Moving without being where you 're not; a non-bivalent way'

Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):235 - 259 (2004)
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Abstract

The classical response to Zeno’s paradoxes goes like this: ‘Motion cannot properly be defined within an instant. Only over a period’ (Vlastos.) I show that this ob-jection is exactly what it takes for Zeno to be right. If motion cannot be defined at an instant, even though the object is always moving at that instant, motion cannot be defined at all, for any longer period of time identical in content to that instant. The nonclassical response introduces discontinuity, to evade the paradox of infinite proximity of any point of a distance with any ‘next’. But it introduces the wrong sort of discontinuity because, rather than assuming the discontinuity of motion, as Quantum Theory does, it assumes the discontinuity of space. Due then to the resulting spacetime disorder, though all else is certainly lost, the Tortoise now turns up at least as fast as Achilles and hence not even this much is rescued. Zeno rejects motion because he shows that a moving object must be where it is not. Hence motion, if to occur, must violate the Law of Contradiction (LNC). Applying the concept of quantum discontinuity, I produce an alternative. If an object is to move discontinuously between two boundary points, A and B, what actually obtains is, rather, that it is nowhere at all in-between A and B. And cannot therefore be at two places in-between A and B. And cannot therefore be where it is not. Thus, LNC is conserved. However, in these conditions, the Law of the Excluded Middle (LEM) fails. To mitigate the undesirability of this effect, I show that LEM fails because LNC holds. Thus, the resulting nonbivalent logic, which is also appropriate for quantized transitions of all kinds, will always turn up nonbivalent, because consistent. And this is not too bad, considering

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