Transgeneric inference

For there are, according to Thomas, two kinds of predication of terms across genera. The first is that of the most general transcendental predicates of 'existence', 'goodness' 'oneness' and the like, which are predicated analogically. The second is that of metaphor. It is of course obvious why no formal demonstration is possible from premises whose terms are literally predicated to conclusions which are metaphorical extensions of them: nothing in the physics of colour could ever strictly entail conclusions about the blueness of a mood, or in the physics of heat about the fieriness of a temperament.12 Nor thus far is the case much different with transcendental terms when predicated by that sort of analogy which we may call 'proportional',13 as existence and goodness can be, and here Aristotle is of course in a limited connection right: what characteristics you describe as making for a good apple provide no grounds for determining what makes for a good time of the day for having a celebration, for the evidence for the one can serve no purpose of evidence for the other. After all, a good time for celebrating is under no requirement to be sweet, juicy and firm, as a good apple presumably must be. Moreover, just so far as concerns the logic of this 'proportional' analogy, Milbank is right too; no possible argument from creatures to God could be generated on the basis of 'analogy' so understood.

Not that all inferences between one genus and another by analogy of proportion are logically impossible, Aristotle notwithstanding. Under certain conditions inference between terms analogically related is of course possible, precisely through their analogically proportional connections of meaning. For even if it is the case that, taken by itself, the description of what makes for a good time for celebrating cannot be derived from what makes for the goodness of an apple, it does not follow that the

12 Though of course we do gain in knowledge from metaphors; we say something true of a temperament when we say it is 'fiery', something else when we say that it is 'volatile'. There are all sorts of ways in which we gain knowledge by transgeneric transfer, and poetry exploits many of them, music others.

13 It is disputed whether Thomas in fact offers any account of what later came to be called 'analogy of proportion', or whether not only the name but also the conception is a later development of late medieval 'Thomist' commentators. In fact it does not matter much whether analogy of this sort is to be found in Thomas. Clearly there is an analogy of this kind, and it is certainly consistent with Thomas's account of the logic of 'transcendental' terms.

meaning of the predicate '. . . is good' as predicated of a time for celebrating bears no connection with the meaning of '. . . is good' as predicated of apples. As we have seen, the predicate '. . . is good' is not, and cannot be, predicated either metaphorically or equivocally. There is always some relation, in fact some 'proportion', determining the meaning common to all such predications.

And as to analogical predication of this kind, the word 'proportion' is used in a sense derived from arithmetical proportions, denoting the equation, a:b::c:d. No variable on either side of the equation is found on the other, yet, given the values of the variables a, b, and c, we can, on certain conditions, derive the value of d. Thus, if a = 2, b = 4, and a = 6, we may derive the value of d as being 12. But we can thus derive the value of d if and only if we know in what relation of proportion a stands to b. For in deriving 12 as the value for d I had simply assumed that the proportion which obtained between a and b was that of multiplication by 2; but of course, if the proportion between a and b were that of the square of, then even though the values of a, b and c remain the same, the value derived for d will be 36, not 12. Given, then, the values for three of the variables and a definition of the proportions in which they stand one to another, we can derive, by analogical argument, the value of the fourth.

It is, therefore, in that same sense in which a's relationship to b is 'proportionally the same' as c's relationship to d that we can say that there is a sameness in which '. . . is good' is predicated of times of the day and of apples, even though there is nothing in common between them by way of descriptive characteristics. For those descriptive characteristics stand in the same relation as each other to what it is for anything to be good, and to know that is to know the definition of 'good' - roughly, for Thomas, the desirability of a thing's realising the potentialities of its nature, the potentialities of the kind of thing that it is. It is because one set of characteristics has to do with an apple's being a desirable one of its kind, and another, wholly different, set of characteristics has to do with a desirable time for celebrating, that, wholly different as they are, these characteristics determine senses of the predicate '. . . is good' which are neither univocally nor yet equivocally related. They are related 'proportionally'.

It is clear, moreover, that the logic of this kind of 'proportional analogy' by which transcendental terms are predicated across genera can hold between created goods without reference to the divine goodness on which, ontologically, they depend. Of course, for Thomas (as Milbank and Pickstock are right to say), the 'full realisation' of a thing is to be found in the divine conception of it - and, in general, anything good is, he says, truly said to be good 'by the divine goodness' itself, as Thomas reports the

Platonici as maintaining:14 that is to say, that any creature is good depends on its participation in the divine goodness. But it does not follow from this, he insists, that, as Milbank and Pickstock infer,15 we can only know the goodness of creatures in so far as we have some already given awareness of their perfect realisation in the divine mind, or that in some way the logic of the predication of goodness of creatures requires some reference to the divine perfection itself. For if it is true that a creature is said to be 'good' by virtue of a likeness to the divine goodness (similitudine divinae bonitatis), nonetheless Thomas is emphatic: that goodness of a creature belongs to the creature itself, and is formally its own goodness, denoting it as such (sibiinhaerente, quae estformaliter sua bonitas denominans ipsum).16 You can know what makes for a good apple without knowing anything of the divine mind, or even that there is a divine mind at all.

To summarise: so far as concerns the meaning of transcendental predicates, it is clear that some 'proportional' analogy holds between all their predications, such that those predicates are never predicated either uni-vocally or equivocally across genera. They are not predicated univocally across genera, because, as we have seen, no two different kinds of thing called 'good' need possess in common any of the characteristics in virtue of which they are thus described. Nor yet are they predicated equivocally across genera, because it is not in any case the simple possession of those characteristics which determines their goodness, but the relation in which those characteristics stand to the full realisation of the sort of thing that it is. Hence, as Thomas says, in the analogical predication of such transcendentals, there is always something in common, and something in which they differ.17

Secondly, so far as concerns inference by proportional analogy across genera, this is possible in so far as two conditions are met: first, that we know the meaning of such predicates, and secondly, that we know the values of three of the variables, from which it is possible to derive the value of the fourth. It is, of course, this second condition which is of significance for theological argument. For since this condition cannot in principle be met in the case of arguments for God, it follows that no knowledge of God can be derived by an inference of'proportional analogy' from our knowledge of creatures, short of our already knowing that God exists.

For while from our knowledge of goodness in one genus of creatures we may be able to learn what goodness is in another - it is common sense that we do thus learn how to use words such as 'good' 'by analogy'

14 ST 1a q6 a4 corp.

15 Milbank and Pickstock, Truth in Aquinas, pp. 28-30.

16 ST 1aq6a4ad1. 17 ST 1aq13a5 corp.

(indeed, how else could we do so?) - this is possible because we know what sort of things both are, and so can come to learn what will count as a good instance of the one from what counts as a good instance of the other. But it is precisely this which is not the case with God, for we do not know what sort of thing God is. Consequently, we cannot construct a valid inference to the existence of a divine goodness by proportional analogy from what goodness is in any creature; all we can know is that the divine goodness must stand in some similarly proportional way to the divine self-realisation, or, as Thomas calls it, the divine 'perfection' - that perfection itself being, of course, equally beyond our comprehension. By this proportional analogy we can know only that if God exists, then to say 'God is good' retains some connection with our ordinary meanings of creaturely goodness; but we cannot argue to the existence of the divine goodness - but only dimly to the 'how' of the divine goodness - by any such analogy with what goodness is in creatures.

Nor does Thomas suppose that we can. It is abundantly clear that Thomas offers no argument to the existence of God by way of analogy, however conceived. Therefore, we ought to examine whether, as it might seem, the case is different with Thomas's own example of those terms whose analogical predication is most directly comparable with the common predications of God and of creatures, namely the predication by what has been called the 'analogy of attribution' - the kind of analogy by which the predicate ' healthy' is predicated in common of a symptom and of its cause.18

Once again, it is clear that Milbank is wrong in attributing to Thomas the view that inference from one term to another related by analogy is in general impossible. For had Thomas thought so, he would have had to suppose that medicine cannot in principle have the character of a science. It is precisely because health in an organism is the cause ofhealthy urine that '. . . is healthy' is predicated analogically of urine; and it is precisely because of that causal connection that the diagnosis of health in the organism from its symptoms in the urine can be scientific. So far from it being the case, as Milbank puts it, that 'scientific demonstration proper depends, for Aquinas after Aristotle, on a univocity of terms answering to a univocity between causes and effects', it is the argument from effect to cause which underpins the validity of the analogical predication 'urine is healthy' - knowing how and why, and under what causal conditions, you can describe urine as 'healthy' just is that in which medical science consists.19 There is nothing in Aquinas' account of the logic of inference and of analogical predication which prohibits, on the Aristotelian ground,

18 ST 1a q13 a5 corp.

19 Aquinas In IV Metaphysicorum, lect. 1, 534, 544.

the inference from health as effect to health as cause, and so from 'health' in the sense of effect, to health in the sense of cause analogically related to it.

Yet it does not follow from this that an argument from creatures to the existence of God is any more possible by means of this kind of analogy than by means of the other; indeed, inference from creatures to God by analogy of attribution is as demonstrably impossible as it is in the case of proportional analogy. For in the case of analogy of attribution, both the meaning of 'healthy urine' in its analogical connectedness with 'healthy organism', and the possibility of inferring the health of the organism from the health of the urine, depend upon our knowledge of the causal mechanisms which underlie that connection. But this is precisely what we do not know about God, in the absence of any already given proof. For even were we to possess some argument which does demonstrate the existence of a cause of the universe - and we should need to know at least that much already if any talk of a theological analogy of attribution is to be justified in the first place - we should thereby know that we have no comprehension of what that causal mechanism is by which God creates the universe. For this reason a causal proofis presupposed to a predication of terms of God by analogy of attribution, not the other way round. And even then, by such analogy we should know no more than that, since God is the cause of the universe, and since there is no knowable causal mechanism by which he causes, it follows that even if we are justified in our predications of God by analogy of attribution, we could not know the meaning of what we are justified in attributing to him. Such a causality being incomprehensible to us, it follows that we cannot know, in advance of a demonstration of God's existence, but only on the strength of one, that any sort of analogy holds between God and creatures.

From this there appears to follow a consequent ordering of logical dependencies. Names predicated of God by proportional analogy are justified through their dependence on predications by analogy of attribution. For it is only if there is some causal link between God and creatures, such as to justify the claim to equivalent proportionality between them, that inference by proportional analogy is possible from what we know about creatures to what we can come to know about such names of God. But if a justification of inference by proportional analogy thus depends upon analogy of attribution, analogy of attribution can, in turn, derive its justification only from such knowledge as we can obtain as to there being a causal link between God and creatures. In short, the justification for analogy of either kind depends on our knowing already that God is the Creator of all things, visible and invisible.

Thus far, then, Milbank is right. None of our human rational procedures for inferring knowledge of God's attributes - and they are all analogical of one sort or another - can stand on their own as inferences demonstrating that there is a God to be thus talking about. You cannot argue to God's existence by analogy. Hence, we are able to conclude that no proof of the existence or nature of God can depend upon our knowing in advance that some analogy between creatures and God could hold.20 To put it in another way, if an argument for the existence of God is to succeed, it cannot depend upon analogy: it must demonstrate analogy; it will be an argument to, not from, analogy. But that, in turn, brings us back to Milbank's strictures against the possibility of such proof as contains terms in the premises connected to terms in the conclusion only by an 'analogy' which stretches across the infinite 'gap' between creatures and God. For even were he to concede that transgeneric inference is possible, it would not, it appears, have to follow that an inference could stretch without breaking across the gap between creatures and God. Nor, Milbank thinks, does Thomas allow it. But on both counts he seems to be wrong.

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