Gods Infinity

Calling God infinite seems, offhand, at least odd because, as Aquinas acknowledges, infinity is associated with quantity (43.356). So he begins his attempt to justify attributing infinity to God by sorting out types of quantity. God could not be infinite in virtue of plurality as regards infinitely many individual gods, infinitely many parts, or infinitely many accidental characteristics. On the contrary, God has already been shown to be unique (1.42), simple (1.18), and utterly without accidental characteristics (1.23). Nor, he says, could God be infinite in virtue of extent, since God has already

been shown to be necessarily incorporeal (1.20).

51 But since Aquinas recognizes the possibility of beginning less time, as we've seen, incorporeality seems an insufficient basis on which to rule out infinity of extent. In order to rule out infinity for time as well as for space, he would have to invoke details of his Boethian concept of divine atemporality, on which see e.g. Stump and Kretzmann 1981, 1987, 1991, and 1992.

Plurality and extent are clearly not the only kinds of quantity, however. Qualities and powers such as colour, heat, and force also vary quantitatively, in ways that provide the bases for our measurements end p.165

Kretzmann, Norman , (deceased) formerly Susan Linn Sage Professor Emeritus of Philosophy, Cornell University, New York

The Metaphysics of Theism

Print ISBN 9780199246533, 2001 pp. [ 166]-[ 170]

of them. Aquinas labels this remaining kind of quantity 'spiritual magnitude', a designation that seems misleading in at least two respects. In the first place, it's certainly not obvious that only material entities can be more than one, or extended; both plurality and extent seem applicable to immaterial (or spiritual) entities, too. In the second place, there's nothing spiritual about, say, degrees of whiteness, one of his own examples (43.357). I think he might have done better to have focused on intensive quantity rather than on 'spiritual magnitude', but I'll stay with his terminology.

'Spiritual magnitude is recognized in two respects: as regards power, and as regards the goodness or completeness of [a thing's] own nature' (43.357). But Aquinas shows that these two reduce to one: 'The magnitude of a power is weighed on the basis of the magnitude of the [corresponding] action or the

things brought about, since one of those magnitudes

52 Following the variant magnitudinum rather than the Leonine and Marietti ed n s. 'magnitudinem.

follows the other. For anything is active in virtue of its being actualized, and so the mode of the magnitude of its power is in keeping with the mode in which it is completed in its actuality. Therefore, we are left with the

conclusion that things are called spiritually great

53 What Aquinas actually says here is: '[S]piritual things are called great.' To preserve what I think he meant, and what is better supported by the context, I'm reading spiritualiter for spirituales.

on the basis of the mode of their completeness' (ibid.). 'Mode' here clearly means the same as 'degree'. The upshot is that if God is properly to be called infinite at all, then, as we've seen, the attribution must be based on the degree of his actualization, which is the universal perfection already argued for: 'there is no limit or end to his perfection . . . And it is in this respect that "infinite" must be attributed to God' (43.358).

Although the infinity of power can be reduced to the more fundamental concept of infinity of being, there are contexts in which it is more natural and convenient to conceive of divine infinity in terms of power. In fact, since the inductive reasoning indispensable to natural theology begins with reasoning from effects to the existence and nature of their cause, divine power is conceptually intermediate between other things and God conceived of as universally, infinitely perfect. An ingenious argument end p.166

in Aquinas's chapter on God's infinity approaches it through a consideration of power. He begins by observing that 'there cannot be infinite power in a finite essence, because everything acts through a form belonging to it, either its essence or a part of its essence, and "power" names a source of action' (43.367). Moreover, 'any agent is more powerful in acting to the extent to which it brings into actuality a [passive] potentiality that is further removed from actuality; for instance, it takes more power to heat water than to heat air' (43.368). On that basis he develops a two-part argument to accommodate, first, the idea that God's effect is a world that began to exist: 'that which is altogether non-existent is infinitely far from actuality and is not in any way in potentiality. Therefore, if the world was made after it was altogether non-existent, its maker's power must be infinite' (ibid.).

'But', he points out, 'this argument works as a proof of the infinity of divine power even for those who posit' a beginningless world.


54 Certain Platonists, according to Augustine, De civitate Dei X.31; see the editors' note to this passage in the Marietti edn.

say that eternal God is the cause of the sempiternal world as a foot would from eternity have been the cause of a footprint if from eternity it had been pressed into some dust. Once that assumption has been made, it nevertheless follows according to the argument we are discussing that God's power is infinite. For whether he produced in time (ex tempore) (according to us) or from eternity (according to them), there can be nothing in reality that he did not produce, since he is the universal source of being. And he produced in a way that presupposes no matter or potentiality. ... We are, therefore, left with the conclusion that since a finite power produces an effect when the potentiality of matter has been presupposed, God's power, which presupposes no potentiality, is not finite but infinite; and so is his

essence infinite. (43.368)

55 My quotation of this extension of the argument omits a passage (at the ellipsis dots) that strikes me as introducing a quite different basis on which to measure active power: 'Now one must arrive at the proportion of active power on the basis of the proportion of passive potentiality. For the greater the passive potentiality that pre-exists or is preconceived, the greater the active power by which it is completely actualized' (43.268).

The basis on which active power is measured in both parts of this argument as I've presented it may be summarized along these lines. In producing a given effect, any agent of course actualizes a certain amount of passive potentiality, and almost every agent also utilizes end p.167


© Copyright Oxford University Press, 2006. All Rights Reserved a certain amount of passive potentiality—the amount that the exercise of the agent's power'presupposes'. Making a drawing on blank paper actualizes more passive potentiality than does tracing an already made drawing. But tracing utilizes more, because in that case the material cause contributes more to the production of the effect, and (so) the efficient cause contributes less. The degree of active power, then, varies inversely with the amount of passive potentiality utilized by an agent.

So far, so good: if Alice produces a drawing of a house and Kate produces a drawing of the same house by tracing Alice's drawing, then on this occasion Alice exhibits a greater degree of active power than Kate does. And if Alice also manufactures her own paper and pencil before producing her drawing, then she exhibits still more active power, and so on.

But can we extrapolate along this line to an infinity of active power? Aquinas's principle of measurement for active power seems to lend itself to a graphic and perhaps not altogether artificial demonstration of such a result. Suppose that in my example we represent the active power in fractions, letting the numerator represent the effect—a drawing of a house—and the denominator represent the amount of passive potentiality the agent utilizes in producing the effect. Then the degree of active power exhibited in Alice's producing the drawing in the first instance might be represented as 1/10, in Kate's tracing it as 1/25, in Alice's producing the drawing after first having manufactured paper and a pencil for that purpose as 1/3. And so, on this model, the degree of active power exhibited in an agent's producing an effect utilizing no passive potentiality at all would be represented as 1/0 (= co). Q.E.D.

end p.168


© Copyright Oxford University Press, 2006. All Rights Reserved

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