Leibniz on the Expression of God Stewart Duncan Draft of 28 August 2014 Leibniz makes frequent use, in his philosophy, of the notion of expression.1 He uses it, for example, in giving his definition of perception as the expression of a multitude in a simple.2 Expression itself appears to be some sort of representation relation. Beyond that, however, it is rather less clear what expression is. Looking at Leibniz's texts, there appears to be a repeated requirement that, for there to be expression, there must be a regular relation between the expressing thing and the thing expressed.3 It remains unclear, however, what this requirement amounts to. As a result, there has been a certain amount of debate in recent literature about what the standards for a 'regular relation' are. In this debate one finds repeatedly the suggestion that Leibniz requires the expressing thing to be isomorphic with the expressed. This is countered by the thought that, taken strictly, that is too strong a requirement. Nevertheless, there remains the suggestion that expression is something like isomorphism, in that it requires a structural similarity between the thing expressing and the thing expressed.4 That sort of view derives some of its support from the 'regular relation' passages, and further support from some of Leibniz's frequent examples of expression. Cases such as 1 I use the following abbreviations in citing works of Leibniz: A (Leibniz 1923-), AG (Leibniz 1989), DM (Discourse on Metaphysics, giving references using section numbers, and quoting the translation of AG), DSR (Leibniz 1992), G (Leibniz 1875-90), L (Leibniz 1970), LA (Leibniz 1967), SLT (Leibniz 2006), WFNS (Leibniz 1997). 2 For example: "perception is the expression of a multitude in a unity" (G 3.69, WFNS 130). 3 For an early version of this notion, and some examples, see "What is an Idea?" (G 7.263-4, L 207-8) 4 For these discussions, see McRae (1976, 20-6), Kulstad (1977), Mates (1986, 37-9), Rutherford (1995, 38-9), Swoyer (1995), Simmons (2001, 41-2), Perkins (2004, 79-81), Puryear (2006, 8-16), Kulstad (2006), and Bolton (2011, 138-40). 2 an ellipse expressing a circle, or even a map expressing a piece of land, seem to fit well with this understanding of expression. There are, however, a variety of other cases in which Leibniz says expression is present.5 Leibniz also talks about speech expressing thought, about an equation expressing a figure, about substances expressing the universe, about substances expressing God, and about God expressing "everything at once, the possible and the actual, past, present, and future".6 Though it may perhaps be possible to understand all these cases as involving the same relation of expression that is seen in the case of the circle and the ellipse, it is far from obvious that this is the case. Indeed one might suspect that there is no overall account of expression that can really capture all the cases.7 I focus in this paper on the curious case of the expression of God.8 Leibniz says that created substances express God, or something closely related to God, such as his resolution to create the world.9 What does Leibniz mean by saying that a substance expresses God? In addressing that question I consider, in particular, the 1686 Discourse on Metaphysics, where Leibniz puts the notion of expression to multiple uses. First, substances are said to express the entire universe. Secondly, expression is used to explain the action of one substance on another. Thirdly, expression is invoked in explaining the distinction between the miraculous and the natural. Fourthly, expression is used in explaining Leibniz's theory of ideas. And fifthly, Leibniz proposes a view – or perhaps two distinct views – about created substances' 5 Kulstad (1977, 57) provides a useful table of Leibniz's examples of expression. 6 WFNS 118. This remark comes from Leibniz's "Reply to the Comments on the Second Edition of M. Bayle's Critical Dictionary, in the Article 'Rorarius', Concerning the System of Pre-established Harmony". There is a version of this at G 4.554-71, but WFNS translates the somewhat different original version from the 1716 Histoire critique de la République des lettres. 7 See Sleigh (1990, 174) and Garber (2009, 216). 8 This has been relatively little discussed in the recent secondary literature on expression, but see Nelson (2005), and also the discussion by Perkins (2004, 83-87) of expression of necessary truths. 9 There is some question as to whether he thought that all, or only some, of the created substances did this. This is discussed below. 3 expression of God. Thus the Discourse illustrates the importance – and also the apparent flexibility – that the notion of expression had for Leibniz, at least at some times. In discussing the expression of God in particular, the Discourse is an important text to consider because it contains several apparently different strands of thinking on the topic: here we seem to find both the thought that all substances express God, and also the thought that only some substances, minds, do; both the thought that substances express God because God is their cause, and the thought that substances express God because they are made in God's image. These apparently different views point to further questions. First, which substances did Leibniz believe expressed God? Secondly, why did Leibniz believe those substances expressed God? And thirdly, did he believe that all substances expressed God in the same way and for the same reasons – or, alternatively, tell different stories about different types of substances?10 1. Central texts The notion of the expression of God appears in three places in the Discourse: in DM 15-6, in DM 26-30, and in DM 35-6. 1.1. DM 15-6 DM 15 aims principally to present a theory of one substance's action on another, or at least of when it can be said that one substance acts on another. This sense of action is explained in terms of expression. As the section summary puts it, "The Action of One Finite Substance on Another Consists Only in the Increase of Degree of its Expression Together 10 Grosholz (2001) discussed the role of expression in the Discourse under the description "theomorphic expression". However, where I focus on finite substances' expression of God, Grosholz focuses on their being like God by expressing other things. 4 with the Diminution of the Expression of the Other, Insofar as God Requires Them to Accommodate Themselves to One Another". Leibniz's story is that when we would usually say that one substance acts on another, what actually happens, speaking more metaphysically correctly, is that the 'acting' substance increases its degree of expression, while the other decreases its. God coordinates all of this, so the changes correspond appropriately with one another. But what is this expression that changes? [T]he efficacy [vertu] a particular substance has is to express well the glory of God, and it is by doing this that it is less limited. And whenever something exercises its efficacy or power, that is, when it acts, it improves and extends itself insofar as it acts. Therefore, when a change takes place by which several substances are affected (in fact every change affects all of them), I believe one may say that the substance which immediately passes to a greater degree of perfection or to a more perfect expression exercises its power and acts, and the substance which passes to a lesser degree shows its weakness and is acted upon [pâtit]. Here the degree of expression is apparently equated with a degree of perfection. To act, and increase one's expression, is also to acquire a higher degree of perfection.11 This is all connected to expression of one particular thing, the glory of God. So to act is, it appears, to express more perfectly the glory of God, and to be acted upon is to express it less perfectly. Thus DM 15 is not merely an account of the coordinated changes of created substances in the pre-established harmony. It also connects the changes of substances to the expression of the divine, in this case of the glory of God.12 11 There are several other passages in which Leibniz gives similar accounts of activity. They do not all invoke the divine in this way. See, for example, the brief discussion of this issue in Kulstad and Carlin (2013), or the longer discussion of Garber (2009, 206-24). 12 One might perhaps suggest that a substance expresses the glory of God by expressing the universe God has created. (Consider DM 9: "the universe is in some way multiplied as many 5 Such connections are made again in DM 16, which distinguishes the miraculous from the natural. The summary of that section offers another example of something expressed: "God's Extraordinary Concourse Is Included in That Which Our Essence Expresses". And the section itself tells us both that "an effect always expresses its cause and God is the true cause of substances" and that "our essence [...] expresses our union with God himself". 1.2. DM 26-30 The language of expression of God occurs again in a series of sections that apparently focus on discussion of Malebranche's views. These sections begin with DM 23, where Leibniz announces that he will discuss ideas, and whether we see all things in God.13 Within this discussion, the notion that our soul expresses God occurs repeatedly. Thus Leibniz says in DM 26 that "our soul expresses God, the universe, and all essences, as well as all existences". Such language occurs again in DM 28 and DM 29. Thus we have ideas of everything in our soul only by virtue of God's continual action on us, that is to say, because every effect expresses its cause, and thus the essence of our soul is a certain expression, imitation or image of the divine essence, thought, and will, and of all the ideas comprised in it (DM 28). In my opinion, this arises from the fact that they have not yet considered sufficiently either what we have just explained about substances or the full extent and times as there are substances, and the glory of God is likewise multiplied by as many entirely different representations of his work".) If that were so, expressing the glory of God would not require expressing God. This deflationary reading would reduce the number of examples of expression of God in the Discourse, but would not change the overall picture: Leibniz says repeatedly that substances express God. 13 I am using this just as a characterization of these particular sections. There is a broader question of whether the Discourse as a whole is intended as a criticism of Malebranche. On this see for example Jolley (2004). 6 independence of our soul, which makes it contain everything that happens to it, and makes it express God and, with him, all possible and actual beings, just as an effect expresses its cause (DM 29). Leibniz appears here to be focused on the human soul, rather than substances in general. Thus what is said here appears to differ from the earlier claim in DM 15 that every substance expresses the glory of God. Some continuity is provided by the claim that every substance expresses its cause, and God is the cause of every substance, which had occurred in DM 16, and is echoed in DM 28 and 29. Meanwhile, the notion that we are imitations or images of God is explicitly connected here to our expressing God – unlike in its previous occurrence in DM 9, where Leibniz talks about imitation of God, and expression of the universe, but not expression of God. So there appears to be a good deal of complexity to the theory by this point. 1.3. DM 35-6 The notion of the expression of God returns later in the Discourse, in DM 35-6. These sections are in a part of the Discourse, which we might see as running from DM 32 to the end in DM 37, in which Leibniz discusses minds and their relationship to God. In both DM 35 and DM 36 Leibniz is concerned to explore the ways in which minds differ from other substances. At times he puts the point in terms of expression. The Excellence of Minds and That God Considers Them Preferable to Other Creatures. That Minds Express God Rather Than the World, but That the Other Substances Express the World Rather Than God (DM 35 summary). For certainly minds are the most perfect beings and best express divinity. And since the whole nature, end, virtue, and function of substance is merely to express God 7 and the universe, as has been sufficiently explained, there is no reason to doubt that the substances which express the universe with the knowledge of what they are doing and which are capable of knowing great truths about God and the universe, express it incomparably better than do those natures, which are either brutish and incapable of knowing truths or completely destitute of sensation and knowledge (DM 35). In this way we may say that, although all substances express the whole universe, nevertheless the other substances express the world rather than God, while minds express God rather than the world (DM 36). Whether the central idea is that minds are better than other substances at expressing God, or that only minds can express God and other substances cannot, is not immediately obvious here. But clearly something in that general area is being said. Before moving on to more detailed interpretive discussions, it is worth emphasizing that the notion of the expression of God occurs repeatedly, in several contexts, and appears to be asked to do a decent amount of work. It is not, at least in the Discourse, a mere trivial detail, but something that Leibniz himself appears to find rather important. For all that, it is not clear just what the notion is, or just how Leibniz thinks this expression works. I have tried to indicate some of the puzzles above. There are certainly others. 2. Expression of causes 2.1. A causal argument for expression of God Why, according to Leibniz, does any substance express God? Well, DM 16 tells us that "an effect always expresses its cause and God is the true cause of substances". Given that, we can construct the following argument. 8 1. An effect always expresses its cause. 2. Every substance is an effect of God. So 3. Every substance expresses God. Similarly, Leibniz said in a letter he wrote that year to Simon Foucher that "Each effect expresses its cause, and the cause of each substance is the decision which God took to create it" (WFNS 53; A 2.2.91). That suggests a slight variant on the above argument. 1. An effect always expresses its cause. 2*. Every substance is an effect of God's resolution to create it. So 3* Every substance expresses God's resolution to create it. The question of what to take the relata of expression – and indeed of causation – to be is visible in the differences between the two arguments here.14 But there is a clear common core. All substances express their causes, and all substances are caused by God, so all substances express God.15 14 Although I have been talking of substances expressing God, the texts give a variety of different, though related, relata to this expression relation. The thing expressing varies: a substance, our essence, our soul, a mind. The thing expressed varies just as much: God, the glory of God, God's extraordinary concourse, our union with God, the divine essence, God's decision to create the expressing substance, and "God and, with him, all possible and actual beings" (DM 29). Elsewhere we find Leibniz talking circa 1680 of substances expressing "the perfection of their creator" ("Conversation du Marquis de Pianese et du Pere Emerey Emerite", A 6.4.2271, on dating see A 6.4.2241). Because Leibniz presents these claims in very similar ways, there is a temptation to take him always to be talking about the same thing, about some created substance or other expressing God. But we should be alert to the possibility that there is more going on: e.g., that the expression of the glory of God is a significantly different thing from the expression of God's resolution to create a substance. That said, the expressing thing is almost always a substance, so perhaps we should be inclined to take the expressed one to be a substance too, and thus to be God rather than any feature of God. 15 Related is the comment in the 1689 "Primary Truths" that "all individual created substances are different expressions of the same universe and different expressions of the same universal cause, namely God" (AG 33). Though this does not explicitly say that the expression is present because of the causation, it does implicitly link the two. 9 This is a claim about all substances.16 As we have seen above, and as I shall discuss below, in places Leibniz appears to say that only some substances express God. But not only do these passages state the opposite, they also state an argument that makes it hard to restrict expression of God to merely some of the substances in the world.17 For every substance was created by God, not just some substances. I discuss the claim that only some substances express God further in section 3 below: it appears that a second sort of argument for expression, and indeed a second sort of expression, is at work in those other passages. For now, however, I consider the reasons for premise 1 above. Why think that substances express their causes? 2.2. Why think that substances express their causes? Given a standard reading of expression as involving, or just being, a sort of structural similarity, it is hard to understand why substances must express their causes. Surely, one might think, one thing can act in a way that changes or gives rise to another, without the second having anything like the structure of the first. Though discussion of examples is complicated, in the Leibnizian context, by Leibniz's denial that there are any genuine causal relations between created substances,18 there is an interpretive puzzle here – one that 16 That is at least, in the context of DM 16, all individual substances. It is hard, at this stage, to see any reason why this should not apply to corporeal substances too, if there are any. We might well also ask why this does not apply to aggregates, phenomena, and anything else in the created world. These are all, after all, effects of God. 17 That said, I note that McRae (1976, 65) argues that "An effect is not essentially an expression of its cause; that it is is a contingent fact discoverable in experience", meaning by this that expressing its cause is not part of the definition of effect. 18 The expression of this point is complicated by the sorts of 'cause' explained in DM 15 and discussed in section 1.1 above. Why not call those 'genuine causal relations'? Well, one might. But then there will be a further sense of 'cause' involved in the observation that Leibniz thinks the relations between created substances involve harmony rather than causation. 10 remains even if we are not attached to the standard reading of expression.19 In this section I explore three readings of Leibniz's motivation for claiming that substances express their causes. Explanation 1: expression and knowledge Those discussing Leibniz's views about expression have often referred to the late-1670s note "What is an Idea?"20 One might hope that it would provide some illumination of the current issue. In the course of his discussion there, Leibniz does say things that might appear to help. In particular, he says that "every entire effect represents the whole cause, for I can always pass from knowledge of such an effect to knowledge of its cause" (A 6.4.1371, L 208).21 So if we have knowledge of an "entire effect" then we will be able to acquire knowledge of the "whole cause" of that effect. That suggests the following argument. 1. If one has knowledge of an (entire) effect, one can acquire knowledge of its (whole) cause. 2. That could only be the case if the effect represented the cause. So 3. All (entire) effects represent their (whole) causes. Some details about 'entire' and 'whole' aside, this gets us close to the Discourse's claim that effects express their causes. However, it is relatively unhelpful as an explanation of why Leibniz held that view in the Discourse. 19 This does suggest the question of whether we should expect Leibniz to have a reason for premise 1 above that would be potentially plausible to people with different views about what actually causes what, or merely a reason to accept the premise given Leibniz's views about what causes what. 20 A 6.4.1369-71, L 207-8. 21 Leibniz uses the language of representation rather than expression here, but in this context appears to be using these terms interchangeably. 11 This is a text from several years before the Discourse, and it is not so clear that the details of Leibniz's views of expression (in particular, expression of God) were all that stable over time. Moreover, the argument seems not tell us why effects express their causes, even if it does show us that it must be the case that they do. Now, premise 1 here might gain some motivation from widespread views of knowledge and understanding that adhere to or approximate the slogan that to know is to know through causes. If one really had knowledge of the effect, the reasoning might go, that would involve knowing the cause and how it produced the effect. But if we think in this way, then the crucial fact appears to be about what knowledge and explanation are, and not to require any representation – or expression – of the cause by the effect. The one who knows the effect must know the cause, but the effect itself does not need to – at least, no reason why it must is given here. Thus, all in all, this appears not a terribly helpful explanation of why, in 1686, Leibniz thought that all effects expressed their causes. Explanation 2: the cause-effect relation as a special case of expression Garber (2009, 216-24) discusses expression, and argues that "The cause/effect relation is a special case of the expression relation" (218), basically because expression requires a "constant and fixed" relationship, and causation is such a relationship.22 Thinking along this sort of line, we might construct another argument for the claim that effects express their causes. 1. The relation of expression holds between two things, A and B, when there is a regular relation between them. 22 See also McRae's claim that "in any cause-effect relations, where it is not thoughts which are expressed, it is possible to see that ordered connection between what expresses and what is expressed to be the sort described by Leibniz" (McRae 1976, 24). 12 2. The cause-effect relation is a regular relation between two things. So 3. When two things stand in the cause-effect relation, the relation of expression also holds between them. So 4. All effects express their causes. Evaluating this is largely a matter of deciding whether causation meets Leibniz's criteria for a regular relation. It doesn't seem to be one of his usual examples.23 And to take causation to be appropriately regular is to make certain assumptions about causation, which it would be helpful, at least, to see filled in. In this connection it is worth noting that efficient causation, at least, seems not to be structure-preserving in the way that expressing relations are often taken to be.24 Overall, there is enough complexity here that we should not take this reading to offer an easily acceptable, simple explanation. And there is another, and good, explanation available. Explanation 3: expression and complete concepts There are yet other Leibnizian reasons to think that an effect will express its cause. Indeed, I suggest that we can find a complete Leibnizian reason for the view in the Discourse itself. Consider the views expressed in DM 8 about predication, complete concepts, etc.25 There Leibniz says that "the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all 23 Though he does, as in DM 15, attempt to explain apparent causal relationships, as between two finite substances, in terms of expression. And the expression of God is not a usual example of expression either. 24 I would not in general want to assume that expression must be structure-preserving, or that the causation being discussed here must be efficient causation – but there is more to say about what is going on. I address closely related issues in section 4 below, where I consider the connection between the relationships of expression and emanation – though similarly, I would not want to assume that all the claims about effects expressing causes are just about emanative causation. 25 There is a lot of literature on this topic. For a shorter account, see Wilson (1989, 88-98). 13 the predicates of the subject to which this notion is attributed". Among the predicates attributed to individual substances will be some that relate it to God. Indeed, these will include predicates about the substance's being an effect of God. Given this, we can reason as follows. There will be true claims of the form 'S is P' that relate any substance to God. Suppose for instance that 'P' is 'an effect of God'. For any created substance this will be true. Thus, by the view about concepts explained in DM 8, an effect of God will be contained in the complete concept of every substance.26 Moreover – given the reasoning at the end of DM 8 – there will be marks and traces in each substance corresponding to this predicate. These marks and traces in the substance are naturally understood as the substance's representations of the things described by the corresponding predicates. So we can at least say that each individual substance represents God. Thus we can see why Leibniz would say that all substances express God. Moreover, if substances had any causes other than God, we could show that the substances would express them too, by similar reasoning. Thus, we could understand the view that all 26 This relies on taking the view about predication and truth to be, as it is stated to be in DM 8, a story about all predication. But one might think it does not apply to predicates about existence, creation, and actuality, such as 'an effect of God'. For one thing, sometimes Leibniz talks about God examining complete concepts and making decisions about creation, in a way that suggests creation does not change the concept. This connects to his saying to Arnauld that "the notion of an individual includes considered as possible what, in fact, is true, that is, considerations related to the existence of things" (G 2.39, AG 70, also translated at LA 41). Though various technicalities arise here, one might at first approximation address this, in my example, by taking the complete concept to contain a possible effect of God rather than an effect of God. This would still get us to the conclusion that all substances express God. More generally, Leibniz appears to have had two rather different ways of approaching complete concepts – by thinking about creation and divine understanding, and by thinking about predication and truth – and we might ask whether these each led Leibniz to precisely the same place. On theological and non-theological approaches to complete concepts, see Di Bella (2005, in particular 265-74). 14 substances express their causes as a consequence of Leibniz's views about substances and language. Moreover, it would be a reason why substances, in particular, express their causes. This sort of reasoning also fits well with Leibniz's claim that we, and other individual substances, express everything (including, but not just) God. For the complete concept view leads to thinking that all individual substances (including ourselves) have concepts that represent everything else. As a reading of the Discourse, or of Leibniz's views in 1686, this approach has the advantage that the resources for explaining why Leibniz thought that substances express their causes are contained in the text itself. Seeing the view that all substances express God as grounded in Leibniz's views about predication, also fits nicely with the view appearing in Leibniz's 1689 "Primary Truths" essay, which attempts to ground many Leibnizian views in his views about language.27 This reading might also help explain why the expression of God is not a persistent feature of Leibniz's statements about substances - as the DM 8 view tends to play less of an explanatory role over time, this view of all substances as expressing God might naturally tend to disappear with it.28 On the other hand, the importance of expressing causes might appear to be minimal on this reading. Substances turn out to express causes simply because they express everything that stands in any relation to them.29 That is somewhat at odds with Leibniz's 27 See note 14 above. 28 See the comment of Garber (2009) on a related issue: "While the claim that individual substances have complete individual concepts is one of the enduring theses of Leibniz's philosophy, and while Leibniz continues to hold the non-communication thesis to the end of his life, the argument for it from the CIC [Complete Individual Concept] seems to drop out of his repertoire rather quickly, by the early or mid-1690s" (198-9). 29 Any relation, not just a regular one, whatever exactly that is. That said, it is unclear if we can find a Discourse-appropriate distinction between regular relations and relations in general, 15 apparent view that causation is distinctive here. So this understanding of why Leibniz says that substances express their causes is not unproblematic, despite its notable advantages. 3. Do only minds express God? Above we have seen Leibniz arguing that all individual substances express God. But as we have also seen, he seems not to have said this consistently, even within the Discourse. Consider the last four sections of the Discourse, which focus on the difference between minds and other substances. Even here Leibniz continues to suggest that all substances express God. Thus in DM 35 we are told that "the whole nature, end, virtue, and function of substance is merely to express God and the universe". But DM 36 appears to deny that all substances express God. For there Leibniz says that "other substances express the world rather than God, while minds express God rather than the world" (DM 36). Something very similar is in the summary of DM 35, and in at least two of Leibniz's subsequent letters to Arnauld (A 2.2.60, 2.2.257). This appears to be the view that only some individual substances, minds, express God. So which is it? Do only some individual substances express God, or all of them? What led Leibniz to assert, apparently, that only minds express God? A few years before the Discourse, Leibniz talked of expression of God in the "Conversation du Marquis de Pianese et du Pere Emerey Emerite".30 There he said that minds, which are infinitely more noble than other things, "express the perfection of their creator in a quite different way than other creatures, which are incapable of this elevation given the view of DM 6 that all arrangements have regular rules, even if we cannot see what they are. 30 Mercer (1996, 107) describes an even earlier view, of April 1676, thus: "Each creature expresses the same essence, but in a slightly different way; that is, each creature will somehow instantiate all the attributes of God", citing "On the Origin of Things from Forms" (A 6.3.518-9, DSR 74-82). 16 (nobility) do" (A 6.4.2271).31 Thus we find minds expressing God, and some difference between the way they express God and the way other substances do.32 Indeed even in the Discourse there are hints that that is what is going on. Thus Leibniz says in DM 35 that "minds are the most perfect beings and best express divinity", suggesting that other beings also express divinity, just not as well. But still, there are more strikingly contrasting passages, which do seem to give rise to a contradiction. One might try to say that comments suggesting only minds express God are not to be taken literally. One way to do this would be to suggest that there is not really a difference between what minds and other substances express, though there are related differences (about, e.g., whether this expression is accompanied by knowledge). Thus Leibniz would simply have given a misleading summary of his point. But, if nothing else, Leibniz says this thing repeatedly. So the prospects for this strategy look rather poor. What else might one say here? One theme in the discussion is that minds are made in God's image, in such a way that a mind "does not merely express the world but it also knows it and it governs itself after the fashion of God" (DM 36). So minds have a sort of resemblance to God that the other substances lack. And for this reason we might say that minds express God, whereas other substances do not. 31 That is: "je suis asseuré que les esprits ont esté bien ordonnés preferablement à toutes les autres choses, qu'ils passent infiniment en noblesse, puisqu'ils expriment la perfection de leur createur d'une toute autre maniere que le reste des creatures incapables de cette elevation" (A 6.4.2271). 32 For another variation on the theme, from perhaps a couple of years later than the Discourse, see the "Specimen inventorum de admirandis naturae generalis arcanis", which the Academy editors date as 1688 (?), and which Parkinson (1974) notes contains several themes familiar from the Discourse. In particular: "Quin imo cum Mens unaquaeque sit divinae imaginis expressio (nam dici potest caeteras substantias magis universum exprimere, Mentes magis Deum)" (A 6.4.1624). 17 That, however, is not straightforward, even just within the Discourse. For back in DM 9 we find Leibniz saying that "It can even be said that every substance bears in some way the character of God's infinite wisdom and omnipotence and imitates him as much as it is capable". So every substance is in some way an imitation of God. Thus it would seem that even non-minds are in some way imitations, images, representations of God. Should one not say that they thereby express God in some way and to some extent, even if not as perfectly as minds? Trying to pull this all together, it appears that there are two distinct theories of expression of God in the Discourse. The first is a causal theory of expression, holding that all substances express their causes. It appears, according to this theory, that all created substances express God equally well, for all are, equally, effects of God. The second is a theory that considers expression of God in terms of being a better or worse image of God. Thinking in this way, minds are better expressions of God than other substances are.33 Still, what should we make of the striking formulation: minds expressing God rather than the world, other substances expressing the world rather than God? Even if we temper our reading somewhat – minds expressing more God than the world, other substances expressing more the world than God – it still does not sit well with Leibniz's other statements. However, one way to think about the formulation is as trying to convey what are the most striking facts about each sort of substance's expression of other things. After all, Leibniz introduces this formulation as something "we may say" (DM 36) rather than simply presenting it as a description. The most notable description of minds' expression is that they 33 Mercer (1996, 108) introduces the helpful notion of a "partial expression", which we might employ here: "for any essence E, whether infinite or finite [...] there is a range of expressions of it, from partial to complete where a partial expression of E is a 'display of a property' of E and a complete expression is a display of every property of E". A different account of partial expression is presented in Mercer (2001) – see section 4.2 below. 18 express God – simply because being made in the image of God is such an important thing, and minds do this better than anything else does. Other substances are less notable in this way – but they still, as Leibnizian individual substances, possess the very notable feature of expressing the whole of the universe. So that, in their case, is something it is reasonable to emphasize. And that gets us to the striking formulation.34 4. Expression and emanation There appear then to be two, largely distinct theories about expression of God presented in the Discourse. But to conclude my discussion, I want to consider a further Leibnizian idea that may connect them. This is the idea that created substances are emanations of God. The language of emanation is not prominent in the Discourse, but does crop up once: "created substances depend on God, who preserves them and who even produces them continually by a kind of emanation" (DM 14). This short text presents three relationships between God and created substances: creation, preservation, and emanation. To consider the relevance of the third relation, emanation, I begin from a summary by Christia Mercer, who argues that this is part of the "Platonism at the core of his [Leibniz's] philosophy" (Mercer 2008, 226).35 The Theory of Emanative Causation claims that, for a being A that is more perfect than a being B, A can emanate its attribute f-ness to B in such a way that neither A nor A's f-ness is depleted in any way, while B has f-ness, though in a manner inferior to the way it exists in A. The emanative process is continual so that B will instantiate f-ness 34 I do not in this paper consider the issue of minds' ability to express possibilia, something we can see briefly in the Discourse, in DM 29. But we can see this as an aspect of the second theory – our minds resemble, and thus express, God in being able to think about possibilia. 35 For all that this is in a way Neoplatonic, there were also aspects of it in scholastic Aristotelianism. Both O'Neill (1993, 36-7) and Fouke (2004, 176-81) show this sort of model being used by Aquinas. 19 if and only if A emanates f-ness to it. The Supreme Being is in the creatures in the sense that it emanates its attributes to them; it remains transcendent from them because it neither loses anything in the emanative process nor gives them any part of itself. The crucial point to understand is that the attributes exist in the products in a manner inferior to the way in which they exist in the Divine. God has the form or Idea f perfectly; creature has it imperfectly (Mercer 2008, 228).36 Suppose one begins with a picture of substances as emanations of God. They will as a result all have the same features that God has, albeit in an imperfect or watered-down way. So the created substances, the effects of God, will also be guaranteed, by the nature of emanative causation, to resemble God. If we're talking about emanative causation, causation and resemblance go together. So, if we talk about emanative causation, expression as resemblance and expression of causes come together. Then, if we take Leibniz to have emanative causation in mind in the Discourse – as DM 14 shows he did, at least sometimes – we can see why he would say two apparently different things about expression – that effects express their causes, and that substances express God by resembling God. Thus we have an explanation for Leibniz's presenting his two different views about expression of God. This is, I grant, a slightly speculative thought about a view of Leibniz's that lies in the background and ties together his two strands of thought about expression. It would not resolve all the puzzles mentioned above, or completely unify the two views. For instance, it does not clear up the issue of Leibniz's sometimes saying that only minds express God, for 36 O'Neill (1993, 32-5) and Fouke (1994, especially 177-8) provide similar accounts of the main aspects of this model of causation. O'Neill thinks that "the Neoplatonic influence model [...] plays a central role in Leibniz's construction of influxus physicus" (1993, 35), i.e. in the construction of a view of causation (within nature) that Leibniz criticized. But one might grant that and still think Leibniz was influenced by the emanative model in his picture of causal relations between God and the created world. 20 non-minds, as well as minds, are emanations of God. But it does help us see why the two theories might both be there. 5. Expression of God before and after the Discourse The theory of emanative causation thus provides a link between two apparently distinct approaches to the expression of God in the Discourse. I conclude, in this section, by looking briefly at how Leibniz thought about the expression of God in earlier and later texts. In particular, seeing a connection between expression and emanation opens up an intriguing possible connection between the Discourse and earlier texts, in particular some from 1676. Mercer (2001, 427-36), in discussing those earlier texts, argues that they contain a different view of expression than the "mathematical and functional account that Leibniz came to use later" (Mercer 2001, 434 n.164). On the 1676 view of expression "S expresses an essence E just in case S is a partial representation of E which means (at least) that to understand S is equivalent to having a partial cognition of E" (Mercer 2001, 436). Moreover, in the 1676 text, every substance expresses God: "because every created substance S (and every state of S) contains the (selected) divine essence, S (and every state of S) will be a partial expression of the divine essence" (Mercer 2001, 436). If we think that emanation is playing the sort of role I have suggested in the Discourse, then we can in fact see something going on there that is very similar to what Mercer argues was going on in the 1676 texts. That sort of expression is indeed different from the "mathematical and functional" account that dominates discussions of expression. But that sort of account – call it mathematical, functional, or structural – is itself not easy to square with the Discourse's repeated talk of expression of God (however exactly we understand it). 21 So it might well be sensible to take the extensive talk of expression of God in the Discourse as a holdover of an earlier view. However, although the views about expression of God in the Discourse might seem to hark back to earlier themes, they might also seem not to be terribly long lasting. Thinking along similar lines, Catherine Wilson has said that "the claim that humans express God rather than the world does not seem to be a consistent theme of Leibniz's, and its appearance here [in DM 36] may represent a transitory moment of enthusiasm" (Wilson 2005, 119 n4). It does seem harder, as we move further away from the Discourse, to find Leibniz saying that all substances express God. As I speculated previously, perhaps this has to do with the connections between the expression of God view and Leibniz's views about language and complete concepts, which themselves appear less prominent over time. The other view, that minds express God in some special way, does have some later echoes. Not, perhaps, in the striking formulation in which they express God but do not express the universe – but then that was never the whole of Leibniz's view. Consider just one case, that of what is probably still Leibniz's most famous later text, the Monadology.37 There the language of expression appears to be confined to talk of substances expressing the universe. Thus Monadology 59 has "every substance expressing exactly all the others".38 But late in the text we come to minds, and in particular the discussion of Monadology 83. Here we find that "minds are also images of the divinity" in addition to being "living mirrors or images of the universe of creatures". This uses the language of images rather than that of expression. But it does seem to make a point familiar 37 This is not the only relevant later text. For example, Leibniz wrote to André Morell in 1698 that "As all minds are unities, it can be said that God is the primitive unity, expressed by all the others according to their capacity" (A 1.15.560, SLT 39). 38 I quote the translation of AG. 22 from the Discourse, that minds like all other substances represent the universe, but minds represent God in some distinctive way. That's not to say all the related thoughts are the same here as in the Discourse, but there does seem to be a continuity here. I do not, in this paper on the Discourse, attempt a complete account of the development of Leibniz's views on the expression of God. But perhaps we can begin to see some patterns. The 1676 view, on Mercer's reading, will tend to have all substances expressing God. As we have seen, the Discourse can seem equivocal about this, though it tends towards that view. 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