3.1 Mereological fictionalism

Why be a fictionalist about composition? Consider the fact that for all we know, mereological nihilism may be true, so it may be the case that strictly speaking nothing composes anything. Or maybe we will never be able to make up our minds about the metaphysics of mereological composition. Should we rid ourselves of thinking and talking about parts and wholes? We might do so when the philosophical stakes are high, but otherwise it is hard to let go of the convenience of everyday talk about parts and wholes. There is an urge to explain the appeal of ordinary mereological talk even if we are convinced of a counterintuitive account such as nihilism; and even in light of possibly unsolvable metaphysical debates. This is the point where fictionalism may start to look promising.

Rosen and Dorr provide an illuminating example that is worth quoting at length here:

When the chemist says that a water molecule is made of two atoms of hydrogen and one of oxygen, he does not take himself to be speaking figuratively. If you ask him whether his claim is meant to express the sober truth, he may well say, ‘Yes, of course; this is serious business.’ Nonetheless, apprised of [the disputes on the metaphysics of composition] he may be inclined to back off from his confident claim about composition. If he is canny he may say, ‘I’m not sure whether what I said is strictly true. But what I am sure of is this: what I said was true on the assumption that composite things such as molecules exist.’ (2007: 169)

As Rosen and Dorr put it, mereological fictionalism conveys pretense with linguistic operators such as ‘according to the fiction of mereology’ or ‘on the assumption that composition occurs’. Notice that the operators are supposed to be tacit in most cases, but we can always make them explicit in order to clarify why we take mereological propositions to be true, even though they may be literally false. Consider the following pair:

1. A water molecule is composed of two atoms of hydrogen and one of oxygen.

2. On the assumption that chemical bonding is sufficient for composition, a water molecule is composed of two atoms of hydrogen and one of oxygen.

1 and 2 are clearly independent from each other: if chemical bonding is not sufficient for composition, 1 is false while 2 remains true. In principle, we could introduce any operator of the form ‘on the assumption that …’. However, the appeal of fictionalism is that it accommodates the pretensions that are related to our interests. So, for example, the truth of 2 from above is not entirely due to its mereological assumption, as it is also contingent on the fact that there is a chemical bond between the atoms.²¹

Notice that this is not entirely different from our attitudes towards figurative speech in general. Rosen and Dorr give the following example for contrast:

Consider the mariner who knows full well that Copernicus was right. When he is navigating he speaks and thinks in Ptolemaic terms. In the midst of a storm, when things are urgent, he may have no conscious reservations about what he says or thinks. Nonetheless, when he says ‘If Venus has crossed the moon, we’re off course’ he is not committed to its truth. His official view, his genuine view, is that Copernicus was right and that his Ptolemaic remark is a useful fiction. (Rosen and Dorr 2007: 170)

So, even if we are convinced that composition never occurs, it makes life easier to assume a sort of folk-mereology according to which chemical bonding is sufficient for composition—just as it is often more practical to pretend that Venus is crossing the moon, even if we know all well that Copernicus was right. After all, we may agree in the case of the chemist that the relevant chemical structure is there, even if we disagree about whether it really is a case of mereological composition.

3.2 Beings of reason

The closest Spinoza gets to contemporary fictionalism is his rich discussion of beings of reason: universals, relations, numbers, shapes, negative properties, etc., are all treated as a being of reason at some point. However, in contrast to contemporary fictionalists, Spinoza retains the medieval terminology of ‘beings of reason’ that stresses the cognitive function of the target discourse as opposed to its usefulness in ordinary language. Perhaps this is most explicit in the CM, where he defines beings of reason as ‘nothing but a mode of thinking, which helps us to more easily retain, explain, and imagine the things we have understood’ (CM 1.1/I:233). For example, consider Spinoza’s treatment of privation (see Ep.21/IV:128; CM 1.1/I:234): the predicate of being ‘blind’ is a privative predicate (i.e., ‘lack of sight’), and in Spinoza’s view it merely conveys our comparisons between people who can see and people with positive features so distributed that they lack the ability of sight.

In addition, it is worth noting that Spinoza distinguishes between the terms ‘fiction’ and ‘being of reason’ (see CM 1.1/I:236): On the one hand, fictional entities are completely invented and their only connection to reality is that people think about them. For example, fictional entities are the likes of the legendary fountain of youth or characters such as Pantagruel. On the other hand, beings of reason are abstract representations of something real, and we rely on these abstract representations in order to perform cognitive tasks.²² As such, paradigmatic beings of reason are mathematical representations of ordinary objects. For example, consider simple geometrical representations of billiard balls that take them to be a prefect spheres in Euclidean space to make it easier to calculate where to hit them for a particular effect. In light of this, Spinoza’s account of beings of reason has more similarities to idealizations in scientific modeling than to fictionalism. That is, while contemporary fictionalism may be understood as prioritizing ordinary language—albeit not independently of its cognitive utility—Spinoza seems to put full emphasis on the cognitive utility of certain abstract ways of thinking.²³

Spinoza seems to make a direct connection between being in error and relying on beings of reason while one is making a case for a certain metaphysical view. One may even argue that for Spinoza, the reification of certain beings of reason is the most severe philosophical error one can ever fall into.²⁴ Consider the following:

We see, therefore, that all the notions by which ordinary people are accustomed to explain nature are only modes of imagining, and do not indicate the nature of anything, only the constitution of the imagination. And because they have names, as if they were of beings existing outside the imagination, I call them beings, not of reason, but of imagination. So all the arguments in which people try to use such notions against us can easily be warded off. (E1app/II:83, emphasis added)²⁵

Let’s stop for a second to assess the main idea here. Somewhat unsurprisingly for a keen rationalist, Spinoza maintains that sense-perception is the only possible source of error (see 2p41). And ‘imagination’ is a technical term that he uses to characterize sense perception and everything else that depends on sense perception in some way or another—for example, memories of sense perception, abstractions from sense perception (including fictional entities), and so on (see, e.g., 2p40s2). The point about names here is nothing new; Spinoza often insists that the nouns we use in ordinary language do not have a one-to-one correspondence with the things that exist in reality:

since words are part of the imagination, i.e., since we feign many concepts, in accordance with the random composition of words in the memory from some disposition of the body, it is not to be doubted that words, as much as the imagination, can be the cause of many and great errors, unless we are very wary of them. (TIE 88/II:33, emphasis added)²⁶

Consider fictional entities: according to Spinoza, the name ‘Pantagruel’ only corresponds to a mental representation and not to a flesh and bone scholarly giant. And Spinoza has a similar attitude towards entities in general that feature in our sense perception, since our mental representations leave it open whether there is anything real that they correspond to. We should resist making metaphysical conclusions about entities just on the basis of having a piece of language that singles them out.²⁷

However, this is not to say that attending to sense perception necessarily leads to epistemic error: Spinoza is clear that he thinks that imagination cannot lead us astray if we are aware of the epistemic status of the representational content of sense-perception. And so Spinoza insists that we are not in error just by, for example, imagining that the sun is 200 feet away from earth, granted that we may be aware that it merely looks as if it is 200 feet away (2p35s; 4p1s). Similarly, we are not in error when we read a fictional novel, given that we do not take it to be an account of events that actually happened.

Remember that we briefly touched upon how Spinoza applies this idea to composition in §2. I would like to put forward another quote here which neatly summarizes his diagnosis that composition belongs to abstract thinking:

If someone should ask now why we are … so inclined to divide quantity, I shall answer that we conceive quantity in two ways, abstractly or superficially, as we imagine it, or as substance, which is done by the intellect alone. So if we attend to quantity as it is in the imagination, which we do often and more easily, it will be found to be finite, divisible, and composed of parts; if we attend to it as it is in the intellect … it will be found to be infinite, unique, and indivisible. (1p15s)²⁸

Clearly, the problem is not that we imagine that some extended thing is composed of parts. This is something we cannot help, since this is just how our sense perception works. So, the point is that even if we can distinguish parts of extension in imagination, this in itself is not sufficient to conclude that these parts are different extended substances. And if we are able to rationally perceive the nature of extension, assuming that Spinoza’s arguments are successful, extended things do not have a part-whole structure.²⁹

My assessment of the evidence so far doesn’t take into account a specific interpretive problem that Spinoza’s discussion of beings of reason presents to his readers. The problem is that after Spinoza repudiates a discourse, he often attempts to reclaim the terms that he diagnoses as beings of reason by introducing new deflationary definitions for them.³⁰ It seems that at least part of Spinoza’s intention in doing this is to make his points accessible, or to explain cognitive life from a human standpoint; but unfortunately this move often backfires since he does not always flag the intended sense of the relevant terms afterwards.³¹ In what follows, I will discuss this issue focusing on Spinoza’s treatment of mereological discourse.

3.3 Perspectivalism

Spinoza dedicates almost an entire letter (Ep.32) to explaining his account of mode-composition. In this letter, he famously invokes a thought-experiment involving a ‘worm in the blood’: according to Spinoza, our everyday experience is comparable to the experience of a microscopic worm living in a bloodstream that encounters microscopic cells. From the worm’s perspective, the cells are separate wholes. But from a different perspective the whole bloodstream may just look like one integrated system with no distinguishable internal structure. By analogy, we may be able to distinguish ordinary objects around us, whereas they are really not all that different from a wider point of view. This is how Spinoza summarizes the takeaway:

I consider things as parts of some whole to the extent [eatenus] that the nature of the one adapts itself to that of the other so that they agree with one another as far as possible. But insofar as [quatenus] they disagree with one another, to that extent [eatenus] each forms in our Mind an idea distinct from the others, and therefore it is considered as a whole and not as a part. (Ep.32/IV:170a–1a, emphasis added)

A natural reading of this passage suggests that Spinoza here treats ‘being a part’ and ‘being a whole’ as a matter of degrees: some objects disagree with each other to some extent and so we represent them as distinct objects in our minds. But these different objects also get represented as parts of a larger whole to the extent that they are in some relative agreement from a different perspective.³² In this sense, the more similar the objects are, the more reason we have to consider them as parts; and the more dissimilar they are, the more reason to consider them as wholes. This account allows for flexibility, since we may adopt different perspectives and our judgments about composition will follow along.³³

There is also a crucial detail about the ‘nature’ of things adapting to each other. Let me unpack this idea with a concrete example: consider Peter helping Paul move his sofa. We may recognize that Peter, Paul, and the sofa exercise relatively dissimilar patterns of motion. To this extent, each of them should be taken to be a whole object on its own. However, Peter and Paul, and to some extent the sofa, work together, so we should also recognize that they have to be able to coordinate and adapt to each other’s patterns of motion. The more similar they become as a result, the more they can be represented as a part of a whole composed by these three individual patterns of motion. But if we zoom in, so to say, we will find out that all of them are in fact just collections of smaller things acting together, much in the same way as Peter and Paul coordinate their motions. And we can also zoom out and adopt wider and wider points of view: we can take their immediate environment into consideration, or other humans performing similar tasks. What is more, the city, the continent, etc., are all exercising some unified pattern of motion that Peter and Paul are parts of. And as we saw in §2, this mental exercise terminates in a representation of the whole of nature as an integrated system of coordinated action.³⁴

Let’s revisit Spinoza’s most direct discussion of mode-composition in the Ethics:

if a number of Individuals so concur in one action that together they are all the cause of one effect, I consider them all, to that extent [eatenus], as one singular thing. (2d7, emphasis added)

When a number of bodies … communicate their motions to each other in a certain fixed manner, we shall say that [dicemus] 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. (2p13sd/II:99–100, emphasis added)

In light of the above, I suggest that these definitions introduce terms that convey comparisons between modes in terms of their joint causal activity from a particular perspective: if some modes act together, then they are becoming more and more similar, and this means that to some extent we can abstractly represent them as having a part/whole structure. This is comparable to the case of the chemist from above. Recall that the chemist tacitly assumes that chemical bonding is sufficient for composition in order to illustrate the structure of a water molecule. Since, for all we know, facts about chemical structure don’t rely on facts about mereological composition, the chemist’s tacit assumption doesn’t make a difference to the point that he is trying to convey by claiming that two oxygen atoms and a hydrogen atom compose water. Similarly, Spinoza considers modes as composing an object because from a limited perspective we may recognize that they are similar to some extent when they act in unison, which is true independently of whether this is really a case of composition.

One may wonder whether adopting perspectivalism about composition means that Spinoza considered the individuals themselves to be abstractions. One may even worry that perspectivalism is yet another way to tacitly attribute acosmism to Spinoza, thereby undermining any plausible motivation for Spinoza to write the Ethics. For example, if there are no individuals, we don’t exist either, so why should we bother with understanding the nature of our affects in order to overcome suffering that isn’t even real in the first place?

Even though I don’t think we should reject acosmist readings just on the basis that it raises these issues for Spinoza’s philosophical project concerning finite entities, it is important to alleviate these worries if possible. Luckily, in my understanding the perspectivalist reading doesn’t imply acosmism. What perspectivalism does imply, is that the application of mereological idioms to actually existing finite modes essentially involves taking up a limited perspective, because finite modes have no mereological structure—they are neither simples, nor composites—independently of some finite mind taking an attitude towards them. Spinoza defines singular things as ‘things that are finite and have a determinate existence’ (2d7), and not as entities that are essentially composed of finite modes. Now although he adds a clause to this definition that many individuals acting together will be considered as one singular thing, from this it doesn’t follow that the entity in question is not a mode that is better characterized with the help of other, more fundamental idioms of ontological dependence. For example, Spinoza defines modes by using inherence (1d5), and perspectivalism can accommodate the reality of modes related by inherence to both the substance and perhaps to other modes. The same goes for the familiar relations of causation and conception. So, as I understand perspectivalism, it is compatible with claiming that there are finite modes that are in causal relations with other finite modes (1p28); or that there are modes that are conceived through God (1p15). As such, adopting perspectivalism doesn’t imply acosmism because it maintains that modes have their fundamental features independently of some finite mind taking an attitude towards them. On the perspectivalist reading, when Spinoza uses mereological idioms to advance a point concerning finite modes, it is an abstract way of describing a set of more fundamental relations between finite modes while ignoring others.

A related objection could be made that perspectivalism appears to undermine certain aspects of Spinoza’s ethical theory. Consider the following:

It is the part of a wise man … to refresh and restore himself in moderation with pleasant food and drink, with scents, with the beauty of green plants, with decoration, music, sports, the theater, and other things of this kind … For the human Body is composed of a great many parts of different natures, which constantly require new and varied nourishment, so that the whole Body may be equally capable of all the things which can follow from its nature. (4p45s, emphasis added)

On the face of it, the passage says that the powers of the human body depend on the powers of its parts. Nevertheless, a perspectivalist can accommodate this point in the following way: from a certain limited perspective, the powers of the human body can be considered as constituted by the powers of a set of discrete finite modes that are considered as its parts. But this is not to say that the human body really consists of a set of discrete parts, independent of perspective. For example, from a different perspective, the human body, with no regard to its intrinsic structure, can be considered as merely a part of some larger integrated whole, for example when it performs a dance with others, or constitutes a state as one of its citizens (see e.g., 4p18s/II:223). However, at the same time, the human body itself isn’t an abstraction, but a finite mode fundamentally related to the substance and other modes through the familiar Spinozistic relations of inherence, conception, and causation.

There is another important objection that we need to address, especially because this objection makes the tacit assumptions behind realist readings explicit. Here is the objection: if Spinoza analyses mereological terms as functions of causal activity, why can’t he be a reductionist about mode-composition after all? Reductionism in this case means that Spinoza simply identifies parts and wholes with modes coordinating their specific motion and rest.³⁵ So, according to this view, it is literally true that modes are parts of a larger whole just in case they ‘adapt’ to the causal activity of other modes. Let’s also grant that the puzzles I discussed in §2 can be played down in some way or another. For example, we may concede that those puzzles only present a genuine challenge to Spinoza’s theory of infinite modes. But if we bracket those issues for now, it seems that we have a perfectly good reductionist and realist account of mode-composition in the realm of finite modes.

To assess this objection, let’s turn to the account of bodies that Spinoza presents in his Physical Digression after 2p13s. Consider the following:

A body which moves or is at rest must be determined to motion or rest by another body, which has also been determined to motion or rest by another, and that again by another, and so on, to infinity. (2p13sl3)³⁶

Spinoza stresses here that bodies always perform their basic activities—motion and rest—in relation to the causal nexus that encompasses the activities of other bodies. However, there are good reasons to think that pairing this with a reductionist account of composition comes with enormous epistemic costs. This is so because Spinoza holds that in order to cognize causal relations we also need to cognize their grounds:

The cognition of an effect depends on, and involves, the cognition of its cause. (1a4, translation altered)³⁷

So, if the causal activity of a finite mode A is an effect of the causal activity of another finite mode B, then we need to cognize B in order to cognize the causal activity of A.³⁸ However, with regard to 2p13sl3 and 1a4, if our goal is to fully understand that a certain body is in a certain motion, we will need to fully understand an infinite chain of causes. As Spinoza puts it:

every body, insofar as it exists modified in a definite way, must be considered as a part of the whole universe, must agree with its whole and must cohere with the remaining bodies. (Ep.32/173a)³⁹

It is possible now to state the main issue with the reductionist reading that I cashed out above. First of all, it is clear that for Spinoza there is a privileged perspective that encompasses all finite modes together and all their specific causal activities. Spinoza has this in mind when he makes the following statement:

I don’t know how [parts of Nature] really cohere and how each part agrees with its whole. To know that would require knowing the whole of Nature and all of its parts. (Ep.32/IV:170a)

Now to make it clear why this is in tension with a reductionist reading, consider the example of a simple billiard ball rolling. According to the reductionist reading, it is strictly true for Spinoza that the billiard ball is composed of particles that are performing similar causal activities, namely that they are rotating in such a way together that they form the shape of a ball. But let’s consider the situation from a wider perspective: it is apparent that the specific motion of any of these particles come from all sorts of distinct causal influences. And taking this into account, we should rather judge that the particles making up the ball from our initial perspective are not uniquely similar after all. This is so because from this wider perspective the relative similarity between them decreases to a certain degree, while at the same time their similarity increases in relation to all sorts of other things. But this also means that on the reductionist reading our billiard ball is a whole to a much smaller extent. And if we consider the situation from the privileged point of view of 2p13l7s and Ep.32 that takes into account the infinite whole of extended nature, it turns out that the particles making up the billiard ball are even more similar to everything else in the whole of nature. So, adopting the widest possible perspective, the reductionist is committed to claiming only the totality of nature appears to be a whole, while everything else is merely a part.⁴⁰

At this point, one may object on behalf of reductionism by pointing out that it is compatible with acknowledging that the composition relation is gradable in this way. The reductionist may even concede that the particles making up our billiard ball are similar to each other to a much smaller extent than the similarity each of them bears to the rest of nature. However, the objection continues, from this it does not seem to follow that the billiard ball is not a whole. Rather, what follows is that the billiard ball is a whole to a much smaller extent than the whole of nature. But notice that even if this is true, from the widest possible perspective the similarity between any finite set of modes is infinitely smaller than the similarity between all of them. So, on a gradable reductionist account of composition, every finite composite, including our billiard ball, is a whole only to an infinitely small degree. If so, if the reductionist still wants to hold that different degrees of composition are grounded in genuine differences in degrees of causal interaction and similarity, they need a story about how Spinoza can accommodate differences between infinitesimal degrees of composition. And even though giving such an account is perhaps not impossible, facing such possibilities in Ep.12 and 1p15s Spinoza goes to great lengths to point out the importance of distinguishing abstraction from reality.

However, the perspectivalist reading has no such issues, because it does not try to reduce mereological notions to specific causal activities. On the contrary, it acknowledges that the truth of mereological judgments depends on assuming a limited perspective. These limited perspectives are abstractions, since they only take into account internal relations, that is, whatever is intrinsic to the causal activity of objects. In this way, we need not cognize the rest of the universe to recognize the harmonized motions intrinsic to, for example, the parts of a human body, a group of people, or particles in a bloodstream.

Lastly in this section, I will compare the perspectivalist reading to Samuel Newlands’s recent interpretation that takes the above observations seriously. According to Newlands,

Conceived narrowly, a region of motion and rest may contain hundreds of individual finite modes … Conceived more broadly, the region might instead contain just a single composite individual … But this implies that there are hundreds of finite modes in a region conceived one way, and that, conceived another way, there is only one finite mode in that region. (2018: 161)

Newlands doesn’t advance a perspectivalist reading since the core idea of his interpretation is that the so-called broad conception of things is not epistemically privileged (see, e.g., Newlands 2018: 155–60). On this reading, we don’t end up committing error just by taking up a limited perspective, and so we can make various seemingly contradictory judgments about composition that are all strictly true depending on the standpoint from which we are evaluating them. As such, Newlands defends a realist and reductionist view about composition that takes each ‘narrow conception’—that is, each particular limited perspective—to have the same epistemic status as the broad conception. It is beyond the scope of this paper to do full justice to Newlands’s interpretation of Spinoza’s mereology, as it is a part of a systematic account of Spinoza’s whole metaphysical project. Nevertheless, in my reading, Spinoza takes the narrow perspectives to have a lesser epistemic status.⁴¹ In what follows, I briefly explore an alternative account—with an admitted focus on Spinoza’s mereological views only—according to which the broader perspective is privileged, even though the narrow, lesser kinds of perspectives may ground useful abstractions.

3.4 Perspectivalism and error

So, how do we avoid falling into error on the perspectivalist interpretation? After all, we may need justification that there are genuine similarities within a perspective which ground Spinoza’s lightweight semantics of mereological terms. Unfortunately neither the Ethics, nor Ep.32 is clear about the details.

One possible clue that I won’t look at in detail is CM 2.5/I:258, where Spinoza discusses things distinguished only by reason. It is unclear whether this line in the CM can be taken as evidence for Spinoza’s own account of composition. The problem is that distinctio rationis in the CM is introduced to explain the distinction between substance and attributes, whereas in the CM Spinoza also maintains the Cartesian line that the parts of extension are really distinct extended substances. This should at least raise suspicion that in the CM Spinoza is discussing a different account of composition than the one in the Ethics.⁴²

Rather, I suggest that Spinoza’s epistemology of ‘common notions’, as it is laid out in the Ethics, may offer a good starting point for an account. According to Spinoza, the common notion of ‘motion and rest’ fundamentally characterizes everything in extension, as anything else they do is reducible to patterns of motion and rest.⁴³ The idea is that it is straightforwardly true that each and every physical body is moving in some way or another:

all bodies agree in that they involve the concept of one and the same attribute (by 2d1), and in that they can move now more slowly, now more quickly, and absolutely, that now they move, now they are at rest. (2p13sl2d)

As such, in case our judgments about composition do not commit us to realism about parts and wholes, they can still be used figuratively to talk about genuine relations of motion and rest. Understood this way, they even express truths with the assumption that coordinated activity from a specific perspective is sufficient for composition.