So much for Scotus on the meaning of terms predicated in common of God and of creatures. Next we must consider what, for Scotus, are the implications of his theory of meaning for inference from creatures to God, and so for the possibility of natural knowledge of God. And immediately, one consequence is clear. Regarding as he does all accounts of analogical predication, whether Henry's or Thomas's, as reducing to equivocation, it follows that natural knowledge of God is possible only if some terms are predicable of creatures and of God univocally.
Scotus appears to take it as axiomatic that natural knowledge of God is possible; moreover, it would seem that what he means by 'natural knowledge' is both that it is rational knowledge (for reason is the means by which human beings 'naturally' know anything) and that it requires proof by inference (for if what is at stake is, properly speaking, knowledge; only such is, properly speaking, knowledge which is supported by a formal demonstration). In short, natural knowledge of any proposition is gained by inference from other propositions which are known to us by our natural powers; that is to say, either because they in turn are self-evidently true, or because they are themselves capable, in turn, of rational demonstration. Now all valid demonstrative inference crosses some kind of 'logical gap' between premises and conclusion; for if the conclusion were self-evidently 'contained in' the premises - that is to say, if the conclusion could be seen by simple inspection of them to be contained in the very meaning of the premises - then no inference would be needed to extract it from those premises, and there would be no 'gap' to be crossed by it.
How one construes this 'gap' between creatures and God, therefore, determines how one construes the logic of inference between them. If you supposed, as it seemed to most medieval interpreters that Anselm did, that God's existence is self-evidently given in the very conception of God, then strictly speaking no argument is needed to demonstrate God's existence, and the conventional description of his Proslogion discussion as the 'ontological argument' is a misnomer. And after all, it is perhaps better to see Anselm's discussion as more in the nature of an exercise in that conceptual ground-clearing which is needed so that the 'fool' can be got to see how God's existence is undeniable, if only he will understand what 'God' means, than as an 'argument' properly speaking. But for Scotus, the natural knowledge of God is gained by inference in a strict sense; and for him, the gap which it is called upon to cross between creatures and God is such that only if some terms are univocally predicable of both could it be closed.
For if terms predicable of creatures and of God are predicated only equivocally - that is to say, without any continuity of sense between them - then no argument from the one to the other can possibly succeed. But since, on Scotus' account of the matter, all accounts of analogical predication reduce to equivocation, it follows that 'every enquiry about God presupposes that the intellect has the same univocal concept that it receives from creatures'.27 For, if you say that the formal notion is other as regards those things that pertain to God [as Henry of Ghent said], a disconcerting consequence results, [namely] that from the proper notion of anything found in creatures nothing can be inferred about God, because the notion of what each has is entirely different; indeed, there is no more reason to conclude that God is formally wise from the notion of wisdom that we perceive in creatures than [there is to conclude] that God is formally a stone.28
27 'Omnis inquisitio de Deo supponit intellectum habere conceptum eundem, univocum, quem accepit ex creaturis.' Ordinatio 1 d3 39; Opera Omnia III, p. 26, my translation.
28 'Quod si dicas, alia est formalis ratio eorum quae conveniunt de Deo, - ex hoc sequitur inconveniens, quod ex nulla ratione propria eorum prout sunt in creaturis, possunt con-cludi de Deo, quia omnino alia et alia ratio illorum est et istorum; immo non magis con-cludetur quod Deus est sapiens formaliter, ex ratione sapientiae quam apprehendimus ex creaturis, quod Deus est formaliter lapis.' Ordinatio 1 d3 3a; Opera Omnia III, p. 27, my translation.
Furthermore, the reason no theological inference is rationally possible without some univocity of terms has to do, simply, with the nature of inference itself; for equivocation is the natural enemy of validity. But here we run up against a problem with Scotus' argument, a problem disguised by the sheer complexity of his exposition. We have seen that Scotus defines univocity by reference to deductive validity: terms are used univocally only if their commonality of meaning is such as is required for a deductive inference to be validly drawn.29 It follows that if we are to know on this criterion that a term is being used univocally, then we must know of a deductive inference in which it occurs that it is validly drawn by some means independently of our knowledge whether the terms in the premises are univocal. But now Scotus asks us to accept that univocity of meaning is itself a presupposition of inferential validity, so that it now appears that a test of an inference's validity is the univocity of its terms. The argument would seem, therefore, to involve a circularity, and it is reasonable to require Scotus to tell us either how inferences can be tested for validity by some means other than the requirement of univocity, or else how univocity can be tested by some means other than the requirement of inferential validity.
But the reason Scotus feels under no obligation to settle this matter one way or the other is that, as we have seen, his theory of meaning is constructed on the basis of a complete disjunction: either univocity or else equivocity. Since there is no other possibility, for the purposes of determining the logic of inference to God, univocity needs no further definition than is given in its contrast with equivocity; so long as terms are not being used equivocally, they are univocal. Since, moreover, everyone will agree that no inference is possible between terms whose meanings are equivocal, it follows that no inference is valid except on condition of the univocity of its terms. Therefore, Scotus says,
No real concept is caused naturally in the intellect in our present state except through those agents which naturally move our intellect. But the natural agents are the sense image - or the object revealed in the sense image - and the active intellect. Therefore, no simple concept naturally arises in our intellect unless it can come about by virtue of these causes. Now the active intellect and the sense image cannot give rise to a concept that, with respect to the object revealed in the sense image, is not univocal, but rather, in accordance with the analogical relationship, is altogether other and higher than the object. It follows that such an 'other', analogous, concept will never arise in our present state. Also it would thus follow that one could not naturally have any concept of God - which is false.30
30 Ordinatio 1 d3, 35, Opera Omnia III, p. 21, my translation.
That being so, we may now ask: if such are the conditions for valid inference from creatures to God, what, on Scotus' account, is the nature of the 'gap' which inference thus closes? On this question we have already made some headway. For Scotus, the ultimately determining difference between God and creatures is that between 'infinite' and 'finite' being. Furthermore, we know that ifsuch is the ultimate 'ontological' distinction between ens and its entia, then it is not one whose logical character is that of genus to species: God is not a kind of being distinct from creatures of other kinds, for the distinction between an attribute predicated of infinite being and that same attribute predicated of finite being is that between the maximal intensive degree of that attribute and some degree of limited intensity of it, and differences of intensity are not differences in kind. For this reason it appears to be mistaken, at least prima facie, to say, as some do of Scotus' account of the difference between God and creatures, being as it is defined within the univocal predication of terms, that it amounts to no more than a 'quantitative' distinction, a 'distinction of degree' as Cross puts it,31 as if to say: God is what creatures are, only writ very large indeed. It seems to be the nub of much criticism of Scotus' natural theology proceeding from Radical Orthodox quarters that if for Scotus God is not different from creatures in kind, yet is rationally demonstrable from univocal concepts in common, then two consequences follow. On the one hand, the divine transcendence is thereby impugned, for the difference between God and creatures is construed as a quasi-created difference, being set on a common scale with creaturely differences - albeit at the 'infinitely maximised' end of it. On the other, by virtue of the divine existence being thus set on a common scale with creatures but in terms of the contrast between infinite and finite, the implication is contained that the difference between God and creatures is represented, paradoxically, as a relationship of exclusion. For if God and creatures belong in any way to a common scale, then whatever part of that scale each occupies, the other must be excluded from that part of it.
But if that were how Scotus' account of the difference between God and creatures had to be understood, it would turn out to the effect precisely opposed to Scotus' manifest intention - which is, through the univocity thesis, to place the existence of God in such degree of continuity with creation that inference from the latter to the former is legitimised. But, it will be argued, if the univocity thesis places God and creatures on the same scale, and the account of their difference is explained as a matter of quantitative degree, then it will follow that far from placing God and creatures in continuity with one another, they will be set disjunctively against
one another; the finite and the infinite will be mutually exclusive terms. And from this there would follow one more conclusion of disturbingly damaging theological consequence, namely the logical impossibility that anything divine could be true of a creature, and equally the impossibility that anything true of a creature could be true of the divine. So much the worse, it would seem, for the incarnation.32
Thus, the judgement on Scotus of some recent critics. But the criticism is at least partly unjustified. It is true that, as Cross says, the 'basic model [of Scotus' infinity] is quantitative', for we proceed to disclose that intrinsic infinite degree of the divine attributes by abstracting 'the concept of infinity from that of spatial extension'.33 But Scotus is not as naive as some of his critics suppose. In fact he uses a quantitative model only so as to demonstrate how the divine infinity altogether transcends our common notions of quantitative infinity.
For the quantitative infinity of, say, an infinite numerical series, is such that you can always add to it and, whatever finite number you subtract from it, there are always some numbers left. Moreover, he says, any quantitative infinity is 'composite', by which he means that it consists of parts each of which is finite. Therefore, no quantitative infinity can be perfect infinity; indeed, in principle any quantitative infinity is created, since it is nothing but the infinite (that is to say, endless) extension of what is finite. And it is precisely this notion of infinity as an infinitely extended version of created finitude which Scotus wants to differentiate from the qualitative, or intensively maximised, infinity of God.
By contrast with such quantitative infinities, therefore, 'qualitative' infinity consists in the maximal intensity of some property which can be possessed in less than maximal intensity. The infinite possession of such a property is its possession such that it has no parts, and so is utterly simple, and thus is such that nothing can be added to it. It follows from the fact that nothing can be added to the infinitely intensive degree of a property that the logic of the 'scale' on which greater or lesser degrees of intensity can be measured cannot be of the same kind as that of the 'scale' on which quantitative degrees are measured. By contrast with the way matters stand with quantitative infinities, 'bright red' is not a given level of redness plus a bit 'more' redness; 'perfectly red' is not 'red' plus endless further additions of redness.34 For you do not get to the notion of a qualitative infinity, as you do in the case of quantitative, by way of
32 For a discussion of this point, see below, pp. 217-18.
34 Not, of course, that 'redness' can change, be more or less. A subject can be more or less red, but not 'redness', as Scotus knows perfectly well.
endlessly adding more of the same to some finite possession of that property. It is hard to know how more explicitly than this Scotus could have rejected the Radical Orthodox criticism of his account of divine infinity, when he says:
While something actually infinite in quantity would not be missing any of its parts or lacking any part of quantity, still each of its parts would lie outside the other and consequently the whole would be made up of imperfect elements. A being infinite in entity ['intensively infinite'], however, would not have any being outside itself in this way. Neither would its totality depend on elements which are themselves imperfect in entity, for it exists in such a way that it has no extrinsic part; otherwise it would not be entirely whole. As for its being perfect, the situation is similar. Although something actually infinite in quantity would be perfect as to quantity, because as a whole it would lack no quantity, nevertheless each part of it would lack the quantity of the other parts. That is to say, an infinite of this sort would not be quantitatively perfect [as a whole] unless each of its parts were imperfect. An infinite being, however, is perfect in such a way that neither it nor any of its parts is missing anything.35
If, therefore, Cross is right to say that the 'basic model' of Scotus' notion of intensive infinity is quantitative, nonetheless it is so only as a starting point to be transcended. Scotus' critics appear to have been misled by the fact that inevitably - for us as much as for Scotus - we have no natural language in which to speak of intensive degrees of a quality except on the deficient metaphor of quantitative degrees - for the word 'degree' is itself a word of quantity. Thus, by way of example, for a medieval thinker such as Scotus, degrees of heat are intensive degrees of a quality, not, as for us, degrees on a numerical scale. But suppose you had confronted Scotus with the modern thermometer, a device which measures degrees of heat quantitatively as different lengths of a column of mercury in a glass tube read against a numerical scale. Then you could have shown him how to translate qualitative degrees of intensity into degrees on a quantitative scale, as a result of our common practice of which we have come to think of degrees of heat exclusively in quantitative terms; thus we read quantitatively what Scotus thought of qualitatively. Scotus' position with regard to intensive magnitudes is rather similar to this; for though we have no recourse but to think of qualitative degrees on a model of the quantitative, to conclude from that - especially in the face of Scotus' explicit denials - that he believes degrees of intensity to be additive quantities is grossly unfair, since it would be to mistake what is a
35 Quodlibet q5 a7, quoted in Frank and Wolter, Duns Scotus, p. 153.
model of measurement for the reality of the thing measured.36 And even if his critics do, Scotus himself had no intention of making that mistake.
That said, it is quite another matter whether all the main Scotist theses which we have examined are fully consistent with one another, which, in summary, are these: first, that a natural theology is possible, that is to say, formally valid inference from creatures to God is possible. Second, that no such possibility exists unless at least some terms are predicable uni-vocally of creatures and of God, among them most particularly 'being'. Third, therefore, that no demonstration of the existence of God is possible on the basis of the analogical predication of terms alone, for in any case all analogy reduces either to equivocity, which yields no possibility of proof, or else to univocity, which does. Fourth, that the most fundamental distinction between God and creatures is that between 'infinite' and 'finite' being. Fifth, that though 'being' is predicated univocally of God and of creatures, 'being' does not stand to 'finite' and 'infinite' being as a genus stands to species; that is to say, God is not some kind of being standing in contrast to creaturely kinds. Sixth, it is possible to say that 'being' is fundamentally divided into 'infinite' and 'finite' consistently with saying that it is univocally predicated of both, because the distinction between 'infinite' and 'finite' is a distinction of intensive qualitative degree; and although we can at best represent that distinction in terms borrowed from extensive magnitudes, the logic of that distinction, and of the scale on which it lies, is quite other, in its nature and consequences, from that of a quantitative scale.
What, finally, are we to say of Scotus' way of determining the 'difference' between God and creatures? On the one hand, taken on its own, the univocity thesis would appear to place at risk the radical 'otherness' of God - and for sure, by comparison with Thomas Aquinas, there is a distinctly more optimistic 'cataphaticism' about Scotus' natural theology, for, as Cross says, 'the result of [this univocity thesis] is that the doctrine of divine ineffability, so strongly stressed by Aquinas... is greatly weakened in Scotus' account. He holds that we can know quite a lot about God "in a descriptive sort of way",37 as he puts it.'38 Moreover, on the same score, it is clear that Scotus believes the possibility of a natural theology - which he takes to be theologically axiomatic - depends upon
36 Thomas agrees with Scotus here, noting that necessarily we think of intensive changes in a quality in terms of quantitative degrees of change. He also notes that we ought not to be misled by this necessity into reducing qualitative degrees to quantitative. See Quaestio Disputata de Virtutibus in Communi, all corp.
37 'Inquadamdescriptione'-Ordinatio 1 d3q1 1-2; OperaOmnia III, p. 40), my translation.
some reduction of what, on his account, he takes to be the excessive apophaticism of Thomas and of Henry of Ghent, which would seem to exaggerate the 'gap' between God and creatures to an extent such that, logically, no inference could possibly cross it. On the other hand, the potential risk implied by the univocity thesis to the transcendence of God is itself explicitly moderated in his account of the intensive infinity of the divine attributes, such that no one can say with fairness, as some have thought they can, that Scotus' God is nothing but a magnified, infinitely extended, creature. No doubt, then, Scotus wishes to have it both ways. But can he do so with consistency?
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