We begin with the theological context of Scotus. Medieval theologians thought that God was infinite and as well there are other finite things that are fundamentally different from God. God’s nature is simple, meaning that it is not composed of parts, and God possesses every perfection, for example, God is infinitely good, infinitely wise, and so on (SH 31a). But when we look at objects that we have access to, objects in the finite world, we see that an object having several properties is a complex object” (SH 31) [unlike God, who has several properties but is a simple thing]. [SH then makes a point about equivocation. It seems the reasoning is this. God is of a fundamentally different nature than finite things. But we use the term ‘good’ for God and for finite things. This one term really refers to two concepts, the good of God and the Good of finite things. Since it is the same term in both cases, we are equivocating. By recognizing it as equivocation, we acknowledge that God is transcendent to our world.]
Now the very fact that a term like ‘good’ operates in these different ways when we use it to describe an object or person in the world or to describe God implies that when we use this term, we are equivocating. That is, that the same term names two different concepts, good-for-God, and good-in-the-finite-world. Such a position has certain advantages – in that it makes clear that God is a transcendent entity that cannot be adequately understood according to our categories of thought – but is ultimately untenable as it renders any relation to or understanding of God impossible.
(31)
[Recall that paronymous meanings refer to a focal meaning. SH refers again to this notion of focal meaning, but now in the context of analogy. (It is not clear to me if paronymous meanings are analogous.) Analogy here is matter of likeness. For Aquinas, if one cause causes two equivocal things, then they are analogous. Thus on the basis of finite good, we can understand by analogy God’s goodness, since God caused both.]
It is here that Aquinas brings in the notion of analogy. As we saw with Aristotle, analogy allows us to relate terms that have something in common (a focal meaning), but yet differ. Aquinas’ use of analogy relies on the likeness of cause and effect (our goodness is caused by God, so there must be some analogy between infinite and finite goodness, since effects resemble their causes). In this instance, therefore, God’s goodness is the focal meaning by which finite goodness gets its own meaning.
(31)
[We now get Scotus’ definition of univocity. But we do not get an example but rather only a counter example, so it as of now a little unclear to me. The counter example is health. It is not univocal. For, since it has a different sense in different applications, any some of those senses can be used in a particular case and others not. Nutrition is a cause of health, but it may not be a sign of health, as perhaps people who are otherwise unhealthy for other reasons can still eat nutritionally.]
It is against this view that Scotus develops his own position: a univocal theory of religious language. He defines univocity as follows: ‘I designate that concept univocal which possesses sufficient unity in itself, so that to affirm or deny it of one and the same thing would be a contradiction’ (Duns Scotus 1978b: 20). Effectively, univocity therefore means that a word is used in the same sense in all contexts, unlike ‘health’, for instance, whose meaning changes depending on what we are relating it to.
(SH 31)
[The implication here seems to be that, contra Aristotle, ‘being’ is univocal in this more absolute sense and not in Aristotle’s analogical sense.] There are two basic reasons Scotus thinks that ‘being’ has this sort of univocity. 1) [In the analogical account of knowledge of God, it might be implied that in order to know that God exists, we might need to see some kind of causal proof of his existence in the world. However,] “we can believe that God exists without knowing anything further about him, even whether he is finite or infinite” (31). And 2) [This one is built on a premise that I cannot explain. For some reason, in order to make the analogy that for example finite goodness is like infinite goodness, we need to have some knowledge of the relationship between God’s nature and his attributes. Perhaps the idea here is that we might see goodness in the finite world, but so long as we do not already have knowledge that God has goodness, we would never make the analogical association between finite and his infinite goodness. I will quote for your interpretation:] “Second, the alternative theory of analogy suffers from a key problem: in order for the analogy to work, we seem to require some knowledge of the relationship between God’s nature and his attributes. Such an analogical argument presupposes some form of understanding of God’s nature” (31d). [The reasoning in the following step is also unclear to me. It seems the thinking is this. To understand God in the Aristotelian / scholastic approach, we need to already know God is infinite and we finite. For otherwise, perhaps, there is no basis to say one is fundamentally different from the other and nonetheless analogical. I am not sure, but perhaps we also here must equate God with being. But if we take God/being to be univocal, we are not concerned with infinite and finite, since God/being is univocal only if it has the same sense in all its applications. I again quote for your interpretation:] “Scotus instead takes being to be univocal and ‘indifferen[t] to what is infinite and finite’ (Duns Scotus 1987a: 2)” (SH 32d). [Perhaps we are also assuming here that both the infinite of God and the finite of our world both have being. This also means that on the basis of the concept of being alone, we cannot differentiate God’s being from our own.] “Now | this raises a problem, since we want to see God as separate from man” (SH 31-32). [But by making the meaning of being dependent on whether or not it is finite or infinite, we seem to be placing it as a higher genus. Thereby, we make it higher in the hierarchy than God. Moreover, now that God is lower than being, we would say that ‘being’ is a predicate to God, in the sense of the sentence: God is a being / God has being / God is. So being is one of God’s attributes. Also, as we noted, God is not finite, so he also has infinitude as one of his attributes (but it is not clear to me if ‘infinite’ is a higher genus).]
This view is clearly heretical, since it appears to be the case that as being is somehow prior to finite and infinite beings, being appears to operate as a genus, with finite and infinite beings as its species. Thus being would seem to occupy a place higher in the Porphyrian hierarchy than God. We might also want to ask how Scotus is able to explain the simplicity of the nature of God, given that God’s nature seems to now be a compound of two different attributes: being and infinitude.
(SH 32)
Scotus has a solution for this problem of possible heresy. To understand it, we need first to return to Aquinas in his Summa Theologica. Here we get a definition of infinite as non limited. The passage adds the complicating issues of form and matter. Both in themselves are infinite, but in their union they limit one another. A form can take any instantiation, but as soon as it is, it is limited to being that particular determination. Matter can take any form, but as soon as it takes one, it is limited to that formation (SH 32c). [The reasoning in the next part is not entirely clear to me. It seems that because infinite and finite are relational concepts, with each co-defining the other, and because they are opposed, then the being must be the highest genus. Perhaps this is because neither one can be said to be higher than the other, but both can be said to have being.]
The concepts of finite and infinite are here relational concepts. The infinite is defined by not being limited, whereas the finite is defined through limitation (by matter). If the finite and infinite are understood in these terms, it is clear that we are going to end up with being as the highest genus, or at best an analogical conception of being, as these two terms are opposed to one another. Rather than finitude being defined by relation to a limit, Scotus instead therefore introduces the notion of an ‘intrinsic degree’ of being.
(32cd)
[Since Scotus does not want to place being above God, he also does not want to co-define infinite and finite. As we saw, this co-definition was based on finite being understood as having a limit and infinite as not having a limit. Thus] Scotus will not define finitude in relation to a limit. We will see how he instead uses the notion of ‘intrinsic degrees’ of being.
SH follows Richard Crosses’ (1999, p.40) account of Scotus’ ‘intrinsic degrees’ of being. [The following is complicated. We first must recognize that the for some reason, infinity for Aquinas is understood as extensive and divisible. This somehow applies also to God’s infinitude and his infinite perfection. But it is not clear to me how Aquinas thinks that God’s perfection is extensive and divisible. Perhaps by saying that the infinite is unlimited and the finite limited, we are saying that the infinite is an indefinite amount of finites, or in other words, that there is no limit to how many finites make it up. But again, how does this apply in the case of perfection? At any rate, we take it for granted that the Aquinas understanding of God’s infinite perfection is extensive and divisible, and we conceive instead that there are different degrees of perfection, none of which are divisible into constituent quantitative parts. They only admit of more-or-less, but not of divisible composition. Thus infinite perfection, and also all finite degrees of perfection, are intensive and indivisible magnitudes.]
Scotus firsts asks us to imagine an infinitely large magnitude. He then asks us to apply this model of extensive infinity to a qualitative perfection, such as goodness. The central claim is that much as we can determine spatial | magnitudes, we are also capable of ranking perfections in such a way that we can conceive of an infinite perfection. In the case of a perfection, however, it cannot be constituted of parts in the way that the extensive magnitude is. An infinite extensive magnitude is constituted from an infinite number of finite extensive parts, but a perfection would not be infinitely perfect if it were composed of finite (and hence imperfect) qualities. The notion of infinity that Scotus is developing is therefore of an intensive, indivisible form of infinity, rather than the extensive, divisible form that Aquinas favours.
(32-33)
[What seems to be important here is the notion that now infinity is no longer a genus, that is something substantial, but rather it is a modality / modification of some substance. Perhaps we might have some reason to say that a human has more perfection than a rock, but infinitely less perfection than God. Perhaps also built into this thinking is that levels of perfection are amounts of being. This way, an infinite amount of being is not higher to God but is equated with God. There is also a somewhat confusing quote of Scotus about degrees of whiteness. We can have different degrees of intensity of white. The quoted material does not mention infinite whiteness. But SH says that infinite being is like infinite whiteness in this example. It is not entirely clear to me what that would be in this example. If we have different degrees of whiteness, then the higher degree, the closer we are to the infinite and also the closer to the absolute. Perhaps we are to think of it like this. Between Black (no degree of whiteness) and White (infinite degree of whiteness) we have an infinity of variations of white. So in order to go from black to white, we need to proceed through an infinity of variations, meaning that the highest one would itself be an infinite variation. But still the situation is not entirely clear to me. Say for example we look just at some middle section of grey variations between black and white. If we can keep finding smaller and smaller variations, would there not be an infinite number of variations within any one limited part or swath of the continuum? So even before arriving at pure white, we would still need to proceed through an infinity of variations of white, thus making the variation just prior to pure white still infinite, in the sense we began with. It must be infinite in some other sense. I can only also think that pure white is an infinite degree of white because there is no limit to how white it is. However, we already ruled out understanding infinity by means of the concept of limit. So one of SH’s points is that in this example, infinite whiteness is not defined by a lack of limitation. Yet I do not know how to conceive of why it is infinite. His second point is that we are not using some external concept to understand whiteness. Likewise for being, it would seem, perfect being, infinite being, and God, which may all be synonymous, do not require another concept for their perfection to be understood. This makes sense, but we might wonder if the infinite degrees of whiteness can be understood without reference to its lowest degree, which is either black or the first variation between black and white. And pure black is different in kind and not degree from pure white, I would think. The main idea we get from this is that finitude and infinity in this understanding are not properties of being, it seems because they are not predicated of being but are rather degrees of being. They thus instead are modes or modulations or modifications of being.]
God is not, therefore, superior to man in the quantitative extension of his being, but rather in the qualitative nature of his being’s intensity. This ultimately allows Scotus to solve the two difficulties of the highest genus and the simplicity of God. Instead of understanding infinity and finitude as species of being, they are rather modes or ways in which being subsists. Scotus gives the following example in terms of colour [the following up to citation is block quotation of Scotus]:
When some reality is understood along with its intrinsic mode, that concept is not so absolutely simple that it is impossible that this reality be conceived apart from this mode, although it is then an imperfect concept of a thing. For example, if there were whiteness in the tenth degree of intensity, however simple it may be in reality, it is nonetheless possible that it be conceived under the concept of so much whiteness, and then it would be conceived perfectly by means of a concept adequate to the thing itself. Or, it is able to be conceived precisely under the concept of whiteness, and then it is conceived according to a concept that is imperfect and lacking in perfection in the thing. But the imperfect concept is common to this and that white, and the perfect concept is more proper. (Scotus, Ord. I, d. 8, pars 1, q. 3 n. 138–9, taken from Hall 2007: 107)
Infinite being is like infinite whiteness in this example. Finite being in turn is like a finite degree of whiteness. In neither case are the notions relational. Infinite whiteness is not defined by a lack of limitation, but positively, in terms of its own intensity. Likewise, a finite degree of whiteness is not defined in relation to some other quality, but is intrinsic to the colour itself. Finitude and infinity are therefore modes, rather than properties of being.
(SH 33)
We recall Porphyry’s Aristotelian system of species and genera. Being would be the highest category. It is higher than humans, since humans exist, and it is also higher than God, since we can as well make the predication “God has being”. This is a problem of course for the medieval theologians, and Scotus has solved the problem. [We can have God as being different from other beings, as an infinite degree of being.] “Scotus’ notion of the distinction allows us to avoid this difficulty. Clearly there is a difference between whitenesses of different degrees of intensity” (34).
[It seems in the following paragraph that we return to the idea of perfection in the previous blocked Scotus quote. Here a concept is imperfect if it does not adequately correspond to what it is a concept of. In our experience, we only see different degrees of whiteness, whether that be finite or infinite. We never see whiteness without it taking on some degree of whiteness. The same it seems goes for being. We see only degrees of being (I am not sure how specifically. What existing things in our world of experience have less being than others?) Therefore, if we formulate a concept of being without involving the notion of its intensity, it is merely a formal conception.]
When we look at the concept of the intensity itself, however, it should be apparent that this notion of intensity cannot be grasped as really distinct from the whiteness itself. If we take away the concept of whiteness, we simply have the concept of ‘degree’, which is meaningless on its own – ‘degree of what?’ Nevertheless, the degree clearly does distinguish different ‘whitenesses’. We can note however, that it is possible to formulate a concept of whiteness that does not make reference to its degree of intensity. Such a concept would, however, be ‘an imperfect concept of a thing’ as whiteness always shows itself with a given intensity. It should be clear that we can apply this conception to the notion of being. Scotus’ claim would then be that being always presents itself with a given degree of intensity which is inseparable from it. While we can therefore formulate a concept of being without reference to its intensity, such a conception is only formal, as actual being is always finite or infinite.
(34)
[We might think of water heated or cooled to different degrees. There is only relative quantitative difference between each degree. But there is a difference in kind if we look at the states of matter the water changes through while its temperature varies. But the intensities themselves do not admit of such categories of difference in kind. So we would think that God and man stand at different degrees of intensity of being, and as such, are not yet understood as being different in kind. It is this understanding of intensity that Deleuze seems to be after. However, Scotus still maintains the theological position that God is fundamentally different than man, and this would be because the infinite perfection is so much greater than our own degree of perfection that an absolute gap divides us. As a result, his understanding of univocity is compromised, since God’s being in the end is a different kind of being than our own, and not just another degree of the same being.]
Intensity as it stands is purely a difference in the degree of something’s being, and is also pre-categorial. As such, it does not constitute the kind of distinction that would allow a proper separation between God and man. Such a position in fact is the one that Deleuze wants to develop in his own philosophy. For Scotus on the contrary, the difference in degree between God and his creation becomes a difference in kind once we recognise that infinite intensity is simply incommensurate with any form of finite intensity. The gap between finite and infinite is therefore still a chasm which allows the separation of God and his creation to be maintained. While being can conceptually be said univocally, in practice, we always encounter being with a given intensity, and so in reality being is always encountered in different forms [the following up to citation quotes Scotus]:
As said of the ten categories, neither metaphysically nor naturally does the term ‘being’ signify one concept; and being is not a genus of these, neither naturally nor metaphysically. However, logically speaking, being is univocal. (Duns Scotus, In De an., q. 22, n. 33 taken from Hall 2007: 20) |
By making this difference a difference in kind, Scotus separates man from God, but at the cost of making the thesis of univocity a purely formal thesis. This is why Deleuze claims that Scotus ‘only thought univocal being’ (DR 39/49).
(SH 34-35)
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