Question Two. Whether in an Angel actually Existing there is Need to posit Something Measuring its Existence that is Other than that very Existence

84. Secondly I ask whether in an angel actually existing there is need to posit something measuring its existence (or the duration of its existence [n.1]) that is other than that existence itself.

85. That there is:

Time differs from motion by the fact that it measures motion (as the Philosopher proves in Physics 4.10.218b13-18 by the fact that ‘time is neither quick nor slow but motion is said to be quick or slow’, and by other reasons); therefore, by likeness, there is something other than the existence of the aeviternal that measures it.

86. Secondly as follows: permanent quantity and successive quantity belong to the same genus - therefore each is something other than its subject, especially if the subject belongs to the genus of substance; therefore just as permanent quantity is other than that of which it is the measure, so also is successive quantity [cf. nn.1-2].

87. On the contrary:

About this ‘other’ I ask by what it endures in being. If by itself then, by parity of reasoning, existence itself will be able to endure by itself formally, because this ‘other’ is not more perfect than that very actual existence, since it is as it were the property of it.

But if it endures in being by an absolute other than itself, there will be an infinite regress in measures and things measured.

I. To the Affirmative Side of the Question

A. The Opinion of Others

88. My response.

The first opinion in the preceding question [n.11] should concede the affirmative side, because aeviternity [according to this opinion] truly posits the idea of measure and quantity in its proper sense [n.48] - and so aeviternity differs from the existence of an angel, which existence is not in itself formally an extension, a quantum, but is indivisible.

89. Likewise, in that existence one ‘now’ of aeviternity succeeds to another; therefore both ‘nows’ differ from the existence of an angel as something absolute (according to this position [nn.19, 49-51, 58]), because they are quasi-indivisibles of the genus of quantity.

90. Likewise some - holding the second opinion in the preceding question (about the indivisibility of aeviternity [nn.39, 42, 33]) - say that aeviternity itself belongs to the genus of quantity, not as a divisible but as an indivisible in that genus; such that from many indivisibles of the same species, measuring namely the existences of several aeviternal things of the same species, a discrete quantity can be composed, which is the number and measure in aeviternal things, just as number in corporeal things is composed of the discrete unities in those things (for this they adduce reasons - look for them).Henry of Ghent Quodlibet 12 a.8, “But someone might ask in what category the measure of angels is. And I say that it is in the category of quantity as the principle of it, in the way that unity and point and instant are in the category of quantity. For just as from diverse indivisibles measuring the diverse thoughts of any angel there is constituted one discrete measure, which is called time, because it is constituted from transient things measuring the being of a transient thing, so from the diverse indivisibles of aeviternities measuring the substance and ‘the being as to substance’ of several angels, differing in number in one species of angels, there is constituted one discrete measure, which does not deserve to be called time, because it is not constituted from transient things measuring the being of a transient thing as it is transient, but rather is constituted from permanent things of a permanent being as it is permanent; and so it is not a species of time but rather of number - and this number is from discrete unities in spiritual things, just as the number that the philosophers posit is from discrete units in corporeal thing. But if it happen that there is only one angel in one species, yet because there can be several angels, as we made clear elsewhere (ibid. 9 q.1), this makes no difference as to positing that such a number is some species of quantity - just as if everything corporeal were one continuum, this would make no difference as to positing that natural number is a species of quantity, since the continuum can be divided (at least by the intellect) and from the continuum something discrete comes to be. So therefore the aeviternity in a species, containing in itself diverse aeviternities measuring the being of diverse angels of the same species, is a discrete quantity and divisible into indivisibles - which indivisibles are the aeviternities of individual angels and differ in number among themselves; and if from the aeviternities of diverse angels differing in species a mathematical abstraction could be made, just as it can be made from the numbers of diverse corporeal things differing in species - then perhaps, just as there is one number ten for ten men and for ten horses (although the tens are not the same), so there is the same aeviternity in species for all the angels diverse in species, although the aeviternals would not be the same in species.” ²⁴

B. Rejection of the Opinion

91. Against this [nn.88-90] there is, as was argued before in 2 d.1 n.262, an argument as follows:

That which, if it were distinct from something, would be naturally posterior to it, is necessarily the same as that something if it is incompossible for it to be without it. Therefore, if it is incompossible for an angel to be without some extrinsic thing (which thing would be the measure of his actual existence), then, since that extrinsic thing, if it were other, would be naturally posterior to the actual existence of the angel, the consequence is that it is not other than his existence; or if it is other, and consequently posterior, the angel’s actual existence will, without contradiction, be able to be without it - and thus there is no necessity to posit it.

92. There is a confirmation of this reason (and it is like the one that mention was made of above at d.1 n.262), that a distinction between things, one of which is properly present in the other, is not deduced save from an actual or potential distinction, or because the things are disposed to each other as those things are of which one is separable from the other.

93. I add this third point, that according to Aristotle, Metaphysics 7.11.1036b22-28 ‘On the parts of Definition’, many have been seduced from the truth by comparison of the younger Socrates who said that ‘if were no circles save bronze ones, bronze would not for this reason fall into the definition of circle’, and inferred by similitude that ‘flesh should not fall into the definition of man, even though there is no man without flesh’ -when it is given, I say, that a separation of these [man and flesh] from each other is impossible. However if these are disposed to each other as are things of which the separation is possible, then the conclusion is that they are separable; for example, if from the proper idea of circle and triangle, of flesh and wood, the conclusion is drawn that circle is disposed to wood as triangle is to flesh, and if separability is proved on the one side, then a distinction will be proved on the other side, and proved that inseparability on that other side is not from its proper idea but from something extrinsic.

94. I take, therefore, that nothing can be proved to be distinct from another thing save because of their actual or potential separation, or because of a proportion of them to some other things of which one is separable from the other. But in the issue at hand [sc. the measure of the existence of angels] none of this holds. For there is not here (for you [sc. those who hold the first or second opinions in the previous question]) any separation, whether actual or potential. Nor are these things [sc. an angel’s existence and the measure of it] disposed to each other as distinct and separable things are, because nothing distinct really from another thing, without which it cannot be without contradiction, is prior to it, but either naturally posterior or simultaneous in nature with it; but this thing which is posited as ‘other’ [sc. the measure of an angel’s existence], if it existed, would be naturally posterior to the angel;     therefore etc     . [n.91].

C. Instance against the Rejection of the Opinion

95. There is objected against this [sc. that there is no distinction between the existence of an angel and the measure of it], that ‘the now as to substance’ is disposed to the substance of a movable thing as that which is posited to be the measure of the duration of the existence of angels is disposed to that existence - because, just as the existence, measured by this indivisible measure, remains the same, so the like is posited on the side of the ‘now’ and the substance of a movable thing; and yet on this side is found a distinction between the substance of the very movable thing and the substance of the ‘now’; therefore here too.

96. Now that one should posit some such ‘now’ measuring the movable thing, the same as it in substance, seems to follow from the intention of the Philosopher in Physics 4.10.281a8-11; there he seems to solve as it were the question he is moving about the ‘now’, by saying that it is ‘one and the same as to substance, but different as to being’.

D. Response to the Instance

97. I exclude this objection [n.95] as follows:

First I show that what it supposes about ‘the now as to substance’ is false and is against the Philosopher’s intention - because the Philosopher proves [Physics 4.11.219b22-25] that “‘the now’ follows what is being moved” by the fact that “we learn from what is being moved the ‘before’ and ‘after’ in motion,” and that from this ‘now’ we learn the ‘before’ and ‘after’ in time. But this is not true of the movable as to substance, but as it is under different changes, because, if the movable is taken as to substance absolutely, we do not from it learn the ‘before’ and ‘after’ in motion.a

a.a [Interpolation] therefore neither do we from the same ‘now’ according to substance learn the ‘before’ and ‘after’ in time, but we do so from different ‘nows’.

98. Likewise, the Philosopher says [Physics 4.11.219b33-20a4], as to the second property about the ‘now’, that it is not without time nor vice versa, because motion is not without the movable nor vice versa; and as motion is to the movable, so the number of motion is to the number or unity of the movable. But that the movable cannot, as to its substance, be without motion is false, but it is true of the movable precisely as it exists under change; therefore if the latter is a movable in the whole motion, then so is the ‘now’ corresponding to it.

99. Further, how could the ‘indivisible now’ flow according to different existences (which would necessarily be indivisible), without its whole flow being a composite of indivisibles? For the Philosopher proves, from his intention in Physics 6.10.241a6-14, that the indivisible cannot move, because then its motion would be composed of indivisibles, because a lesser or equal part of it would pass by before a greater did;     therefore time would be a composite of indivisibles, which is against the Philosopher [Physics 6.9.239b8-9].

100. To prove this [sc. that an indivisible ‘now’ cannot flow according to different existences] there are two reasons from the Philosopher [Physics 4.10.218a21-30],a one of which is of this sort: ‘those things are said to be at once which are in the same indivisible instant etc     .’b

a.a [Interpolated note] In the Reportatio, “these reason are left unsolved, though they may apparently be solved.”

b.b [Interpolation]     therefore if the instant is the same in substance, all instances are equally present and at once, both those now and those a thousand years from now (Averroes Physics 4 comm.92).

101. The other reason is that ‘of any continuous thing there are two distinct terms etc     .’ - which reason I clarify as follows:

Because to ask whether the substance itself of the ‘now as to substance’ is movable is only to dispute about words. But if the ‘now’ is other than the substance (namely, something indivisible in the genus of quantity), I ask of which continuous thing or of which discrete part it is the term - because everything indivisible that is per se in the genus of quantity is either a term of continuous quantity or a part of discrete quantity. If the now is part of discrete quantity then time is discrete, which the Philosopher did not concede [n.99]; if it is a term of continuous quantity, then it must be two (according as it is the term of this and of that part of the continuous), because it is impossible for ‘the same thing as to substance’ to be per se the end and the beginning of one and the same quantity.a

a.a [Interpolation] Again, the Commentator makes the following argument at Physics 4 comm.91: an instant is end and term of something finite; but everything finite has two terms and two ends; therefore it also has two instants.

102. And if you say that it is the term ‘according to diverse existences’ - then since those existences are accidents of the ‘now’ the same in substance (because for you it remains the same under diverse existences [n.95], and consequently those existences are accidents of it), and since everything indivisible in the genus of quantity is the per se term of a quantity (or is a part of what is discrete), it follows that that ‘now’ is not an indivisible per se in the genus of quantity, since it is not per se a term.

103. Further, I ask to what genus those ‘existences’ belong. If they are indivisibles of the genus of quantity, then they are sufficient to be the terms of the continuous proper without the ‘now as to substance’, which is unacceptable (the proof of the consequence is that nothing indivisible is per se a term ‘because there is a term of a second indivisible’). But if they belong to another genus, namely of quality - then a quality will be per se the idea of terminating the continuous in the genus of quantity.

104. And further, how would the ‘now as to substance’ not undergo change according to diverse existences? And then one would have to ask about the measure of it and of its changes, and so on ad infinitum.

105. Further, is the ‘now as to substance’ the same in any motion whatever or in a single one precisely?

106. To the Philosopher [n.96] I say that he does not intend the ‘now’ to remain the same in substance, but the opposite follows from what he said; but any ‘single now’, considered in itself, is the same, and this is said to be ‘the same in substance’ - but considered in order to past and future time, since it is the end of the past and the beginning of the future, it is said ‘to be distinguished in being’ [Physics 4.13.222a10-15].

107. And to make this clear, there is the likeness about the movable thing, that it remains the same [n.95]; not indeed the movable thing as it absolutely precedes change (for in that case, the ‘now’ is not the measure of it and it does not belong to time [nn.97-98]), but the movable thing as it is under a change is ‘the same as to substance’ - that is, according to the being of the change considered in itself -, and is ‘different as to being’ -that is, as under the change it is the term of the past and the beginning of the future, and in this respect it is said to be here and to be there. Not indeed actually so, but in one intermediate ‘where’ between the extremes (insofar as this intermediate ‘where’ ends the motion as to the prior ‘where’ and begins the motion as to the later ‘where’) - in this it is said to be here and there, because ‘to change’ is to have something of both extremes; hence the Philosopher in Physics 6.4.234b17-19 maintains that, although something may be in a single intermediate, yet it is ‘other’ according to each extreme.

108. But how will this solve the question of the Philosopher, which he moves in the Physics [n.96], ‘whether the same ‘now’ in substance remains in the whole time or not’?

I say that the Philosopher nowhere expressly solves this other question, about ‘whether time is’, but he does say a few things from which its solution can be collected [Physics 4.10.217b31-18a8] - and so it is in the case of this question: for if any movable thing whatever has sameness precisely as to substance (that is, relative to itself) and difference as to being (that is, in its order to different parts of motion), then things are the same about an instant with respect to the parts of time; and there is not as much sameness to the instant in the whole of time as there is to one instant; therefore the instant in the whole of time is ‘different things’ as to substance.

109. I say then to the objection [n.95], that if any ‘now’ is similarly disposed to the substance of the movable thing as aeviternity is to the substance of an angel, then that ‘now’ is not other than that substance, nor is it an indivisible in the genus of quantity; and if some ‘now’ in the genus of quantity is imagined for measuring the movable thing as to substance, then there is no such thing in an angel actually existing, as was proved before [n.91].

110. But I argue against this [sc. the imagining of a now in the genus of quantity etc., n.109] as follows:

The movable thing can be considered in three ways: either as it exists under the end points of change, or as it exists under the in-between of change, or as it is prior to motion and change (though able to receive them). In the first way there correspond to it diverse ‘nows’ as to being, in the second way there corresponds to it the time between those ‘nows’ - so in the third way there will correspond to it some proper measure, but this measure is only the ‘now as to substance’;     therefore etc     .

111. I reply.

If time has to differ from motion, and consequently the instant has to differ from change, yet there is not a like reason for positing something different from the existence itself of a uniform angel in order to be measure of it.a For if time differs from motion, the reason for this is that the parts of the same proportion of some motion are not necessarily equal in number and quantity to the parts of the same proportion of time; but no quantity is the same as another quantity unless the parts of the same proportion in it are equal to the parts of the same proportion in the other quantity, and that equal both in number and in magnitude (though, when speaking of the quantity that is in motion, it has this from the part of the magnitude or form by which it is motion). However, parts of a motion, to wit ten parts integrally forming a whole motion, can exist with ten parts of time, and yet they are not the same as the parts of time, because there could exist, along with the same parts of time, a greater number of parts of motion equal in magnitude to the prior parts of the motion, or as many again; for if a double force were to move the same movable thing, and consequently move it twice as quickly, there will be no part in the slower motion that does not exist in the quicker motion (speaking of the parts that the motion has in magnitude, according to the form according to which it is a magnitude), because what moves a movable thing with a quicker motion does not make any parts of the magnitude pass by simultaneously but makes them precisely pass by one after the other; therefore there are as many and as large parts in a quicker motion (speaking of this quantity) as there are in a slower motion. But the same time (possessing the same parts) cannot exist along with the former motion and also with the latter; therefore the parts of time will not be the same as the parts either of the former or of the latter, because the parts of time are not disposed to the whole in the same proportion as, and equal with, those other parts of the whole.

a.a [Interpolation] in the way that is posited on the other side about time and the instant with respect to motion and change as to their measures.

112. If this is true, the conclusion from it is that an indivisible of one quantity is not the indivisible of another quantity, but the conclusion from this conclusion is not that in anything ‘that remains always uniform in being’ one must posit something else different from it, because there the argument about the magnitudes and their parts does not hold. There is then a fallacy of the consequent involved in arguing affirmatively from the lesser thing: ‘if change and motion have measures other than themselves, then the substance too itself - which is prior to motion and change - has a measure other than itself’ [n.110]; for there seems to be less distinction (or lack of sameness) in a permanent thing than in a thing in flux (or in motion) and its measure.Tr. To argue from a distinction between change and its measure to an equal distinction between a permanent thing and its measure is to argue from a less permanent thing to a more permanent one, which is fallacious here because there is no reason to suppose that a more permanent thing should have the same distinctions as a less permanent one; rather it would seem intuitively to have fewer distinctions. ²⁵

113. But if one is pleased to grant some measure to the movable thing insofar as it is in itself prior to motion and change, then that measure will be aeviternity, as will be plain in the question about the measure of the operations of an angel [nn.167, 171-76].

114. And if you look for another measure of it insofar as it is in itself and insofar as it is susceptive of motion and change, I say that it is not other, because the subject insofar as it is in itself is susceptive of its proper accident - and likewise, if there is any measure, it is the same; hence there is not another measure of a surface insofar as it is a surface and insofar as it is susceptive of whiteness and blackness. So I say that if the substance of the first movable (or of any other movable) is measured by aeviternity, there is no other measure of it insofar as it is naturally prior to motion and change and insofar as it is receptive of motion and change.

115. But if you say that insofar as it is at rest it will have a measure other than aeviternity, this is false as will be clear later [nn.167, 171-76].

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).

III. To the Principal Arguments

124. As to the first principal argument [n.85], it is plain that the consequence about time and motion is not valid when making comparison with the existence of an angel (and the reason was stated before, when replying to an argument [nn.110-112]), because an argument that would prove a difference between motion and time [n.111] does not here prove that there exists anything distinct and different from the actual existence of an angel; so neither that there is any measure distinct and different.

125. As to the second [n.86], it is plain that nothing is conceded to be in the actual existence of an angel that may properly be a quantity or an indivisible in the genus of quantity - because his existence seems able to be known by itself without anything else added.