Abstract
There is a strong intuition that for a change to occur, there must be a moment at which the change is taking place. It will be demonstrated that there are no such moments of change, since no state the changing thing could be in at any moment would suffice to make that moment a moment of change. A moment in which the changing thing is simply in the state changed from or the state changed to cannot be the moment of change, since these states are respectively before and after the change; moreover, to select one of these moments over the other as the moment of change would be arbitrary. A moment in which the changing thing is neither in the state changed from nor in the state changed to cannot be the moment of change, since there are changes for which it is impossible for something to be in neither state. Finally, the moment of change cannot be a moment in which the changing thing is in both the state changed from and the state changed to, as suggested by Graham Priest and others. Even if, like proponents of this view, we are willing to accept the contradictions that the account entails, it is demonstrated that on such a model, every change would require an infinite number of other changes, every change would take an infinite amount of time, and some changes would occur without occurring at any time. Further, the model is grossly counterintuitive, with the exact nature of the counterintuitive element depending on what model of time and space one endorses. Finally, it is demonstrated that this model is incompatible with the Leibniz Continuity Condition.
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Notes
I am assuming that micron is not itself a vague concept, since it can be defined as the distance traveled by light in a vacuum in 1/299,792,458,000,000 of a second, while a second may be defined as the time needed for a cesium-133 atom to perform 9,192,631,770 complete oscillations. The concept of a cesium-133 atom might be vague, but if so, we can at least theoretically define a second in terms of the oscillations of an atom that exists in a universe that contains nothing else, so that there is no question as to what matter is part of the atom and what matter is not. If we are further concerned that an atom can only oscillate relative to some other object, we can introduce an object for reference, placing it sufficiently far away from our atom that there is no vagueness about which object any given piece of matter belongs to.
It might be objected that the word “teleport” is inappropriate here, on the grounds that teleportation involves an object moving from one place to another on a line without passing through the places between them, whereas on this model, every actual place on a line is occupied by any object moving down the line. However, to say that space is “finitely divisible” is to say that fewer positions exist in a dimension than we can represent mathematically. For instance, let us say that S is an indivisible extension of space. Because S is indivisible, there is only one place in S—that is, S itself. Despite the fact that there is only one place in S, we can represent an infinite number of places in S mathematically. For instance, we can represent the place “halfway through S” on any mathematical model of S, and once we specify a direction, we can add “a third of the way through S,” “a quarter of the way through S,” and so on infinitely.
Because of this abundance of mathematically identifiable places within any actual place, the movement of an object through finitely divisible space must be, in some sense, mathematically discontinuous. That is to say, the object leaps from one cluster of mathematically possible spaces to another cluster of mathematically possible spaces, rather than moving smoothly through each of them in turn as it would in infinitely divisible space. I think that such movement deserves the label “teleportation,” but nothing hangs on the adoption of that term. The important point is simply that movement through finitely divisible space is discontinuous in a way in which movement through infinitely divisible space is continuous. Such discontinuity should strike us as odd, regardless of what we call it. Certainly, we intuitively think of movement of an object down a line as requiring the passage of that object through every place we can identify on that line, in order. This order may be complicated by the fact that an extended object may occupy more than one place at a time, but at the very least, the object should enter identifiable places on the line in strict order, and leave those places again in the exactly the same order.
As Graham Priest suggests in In Contradiction, ( 2006 ): 160.
Not all philosophers would agree, of course. Most famously, John M. E. McTaggart, “The Unreality of Time”, Mind 17 (1908): 457–74, concluded that change, like time itself, is not real.
English translation in Leibniz philosophical papers and letters, ed. L.E. Loemker, (Dordrecht: Reidel 1969: 351).
English translation in Leibniz philosophical papers and letters, ed. L.E. Loemker, (Dordrecht: Reidel 1969: 352–3).
References
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Leibniz, G. (1687). Letter of Mr. Leibniz on a general principle useful in explaining the laws of nature through a consideration of the divine wisdom; to serve as a reply to the response of the Rev. Father Malebranche. (English translation in Leibniz philosophical papers and letters, (ed) L. E. Loemker, Reidel, 1969.)
McTaggart, J. E. (1908). The unreality of time. Mind, 17, 457–74.
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Priest, G. (2006). In contradiction: A study of the transconsistent. Oxford: Clarendon Press.
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Littmann, G. Moments of Change. Acta Anal 27, 29–44 (2012). https://doi.org/10.1007/s12136-011-0123-3
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DOI: https://doi.org/10.1007/s12136-011-0123-3