II. To the Negative Side of the Question

116. As to the second side of the question wherein is asked ‘whether there should be posited in an existing angel something measuring his existence’ [nn.84, 87], I say that ‘to measure’ is to make an unknown quantity certain through a more known quantity; but making certain can be done by a quantity existing in reality or in imagination.

117. In imagination as when a skilled artisan measures by a quantity that he has in his imagination some quantity that is presented to him.

118. But sometimes the measuring can be done by some real quantity, and that in three ways:

Either by an exceeding quantity, and then the intellect is made certain about a lesser quantity through its approach to or departure from a greater quantity. And in this way is a measure imposed on the quiddities of things, and the measure is more perfect than the measured and must be naturally more known than it - the way whiteness is imposed as the measure in the genus of colors and is called the first measure in everything that is in that genus [Metaphysics 10.2.1053b28-34, 54a9-13].

119. In another way the known quantity is lesser and part of the greater quantity (which is less known), and then the lesser quantity measures the larger whole by reduplication of itself. And in this way a lesser motion can, from the nature of the thing, be the measure of a greater motion.

120. In a third way an unknown quantity is measured by some known quantity that is equal to it, and this is done by applying or superimposing it; and because that which, from the nature of the thing, is the measure first should be naturally more known than the thing measured, so in this way one of the equals is not the measure of the other unless it were, from the nature of the thing, more known. And in this way time, if it is a quantity other than motion and more known than it, can be from the nature of the thing the measure of motion.

121. However, for some intellect what is not the measure by the nature of the thing can be a measure; for example, if the length of the arm is known to someone and the length of a piece of cloth unknown, the length of the arm (because it is known) can be for him the measure of the length of the cloth,a although neither length has, from the nature of the thing, greater certitude than the other.

a.a [Interpolation] About the mensuration of one thing by another by a measure more known simply or more known to us, note Averroes Physics 4 comm.112-114 about time, where he shows how time measures motion by a number of it that is more known, and the whole motion by that part.

122. Applying this then to the issue at hand, I say that in the actual existence of an angel there is no need to look for some intrinsic measure different from the nature of the thing itself that is measured, because - as was already proved [n.91] - nothing is there really other than the nature of the measured thing; but a measure is, from the nature of the thing, other than the thing measured, and plainly, if some measure were posited in an angel, it would not be posited in him save in the third way (for it neither exceeds nor is exceeded but is equal [nn.118-120]). And in addition, the existence of an angel does not seem able to be its own measure the way that in other things a quantity more distinctly known can be the measure of itself as to its own confusedly known parts; it is not so with an angel, since his existence is indivisible and cannot contain parts confusedly in itself, since it has no parts.

123. Likewise therefore, there is no need to posit in an existing angel anything to be the measure of actual existence other than his actual existence. And if plurality is not to be posited without necessity, and here there is no necessity, plurality does not seem it should here be posited; but not only is it not necessary to posit anything absolute as measure, it is also not necessary to posit any relation other than relation to the efficient or conserving cause - and that relation is not different from the foundation (from 2 d.1 q.5 nn.260-71).