:
McLaughlin, W.I. , Miller, S.L. (1992). An epistemological use of nonstandard analysis to answer Zeno's objections against motion. Synthese 92 (3), pp. 371-384.
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