Synthese 92 (3):371 - 384 (1992)

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.
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DOI 10.1007/BF00414288
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References found in this work BETA

Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
Plato's Parmenides.R. E. ALLEN - 1983 - Duke University Press.
A Note on Zeno's Arrow.'.Gregory Vlastos - 1966 - Phronesis 11 (1):3-18.

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Citations of this work BETA

Set Theory and Physics.K. Svozil - 1995 - Foundations of Physics 25 (11):1541-1560.
The Tortoise is Faster.Constantin Antonopoulos - 2003 - Southern Journal of Philosophy 41 (4):491-510.

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