An instant, or changing in an instant, it can be in motion



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    • Imagine that there is an archer with an arrow that is ready to be released who has been in that state of affairs for all eternity.  Then, as an act of free will, the arched executes his timeless intention to release the arrow and set the arrow into motion.  Now, the question becomes, when did the arrow change from being at complete rest, to being in motion.  Motion, just as change, takes time.  However, if we assume that time is composed of instants, and there cannot be any first instant of motion or change, and if we assume that time is infinitely divisible into more and more instants, then there is no answer to this question; indeed, Angra Mainyu's objection would prove that motion, and change itself is impossible.  Clearly then, Angra Mainyu has landed himself in Zeno's paradox.  The solution to these kinds of paradoxes is that while it is true that an object cannot be in motion in an instant, or changing in an instant, it can be in motion at an instant in the sense of having a speed at that instant, provided the object occupies different positions at times before or after that instant so that the instant is part of a period in which the arrow is continuously in motion.  The same is true of change. Moreover, as was already mentioned, the present isn't actually composed of durationless instants.  Likewise, the duration of the first moment at which God enters into time is logically prior to any divisions, or point instants that we conceptually impose on this moment.  On Craig's view, the duration of the present doesn't have an answer apart from a universe of discourse; so it only makes sense to ask how long is the present second, minute, hour, etc.  If one doesn't like that view, then one can be an atomist which would mean that the present is composed a finite non-zero interval of time that cannot be further divided in reality.  In either case, God enters into time at that first moment and changes simultaneously with His creating the universe; just as the arrow begins to move at some conventional first moment which is simultaneous with the release of the arrow.  As David S. Oderberg writes:

      "The question to be considered is whether time is made up of durationless instants. The short answer to the question is that it cannot be, for the reason Zeno originally proposed in respect of lines: if a temporal interval or a line segment were composed of durationless instants or points of zero length respectively, then neither the interval nor the segment could have a length greater than zero.  Change takes time. And yet in another sense it takes no time at all. It may take an hour to paint a red wall green. But if we ask, “When, exactly, did the wall become green?”, what are we to answer? We might say, “When the last coat of green paint was applied.” But when, exactly, was that? “When the last lick  of paint was applied to the coat.” And when, exactly, was that? “When the last drop of paint from the last lick hit the surface of the wall.” But we need not stop there.  We can get more and more precise, and if we like we can fetch the latest in microscopic instruments to determine when the last molecule of green paint touched the surface of the wall. We might even start doing some quantum theory. But to the determined enquirer, that till will not be enough. Note that the sort of question I am posing here is not the same as the question of vagueness. The latter is a question about, in our example, what counts as the wall’s becoming green – is it the first coat of green paint, the last, the last swipe of the brush across the surface, the last droplet of green paint on it? And so on. But even if we stipulate one event or another, and even if the event takes place at the molecular or sub-molecular level, there is still a question about locating the exact time at which the change takes place. This is not a matter of vagueness but of the possibility of ever greater precision.…we could say, since we are...moving closer and closer together from opposite directions, that the stopping point is the one at which x changes instantaneously from F to G. But what point is that? It cannot be a point at which Fx, since, if x is genuinely changing at that point, it cannot be F, at least not wholly. Similarly it cannot be a point at which Gx, since if that were the case x would have already changed. So is it a point at which x is partly F or partly G? But that would only push the problem a stage back and we would have to locate the point at which x changed from being F to being partly F or partly G. Could the instant at which x changes be the instant at which it is neither F nor G? But now we need to know at what point, exactly, x passes from being F to being not-F, since this too is a change, and also the point at which it passes from not-F to G. Further, are we really to suppose that there is an instant at which – to continue with the example of the red wall that changes to green – the wall is neither red nor green? But then what color is it? Not blue or purple. But it cannot be colorless either, since all material objects have to have some color or other.

      Here we run up against one of the governing principles of change: the generation of one thing is the corruption of another, and the corruption of one thing is the generation of another.  We seem, then, to run up against serious obstacles in seeking to characterize instantaneous change in terms of an actual instant of change. But perhaps the most serious was already implicitly stated in the previous section: there are no actual instants. It is otiose to speculate at too great a length on what things are like at the instant of change if there is no such thing. Rather, we can speak of “change at an instant,” but if the earlier considerations are correct then this can only be given the


      same metaphysical interpretation as “velocity at an instant” or “acceleration at an instant.” The instant is a limit, and the limit is only a potentiality, not an actuality: it is the potential result of an infinite process of division, not an actual moment of time at which objects exist in certain states or configurations. But the crucial question now is: how do we reconcile the thought that change is instantaneous with the thought that there are no actual instants? We can take our
      cue from Aristotle:

      Again, since a thing that changes continuously and has not perished or ceased from its

      change must either be changing or have changed in any part of the time of its change, and

      since it cannot be changing in a moment [emphasis added], it follows that it must have

      changed at every moment in time: consequently, since the moments are infinite in

      number, everything that is changing must have completed an infinite number of

      changes.34

      So that which has changed must have been changing and that which is changing must
      have changed, and a process of change is preceded by a completion of change and a
      completion by a process: and we can never take any stage and say that it is absolutely the
      first [emphasis added]. The reason of this is that no two things without parts can be
      contiguous, and therefore in change the process of division is infinite, just as lines may be
      infinitely divided so that one part is continually increasing and the other continually
      decreasing.35

      Our next point is that no process of change is infinite: for every change, whether between

      contradictories or between contraries, is a change from something to something. Thus in
      contradictory changes the positive or the negative, as the case may be, is the limit, e.g.,
      being is the limit of coming to be and not-being is the limit of ceasing to be: and in
      contrary changes the particular contraries are the limits, since these are the extreme
      points of any such process of change….

      There is, on the Aristotelian view, no first stage of change. Change involves limits,

      and limits involve infinite divisibility; since there are an infinity of instants –

      understood only potentially – everything that changes must have completed an

      infinite number of changes. It is, I propose, by means of the sketch I have given

      above of the metaphysics of change and the metaphysics of time that all of these

      thoughts can be put together into a coherent whole.

      When an object x changes fromF to G, or from F to not-F, the period of time in which the change takes place is full


      of forms, and the only forms which are present are the forms of Fness and Gness or the forms of Fness and whatever form entails non-Fness. In the case of substantial hange, the forms are substantial forms; in the case of accidental change, they are accidental forms. There is no void, no period of any duration during which x is neither F nor not-F, neither F nor G; still less is there a durationless instant at which this is the case. But there is change at an instant, as long as instants are understood derivatively just as motion at an instant or velocity at an instant are understood derivatively, these being in fact just special cases of change. Our model of change is thus:

      ________F_________.…FFFF……GGGG….________G___________


      where FFFF and GGGG approach each other infinitely – there never being adjacent F and G, there never being a void, and there never being a point of simultaneous, contrary F and G. There is no first moment of change since there is no last moment of F, and by parity of reasoning, no last moment either since there is no first moment of G.

      I have defined the essence of change as the actualization of a pre-existing potentiality. I have also defined
      instants as the limits of a process of in finite potential division. It is my contention that these two potentialities are but different aspects of one and the same radical potentiality that lies at the heart of nature itself. Both are necessary for the
      explanation of change.  The actualization of potentiality would not be possible without the potentiality that characterizes time; and if, as I would also contend (without space for a defense here) there is no time without change, the potentiality at the root of time would not be possible without the eduction of form from potentiality that is the essential note of change. In change, form succeeds form: every coming-to-be is a passing-away and every passing-away is a coming-to-be. Change is, then, a continuous process of loss and gain that is without gap and without contradiction. Change is instantaneous: without instants as limits it could not take place. To search for an actual instant of change, however, is to search in vain, for there are no actual instants at all. To search for a transition that does not consist in the actualization of potentiality is to search for a chimera. Transition there must be, and without the exceedingly small there is no transition; but to look for it in the exceedingly small is to miss its presence in the process at large. Ultimately the process is unfathomable –as unfathomable as the very potentiality that explains the finitude of the material universe and everything within it. In metaphysics, this is all the explanation we need."

      There is a second route one could take here as well.  According to Craig, God changes EXTRINISICALLY upon the moment of creation in virtue of being related to the universe.  Even though God’s knowledge switches from knowing all tenseless facts to knowing all tensed facts (and believing no false tensed facts), this type of change isn’t intrinsic because God remains omniscient throughout.  Moreover, since time wouldn’t exist in the absence of the relations of events, it seems that God’s changing from being timeless to temporal is also an extrinsic change.    

      According to David Lewis, ‘The intrinsic properties of something depend only on that thing; whereas the extrinsic properties of something may depend, wholly or partly, on something else.’  Thus, God’s changing in the above two ways depends wholly on the act of creating the universe, and thus are extrinsic.  So then, God seems to go through a Cambridge change at the moment of creation, and it seems much easier to conceive of extrinsic change as instantaneous, even if intrinsic change cannot be (such as the property of ‘taller than’).

      There is yet a third route that one could take which would be to grant that change qua change is an inconsistent phenomena that permeates all of reality.  As Quine taught us, we must be willing to revise our a prior concepts in light of empirical evidence to the contrary.  So, given that change is an empirical fact, and if one is not satisfied by any of the solutions to Zeno’s paradoxes, then one could simply accept that change is real, but that it is also inconsistent.  Indeed, a number of philosophers take this position:



      Mortensen, Chris, 1985, “The Limits of Change,” Australasian Journal of Philosophy, 63: 1–10.
      –––, 1997, “The Leibniz Continuity Condition, Inconsistency and Quantum Dynamics,” The Journal of Philosophical Logic, 26: 377–389.

      • Priest, Graham, 1987, In Contradiction, Dordrecht: Nijhoff; second edition, Oxford: Oxford University Press, 2006.

      • Von Wright, G.H., 1968, Time, Change and Contradiction, Cambridge: Cambridge University Press


TO SEE THE FULL EXPLANATION OF THE POINT I AM TRYING TO MAKE, READ THE REST OF THE FOLLOWING ARTICLE:  Instantaneous Change Without Instants by David S. Orderberg (http://www.reading.ac.uk/AcaDepts/ld/Philos/dso/papers/Instantaneous%20Change%20without%20Instants.pdf)


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