Spinoza on composition and priority (PENULTIMATE DRAFT)1 Ghislain Guigon Spinoza held that there is only one possible substance, God or Nature, and that this unique substance is an extended one. By doing so he departed from the Cartesian doctrine according to which God is not extended because God is simple and indivisible while no extended thing is mereologically simple.2 Spinoza was aware that his Cartesian fellows would challenge his attributing extension to God. So he addressed this challenge by arguing, in the demonstrations and scholia that immediately precede and follow his affirmation of Substance Monism, that no substance is divisible and that the extended substance, in particular, is mereologically simple.3 1 I would like to thank Jonathan Schaffer whose work and encouragement motivated this chapter. This work also benefited greatly from comments by Andrew Arlig, Richard Glauser, Philip Goff, Jessica Leech, Christiaan Remmelzwaal, and Gonzalo RodriguezPereyra; I thank them all. 2 Principles I: 23. 'Principles I: 23' refers to article 23 of part I of Descartes's Principles of Philosophy. 3 Substance Monism is affirmed in E Ip14d. Spinoza's reply to the Cartesian challenge to Substance Monism is displayed in E Ip15s and relies on his demonstrations of the indivisibility of substances offered in E Ip12d, E Ip13d, and E Ip13s. Thus I agree with Curley (1985: 422) and others that Descartes is the opponent Spinoza is targeting at in E Ip15s and that Wolfson's (1962: 262-295) argument to the contrary is unconvincing. Unless otherwise marked, all references to the Ethics [E] and the early works of Spinoza are to Curley 1985. In reference to letters of Spinoza, I have used the Unabridged R.H.M. Elwes Translation. The arrangement of letters is as found in the Opera Posthuma while numbers in parenthesis are as arranged in Van Vloten's edition. I use the following standard abbreviations for Spinoza's works: KV = Short Treatise on God, Man, and His Well-Being = Short Treatise; Ep. = Letters; PP = Parts I and II of Descartes' Principles of Philosophy; CM = Appendix Containing Metaphysical Thoughts = Metaphysical Thoughts; E = Ethics. Passages from the Ethics will be referred to by means of the following standard abbreviations: initial Latin numerals stand for part numbers; 'a' for 'axiom'; 'c' for 'corollary'; 'p' for 'proposition'; 's' for 'scholium'; 'd' stands for either 'definition' (when it appears immediately to the right of the part of the book), or 'demonstration' (in all other cases); 'pos' stands for 'postulate', and 'l' for lemma. Hence, 'E Ip14d' refers to the demonstration of proposition 14 of part I of the Ethics, and 'E Ip15s' refers to the scholium of proposition 15 of part I of the Ethics. 2 But scholars have found Spinoza's answer to the Cartesian challenge to Substance Monism inconsistent with passages wherein Spinoza talks of Nature as if it were composed of parts. In this chapter, I shall argue that Spinoza has a consistent view on composition. Given the importance Spinoza attached to the Cartesian challenge to Substance Monism, my interpretation of Spinoza's discourse on composition should shed some new light on Substance Monism itself. Working out what view on composition Spinoza held is not just a matter of interest for historians of philosophy. In a series of articles,4 Jonathan Schaffer has defended Priority Monism-the thesis that the most comprehensive concrete thing (the cosmos) is more basic than any of its proper parts- against Existence Monism-the thesis that there is exactly one concrete thing-and Priority Pluralism-the thesis that the cosmos's proper parts are more basic than the cosmos itself. In these articles, Schaffer argues that authors in the monistic tradition are better interpreted as Priority than as Existence Monists. In this chapter, I shall give evidence that Spinoza's Monism is neither an Existence nor a Priority Monism. For in according to Spinoza's Monism, (i) there is exactly one basic concrete thing, (ii) there are many less basic concrete things, and (iii) parts are more basic than the whole they compose. If the conjunction of (i) and (ii) is incompatible with both Existence Monism and Priority Pluralism, the conjunction of (ii) and (iii) is incompatible with Priority Monism. So the insight of this chapter goes beyond history of philosophy. For it shows that the contemporary debate among monists in fundamental metaphysics is not exhausted by the debate between Existence and Priority Monists. There is room for a third kind of Monism, which is a Substance Monism. In section 1 I argue that Spinoza agrees that there are many concrete things though there is only one fundamental concrete thing. In section 2 I argue that Spinoza's view is that the fundamental concrete thing, the extended substance, is mereologically simple. However, this interpretation of Spinoza faces two challenges that I shall explore: a puzzle about the occurrence of composition in extended reality, and a puzzle about substantial simplicity. Sections 3 and 4 provide conceptual tools that will allow me to address these two challenges in sections 5 and 6: section 3 introduces Spinoza's threefold distinction between kinds of composition and section 4 is a study of Spinoza's doctrine about beings of reason. 4 See in particular Schaffer 2008 and Schaffer 2010. 3 1. Preliminaries I start with an introduction to various Monist and Pluralist theses; then I will display fundamental claims of Spinoza's prime philosophy. These claims will allow me to settle precisely the disagreements between Substance Monism and other forms of Monism. In particular, they shall allow me to contend that what Substance and Priority Monists disagree about is the mereology of the concrete world. The remainder of this article, which develops an original interpretation of Spinoza's discourse on composition, can be understood as a defence of this contention. 1.1 Monisms and Pluralisms Existence Monism (EM) is the thesis that there is exactly one concrete thing, the cosmos or Nature (Schaffer 2010). Existence Monism is opposed to Existence Pluralism (EP) according to which there are many concrete things. So what Existence Monists and Existence Pluralists disagree about is the cardinality of the concrete world. We should distinguish between two forms of Priority Monism, a weak and a strong one, which are both distinct from EM. Weak Priority Monism (WPM), on the one hand, is the thesis that there is exactly one basic, fundamental, concrete thing (where, for any x, x is a basic concrete thing if and only if no concrete thing is ontologically prior to x). WPM is opposed to Weak Priority Pluralism (WPP), which is the claim that there are several basic concrete things. So what Weak Priority Monists and Weak Priority Pluralists disagree about is the cardinality of the basic concrete world. If there is exactly one concrete thing, there is exactly one basic concrete thing. So EM entails WPM. However, WPM is consistent with EP. On the other hand, Strong Priority Monism (SPM) is the thesis that (i) every concrete thing distinct from the cosmos or Nature is a proper part of it and (ii) the whole is prior to each of its proper parts. Since SPM is not committed to the existence of several concrete things, it is compatible with EM. Moreover, SPM entails that there is exactly one basic concrete thing, namely the cosmos or Nature. So SPM entails WPM. However, WPM does not entail SPM since a Weak Priority Monist might deny that Nature is a composite whole whose parts are the less basic concrete things. SPM is opposed to Strong Priority Pluralism (SPP), namely the view that (i) every concrete thing 4 distinct from the cosmos or Nature is a proper part of it and (ii) proper parts are prior to the whole they compose. SPP entails WPP only on the further assumption that EP is true. For SPP is compatible with EM which entails WPM. So what Strong Priority Monists and Strong Priority Pluralists disagree about is the direction of the priority relation among parts and whole. So far I have distinguished three forms of Monism. Which of these three corresponds to Schaffer's Priority Monism? Schaffer's (2010) definition of Priority Monism is the following (where the quantifier is restricted to actual concrete things): (PM) (∃!x) Bx & Bu which means that there is exactly one basic concrete object, u, which is defined as the thing all actual concrete objects are parts of. Schaffer's Priority Monism is a Strong Priority Monism about the actual world. So, given that Schaffer does not distinguish between the strong and the weak forms of Monism that I introduced, I shall reserve the label "Priority Monism" (and cognates) for the strong version of Priority Monism. Schaffer suggests that Spinoza is better interpreted as a Priority Monist than as an Existence Monist because of his apparent commitment to concrete parts of Nature in his letter Ep. 15(32) to Oldenburg: A third main thread in the monistic tradition is that of the world as an integrated system. Arguably the seed of this idea can be found in what Spinoza wrote to Oldenburg: "Concerning whole and parts, I consider things as parts of some whole insofar as the nature of the one so adapts itself to the nature of the other that so far as possible they are in harmony with one another" (1994, 82-3). And thus: "[E]ach body, in so far as it exists modified in a certain way, must be considered as a part of the whole universe, must agree with the whole to which it belongs, and must cohere with the remaining bodies" (1994, 84) [...] The idea of the cosmos as an integrated system is incompatible with Existence Monism. For Existence Monism denies that there is anything other than the cosmos. Hence it denies that there are any things to be integrated into the cosmos. Thus any historical monist who claims that the cosmos is an integrated system is committed to the existence of the parts, as what are integrated in the whole. (Schaffer this volume) 5 I agree with Schaffer that Spinoza is not an Existence Monist since he maintains that there are several bodies. However, Spinoza's discourse of bodies as being parts of the universe in this passage is a mere figure of speech and does not commit him to Priority Monism, or so I shall argue in this chapter. Considering the varieties of Monism and Pluralism I have introduced so far, I shall interpret Spinoza as agreeing with EP and WPM but as denying both SPM and SPP. This is a coherent view if according to it the many concrete things stand in substance-mode relations but one denies that modes of substances are component parts of substances. This view is Spinoza's Substance Monism. In the next preliminary I shall explain why I believe that Spinoza agrees with both EP and WPM. My argument for the claim that Spinoza rejects both SPM and SPP is the core of this chapter. 1.2 Substance and modes According to Spinoza, there are two categories of extended beings: extended substances and modes of extension. Likewise, there are two categories of thinking beings: thinking substances and modes of thinking. A substance is defined as "what is in itself and is conceived through itself, i.e. that whose concept does not require the concept of another thing, from which it must be formed" (E Id3). Substances have attributes, which are defined as "what the intellect perceives of a substance, as constituting its essence" (E Id4). Thus extension is an attribute of extended substances and thought is an attribute of thinking substances. Finally, modes are understood as "the affections of a substance, or that which is in another through which it is also conceived" (E Id5). Modes of extension are of two kinds. First, there are bodies (E IId1), which are extended in space and time-and thus are concrete, according to our contemporary use of 'concrete'. Bodies are finite, have a determinate existence, and are regularly called "individuals" by Spinoza (E IId7, E IIp13a2''). Second, there are affections of bodies (E IIId3) that should be understood as extended modes of extended modes of extended substances, i.e. second-order modes of extension. Modes of thinking are of various kinds: ideas of objects, affections of minds that are ideas of affections of bodies (E IIId3), but also beings of reason and mere fictitious beings. Ideas of objects are the basic modes of thinking because any further mode of thinking depends on an idea of an 6 object (E IIa3). The networks of modes of extension and of these modes of thinking that are ideas are causally isomorphic (E IIp7d).5 Modes that stand in correspondence in parallel networks are identical to one another (E IIp7s). So there are various ways substances are affected. But while there are so many modes, there is only one substance, God or Nature, which is an extended and thinking substance (E Ip14). Every mode, then, is either a mode of the unique substance or a mode of a mode of the substance conceived through a certain attribute. The main thesis about the relationship between substances and modes is introduced as the first proposition of the Ethics: substances are prior in nature to their modes (E Ip1). This proposition, which, Spinoza claims, directly follows from his definitions of substance and mode, plays a central role in Spinoza's account of the mereology of the concrete world that I will display in the next section. Therefore, admitting that extended individuals are concrete, there are many concrete things in Spinoza's system: Nature-the unique extended substance-and bodies-first-order modes of Nature. Hence Spinoza agrees with EP and denies EM. Since only one of these concrete things is a substance and since any other concrete thing is a mode of this extended substance, it directly follows from E Ip1 that there is exactly one basic concrete thing: Nature. So Spinoza agrees with WPM. But is Spinoza a Priority Monist? If there is exactly one basic concrete thing and if bodies are concrete things distinct from the basic concrete thing, then the further assumption that bodies are parts of Nature yields Schaffer's Priority Monism. However, we shall see that Spinoza denies that Nature has any component part. 2. A simple substance The Cartesian challenge to Substance Monism is the following valid argument (reconstructed from Descartes' Principles I: 23 and Spinoza's KV I: 2[18]6 and E Ip15s): 1. God, being perfect, is indivisible and does not consist of parts. 2. The extended substance is divisible and consists of parts. 3. Therefore, God and the extended substance are numerically distinct. 5 This is the so-called thesis of parallelism; see, for instance, Della Rocca 1996, Chapter 2. 6 'KV I: 2[18]' stands for paragraph 18 of chapter 2 of Part I of the Short Treatise. 7 The conclusion of this argument clearly conflicts with the main thesis of Substance Monism, according to which there is exactly one substance. So Spinoza addresses this challenge in many places by rejecting the second premise, i.e. by arguing that no substance is divisible and that Nature, the extended substance, is simple. Spinoza argues that no substance is divisible into parts in the demonstrations and scholia (E Ip12d, E Ip13d, and E Ip13s) that immediately precede the affirmation of Substance Monism in E Ip14.7 These demonstrations appeal to the following claims: • Wholes could neither be nor be conceived without their parts.8 • Each substance is infinite (demonstrated in E Ip8d, and E Ip8s); • Each substance is its own cause (demonstrated in E Ip7d); • No two substances can have an attribute in common (demonstrated in E Ip5d); • Each substance is eternal (demonstrated in E Ip7d). In E Ip15s[IV], Spinoza maintains that his demonstrations of substantial indivisibility (in E Ip12d and E Ip13d) establish that the "supposition that corporeal substance is composed of parts [...] [is] absurd". In other terms, these demonstrations, if sound, establish not only that Nature is indivisible but also that Nature is mereologically simple.9 Indeed, the claim that wholes could neither be nor be conceived without their parts, together with the definition of a substance as an independent and independently conceived being, entails that no substance is composed of substances and, together with the definition of a mode and E Ip1, entails that no substance is composed of modes. Spinoza offers further arguments in favour of the simplicity of God (CM II: 5, Ep. 40(35)), or of the extended substance (KV I: 2[19]-[20]).10 The first argument of KV I: 2[19] appeals to the 7 Spinoza also argues that God is indivisible in Ep. 40(35), IV. This argument is a summary of the arguments of E 1p12d, E Ip13d, and E Ip13s. 8 E Ip12d: "Furthermore, [if the parts of the divided substance will retain the nature of the substance] [...] the whole (by d4 and p10) could both be and be conceived without its parts, which is absurd, as no one will be able to doubt." 9 Notice that, for Spinoza, division, unlike composition, is a process. By dividing a whole into parts, the whole ceases to exist. Division being thus conceived, it is logically possible that some whole is composed of parts and yet indivisible. I am grateful to Jonathan Schaffer for pointing out this possibility. However, Spinoza's view is that substances are both indivisible and simple. 10 In KV I: 2[19]-[20], Spinoza offers no less than three arguments to the conclusion 8 assumption that wholes could neither be nor be conceived without their parts. Moreover, Spinoza's demonstrations of God's simplicity in CM II: 5 and Ep. 40(35) essentially appeal to the equivalent claim that component parts are (CM II: 5), or must be (Ep. 40(35)), prior in nature and knowledge to the whole they compose.11 However, despite his systematic and essential use of the assumption that wholes could neither be nor be conceived without their parts, Spinoza offers no justification in favour of this assumption. Indeed, he declares it "clear through itself" (CM II: 5) and its negation "absurd as no one will be able to doubt" (E Ip12d). Why does Spinoza judge so? Plausibly, his reason for thinking this is that this assumption is in line with the Aristotelian tradition he is familiar with. Aristotle himself seems to be arguing in chapters 10 and 11 of Metaphysics Z that concrete substances (made of matter and form) perish into material parts from which they are constituted as principles, that parts of concrete substances are anterior to their composites, and that the definitions of material parts of concrete substances will occur in the definition of their composite (Heinaman 1997). Boethius (1998: especially 879c) also claims that the whole is posterior to its parts, a claim assumed by medieval thinkers in their demonstrations of God's simplicity (e.g., Anselm Proslogion 18; Aquinas Summa Theologiae I, q. 3, a. 7). Likewise, late medieval thinkers, including William of Ockham (1967-1986: Quaestiones in Librum Quartum Sententiarum, q. 13), John Buridan (2010: 1.13), and Albert of Saxony (1999: in particular Quaestiones in Phys. 1.8), share the view that objects like rivers, houses, and cats are dependent upon their parts.12 So Spinoza's insistent appeal to the claim that parts are, or must be, prior in nature and knowledge to the whole they compose in his demonstrations of substantial simplicity is in line with the Tradition. Given Spinoza's definition of a substance (E Id3), it is impossible that a substance depends on another substance (or is conceived through it). So, Spinoza concludes, parts of a substance cannot be substances themselves since composites can neither exist nor be conceived without their parts. that the extended substance is simple. 11 CM II: 5: "It must be shown, therefore, that God is not something composite [...]. For since it is clear through itself that component parts are prior in nature at least to the thing composed, those substances by whose coalition and union God is composed will necessarily be prior in nature to God himself [...]. But since nothing more absurd than this can be said we conclude that God is not composed of a coalition and union of substances." Ep. 40(35): "II. It [God] must be simple, not made up of parts. For parts must in nature and knowledge be prior to the whole they compose: this could not be the case with regard to that which is eternal." 12 On medieval views about composition and priority I have benefited greatly from Andrew Arlig's forthcoming works 'Nothing other than the parts' and 'Medieval Mereology'. 9 But parts of a substance cannot be modes either. For by E Ip1 substances are prior in nature to their modes, whereas parts are prior to the whole they compose. So neither modes nor substances can be parts of substances, and we must conclude from Spinoza's agreement with the Aristotelian doctrine of the priority of the parts that substances are mereologically simple. Therefore, we have abundant evidence that Spinoza holds the view (i) that parts are or must be prior to the whole they compose13 and (ii) that there is exactly one basic concrete thing, Nature, which is mereologically simple.14 This view conflicts with Schaffer's Priority Monism according to which the basic concrete thing is the thing all actual concrete objects are parts of. For suppose for reductio that there is a thing all actual concrete objects are parts of in Spinoza's Monism. Then, given Spinoza's commitment to the priority of the parts, this composite thing is not a substance and so is not basic. In other terms, Spinoza's Nature is not Schaffer's cosmos and there is nothing like Schaffer's cosmos in the ontology of Substance Monism since there is no composite whole that is also basic. Nevertheless, since Spinoza's Substance Monism entails both EP and WPM, Spinoza is neither an Existence Monist nor a Priority Pluralist. But puzzling passages in Spinoza's writings threaten this interpretation. These passages give rise to two challenges that I shall explore. First, Spinoza's commitment to the view that Nature is mereologically simple motivates his claim that, "part and whole are not true or actual beings but only beings of reason; consequently in Nature there are neither whole nor parts" (KV I: 2[19]).15 This suggests that Spinoza denies that composition occurs in extended, mind-independent, reality. However, on some occasions Spinoza talks as if composition takes place between extended modes. Thus he writes in E IIp13pos1 that, "the human Body is composed of a great many individuals of different natures, each of which is highly composite." But how could the human body be composed of parts if part and whole are beings of reason? 13 See KV I: 2[19], CM II: 5, E Ip12d, Ep. 40(35). 14 See KV I: 2[19]-[20], CM II: 5, E Ip12 and E Ip12d, E Ip13 and E Ip13d, E Ip13c, E Ip13s, E Ip15s, and Ep. 40(35). 15 This is clear from the argumentative structure of KV I: 2[18]-[19]. The Cartesian challenge to Substance Monism is displayed in KV I: 2[18]. KV I: 2[19] is Spinoza's reply to this objection and begins as follows: "To this we reply: 1. That parts and whole are not true or actual beings, but only beings of reason; consequently in Nature there are neither whole nor parts". In a note, Spinoza makes it clear that by "Nature" here he means substantial extension. The remaining of KV I: 2[19] consists in Spinoza's first and second arguments for the simplicity of extension, making clear that these arguments are intended to support the thesis that part and whole are beings of reason. 10 Second, although Spinoza holds that the extended substance is mereologically simple in several writings, we find him talking of God or Nature as being composed of parts on three separate occasions. First, Spinoza writes in KV II: 22[7] that, "[the effect] is so united with [its cause] that together they form a whole" where God is the freest cause of all to which Spinoza is referring here. Then, in Part II of the Ethics Spinoza writes: And if we proceed in this way to infinity, we shall easily conceive that the whole of nature is one Individual, whose parts, i.e., all bodies, vary in infinite ways, without any change of the whole Individual. (E IIp13l7s) Finally, in a letter he writes to Oldenburg: Hence it follows that each body, in so far as it exists as modified in a particular manner, must be considered as a part of the whole universe, as agreeing with the whole, and associated with the remaining parts. [...] But, in respect to substance, I conceive that each part has a more close union with its whole. (Ep. 15(32)) It is even more puzzling that in this letter Spinoza seems to deny what he vigorously affirms elsewhere, namely that parts are prior to the whole they compose: For, as I said in my first letter [...], substance being infinite in its nature, it follows, as I endeavoured to show, that each part belongs to the nature of substance, and, without it, can neither be nor be conceived. (Ep. 15(32)) On the balance of evidence, these texts should not induce us to doubt that Spinoza's official doctrine is that Nature is mereologically simple and that parts are prior to the whole they compose. Still, interpreters of Spinoza's discourse about parthood have to address these challenges. In order to do so, I shall first introduce Spinoza's threefold distinction of kinds of composition and his doctrine of beings of reason. 3. Three kinds of composition Chapter 5 of part II of Spinoza's Metaphysical Thoughts is devoted to the demonstration of God's 11 simplicity. There, Spinoza introduces and distinguishes three kinds of composition. I shall introduce labels for these three kinds of composition. Then, paying attention to which kind of composition is involved in which context, I will be able to solve the difficulties met at the end of the last section. First, some preliminary remarks about the interpretation of CM II: 5 are required. CM is the appendix of Spinoza's Exposition in the geometrical manner of Descartes' Principles of Philosophy. Spinoza offers in PP an axiomatic presentation of theses that are demonstrated by Descartes in the first and second parts of his masterpiece, whereas he offers in CM original demonstrations of theses that are endorsed without demonstration by Descartes. The result is that in CM Spinoza often asserts statements he disagrees with in order to demonstrate Cartesian theses. There is little doubt that Spinoza sees the threefold distinction between kinds of composition that is displayed in CM II: 5 as presupposed by Descartes' metaphysics. For he claims there that this distinction directly follows from Descartes' three kinds of distinction: real, modal, and of reason. However, that Spinoza conceives of the threefold distinction of kinds of composition as being presupposed by Descartes' philosophy does not mean that he would deny this distinction. And while there is no textual evidence that Spinoza disagrees with it, there are good reasons to believe that Spinoza endorses it. For Spinoza agrees with Descartes that beings are divided into substance and mode and he thinks that admitting this division of beings yields Descartes' three kinds of distinction. So by transitivity the threefold distinction between kinds of composition is derived from the division of beings into substance and modes Spinoza is committed to. Moreover, assuming that Spinoza agrees with the threefold distinction between kinds of composition provides an adequate account of his discourse about composition in his more original works, as I shall argue in subsequent sections. Spinoza begins his demonstration of God's simplicity in CM II: 5 by reminding us of Descartes' three distinctions: We proceed to the simplicity of God. In order to understand this attribute of God rightly, we need to recall what Descartes has taught (Principles I, 48, 49), viz. that there is nothing in nature but substances and their modes. From this a threefold distinction of things is deduced (I, 60-62), viz. real, modal, and of reason. The real distinction is the distinction by which two substances are distinguished from one another 12 (Principles I: 60). The modal distinction is the one by which different modes of a same substance, on the one hand, and a substance and its modes, on the other hand, are distinguished from one another (Principles I: 61). The third distinction, called distinction of reason, is in Descartes the one by which a substance and its principal attribute are distinguished (Principles I: 62). Spinoza writes that, "From [Descartes'] distinctions, all composition arises" (CM II: 5). Then he distinguishes three kinds of composition on this basis. The first kind of composition, which I shall call substantial composition, is introduced thus: The first sort of composition is that which comes from two or more substances which have the same attribute (e.g., all composition which arises from two or more bodies) or which have different attributes (e.g., man). (CM II: 5) He then claims that "the second [sort of composition]", which I shall call modal composition, "comes from the union of different modes". Finally, about the third kind of composition, which I shall label composition of reason, Spinoza writes that it "does not occur, but is only conceived by the reason as if it occurred, so that the thing may be the more easily understood". So composition is either substantial, modal, or of reason. Spinoza concludes by affirming that, "whatever is not composed in these first two ways should be called simple" (ibid.). Thus, according to this threefold distinction of kinds of composition, only two of them are genuine kinds of composition: substantial composition and modal composition. It should be noticed that as Spinoza is, in CM, demonstrating theses held by Descartes, it is not surprising to find him asserting in this context that substantial composition occurs. For Descartes agrees that composition does occur between bodies, which are substances in his system. However, Spinoza denies that bodies are substances16 and that substantial composition occurs. Indeed, if there is only one substance, if Substance Monism is true, then no substance can be composed of several substances! So, despite the fact that Spinoza describes substantial composition as occurring in the Cartesian context of CM II: 5, it is clear that his own view is that, necessarily, substantial composition never occurs. The distinction of reason is not a distinction that occurs in reality but is merely a product of the mind thinking of two ways of conceiving a single entity as if they were two entities. Likewise, composition of reason does not occur but is merely conceived by reason as if it occurred. For things 16 See section 1.2. 13 that are merely conceived by reason as if they were wholes composed of parts are, strictly speaking, mereologically simple. And just as it is literally false to say of things that are only distinguished by reason that they are numerically distinct, it is literally false to say of a thing that is merely composed by reason that it is a composite. Nevertheless, according to Spinoza, composition of reason might play some useful theoretical role: it can help us to understand things more easily. So we can talk of simple things as if they had component parts if it helps us, for instance, to understand more easily a difficult philosophical thesis. In contemporary debates between realists and anti-realists, we say that someone is a fictionalist about a region of discourse if she takes all positive statements about this region of discourse to be literally false but nevertheless worth using for some theoretical purpose.17 In this sense, it is not inappropriate to regard Spinoza as a fictionalist about mereology when, and only when, the mereological vocabulary is to be interpreted in terms of composition of reason. If so, careful examination might reveal that, in some contexts at least, Spinoza asserts statements of the form "x is a part of y" because they are useful but without being committed to the truth of these statements. What is at stake there is composition of reason. So, according to Spinoza's distinction between three kinds of composition and given his commitment to Substance Monism, positive mereological claims are literally false when the mereological vocabulary they contain ('part', 'whole', and cognates) is interpreted either in terms of substantial composition or in terms of composition of reason. In the latter case, positive mereological claims can be worth using to play theoretic roles despite their falsity. It remains to be considered whether positive mereological claims can be true when the mereological vocabulary they contain is interpreted in terms of modal composition. But first I have to introduce Spinoza's doctrine about beings of reason. 4. Spinoza's doctrine of beings of reason Spinoza's doctrine of beings of reason is displayed in the first chapter of CM.18 Spinoza's starting 17 In this sense Hartry Field (1989) is a fictionalist about mathematics since he holds that statements committed to the existence of mathematical entities are all false although many of them are very useful. 18 So one may wonder whether the doctrine that is displayed in CM I: 1 is Descartes' or Spinoza's view. The account of beings of reason which is displayed in this text is largely 14 point is a definition of a being as "whatever, when it is clearly and distinctly perceived, we find to exist necessarily, or at least to be able to exist" (CM I: 1 'The definition of Being'). It follows from this definition, Spinoza claims, that beings of reason are not beings but "mere modes of thinking" (ibid. 'Chimaeras, Fictitious Beings, and Beings of reason are not beings'). Mere modes of thinking are modes of thinking that are not ideas. Thus beings of reason are not ideas but are wrongly taken to be ideas because they directly follow from ideas (CM I: 1 'Why beings of reason are not Ideas of things and are nevertheless taken to be ideas'). Since beings of reason are not ideas, "they also have no object that exists necessarily, or can exist" (ibid.). In other words, beings of reason represent neither the extended substance nor any of its modes in the way expressed by the thesis of parallelism (E IIp7). In a slogan: modes of extension are sparse, modes of thinking are abundant. Only ideas correspond to modes of extension. And since beings of reason "cannot be called ideas", they cannot "be said to be true or false, just as love cannot be called true or false, but [only] good or bad" (CM I: 1 'In what sense Beings of reason can be called a mere nothing, and in what sense they can be called real Beings'). The relevant consequence of Spinoza's claim that beings of reason are not ideas is that beings of reason have no real definition but only have stipulative ones. In his letter Ep. 9(27) to Simon De Vries, Spinoza explains that there are two kinds of definition. Definitions of the first kind, which I call real, "ought to be true" and explain things as they are outside the intellect in that these definitions are "concerned solely with the essences of things or their affections". Definitions of the second kind, which I call stipulative, explain things as we conceive, or can conceive, them and "need not [...] be conceived as true" but only need to be conceived. Then Spinoza explains to De Vries that a good definition need not be a real one: If I say that each substance has only one attribute, that is only a proposition and requires a demonstration. But if I say "By substance I understand what consists of one attribute only," that will be a good definition, provided that afterwards beings that of Suárez (1994). But Freudenthal (1887: 108) argues that Suárez is the target of Spinoza when he argues in CM I: 1 that, "many wrongly confound beings of reason with fictitious beings". Since no such attack is to be found in Descartes' writings and since the distinction between beings of reason and fictitious beings is not relevant to the content of Descartes' Principles I and II, there seems to be no reason why Spinoza would ascribe this attack to Descartes. Moreover, the Cartesian Heereboord (1680: 222 and 225) seems to be the target of Spinoza's criticism that, "those who say that a being of reason is not a mere nothing speak improperly". All this indicates that the doctrine of beings of reason that is displayed in CM I: 1 is not Descartes' but Spinoza's doctrine. 15 consisting of more attributes than one are designed by a word other than substance. (Ep. 9(27))19 Spinoza accounts for truth in terms of correspondence: a truth is an affirmation or a denial about something that corresponds to the thing itself, whereas a falsity is an affirmation or denial about something that does not correspond to this thing.20 So if beings of reason are modes of thinking that have no object they can represent, their definitions are not truth-apt because there is nothing to which these definitions can correspond. A fortiori then, if part and whole are beings of reason, then definitions we can offer for "part" and "whole" must be stipulative: definitions that are neither true nor false but can still be good definitions if we regiment our discourse accordingly. If beings of reason are not ideas, what kind of modes of thinking are they? Here is Spinoza's answer: Finally, a Being of reason is nothing but a mode of thinking, which helps us to more easily retain, explain, and imagine the things we have understood. (CM I: 1 'Chimeras, Fictitious Beings, and Beings of reason are no beings') Distinct beings of reason can play distinct cognitive roles. Some beings of reason help us to keep present to our memory what we have understood. Among these we find the modes of genus and species (ibid. 'By what modes of thinking we retain things'). Some beings of reason "serve to explain a thing by determining it through comparison to another" (ibid. 'By what modes of thinking we explain things'). As examples of these beings of reason whose purpose is explanation Spinoza offers time, number, and measure. Finally, some beings of reason help us "to depict in our fantasy images of whatever we understand" and to "imagine nonentities positively, as beings" (ibid. 'By what modes of thinking we imagine things'). So it happens, Spinoza claims, that we imagine, as if they were beings, modes that are used by the mind for negating things: blindness, extremity or limit, term, darkness, etc. (ibid).21 Assuming that part and whole are beings of reason, what is their cognitive purpose? Much evidence 19 Notice that Spinoza denies the proposition that it is impossible for a substance to have more than one attribute; see E Ip9. 20 See KV II: 15[1], CM I: 6, and Spinoza's argument against ghosts in Ep. 60(56). 21 Spinoza is in line with the Aristotelian tradition when he denies that nature is negatively affected and claims that negative affections are mere beings of reason. See Suárez 1994, section 5. 16 indicates that, according to Spinoza, part and whole are beings of reason whose purpose is to help us to more easily imagine things we have understood. First, Spinoza accounts for wholes and composition in terms of agreement in his letter Ep. 15(32) to Oldenburg. But in CM I: 5 he claims that agreement is a "mode of thinking by which we retain or imagine the things themselves more easily". Second, in KV I: 2nd dialogue[9], Spinoza accounts for the claim that part and whole are beings of reason by exhibiting the close similarity between wholes and universals. Yet Spinoza contends that universals are products of our imagination (E IIp40s). But the main evidence is perhaps what Spinoza says in E Ip15s[V]. There, Spinoza claims that the reason why we tend to think of matter as being divisible and composed of parts is because we conceive of it "as it is in the imagination". Therefore, when Spinoza claims that part and whole are beings of reason, his aim is to emphasise that part and whole are not ideas. They are modes of thinking that do not correspond to any mode of extension. For this reason, definitions of mereological vocabulary are stipulative instead of real ones. Nevertheless, mereological discourse may play an important cognitive role, which is to help us imagine things. 5. Modal composition and beings of reason Spinoza claims that part and whole are beings of reason. His reason appears to be his belief that Nature is mereologically simple. We have been puzzled by the fact that Spinoza's claim that part and whole are not true beings but only beings of reason seems prima facie incompatible with passages in which Spinoza seems to assert that composition occurs in extended beings. However, the displayed elucidation of Spinoza's notion of a being of reason shows that there is no inconsistency in maintaining both that part and whole are beings of reason and that composition can occur in extended reality. In particular, modes of extension can compose further modes of extension. Consider blindness. According to Spinoza, who follows Suárez on this point, blindness is like every negative mode of thinking a mere being of reason. Obviously, this does not mean that Spinoza, a specialist of optic, denies that there are blind people. So what does it mean? Spinoza would probably admit the following definition of a blind person: a blind person is a person who lacks visual perception due to physiological factors. We can regard this as a good definition of a blind 17 person according to which there are blind people. Nevertheless, for Spinoza this definition of a blind person is stipulative. For blindness being a being of reason definitions of "blindness" cannot be truth-apt. In other words, the offered definition is stipulative because no mode of extension parallels the mode of thinking that is absence of visual perception due to physiological factors. There is no such mode of extension because every mode of extension is positive. This is what Spinoza means when saying that blindness, and in general negative modes of thinking, are beings of reason. By contrast, the positive mode of having visual perception is an extended mode of human bodies: a second-order mode of extension. So, according to the stipulative definition of blindness, blindness occurs in human bodies whenever people fail to have, for physiological reasons, the extended mode of having visual perception. Since it is an objective and determinate fact that some people fail to have this mode of extension, it is literally and objectively true that some people are blind. Therefore, according to the displayed account of Spinoza's doctrine about beings of reason, there is no inconsistency between the claim that blindness occurs in bodies, which are modes of extension, and the claim that blindness is a being of reason.22 Now Spinoza's view is that blindness, part, and whole are modes of thinking of the very same category: they are beings of reason whose purpose is to help us to more easily imagine things we have understood. So if propositions of the form "x is blind" can be literally true even though blindness is such a being of reason, a fortiori propositions of the forms "x and y compose a whole" and "y is a composite whole" can be literally true even if part and whole are beings of reason. So suppose that one stipulates that, for any extended x and y, x and y compose a whole if and only if x and y are affected in a particular given way. Then it turns out to be literally true that x and y compose a whole if they are affected in this particular given way. So, as for blindness, there is no inconsistency between the claim that composition occurs in modes of extension and the claim that part and whole are beings of reason. Modal composition is the kind of composition that occurs between modes. Hence, the claim that part and whole are beings of reason is consistent with the claim that modal composition occurs in extension. And so is solved the first puzzle about parthood that I introduced at the end of section 2: Spinoza's postulate that "the human Body is composed of a great many individuals of different natures, each of which is highly composite" does not conflict with the claim that part and whole are mere beings of reason. 22 This view should be compared with the treatment of negative predications in sparse theories of properties. For instance, Armstrong (1978: 23-9) endorses a sparse view of properties according to which there are no negative properties. But there are true negative predications, of course. So things truly can truly satisfy a negative predicate to which no property corresponds when they lack the corresponding property. 18 We have abundant evidence that Spinoza believes both that modal composition occurs and that part and whole are beings of reason. In chapter 2 of part I of KV, Spinoza both claims that part and whole are not true or actual beings but beings of reason (KV I: 2[19]) and that composition never occurs in the substance but always and only in the modes (KV I: 2[21]-[22]). This suggests that Spinoza does not take these two claims to be contradictory and that he believes that modal composition occurs. The content of the fifth scholium following E Ip15 also indicates that, according to Spinoza, composition occurs between modes of extension. There Spinoza distinguishes two ways of conceiving of matter. We can, he says, "conceive of it as it is in the imagination", and in this case it will be found finite, divisible, and composed of parts. But we can also conceive of matter as it is in the intellect, in which case matter is found to be infinite, indivisible, and simple. Then Spinoza illustrates this claim by adding the following: Parts are distinguished in [matter] only insofar as we conceive matter to be affected in different ways, so that its parts are distinguished only modally, but not really. For example, we conceive that water is divided and its parts separated from one another- insofar as it is water, but not insofar as it is corporeal substance. For, insofar as it is substance, it is neither separated nor divided. (E Ip15s[V]) Spinoza's appeal to the modal distinction in relation to imagination in this passage makes it clear that he relates modal composition to our faculty of imagination. But the main evidence that Spinoza agrees that modal composition occurs in extended modes is his definition of a composite body in the Ethics: Definition: When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon another, or if they so move, whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or Individual, which is distinguished from the others by this union of bodies. (E IIp13a2") This definition provides meaning to the postulate that, "the human Body is composed of a great many individuals of different natures, each of which is highly composite" (E IIp13pos1). If my 19 understanding of Spinoza's doctrine of beings of reason is correct, then this definition of a composite body must be stipulative. Indeed, what Spinoza does in this definition is to introduce new theoretical terms. For he is explaining how he will thereafter use the phrases "union of bodies" and "individual composed of parts". Now Spinoza believes that, sometimes, bodies lie upon one another or move in such a way that they communicate their motions in the relevant fixed manner. So, given Spinoza's definition of a composite body, the concrete world is such that, sometimes, bodies unite so as to form a composite body. And so for Spinoza some propositions of the forms "x is a part of y" and "y is a composite whole" are literally and objectively true. Such propositions are literally true when being a part of and being a composite whole are understood in terms of modal composition and when bodies satisfy the stipulative definition of an individual composed of parts. Spinoza's definitions of the union of modes and of a composite individual in E IIp13a2'' are similar to the definitions he couched in less precise terms in his letter to Oldenburg: By the association of parts, then, I merely mean that the laws or nature of one part adapt themselves to the laws or nature of another part, so as to cause the least possible inconsistency. As to the whole and the parts, I mean that a given number of things are parts of a whole, in so far as the nature of each of them is adapted to the nature of the rest, so that they all, as far as possible, agree together. On the other hand, in so far as they do not agree, each of them forms, in our mind, a separate idea, and is to that extent considered as a whole, not as a part. (Ep. 15(32)) It is plausible to think that what Spinoza describes here as the adaptation of the laws of parts to the laws of other parts is what he described in the Ethics as bodies communicating their motions to each other in a certain fixed manner. And so it is plausible to think that what Spinoza calls "the association of parts" is what he calls the "union of bodies" in the Ethics. It should be noticed that immediately before he defines the association of parts in Ep. 15(32), Spinoza writes: I will premise that I do not attribute to nature either beauty or deformity, order or confusion. Only in relation to our imagination can things be called beautiful or deformed, ordered or confused. Yet, in CM I: 5, Spinoza claims that order is a mode of thinking by which we either retain or 20 imagine things we have understood. Likewise, in the Appendix [III.] of E I, Spinoza argues that order is a mode of imagining. Plausibly, there cannot be any adaptation between the laws of bodies, if the extended world is devoid of order. So Spinoza's premise to his definition of the association of parts shows that he is assuming in his letter to Oldenburg that part and whole are beings of reason by which we imagine things. Therefore, Spinoza agrees that modal composition occurs between bodies, which are modes of extension, despite his commitment to the view that part and whole are beings of reason, and it is consistent for him to do so. 6. The challenge to substantial simplicity Spinoza has been busy arguing that Nature is mereologically simple on the basis of the principle that parts are or must be prior to the whole they compose. Yet on two occasions he claims that Nature is composed of parts that are bodies (in E IIp13l7 and Ep. 15(32)). And on one of these occasions (Ep. 15(32)) he also claims that parts of the substance can neither be nor be conceived without the whole they compose. Does Spinoza contradict himself about substantial simplicity and the priority of the parts? I shall argue on the basis of his threefold distinction between kinds of composition that Spinoza's discourse about composition and priority is thoroughly consistent. So far I have argued that Spinoza's claim that part and whole are beings of reason is consistent with the view that composition occurs in the modes of the extended substance. Also I have argued that Spinoza makes use of mereological discourse to describe affections of extended modes: for instance, in his definitions of the union of modes and of a composite individual in E IIp13a2''. This does not mean, however, that each time Spinoza makes use of mereological discourse he should be taken at face value. The correct understanding of Spinoza is, I think, the following. Whether the definition of the union of bodies (E IIp13a2"), or of the association of parts (Ep. 15(32)), captures a kind of composition that occurs in concrete reality depends on the domain of individuals on which we apply this definition. If we apply it on a domain of finite individuals, the definition captures the modal kind of composition that comes from the union of bodies. But if our imagination keeps applying this definition to an infinite being, then what we do is merely conceive of a simple being as if it were a 21 composite one. In other words, when applied to an infinite entity, our stipulative definition of the union of bodies no longer captures the kind of composition I called modal, but only captures composition of reason. For infinite beings are incapable of being divided and composed of parts as Spinoza repeatedly argues in KV I: 2[19]-[20], E Ip12d, E Ip13d, and the whole scholium of E Ip15. There is no direct textual evidence that Spinoza is talking of composition of reason in passages where he claims that God forms a whole with its effects (KV I: 2nd dialogue[3]), that "if we proceed to infinity, we shall easily conceive that the whole of nature is an Individual" having parts (E IIp13l7), and that we ought to conceive each body as a part of the extended substance without which they can neither be nor be conceived (Ep. 15(32)). Nevertheless, there are some clues, and Spinoza's demonstrations of Nature's simplicity and his distinction between three kinds of composition show that we can, and I think that we ought to, interpret him as talking of composition of reason in these puzzling passages. According to Spinoza, a substance is prior in nature and knowledge to its modes (E Ip1). So Nature, the extended substance, is prior in nature and knowledge to bodies, which are first-order modes of extension. Thus bodies can neither be nor be conceived without Nature. If so it is not surprising that, when Spinoza allows himself to describe the substance-mode relation between Nature and bodies in mereological terms in Ep. 15(32), he maintains that Nature-described as "the whole"-is prior in nature and knowledge to bodies-described as "parts". The question is: Is the kind of composition that arises between Nature and bodies a kind of composition that occurs? The answer must be negative. We have seen that Spinoza denies that substantial composition occurs.23 And we have seen him affirming that no mode can be a component part of a substance.24 Therefore, whenever modes compose anything, the thing they compose must itself be a mode. So the kind of composition that arises between Nature and bodies is neither substantial nor modal composition. In other words, the composition of Nature by bodies must be a composition of reason. Furthermore, we have seen that when Spinoza argues that Nature or God is simple and not divisible, he does so by appealing with insistence both to the infinity of Nature and to the principle that parts are prior to the whole they compose. So it would be absurd for Spinoza to maintain thereafter that Nature is not simple even though it is infinite and prior to its modes. If Spinoza had changed his mind regarding the simplicity of Nature, he should also, given his arguments for substantial 23 See section 2 and section 3. 24 See section 2. 22 simplicity and indivisibility, have changed his mind regarding the infinity of the substance and the priority of the substance. But Ep. 15(32) shows that Spinoza did not change his mind on the latter issues. So there is no good reason to think that he changed his mind on Nature's simplicity.25 However, if it is true that Spinoza's talk of Nature as if composed of bodies is to be interpreted in terms of composition of reason, then Spinoza must have some theoretical reason to talk of a simple thing as if it were a composite one. For we have seen (section 3) that the purpose of composition of reason is merely to help us to understand things more easily. So what is it that Spinoza wants us to understand more easily when he talks of Nature as if it were a composite? Of course, we can only speculate as to what Spinoza's intentions were; still there are some clues. When he claims in KV that God forms a whole with its effects, Spinoza's purpose is to help us to understand that God is an immanent cause instead of a transitive one. For in this text Spinoza always uses this metaphor in addition to arguments for the view that causation is immanent.26 And indeed the image of God forming a whole with its effects provides a powerful means to illustrate the idea of an immanent cause. But it is a mere figure. What is Spinoza's purpose when he claims, in the Ethics, that if we proceed in this way to infinity, then we shall easily conceive that the whole of nature is one individual having parts that are affected in many ways without any change in its form? I think that his purpose here is to help us to understand more easily the iterative character of his definition of a composite individual. For, immediately before making this claim in E IIp13l7, he writes that if we take two arbitrary individuals and form from them a third one according to his definition of a composite individual, we should see that the composite individual has the characteristic feature of being affected in many ways without any change in its form. So the phrase "if we proceed in this way to infinity" plays the role of an "and so on to infinity": no matter how complex individuals are, any composite individual has this characteristic feature of being affected in many ways without any change in its form. In any case, Spinoza does not contend in E IIp13l7 that we have to proceed in this way to infinity. So, in the Ethics, Spinoza never affirms that the substance is composed of parts. 25 Notice also that Ep. 40(35), in which Spinoza asserts that God is simple because parts must in nature and knowledge be prior to the whole they compose, is posterior to Ep. 15(32). So if Spinoza has changed his mind on this issue, it is in favour of the simplicity of the substance. 26 In KV I: 2nd dialogue[3], and in KV II: 22[7]. 23 It is for the same purpose that Spinoza allows himself to talk as if Nature were composed of bodies in his letter to Oldenburg. For he begins there to illustrate his definition of the association of parts to the composition of the blood and goes on to more and more complex individuals so as to emphasise the iterative character of his definition. However, in this text Spinoza contends that we ought to conceive each body as being a part of the infinite substance. Why does he claim this? Here is my attempt of an explanation. The opening paragraph of Ep. 15(32) shows that Spinoza's remarks on composition in this letter are introduced to answer a question asked by Oldenburg: You ask me my opinion on the question raised concerning our knowledge of the means, whereby each part of nature agrees with its whole, and the manner in which it is associated with the remaining parts. (Ep. 15(32)) The view that Nature is composed of parts is common among the founders of the Royal Society. Then it is not surprising that Oldenburg, secretary of the Royal Society, asks his question in mereological terms. So presumably Spinoza talks of the extended substance as if it were composed of parts in this letter simply because Oldenburg's question is formulated in these terms. Strictly speaking, bodies are modes, not parts, of Nature since there is only one substance and since modes of a substance are not parts of a substance. So when Spinoza claims that each body ought to be conceived as a part of the infinite substance, he aims to claim that each body ought to be conceived as a mode of the infinite substance. But Spinoza might have thought, with reason, that talking of bodies in terms of modes of Nature would make his answer to Oldenburg's question more difficult to understand and perhaps less convincing.27 So he allowed himself to answer it without entering into irrelevant peculiarities of his monistic doctrine. In other words, he allowed himself to talk of bodies as if they were parts of Nature so as to make his answer more easily understandable to his reader. This is the purpose and nature of composition of reason. If I am right that Spinoza's talk of the substance as if it were composed of bodies is to be interpreted in terms of composition of reason, then there is no inconsistency between his commitment to the view that Nature is mereologically simple and his sparse talk of Nature as having bodies for parts. For use of composition of reason is non-committal. It allows us to talk of a simple entity as if it were composed of parts, if we need to, for cognitive or theoretical purposes. 27 It should be noticed that Spinoza concludes his answer to Oldenburg's question by writing, "I am afraid that I may have mistaken your meaning, and given an answer to a different question from that which you asked" (Ep. 15(32)). 24 7. Conclusion Spinoza holds that Nature is mereologically simple because it is absolutely infinite and prior to any other concrete being. Since he denies mereological complexity to Nature, he maintains that parts and whole are beings of reason, so that neither "part" nor "whole" has a real definition. Still he allows himself to introduce stipulative definitions of composite individuals in such a way that, according to his doctrine, composition occurs in the concrete modes of Nature. However, applying these stipulative definitions to an infinite being results in a kind of composition that is merely of reason: a kind of composition that does not occur but that we can conceive of as if it occurred for theoretical reasons, i.e. to help us to understand more easily difficult issues. According to the interpretation of Spinoza I have displayed in this article, Spinoza is not a Priority Monist, nor is he an Existence Monist or a Priority Pluralist. He is not an Existence Monist because he agrees that there are many concrete, extended, individuals: Nature and bodies, which are modes of Nature. Of course, Spinoza is committed to the thesis that I called Weak Priority Monism given that, according to him, there is exactly one basic concrete thing, namely Nature. But Spinoza's Nature is not Schaffer's cosmos as the former is mereologically simple while the latter is composed of parts. Since Spinoza commits himself to the Aristotelian principle that parts must be prior to the whole they compose, he would have been a Priority Pluralist if he had endorsed the view that each body is a component part of Nature. But since Spinoza denies that Nature has any component part, he is neither a Priority Pluralist nor a Priority Monist. Therefore, Spinoza's Monism is neither an Existence nor a Priority Monism. It is a Substance Monism, a Monism according to which there is a unique simple substance modified in an infinite variety of ways. References Albert of Saxony. 1999. 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