Saturday, 23 July 2011

Question 53 - The Local Motion of Angels

Why this Question Matters.

In Ia.q52 Aquinas has argued that we can consider angels to be “in place” in a sense that is determined by the way that they exert their power in the world; they are where they act. Having dealt with the topic of statics, it would seem entirely reasonable to turn to the field of dynamics; in what way can we say that angels move? Local motion through space naturally involves time; indeed it is motion that, in the general sense of change, determines what we understand as time. Recall from the discussion in Ia.q10, that God is in eternity, angels are in aeviternity and matter-form composites are in time. If we ask the question of how angels can be considered to move in space and time, then we have to ask about what the interface between time and aeviternity might look like.

The Thread of the Argument

A1: The first question that Aquinas has to turn his attention to is whether it makes any sense to talk about an angel moving from place to place. In considering this question, he first of all thinks about what we mean by local motion in the case of ordinary material objects. When we think about objects moving we notice that their movement is continuous both in space and in time; things simply don’t jump from one place to another instantaneously. Indeed, it is this fact that leads us to model time and space as continua and to model motion by using considering location to be a continuous function of time. There is always a point in time between two different points in time; on any path between two places there is always an intervening point between any two different points.

When we turn to the angels we have to remember that they are said to be in place simply by the fact of their exercise of power in that place. If we are to say that they move, we are simply saying that the location of their exercise of power moves. As such, there is no reason whatsoever that impels us to think of that motion as being continuous. If they exercise their power, first in this place and then in that place, the change of place from one to another need not be continuous. Of course, it is perfectly possible that their motion may be continuous if it involves the continuous movement of the location of the application of their power. So Aquinas’s answer to this question is a guarded yes; we can consider angels to move locally, but we must be very careful not to confuse such motion with the local motion of material bodies.

A2: A corollary of the possible discontinuity of the local motion of an angel is that, unlike the local motion of a material body, he need not pass through intermediate points between here and there in his motion. To us, centuries after the invention of the calculus and more than a century after the careful analytical investigations by nineteenth century mathematicians into the nature of continuity, this is completely unsurprising and not at all difficult to prove. But Aquinas was writing before even the Oxford Calculators had started their seminal work; he spends a careful paragraph or two describing what it means for the motion of a material body to be continuous and he shows that if a motion is not continuous then the “intermediate” property of continuous motion fails. His analysis may not possess modern rigour, but what he could do is rather humbling.

A3: The other part of the equation when considering the possibility of discontinuous motion is that it must surely involve an instantaneous “jump” from one place to another. However, there is a problem with this.

Suppose we are timing material motion with a stopwatch. If we time a runner running the hundred metres race, we start the stopwatch at t = 0 when the gun fires and the runner starts running. The runner runs (continuously) from the start line to the finish line and arrives at the finish line at (say) time t = 10. Because the motion is continuous, the runner is at a particular place at every time between zero and ten seconds. Now let us try to do the same thing with an angel who moves discontinuously from the start line to the finish line. Let us suppose the angel arrives instantaneously at the finish line at time t = 10. Where is he at t = 9.9? He is at the start line. What about 9.99 seconds? Similarly he is at the start line. What about 9.999 seconds? There’s a pattern emerging here! There is no last time at which the angel is at the start line before he transitions to the finish line. The problem is that our very notion of modelling the motion of material objects using spatial and temporal continua is predicated upon the continuity of that motion. When we run into an example like angelic motion that is discontinuous, we must realize that this fails.

Aquinas draws the obvious conclusion: we cannot model discontinuous angelic motion using continua (there no problem with continuous angelic motion). The discontinuous motion of angels takes place in a discontinuous or discrete time. At one discrete time point an angel is here and at the next discrete time point the angel is there; we cannot say that this motion is instantaneous because there are no time points (for the angel) between the start and finish times.

Handy Concepts

  • Angels can be said to move in space insofar as their power is exercised first in one place and then in another. This movement can be continuous or it can be discontinuous.
  • In discontinuous motion an angel need not pass through intermediate places between his start and his destination.
  • An angel’s discontinuous motion cannot be measured by continuous time; rather it is measured by a discrete time. Hence we cannot say that discontinuous motion occurs instantaneously.


  • Aquinas’s solution in the third article is a fascinating anticipation of some the problems of time that arise in quantum mechanics. In some quantum mechanical systems, it does seem to make sense to model time and space as discrete variables.
  • Perhaps Aquinas’s solutions to the problems raised by angelic motion are a little more restrictive than they need be. The fundamental insight that an angel may be considered in place by the exercise of his power there, or by his potential to exercise power there, remains of fundamental importance. But Aquinas doesn’t seem to push some of his ideas far enough. For example, he asserts that an angel cannot be in more than one place at a time, but allows that that place may be spatially quite complex (the fundamental issue being that the place is determined by the needs of the determined exercise of power rather than anything to do with how the actors in that exercise of power are arranged). This being so, the movement of an angel from place to place corresponds to the shift of focus from one act of determined power to another. The act of determination of the angel to its act of power may be instantaneous, but does this force the application of that act of power in the material world to be instantaneous? Might we not consider such acts of power as coming-to-be in time in the material world? Pictures such as a spherical surface descending to intersect a plane surface may then be helpful. Elaborations of this picture are then helpful in eliminating the implication that angels’ discontinuous acts need to occur in discrete time.
  • Aquinas never really ties up the connection between time and aeviternity in this article, which is a bit of a disappointment!

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