Article

Leibniz on Possibilia, Creation, and the Reality of Essences

Authors
  • Peter Myrdal orcid logo (University of Turku)
  • Arto Repo orcid logo (University of Turku)
  • Valtteri Viljanen orcid logo (University of Turku)

Abstract

This paper reconsiders Leibniz’s conception of the nature of possible things and offers a novel interpretation of the actualization of possible substances. This requires analyzing a largely neglected notion, the reality of individual essences. Thus far scholars have tended to construe essences as representational items in God’s intellect. We acknowledge that finite essences have being in the divine intellect but insist that they are also grounded in the infinite essence of God, as limitations of it. Indeed, we show that it is critical to understand that this dependence on God’s essence is prior to the dependence on God through divine ideas. Here it is crucial to distinguish questions concerning the ontological status of essences from questions concerning their reality. This yields a fresh view of Leibniz’s theory of creation, which takes seriously his claim that the same thing is first a mere possibility but after creation an actually existent substance.

Keywords: Leibniz, Descartes, metaphysics, epistemology, rationalism, ontology, modality

How to Cite:

Myrdal, P., Repo, A. & Viljanen, V., (2023) “Leibniz on Possibilia, Creation, and the Reality of Essences”, Philosophers' Imprint 23: 17. doi: https://doi.org/10.3998/phimp.1697

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20 Oct 2023
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1. Introduction

Leibniz famously holds that, in creating the world, God chooses between possible worlds, actualizing one of them — the most perfect one. Possible worlds are constituted by possible individual substances. Creation thus amounts to God’s choosing to actualize some of all of the possible individuals and presupposes “an infinite number of series of possible things” only some of which “attain existence” (A VI.iv, 1651/AG, 29).1 This paper proposes to radically reconsider Leibniz’s conception of the nature of possible things (possibilia), as well as the very ground of possibility.

There is a close connection between Leibniz’s idea of possible things and his idea of finite individual essences.2 That there is a genuinely possible thing, apt to be created, means that there is an individual essence endowed with a degree of reality or perfection. To ask about the nature of possible things is thus to ask about the nature of essences and their reality. Our main focus will be on what Leibniz understands by the reality of essences. We believe that this central element in Leibniz’s system has thus far not been correctly interpreted and that the main reason for this is that his readers have tended to see Leibniz’s concern with the reality of essences as primarily a concern about their ontological status, or the kind of being or existence they have. In contrast, we shall argue that the question concerning the ontological status of essences is importantly different from that of their reality, which pertains to the very ground of possibility. Here we depart from a common view according to which Leibniz works with a purely logical conception of possibility: we believe that it is crucial to his metaphysics of modality that possibility has a ground in essences, conceived in what may called pre-logical terms. The failure to appreciate this central dimension of his thought has led to interpretations of essences as representational or conceptual items. We propose that in order to understand the Leibnizian notion of the reality of finite essences, it is of paramount importance to pay attention to the way in which those essences depend upon God’s essence. This is a type of dependence fundamentally different from the ontological one on divine ideas, and is, in fact, prior to it. Taking seriously the distinction between the reality of essences and their ontological status will further allow us to revisit a common picture of Leibniz’s view of creation, on which the finite essences in God’s intellect and actual existing creatures are related to each other as concepts to their instantiations.

The paper will unfold as follows. In Section 2, we examine some key passages concerning the nature of possible things and finite essences. In them, Leibniz presents two main theses, namely that essences (or possibilia) are located in the intellect of God, and that the reality of essences is grounded in, or derived from, the infinite essence of God. In Section 3, we critically discuss the tendency in recent scholarship to downplay, if not ignore, the second of these two theses. Section 4 introduces our new interpretation. We argue for the importance of making a firm distinction between questions concerning the ontological status of essences and questions concerning the reality of those essences. With regard to the former, essences have objective being in divine ideas. Yet, for Leibniz, finite essences also come with different degrees of reality in virtue of being limitations of the divine essence. In fact, the notion of essences as real or as having reality is, as we shall see, presupposed by the conception of them as having objective being in the divine intellect. Section 5 argues that a certain conception of the grounding role of space in geometry is of crucial help in understanding the dependence of the essences of possible things on God. Section 6 elaborates on the implications of our interpretation for understanding the act of creation. We also indicate how Leibniz can be cleared of the well-known charge that his notion of existence is equivocal.

2. The metaphysics of merely possible things

The two most important Leibnizian theses concerning the metaphysics of possible things are as follows. First, possibilia or essences have their being in the understanding of God. Second, finite essences involve reality or perfection in different degrees in virtue of being grounded in (the essence of) God. Both theses can be found in texts from different periods of Leibniz’s philosophical career, which makes it unlikely that there is some kind of development from one thesis to the other. In this section, we shall first take a look at some of the relevant passages in which Leibniz formulates these theses. The first thesis has dominated scholarship to such an extent that the importance of the second thesis has not been properly recognized, although it is actually the more fundamental one.

In the Discourse on Metaphysics and the ensuing correspondence with Arnauld, Leibniz famously frames his account of substances, creation, and possible things in terms of complete individual concepts . The basic idea is that in God’s mind there is a completely determined concept of every possible individual substance. The complete concept of Adam, one of the substances belonging to the world God decided to create, contains every predicate true of Adam, and any variation in that concept would result in a distinct complete concept of a different possible individual. In April 1686, Leibniz writes to Arnauld:

There is a possible Adam whose posterity is such and such, and an infinity of others whose posterity would be otherwise. Isn’t it true that the possible Adams […] are different from one another; and that God chose only one who is precisely our own? (A II.ii, 19–20/LA, 25)

Arnauld’s main worry is that this doctrine leads to necessitarianism, but he also complains that the notion of purely possible substances escapes him:

I have no idea of these purely possible substances, that is, the ones that God will never create. […] [T]hey are chimeras we frame and […] everything we call possible substances, purely possible, can be nothing whatever but God’s omnipotence, which, being a pure act, does not allow there to be any possibility within it. (A II.ii, 36/LA, 51)

Leibniz, however, thinks that the notion of merely possible things does not lead to any extravagant ontological commitments. In his notes on Arnauld’s letter, Leibniz explains that he agrees that “there is no other reality in the pure possibles than the one they have in the divine understanding” ( A II.ii, 51/ LA , 73). He expands on this claim in his subsequent reply to Arnauld:

In order to call something possible it is enough for me that a concept can be formed of it, even if it would only be in the divine understanding, which is, so to speak, the land of possible realities. […] [I]f we wanted to reject pure possibles absolutely, we would destroy contingency and freedom. For if there were nothing possible but what God has in fact created, what God creates would be necessary[.] (A II.ii, 79/LA, 109)

This passage seems to offer a clear expression of the aforementioned first main thesis concerning possibilia. Even though the notion of a complete individual concept central to the Discourse seldom explicitly appears in Leibniz’s later texts, the tenet that possible things have their being in the divine understanding never loses any of its importance. Instead of the notion of complete concepts, Leibniz later uses the notions of (divine) idea and essence to describe the realm of possibilia: God’s creative act requires that there are ideas of finite individual essences in his understanding. Like complete concepts, ideas of individual essences of possible creatures — as well as eternal truths based on relations between those ideas — have being in, and are dependent on, the understanding of God.

Given divine omniscience, this kind of view is certainly reasonable: as everything (even the merely possible) is known by God, God must have an idea of every possible individual essence. The first main thesis yields an account of the ontology of finite essences: they are given, as it were, a metaphysical location in the divine intellect (“the land of possible realities”). In this way, a theocentric metaphysics such as Leibniz’s can, as Robert Adams (1994, 180) has noted, avoid the problematic features of genuine or robust Platonism.

Such a focus makes it natural to take Leibniz’s talk of possibilia as real simply to mean that they have a mode of being and a location in the divine intellect. The problem is that this fails to capture the sense of reality at work in the second main thesis, according to which the reality of finite essences is ultimately grounded in God’s infinite reality. To begin with, it is central here that the reality of finite essences derives from the entire reality of God and not only from the divine intellect or omniscience, which is just one of the divine attributes — God is the most perfect or real being, the ens realissimum, and thus necessarily has all perfections. In the preface to the Theodicy, Leibniz offers us a piece of philosophical poetry to drive the point home: “The perfections of God are those of our souls, but he possesses them in boundless measure; he is an ocean, whereof to us only drops have been granted” (G VI, 27/H, 51).3 As necessarily limited or bounded, creatures have some degree of God’s absolute perfection. It should further be noted that the idea of perfection or reality as coming in degrees clearly differs from that of having being in the divine intellect, which is something an essence either has or lacks — either it is or is not cognized by God.

While distinct from the first main thesis, the view of God as the source or ground of the reality of finite essences is still closely connected to it. Consider the following sections of the Monadology :

§43. God is not only the source of existences, but also that of essences insofar as they are real, that is, or the source of that which is real in possibility. This is because God’s understanding is the realm of eternal truths or that of the ideas on which they depend; without him there would be nothing real in possibles, and not only would nothing exist, but also nothing would be possible.

§44. For if there is reality in essences or possibles, or indeed, in eternal truths, this reality must be grounded in something existent and actual, and consequently, it must be grounded in the existence of the necessary being, in whom essence involves existence[.] (G VI, 614/AG, 218, emphases added)

The reference to God’s understanding and divine ideas (in §43) may seem to square well with the first main thesis. Yet the way in which Leibniz elaborates his view (in §44) suggests something stronger: instead of emphasizing the dependence on God’s understanding Leibniz claims that essences can have reality only if they are grounded in the actual necessary existence of God. God’s existence is, of course, a necessary presupposition of the existence of God’s understanding, but this is not the point. Leibniz is not so much concerned with the ontology of possibilia — with the way in which they exist — as with the ground of possibility: the space of creaturely possibilities must ultimately be determined by the actually existing necessary being . This means that finite essences, in addition to being ontologically dependent on the divine ideas , have reality derived from God as the fundamental actual entity. 4

Finite essences thus depend on God in two ways: not only as residing in the divine understanding but also as directly related to the infinite essence of God, the foundation of their reality (A VI.iv, 1635/SLT, 30–31). In what follows, we shall further elaborate this distinction and also dispel the impression that Leibniz’s talk of the reality of essences is ambiguous — that he is speaking of essences, on the one hand, as real in the sense of having being in the divine intellect, and, on the other, as real in the sense of expressing the infinite perfection or reality of God in limited ways. We shall argue that the latter is the central import of Leibniz’s talk of the reality of essences — even in passages, which at first blush are concerned with the location of possibilia in the divine intellect.

Unfortunately, in discussing Leibniz’s theory of possibilia, commentators often downplay or even completely ignore the second main thesis. This has led to a distorted picture of his position. Not only should the second thesis be taken seriously, but it constitutes the very basis of Leibniz’s metaphysics of modality. In fact, we surmise that the idea of essences as real in the sense of deriving from God’s reality (as articulated in the second main thesis) is also critical to a proper assessment of the first main thesis.

3. Representationalist approaches

As already noted, the view that possibilia, essences, or eternal truths have their being in the understanding of God can be seen as providing an alternative to robust Platonism. The idea that essences reside in the mind of God is, of course, in itself nothing new — it can be traced all the way back to Augustine and was, in different forms, accepted by several scholastics. According to one traditional line of interpretation, Leibniz espouses what we could call a representationalist version of this idea, leading to a decidedly deflationary understanding of finite essences. Most recently, such a reading has been defended by Ohad Nachtomy:

According to Leibniz, the platonic realm of essences and intelligible entities becomes a realm of pure logical possibilities. […] [This] signifies a crucial turn in the history of the notion of possibility. Possibilities need no longer be seen as entities subsisting in God; they need no longer be seen as some type of shadowy entities at all. Rather, Leibniz [sees] […] possibilities […] as mere thoughts in God’s understanding. With this deflation, the very notion of intelligibility is transformed as well: from its platonic sense of true Being to that which can be understood by a perfect mind — regardless of whether it exists or not. (Nachtomy 2017, 69)

To say that the realm of possibilities is a “realm of pure logical possibilities” means that possibility merely requires the absence of formal contradiction. Possibilities arise through a combinatorial process, whereby simple concepts are combined into complex ones — ultimately into complete individual concepts — in accordance with the principle of non-contradiction.

Nachtomy does acknowledge that there is a sense in which the ground of possibility goes beyond logic: as he reads Leibniz, God arrives at simple concepts by reflecting on the simple forms or attributes that constitute the divine essence. In this way God’s attributes may, as Nachtomy puts it, “be seen as the material or the actual basis out of which possibilities arise in his mind by virtue of God’s mental combinations and reflections” (2007, 23). The ground of possibility is nonetheless purely logical in that once the simple concepts are in place, possibility is only a matter of combinatorics, of absence of formal contradiction.5 This is why the realm of possibility is to be understood as a mere “conceptual realm” (Nachtomy 2017, 71): Leibniz’s frequent talk of essences should not be taken at face value, for essences (or possible things) are to be reduced to — or identified with — concepts.6 When Leibniz characterizes finite essences as limitations of God’s essence, all this means is that possibilia are built up from simple concepts derived from the divine attributes.

It may be thought that the doctrine of complete concepts lends support to such a reductivist approach to essences, as the former can be taken to imply a picture of God’s creation as a matter of choosing between descriptions of possible worlds, constituted by complete concepts. God has conceptual representations or blueprints of possible worlds in his understanding, and the actual world corresponds to one of these representations — the one describing the best possible world — so that actual things are to be seen as instantiations of divine concepts. What is “located” in God’s mind, on this picture, are basically just representational items.

Yet it is anything but clear that Leibniz’s notion of complete concept licenses a representationalist reduction of possible things or their essences. We have already seen that he often frames his views of substances, creation, and possible things by stressing the notion of essence without adding any deflationary or reductivist qualifications. It is true that Leibniz often describes God’s intellect as the realm of ideas, but it is important to keep in mind that ideas, for Leibniz, are in the first place immediate objects of thought, as he explains in the New Essays: “If the idea were the form of the thought, it would come into and go out of existence with the actual thoughts which correspond to it, but since it is the object of thought, it can exist before and after the thoughts” (A VI.vi, 109/RB, 109). It is thus misleading to characterize, as Nachtomy does, possibilities or essences as “mere thoughts” of God.

We are not the first to note the limitations of reductivist readings of essences. Samuel Newlands (2013, 165n26) is overtly critical of attempts to “flatten Leibniz’s ontology on this point.” He tries to do justice to the central place of essences in Leibniz’s thinking about modality, while at the same time steering clear of committing him to genuine Platonism. Newlands argues that “essences are the objective beings of God’s ideas,” which he takes to be equivalent to saying that essences are the intentional objects or representational contents of divine ideas (2013, 165). It is crucial to Newlands’s point that merely possible essences are, as he puts it, “purely intentional objects” (2013, 165), that is, that they have mere objective being and not, to use the traditional terminology, formal being, or actual existence. The difference from the reductivist interpretation is that essences are intentional objects of God’s thoughts and not, as they are for Nachtomy (2017, 69), “mere thoughts in God’s understanding.” Without committing Leibniz to genuine Platonism, we are nevertheless offered an ontology of essences: they have a way of being in the divine understanding.

On the basis of such a minimalist reading Newlands ascribes a bipartite grounding thesis to Leibniz: (i) finite essences are truth-makers for modal propositions; (ii) as essences are purely intentional objects of divine ideas, the latter constitute the ontological ground of the former, which means that “divine ideas provide the reasons in virtue of which essences have their reality” (Newlands 2013, 172). On this picture, divine ideas are the ultimate explanation for finite essences, for the space of possibilities is determined at the level of divine ideas — the ground of possibility lies, as it were, in divine psychology. Essences are real insofar as they have an ontological status in the divine intellect — indeed, Newlands explicitly talks of the “ontological status or ‘reality’” of essences (2013, 165). His interpretation can thus also be characterized as representationalist in that it is based on the first main thesis alone — that essences reside in the divine intellect.

Although we also find essences crucial to Leibniz’s modal metaphysics, we believe that Newlands takes this idea in the wrong direction. In our view, the right way to proceed is to take the second main thesis seriously. That is, we propose that finite essences themselves — and not only simple concepts, as Nachtomy’s logical approach would have it — have what we shall call a pre-logical ground in the divine essence.7

In attributing a purely logical conception of possibility to Leibniz, commentators typically draw on his assertion that “all truths that concern possibles or essences and the impossibility of a thing or its necessity (that is, the impossibility of its contrary) rest on the principle of contradiction” (A VI.iv, 1445/AG, 19) so that “anything that, in itself, implies no contradiction” is “possible in its nature” (A VI.iv, 1447/AG, 21). Such a reading is far from obvious, however. The scholastics widely shared the idea that absence of contradiction is sufficient for possibility. Yet this is not to say that all medieval thinkers subscribed to a purely logical conception of possibility: the key issue concerned the basis of contradiction, namely whether it is purely formal or instead metaphysical in nature. A prominent case in point is Aquinas. As John Wippel (1984, 168) explains, although Aquinas sometimes expresses the most basic kind of possibility (absolute possibility) “by appealing to the absence of incompatibility between the terms which describe such a thing, the possibility in question is not merely linguistic, nor merely logical, but ontological.” The ultimate ground for possibility “is the divine essence itself insofar as it is viewed by God as capable of being imitated in a certain way” — the divine essence “accounts for the fact that a possible is not self-contradictory and is therefore possible in the absolute sense.”

We take Leibniz’s second main thesis to express broad agreement with Aquinas on this score: the divine essence is ultimately what determines the space of possibilities.8 However the details of Aquinas’s own account are to be spelled out, we further take it that the grounding of the reality of essences in the divine essence is not for Leibniz a matter of offering an ontology of finite essences. This marks our second point of disagreement with Newlands: not only are essences not fundamentally representational or psychological, but they are not fundamentally existents at all.

This may sound surprising. It is natural to think that rejecting a purely logical conception of possibility in favor of grounding modalities in essences implies a commitment to some kind of ontology of essences: we easily construe the alternative to a purely logical conception of modalities in terms of a need for truth-makers of modal propositions, where a truth-maker is understood as an existing entity that makes a proposition true. Traditionally there was, however, a different view of the real ground of possibility. On this view, the relevant notion of reality was what can be called pre-ontological. We believe that this sort of approach underlies Leibniz’s second main thesis. Understanding this point requires a firmer grip on the notion of reality itself.

4. The reality of essences

We hold that there are two orthogonal metaphysical dimensions that are relevant in understanding Leibnizian essences: the grade of reality and the ontological status. When discussing the former — the reality of essences — Leibniz is not concerned about whether they have merely objective being in God’s understanding, or whether they instead have some mind-independent being, some sort of formal being in a Platonistic realm of essences. Rather, his focus is on the nature and determination of whatever has objective being in divine ideas and what also in some cases acquires formal being, or actual existence, in the created universe.

We should thus resist the temptation to think of objective being in terms of modern notions of mere representational content or purely intentional objects. God’s understanding does not conjure finite individual essences out of nowhere: God’s infinite essence is the ultimate source of finite essences, of all limited possibilities. In this way, essences are metaphysically prior to God’s ideas of them; essences are realities that acquire an objective mode of being in divine ideas. This proposal obviously requires some unpacking. We shall first outline the general distinction between reality and ontological status, and then consider more closely the role of the notion of reality in Leibniz’s account of the relation between finite essences and God.

4.1 Reality vs. ontological status

In contemporary metaphysics “reality” typically denotes some mode of existence and “existence” means actual existence, expressed by the standard existential quantifier. While the view that there are also other modes of being or existence (e.g. intentional being) has recently become more popular, what we propose is something entirely different, namely that reality is not to be conceived of as any way of being, not in terms of any kind of ontological status. The notion of reality is sui generis and is in fact presupposed by the notion of way or mode of being — what has a way of being, an ontological status, must be something real, some reality.

Such a notion of reality, which we shall henceforth call pre-ontological, may sound mysterious. At the same time, it is a historically important notion. It can be considered to underpin the Aristotelian view of cognition as involving a formal identity between the cognizer and the cognized, where the form is metaphysically prior to its mode of existence, the very same form existing in one way in, say, a birch (formally or actually) and in another way (objectively) in the mind cognizing the tree.

To be sure, Aristotelians still thought of forms as closely depending on actual exemplification: birch form requires that there are birches in the world. Such a view had, however, become less prevalent by the early modern period, partly owing to theological considerations: when God considers what to create, the focus is on the forms or essences of possibilia, and so they cannot depend on the actual existence of things, which is supposed to result from creation. Yet the independence of reality of any ontological status also has a more intuitive appeal quite apart from theology. To see this appeal, we shall turn to Descartes’s famous Fifth Meditation discussion of true and immutable natures . As John Carriero (2009 , 282–83) has shown, Descartes’s main aim here is to distinguish genuine thinking about something endowed with an essence from thinking about a mere chimera, something that does not have an essence and cannot actually exist; or as Descartes puts it:

When, for example, I imagine a triangle, even if perhaps no such figure exists, or has ever existed, anywhere outside my thought, there is still a determinate nature, or essence, outside my thought, or form of the triangle which is immutable and eternal, and not invented by me or dependent on my mind. (CSM II, 44–45)

In contrast to things invented by us, true and immutable natures are something our cognition tracks : we can examine them, focus on them in our thoughts, and discover surprising non-trivial truths about them. The difference between mere inventions and genuine thought is not formal in nature: on the logical surface, thinking of a triangle (a plane figure enclosed by three straight lines) seems to be no different from thinking of a biangle (a plane figure enclosed by two straight lines). However, in the Euclidean context the latter is not anything that one can genuinely think about — it is impossible, a mere chimera, a non-thing — whereas the former is something that geometers have been working on for centuries; it has, one could say, non-trivial and consistent structural depth. To capture this difference a more metaphysically robust notion of reality is needed. In thinking of a triangle, as opposed to a biangle, what my thought latches onto is an underlying reality, a nature or essence “outside my thought.”

Here Descartes draws on a broadly Aristotelian view of essence as, in Carriero’s (2016, 135) terms, “a thing’s intelligible structure” — as a bridge between the world and human cognition, something capable of existing in the thing determining what the thing is, but also in the mind as that which the mind grasps when it has a true idea of something. To put it more technically, the very same reality, essence, is capable of having objective being in the mind, and formal or actual being in the world.9

In the Aristotelian tradition, there is a close connection between the notions of reality and perfection. The basic point is that not any true predication picks out something real: indeed, to be an ingredient of reality is to be something positive, a perfection, in contrast to mere negations or privations.10 This line of thought remains central also to Descartes: for instance, in stating his causal principle of cognition he relies precisely on the idea that “what is more perfect — that is, contains in itself more reality — cannot arise from what is less perfect” (CSM II, 28).

Taking geometry as the starting-point further indicates that the realm of things with intelligible structures is wider than the one of actually existing things — as Descartes himself emphasizes. This makes it plausible to see essences as eternal and independent of actual temporal existence of (created) things. At this point, Descartes’s readers have traditionally lamented the fact that he remains mostly silent about the ontological status of true and immutable natures. A central worry has been that such eternal and abstract natures have no place in Descartes’s ontology that builds on the notions of substance, principal attribute, and mode.

Yet, as Carriero (2009, 313–14) notes, this may not be a fundamental lacuna in Descartes’s discussion concerning true and immutable natures. In claiming that these natures are “not nothing but something,” he is not concerned with their ontological status, but their reality, which is a metaphysical feature distinct from any ontological status.11 For instance, that there is a true and immutable nature of the triangle depends neither on actually existing triangles, nor on a Platonic idea of a triangle existing in a special realm beyond minds and bodies: the question does not concern the manner such essences exist — in this context, we might say, the quantifier “there is” does not imply any existential commitment.

The question of the reality of mathematics is thus very different from the familiar question of whether the objective truths of mathematics entail the existence of abstract entities that are truth-makers for mathematical propositions. The key idea here differs significantly from those found in modern-day Platonist approaches: while ontologically more cautious, it is in another way richer. The focus is not simply on objectivity and truth, but on structural or explanatory depth, absent from discussions of whether abstract entities exist. Working with a pre-ontological notion of reality, Descartes’s silence about ontological status is exactly what one would expect: the claim about the reality of true and immutable natures is not a claim about their ontological status.

4.2 Essence and reality-dependence

The Cartesian context obviously diverges from the Leibnizian one: Descartes is setting the stage for his second proof of the existence of God, using geometrical cognition as the model for understanding the way a thing’s essence allows us to derive further truths about the thing. In contrast, Leibniz thinks that by beginning with the idea of essences, we can obtain a direct argument for God’s existence. “On the Reality of Truth” (1677) offers an early version of this argument, premised on the Cartesian point concerning the independence of geometry from our own thinking. The argument merits close attention:

It is true or rather it is necessary that a circle is the most capacious of isoperimetric shapes, even if no circle actually exists. Likewise if neither I nor anyone else of us exists. Likewise even if none of those things exist which are contingent, or in which no necessity is understood, such as is the visible world and other similar things.

Therefore because this truth does not depend on our thinking, it is necessary that there is something real in it. And because that truth is eternal or necessary, this reality that is in it independent of our thinking will also exist from eternity. This reality is something existing in actuality. For this truth always subsists in actuality objectively [actu a parte rei].12 Therefore a necessary being exists, or one from whose essence there is existence. (A VI.iv, 18/SLT, 181)

The truth that a circle is the most capacious of isoperimetric shapes is independent of the actual existence of any contingent being. Like Descartes, Leibniz concludes from the independence of the truth to its reality. He then takes two further steps: from the reality of the truth about the circle, he infers the eternal objective existence — i.e. existence in an intellect — of that reality. From there he infers the existence of an eternal being, God — and here presumably the thought is that eternal objective existence requires the existence of an eternal intellect.

Leibniz’s argument may seem to run against the distinction we have urged between reality and ontological status or mode of being. It is important to be careful here, however. To begin with, Leibniz asserts that the reality of a truth requires that there is something real “in” it and further that “[t]ruths arise from natures or essences” (A VI.iv, 19/SLT, 182). This suggests that for truths to have reality “in” them is for them to be based on natures or essences; for instance, truths about circles are based on circle nature. In other words, natures or essences are fundamental realities, whereas truths are derivatively real insofar as they contain or are based on natures or essences.

Secondly, Leibniz seems to be working with a traditional view of truth as something that essentially depends on having being in an intellect; on this view (in contrast to the later, Fregean view), truth presupposes an intellective act (or judgment).13 As far as eternal truths are concerned, the intellect on which they depend can only be the divine intellect. This is not to say, however, that we should identify the reality of such truths with their mode of being. The reason why the reality (such as the circle essence) is something “existing in actuality” is that the truth which is based on it — the truth that a circle is the most capacious of all isoperimetric figures — has objective being: it is “because that truth is eternal or necessary” that “this reality that is in it independent of our thinking will also exist from eternity.” This move presupposes a distinction between ontological status and reality. If essences come to acquire objective being in virtue of being “contained in” truths — in virtue of being thought of by God — this arguably requires that essences are real prior to obtaining an ontological status.

This point is crucial for appreciating a subtly different line of argument Leibniz offers from essences to the existence of God. In addition to arguing from eternal truths — and thus from the objective existence of essences or realities — he argues directly from the reality of essences to God as the source of their reality. The idea is that the full metaphysical account of the reality of finite essences must ultimately involve a reference to an actually (indeed necessarily) existing entity, the source of all reality. We shall call this determinative grounding relation between God, or God’s infinite essence, and finite essences reality-dependence . Consider, for example, the following 1689 note:

[T]here must be in reality an existing source of existence-demanding essences; otherwise there will be nothing in essences except a figment of the mind, and since nothing follows from nothing, there will be a perpetual and necessary “nothing.” But this source cannot be anything other than the necessary being, the foundation of essences, the origin of existences, i.e. God […], because all things are in him and come from him[.] (A VI.iv, 1635/SLT, 30–31, emphases added)

Leibniz elaborates this point in “On the Ultimate Origination of Things”:

[A]ll possibles, that is, everything that expresses essence or possible reality, strive with equal right for existence in proportion to the amount of essence or reality or the degree of perfection they contain, for perfection is nothing but the amount of essence. (G VII, 303/AG, 150)

Our concern here is not with the details of Leibniz’s well-known view of essences as striving for existence. For our purposes, the important point is simply that this striving — be its exact nature what may — is a function of the degree of the reality of possibles. This is so because what it is for something to be possible in the first place is for it to “express essence or possible reality” — this is what grounds its very possibility. We take it that this is the background of the contrast he draws between a reality and a figment of the mind. 14 Not unlike Descartes, Leibniz wants to contrast that which is real — a genuine possibility — to something merely invented. At the same time, Leibniz goes beyond the Fifth Meditation, insisting that without a ground in divine reality, we are left with figments of the mind, which renders thinking fundamentally empty.

The argument from the reality of essences to the necessary existence of God is markedly different from the argument from the independence of eternal truths to the existence of God. According to the latter, these truths exist eternally because there must be an eternal being in whose mind they exist objectively. According to the former, it is instead the nature of essences themselves — their explanatory or structural depth — that needs to be explained in terms of God’s essence, in terms of the ens realissimum. This may well be why Leibniz finds it so natural to move from discussing the degrees of reality (or perfection) to quantity of essence: the degrees of reality are in some sense degrees or limitations of God’s essence.

In what follows, we shall attempt to elucidate the reality-dependence of finite essences, possibilia, on God. Already at this point we are, however, in a position to see more clearly how the two main theses relate to each other and why Leibniz in many passages treats them jointly. The omniscient God must have an adequate idea of, and form all the truths about, every possible reality or essence, which means that these realities necessarily have objective being in the divine ideas. The first main thesis thus complements the second.

We can further mitigate the worry that Leibniz’s use of “reality” is ambiguous between ontological and pre-ontological senses. The primary and dominant meaning of the talk of essences as real is pre-ontological: they are endowed with degrees of reality, as limitations of God’s essence, and function as the ground of possibility. Even in passages mainly concerned with the first main thesis we should not read “reality” as denoting an ontological status. To take a notable example, consider the claim to Arnauld that “there is no other reality in the pure possibles than the one they have in the divine understanding” (A II.ii, 51/LA, 73). Arnauld, as we have seen, presses Leibniz on whether his notion of pure possibles commits him to genuine Platonism. This is something that Leibniz denies: pure possibles do not have any existence outside the divine intellect. But this does not mean that we should identify possibles or essences with their mode of being. Leibniz’s formulation is perfectly consistent with a distinction between reality and ontological status. His thesis is that pure possibles are real or realities, but if asked where they “have” this reality — where is this reality located — the answer is merely that it resides in the divine understanding.15

Still, even though the two main theses are complementary, there is nonetheless an order of priority from the second to the first. God has, as Leibniz puts it, “an infallible vision” of all the contingent truths concerning possible creatures. Yet — and this is crucial — he has this vision because he sees “possibles by a consideration of his own nature” (A VI.iv, 1658/AG, 97, emphasis added). In other words, divine ideas of possibilia are based on God’s self-understanding. Not only does Leibniz then subscribe to a traditional view that possibilities are grounded in the divine essence, but his specific way of developing the idea reflects Aquinas’s view that God knows finite essences through considering his own essence.16 To the extent that Leibniz differs from Aquinas, this is not (pace Nachtomy) because he endorses a purely logical conception of modalities. Instead the difference is that for Aquinas the route from God’s essence to individuals goes via genus and species forms (e.g. ST I, q. 15, a. 2, co.), whereas for Leibniz there is a direct path from God’s essence to individual essences. This may be why Leibniz characterizes the relationship of finite essences to God in terms of limitation and not only, as Aquinas does, in terms of participation, imitation, or likeness.

It may be thought that seeing the relationship between God and finite essences in terms of limitation Leibniz runs the risk of coming too close to Spinoza. This worry provides the primary rationale for Newlands’s minimalist reading. According to Newlands (2013, 177), if the grounding of possibilities by God amounts to anything more than just the claim that God thinks of all possibilities, we end up with the view that God must exemplify any possible creaturely property. However, a careful look at Leibniz’s understanding of the nature of the limitation relation shows why he might well have considered such worries misplaced.

5. The nature of limitation

In this section, we aim to explicate the nature of the limitation relation. Thereby we will come to better understand Leibniz’s argument for the claim that finite essences depend upon God’s essence for their reality.

As we saw, even the logical approach acknowledges the importance of the idea that finite essences are in some sense limitations of God, but it is far from clear that it can give an adequate account of what limitation involves. As Sebastian Bender (2016, 140) has shown, mere logical means are insufficient to explicate the limitation relation.17 A finite individual can only either completely lack or completely possess the perfection expressed by some simple concept, depending on whether that simple concept is either denied or affirmed in the complete concept of that individual. Bender’s (2016, 143) own response to this problem is to try to amend the logical approach by adding a pre-logical level to the thought-processes of God: before the combinatorial process begins, God’s intellect produces limited versions of his own attributes. This is a crucial insight, but in our view it should be taken a step further. Without denying the importance of combinatorial ideas in Leibniz’s views concerning the nature of thought, it is actually unclear whether even a metaphysically enriched combinatorics of Bender’s sort is enough to capture the core of Leibniz’s notion of essence.

The logical approach relies on what may be called an aggregative conception of essence, a view of both divine and creaturely essences as ultimately consisting in collections of attributes or perfections. But it is difficult to see how this could be the fundamental story about God’s essence, which is supposed to be simple. Indeed, in some places Leibniz explicitly emphasizes God’s simplicity or unity in characterizing the relationship between finite essences and God, for instance when he famously claims that all things can be analyzed “into God and nothing” (A VI.iv, 158–59/MP, 3). The aggregative view is also unable to capture what is arguably Leibniz’s considered view of the essence of a substance as what he calls a law of the series — that is, as the explanatory ground of various features (or properties) belonging to the substance rather than a mere collection of such features.18

We believe that to make sense of creaturely essences as limitations of God’s essence it is not enough to have a pre-logical level of limited predicates , which are then combined by logical means into finite essences. Rather, we need a pre-logical or pre-combinatorial account of how finite essences themselves directly result from or are limitations of God’s essence. Here we would like to draw attention to an important, but largely neglected, analogy Leibniz uses throughout his career in order to explicate the relationship between the infinite essence of God and finite essences: the reality-dependence of finite essences on the infinite essence is to be considered in significant respects analogical to the relation between space and geometrical figures . 19 A notable example is “De abstracto et concreto” (1688), where Leibniz elaborates the analogy in an attempt to dispel the worry that he risks ending up in Spinozism:

[A]s all the reality of creatures is in God, it seems to follow that all creatures are in God. But […] the reality of creatures is not that which is absolutely in God but that which is limited, which in fact forms the essence of the creature. This can be illustrated with the image of space and a body: the extension of space and that of a creature [i.e. a body] differ in that the extension of space is in itself absolute, unbounded, indivisible, without any change[.] […] In contrast, the extension of a body is limited with respect to all of its modes. (A VI.iv, 990)20

Leibniz’s use of the analogy should not come as a surprise. There can hardly be any doubt that he was familiar with the suggestion that thinking about the way in which infinite extension gives rise to geometrical figures can help us to understand how God’s essence is related to finite creaturely essences: after all, this idea was prominent among his contemporaries, especially Spinoza and Malebranche. 21 Leibniz even explicitly defends the latter’s claim that God is “being in general” by saying that by this Malebranche “did not understand a vague and indeterminate being, but absolute being, which differs from particular limited beings as absolute and boundless space differs from a circle or a square” ( RML , 481/ W , 556).

Admittedly, one could complain that what Leibniz offers us is just an analogy, a model. At the same time, it is also a very intuitive model of some of the key features of Leibniz’s view of divine and finite essences and their relationship. Space in itself is to be conceived of as infinite, unified, and indivisible. As the ground of the possibility of an unlimited number of geometrical figures, it is — prima facie paradoxically — both in an important sense simple and infinitely abundant. The abundance means that everything geometrically possible is contained in the infinite space in the sense of being constructible in it, which is about delimiting the space rather than adding something to it. For instance, a triangle can be produced because the Euclidian space can be delimited by devising three intersecting lines, and this construction procedure fixes the essence of a triangle from which all its properties follow.

In this way, the geometrical model allows us to take seriously the idea that the infinite essence, conceived of as unitary and simple, can be the source of a multitude of finite essences via a process describable as limitation — the idea that finite essences can be analyzed “into God and nothing.”22 Moreover, the products of this process, finite figures, are not conceived of as collections of features, but rather are determined by a construction procedure from which other properties follow, i.e. something close to the conception of essence as the law of the series.

The analogy also throws light on why the question concerning reality-dependence is so important to Leibniz — why he thinks that the nature of finite essences needs to be explained via the essence of God. This involves what can be called the unity of geometry. Not only must there be a single grounding space for the whole variety of geometrical objects — or one space for one geometry, as we might prefer to say, knowing that there are many possible geometries — but all geometrical objects are thoroughly interconnected: they all must conform to the constraints, principles, or laws of the single space. Conversely, we may say that precisely because they display such a deep interconnectedness, all geometrical figures are of the single space. The geometrical model thus makes it natural to infer from the interconnectedness of essences to a common source of their reality, or as Leibniz says, the reality of both essences and existences “can be sought in but one source, because of the interconnection among all of these things” (G VII, 305/AG, 152).

Leibniz’s claim that essences as limitations have different degrees of reality, where this is understood as having an “amount of essence or reality” (G VII, 303/AG, 150), is easily read as suggesting a scalar picture of the metaphysical hierarchy, where each finite essence corresponds to some quantum of God’s essence. Yet the geometrical analogy offers a more sophisticated way of understanding metaphysical “density.”23 In geometry we do not equally focus on all possible geometrical figures: interesting theorems can be proven of such things as circles and triangles, but there are also endless varieties of shapes of which there is little to be said. The significance we attribute to circles and triangles has arguably to do with the fact that they simply are more important as geometrical objects, revealing, or expressing, more of the nature of space than some other objects, and as such they have a higher degree of reality or contain a greater “amount” of the essence of space.

How then does the analogy help with the worry that if “all the reality of creatures is in God” then “creatures are in God”? We think that, for Leibniz, being the ultimate source of the reality of geometric figures does not endanger the infinite nature of space itself: something finite and limited is possible by virtue of space, but this does not take anything from space — space as such does not become limited or diminished. This also suggests that it is not so clear (pace Newlands) that a more robust form of grounding of possibilities in God means that God must exemplify possible creaturely properties. The possibility of, for instance, triangular figures certainly does not require that the infinite space exemplifies triangularity. Still, the infinite space is what grounds the possibility of triangularity. Although this leaves leeway for interpretation, the analogy clearly shows how something infinitely rich can ground the possibility of an endless variety of finite things without itself exemplifying their properties.

6. Creation and the nature of actual existence

We have argued for the need to distinguish two kinds of dependence of finite things on God. The fundamental one (expressed by the second main thesis) is reality-dependence, the dependence of finite essences on the infinite essence of God. The other one (expressed by the first main thesis) is the dependence of finite essences on God’s understanding, that is, on divine ideas, which gives us an account of the ontological status of essences regardless of whether they are actualized or not.

There is of course a further way in which finite things depend on God: creatures must be created, they could not actually exist without the necessarily existing infinite being having “produced” them. It is important to note that this type of ontological dependence of creatures on God — the way creatures depend for their existence on God — presupposes the reality-dependence of finite essences on God. There could not be actually existing creatures without prior finite individual essences, because divine creation is not blind: God must have something from which to choose what to create.

The priority of reality-dependence deeply affects the way in which we understand the nature of creation. If we regard the realm of essences as merely conceptual (or representational), we are naturally led to a conception of that realm as in need of some kind of activation by God, or as Nachtomy puts it: “[A]ctualization requires that a unique and well-defined course of action, corresponding to a possible individual, be given power to act and thereby make it actual” (2007, 132).24 In this picture, actual existence has the following meaning: to actually exist is to be an essence to which power or agency is added, which turns an abstract essence into an agent.

Yet such a reading sits ill with textual evidence. Take, for example, the two central Leibnizian notions, the law of the series and primitive force. On the representationalist approach, the law belongs to the abstract level, the primitive force to the concrete. However, Leibniz himself instead identifies the law of the series with the primitive force: “The essence of substances consists in the primitive force of action, or in the law of the sequence of changes” (A VI.3, 326/L, 155, emphasis added).25 Indeed, it is the universe itself — the collection of substances — that God brings out of possibility, as Leibniz insists in a letter to Clarke: “properly speaking, there is but one decree for the whole universe, whereby God resolved to bring it out of possibility into existence” (G VII, 407/LC, 78).26

Nachtomy (2007, 129) holds that such passages involve confusion. But in our view, there is nothing problematic here: the absence of a distinction between an abstract level of essences and a concrete level of actuality is just what one should expect. Recall that the notion of the reality of essences is not to be seen as an attempt to characterize their ontological status, for reality derived from the infinite essence is what constitutes a finite essence as something possible that can have any ontological status in the first place. In actualizing a finite essence, God does not consider and compare mere conceptual complexes. God considers possible substances — realities or essences — he is about to create, akin to the way for Descartes the triangle itself is in our minds when we perceive or think about it (CSM II, 44–45). In creating one of the possible worlds God does not add some new feature (e.g. power) to essences, but gives them a new ontological status. One and the same reality is first a mere possible substance and after creation an actually existent substance.

In a remarkable passage Leibniz inquires how possibilia differ from actual existents. He begins by claiming that “an existent is an entity, i.e. a possible, and something else,” which may at first sight suggest a view of actualization as involving adding something to an essence. Consider, however, what he says next:

“[E]xistent” is what would please some mind, and would not displease another more powerful mind, if minds of any kind were assumed to exist. So […] there is said to “exist” that which would not displease the most powerful mind, if it should be assumed that a most powerful mind exists. (A VI.iv, 763/P, 65–66)

Not unsurprisingly, many have found mysterious the claim that existence consists in pleasing God. It is tempting to assume that God’s actualization of an essence must follow from the fact that the essence pleases God. But Leibniz no doubt finds our common sense way of thinking about willing to do something and then doing it inapplicable to God. However the exact details are to be worked out, one benefit of trying to take literally Leibniz’s claim is that it throws light on what a change in ontological status amounts to. To say that existence is about pleasing God is simply a figurative way of saying that the actualization of a finite essence consists in its coming to stand in a completely new relation to God, rather than in its acquiring some new feature .

One virtue of adopting such a relational interpretation of actualization is that it allows Leibniz to fend off the charge according to which he endorses an equivocal notion of existence. Bertrand Russell (1900, 174) famously argues that in formulating the ontological argument for God’s existence, Leibniz holds that existence is a perfection and thus included in the divine essence. In contrast, in the case of creatures existence is a second-order notion: a created substance exists when its individual concept is instantiated. Yet, on the relational interpretation, fundamentally the same notion of existence is applicable both to creatures and to God. For both, existence can be seen as a status of essences that depends on standing in a special kind of relation to God.27 The difference is that in God’s case nothing beyond the infinite essence is needed: because the divine essence is in some sense self-related (pleasing to itself, as it were), it necessarily exists by itself. In contrast, the existence of creatures requires that they are related to God and thus to something beyond their own essences.

7. Conclusion

The idea that creaturely essences have their metaphysical location in the divine understanding is part and parcel of well-established Western philosophical theology. This thesis plays an important role in Leibniz as well. In this paper, we have emphasized that Leibnizian essences are not merely conceptual or representational items residing in the divine mind but rather possible individual substances.

In order to understand Leibniz’s position we must carefully distinguish between questions concerning, on the one hand, ontological status, and, on the other, reality. The requirement of reality has to do with the fact that the ground of possibility cannot be understood in purely logical or formal terms; instead, it must be understood metaphysically. Essences have reality prior to God’s ideas of them, and their reality is derived from the unlimited reality of the infinite essence. On this view, essences are realities that acquire objective being in God’s understanding. To say that the reality of essences is prior to God’s ideas of them does not thus alter the view of Leibniz’s basic ontological stance toward finite essences — it does not commit him to robust Platonism. Even though their reality is prior to God’s ideas, only the ontological status of having objective being in the divine mind pertains to essences as possibilia. In creation, it is the ontological status of essences that changes into actual existence. Thereby we can make sense of an intriguing, but lamentably often overlooked, aspect of Leibniz’s theory of creation: the idea that one and the same thing is first a mere possibility but after creation an actually existent substance.28

Notes

  1. When available we cite English translations, although we have occasionally modified them.
  2. “Finite” is to be understood in contrast to God’s absolute infinity (though there are other ways in which also created things can be infinite, see Antognazza 2015).
  3. Cf. G VI, 613/AG, 218; G VI, 602/AG, 210.
  4. The general distinction between questions concerning the ground of possibility and those concerning the ontological status of possibilia is helpfully stated by Mondadori (2014). However, he problematically ignores the difference between ontological status and reality (see Sections 3 and 4 below).
  5. Mondadori even denies that, for Leibniz, possibility has any ground in God’s essence (2014, 231; cf. 2000, 217–20). This is implausible given many passages (rightly highlighted by Nachtomy) in which Leibniz connects primitive or simple concepts to divine attributes (e.g. A VI.iv, 590/AG, 26).
  6. See Nachtomy 2002, 32. Cf. Mates 1986, 76.
  7. What then about the modal status of the divine essence itself? Leibniz does not, as far as we are aware, explicitly address this issue. One option is to view the necessity of God’s essence as an ungrounded modal fact. Another option — perhaps more in the spirit of Leibniz’s overall position — is that the necessity of the divine essence is self-grounded, just as necessary existence was traditionally supposed to follow from God’s essence itself.
  8. Some medieval thinkers, such as Duns Scotus, held a purely logical view of modalities, rejecting any foundation in the divine essence (Mondadori 2016, 231). In our view, Leibniz does not agree with Scotus (pace Nachtomy and Mondadori).
  9. On the importance of the notion of sameness of reality or essence to Descartes’s account of cognition, see also Myrdal and Repo 2019.
  10. Carriero 2009, 140.
  11. Cf. Adams (2007, 102–3), although our claim about reality is stronger than his: attributing reality to a thing is prior to any attribution of ontological status, either actual existence (i.e. formal being) or objective being.
  12. “A parte rei” has the general meaning of “in reality.” Yet Leibniz goes onto explain that what he has in mind here is specifically objective being: “a parte rei seu ut vocant objectivae” (A VI.iv, 19), as Lloyd Strickland notes (SLT, 209n3).
  13. On traditional debates concerning bearers of truth, judgment, and predication, see Nuchelmans 1983. Although Leibniz often endorses the intellective act view of truth (A VI.iv, 1394; cf. A VI.iv, 528), some commentators have argued that his considered position comes closer to Frege’s (see, e.g. Barth 2020). Without entering into this complex issue, notice that a Fregean reading makes Leibniz’s claim that eternal truths have being in the divine intellect harder to motivate.
  14. Our reading of this passage differs from Mondadori’s (2014, 219–20). The problem is that he completely overlooks the way in which Leibniz ties possibility to expressing reality.
  15. Cf. Theodicy, §184, where Leibniz says that the divine understanding “gives reality to the eternal truths” (G VI, 226–27/H, 243–44). In related contexts he uses the Latin realisentur, best translated as “realized” in the sense of being given a mode of existence (e.g. G VII, 305/AG, 150).
  16. Another important thinker in this tradition is Henry of Ghent. In contrast to Aquinas, Henry (following Avicenna) holds that the way in which finite essences depend on God involves their having reality of their own, an esse essentiae (see Wippel 1984, 173–84). The details of this disagreement are complex, and it is not clear to us whether Leibniz’s position comes closer to Aquinas’s or Henry’s.
  17. Adams (1994, 116–18) briefly raises a similar concern.
  18. See, e.g. A VI.3, 326/L, 155; G IV, 512/AG, 162–63. Even Nachtomy (2007, 69–71) acknowledges the difficulties in reconciling the notion of law of the series with a purely combinatorial picture.
  19. Bender (2016, 142) uses the analogy in reformulating Nachtomy’s combinatorial approach. We instead take the analogy to offer an alternative to a combinatorial view of the relation of finite essences to God.
  20. In a 1702 note, Leibniz explains how substantial forms or primitive entelechies “result from the divine perfections through limitation as figure from unlimited space” (VE, 2657). Cf. A VI.iii, 519/DSR, 77.
  21. For Spinoza, see Ethics II, proposition 8; for Malebranche, see The Search After Truth, Elucidation X. For discussion on geometry and Spinoza’s ontology, see Viljanen 2018 and 2020.
  22. In illustrating the idea of an analysis into “God and nothing,” Leibniz usually appeals to the way all numbers can be represented in the binary system, as just series of ones and zeros (A VI, iv, 158–59; A I.xv, 560). We think that the geometrical model offers a more concrete way of fleshing out the same point.
  23. Cf. Wippel’s (1984, 180) notion of “ontological density.”
  24. See also Look 2005, 40. Although Newlands’s version of representationalism differs from this, he too needs to sharply distinguish between the objective level of contents and actually existing creatures.
  25. Cf. G IV, 512/AG, 162–63; A VI.iv, 1667/AG, 102.
  26. See also A VI.iv, 1667/AG, 102.
  27. Our proposal is one way of developing Adams’s (1994, 163) suggestion that for Leibniz “existence must be connected with the essence of the necessary being, not primarily as a part of the essence, but by virtue of a second-order, and probably holistic, property of the essence.”
  28. We are especially grateful to John Carriero for invaluable comments on several drafts. We would also like to thank the two anonymous reviewers for their encouraging and useful reports, which helped to improve the final version. Finally, we would like to acknowledge that our work on this article has been financially supported by the Emil Aaltonen Foundation and (in Myrdal’s case) the Turku Institute for Advanced Studies (TIAS).

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