Hylomorphism Got the Facts Wrong

Home , Hylomorphism, Mereological nihilism

ON HOW PERSPECTIVAL HYLOMORPHISM GOT THE FACTS WRONG

Abstract

This thesis proves the essential relevance of Aristotelian mereology, in particular of its notion of form, within the contemporary debate about ordinary objects. I focus on Sattig’s theory of perspectival hylomorphism (Sattig, 2015) and its analysis of ordinary objects. I criticize the key notion of this theory, namely thAT of K-Path for it entails an unnecessary commitment to the “questionable” category of facts. My criticism of facts, in general, follows Betti (Betti, 2015). I argue that K-Paths as complex facts are not able to perform the role of individual form ascribed to them by Sattig. On the contrary, I suggest that the Aristotelian notion of form is a better fit for Sattig’s novel framework while avoiding the problems deriving from its involvement of facts. Chapter 1 introduces the notion of ordinary objects and outlines several approaches in which ordinary objects have been analyzed. Chapter 2 describes the metaphysical account of Perspectival Hylomorphism, namely Q-hylomorphism, and the notion of K-Path. Chapter 3 deals closely with Aristotle’s hylomorphism and mereology. Moreover, in chapter 3, I offer my own interpretation of Aristotle’s notion of form. Chapter 4 compares the notion of K-Paths with Aristotle's form. It shows that the notion of Aristotle’s form can play the same role as a K-path while avoiding the commitment to facts.

Table of Contents

1 Introduction 3

2 Perspectival Hylomorphism 8

2.1 Q-Hylomorphism 8

2.1.1 Classical Mereology 9

2.1.2 Aristotelian Hylomorphism 17

2.2 K-paths and Complex facts 18

3 Aristotle’s Hylomorphism 24

3.1 Form, Matter, and Compound 25

3.1.1 Form and Matter 26

3.1.2 Compound 29

3.2 Part and Whole 30

3.2.1 Part 31

3.2.2 Whole 33

4 Aristotle’s Forms versus K-Paths 35

4.1 Horizontal and Vertical Unity 37

4.2 Forms and K-Paths 41

4.3 What is a K-path? 46

Conclusion 51

1 Introduction

Ordinary objects, among other things, are part of the furniture of our everyday world. Along with being objects of common use, they have always been highly disputed in philosophical debates, especially in metaphysics. The metaphysical debate about ordinary objects is extremely vast and variegated. For the purpose of this thesis, I focus on what we usually call “things” every day, namely ordinary material objects, e.g. the laptop in front of you, the sandwich you had for lunch, and also you yourself. My metaphysical analysis of ordinary objects is based on a number of assumptions that although are not fully discussed in this work, I shall make them explicit in what follows. First, the existence of objects, and especially of ordinary objects, is here taken for granted. I assume that ordinary objects exist and that they are involved in our everyday life because their existence is exactly what makes them interesting and relevant in metaphysics. Most of the controversial issues about ordinary objects simply evaporate as soon as the existence of ordinary objects is denied, and the debate becomes flat. If there are no objects, then there is no object to be discussed. In particular, I assume that ordinary objects exist and that they have parts. In this thesis, I examine the mereology of ordinary objects, that is how ordinary objects considered as wholes relate to their parts (Korman, 2016; Varzi 2016). Second, when I talk about ordinary objects, I have in mind the category of concrete particulars or, to put it differently, of particular material objects. As in Loux (2006, p.85), concrete particulars are objects with the following features. They are (i) particulars entities that exemplify a number of attributes. In other words, concretes particulars are objects with a given number of properties. Moreover, their existence is limited in time (ii), that is they come into existence, exists and then go out of existence. In addition, concrete particulars are subject to change during their existence (iii), i.e. they can have different (and even incompatible) attributes at different times. Furthermore, concrete particulars are located in a unique region of space at each time of their existence (iv)— i.e. they cannot be in different places at the same time— that makes them individual. Finally, concrete particulars are objects with physical parts that occupy a determined region of space (iv), namely they have material parts. Therefore, in this work, I leave aside other ontological categories, such as abstract objects, universals, events, etc. On the basis of this description of ordinary objects as concrete particulars, my aim is to investigate the mereological composition of these objects, i.e. how they relate to their parts.

In this thesis, I will closely examine a specific theory of ordinary objects, namely Perspectival Hylomorphism (Sattig, 2015). To be precise, I will focus on the metaphysical account of this theory, that of Q-hylomorphism or quasi-hylomorphism. The latter claim that ordinary objects are compound of form and matter — they have a formal and a material part (Sattig, 20015, p.13). As it will become clearer in the next chapter, ordinary objects are described in this way also according to another metaphysical account, that of Aristotle’s hylomorphism. However, Q-hylomorphism characterizes the notion of form in a completely different way Aristotle’s characterization. It maintains that forms are K-paths, namely complex facts about a material object (ibid.). Conversely, I will contend that there is no need to appeal to complex facts and that my interpretation of Aristotle’s notion of form can play exactly the same role. I will argue that Aristotle’s notion of form is to be understood as the relation obtaining among the material parts of an object. Let us take a step back to place in context my argument. I shall give a brief summary of the theories of ordinary objects. Needless to say, this is not an exhaustive overview of all theories of ordinary objects. However, it is useful to outline the broader debate in which the topic of this thesis is placed. At this point, my starting question is: “Is there only the category of ordinary objects?”. There are multiple answers to this question and they branch out into many theories of objects. I will take into account the three most general answers to my question and give an outline of the theories they include. First, conservatism answers positively to my question. According to it, the only category of objects that exists is that of ordinary objects (Korwan, 2016, Sec. 1.1). Ordinary objects are entities that belong to kinds that we ordinarily recognize as being exemplified in our everyday life, e.g. human being, tree, statue (ibid.).This view relies on common sense as it identifies existing objects with ordinary objects that we are familiar with and that we perceive by the senses. Conservatism has been endorsed (among others) by Elder (2004, 2011), Hirsch (2005), Lowe (2007), Markosian ( 008, 2014), Korman (2010), Koslicki (2008), Simons (2006). Second, eliminativism answers negatively to my question “Is there only the category of ordinary objects?”. It claims that there are fewer categories of objects and denies the category of ordinary objects (Korwan, 2016, Sec. 1.2). Eliminativism has many variants and it is usually combined with nihilism, namely the view that there are no composite objects (ibid.). If ordinary objects are conceived as composite objects, i.e. objects that have parts, then eliminativism together with nihilism implies that no ordinary object exists (ibid.). Mereological nihilism is a version of eliminativism that endorses nihilism as it denies the existence of composite objects, but that accepts the existence of simple objects, namely atoms (e.g., Hossack, 2000; Contessa, 2014). This view maintains that what exists are (infinitely) many microscopic objects. By contrast, existence monism argues that there exists only one single object, that includes everything else and that is simple at the same time (e.g., Horgan & Potrč, 2000; Rea 2001). Additionally, there is also a version of eliminativism that denies the existence of objects tout court, namely extreme nihilism (e.g, Turner, 2011). Nonetheless, there

are also versions of nihilism that deny nihilism and agree that there are some objects that are composite. Therefore, while endorsing that there is no category of ordinary objects, this kind of eliminativism accepts that some objects have parts. A well-known version of this view is organicism and it claims that organisms are the only composite objects that exist (e.g. van Inwagen, 1990)(Korwan, 2016, Sec. 1.2). Before moving on to the third possible answer to my question “Is there only the category of ordinary objects?”, I shall make clear on one point. In this thesis, I will leave aside eliminativism for it is not relevant for my purpose. I will examine ordinary objects considered as composite objects, while eliminativism (or the many versions of it) deny their existence. Nevertheless, I summarized eliminativism to show the variety of the theories of objects, and especially to place my thesis in this broader scenario. We shall now give particular attention to the third (and last) answer left as the debate of this work finds its place there. Permissivism denies that there is only the category of ordinary objects and it maintains that there are more categories than the category of ordinary objects (Korman, 2016, Sec.1.3). The idea of permissivism is that ordinary objects are a special class of objects within the wider category of objects, that also includes, for example, abstract objects, material objects, fictional objects, etc. In this thesis, I will examine a permissivist version of hylomorphism. In general, hylomorphism is the metaphysical position that takes ordinary objects to be compounds of form and matter (Rettler, 2017, Sec. 3.2.1; Koslicki 2018, p. 337). In its permissivist version, hylomorphism implies that every category of objects is composed in this way. Therefore, all objects are composed of matter and form, but only some of them are ordinary objects (Sattig, 2015, p.25). Permissivist hylomorphism has two variants depending on how the composition of the object is conceived. Mereological hylomorphism explains composition in mereological terms, that is matter and form are (proper) parts of the objects (e.g., Haslanger, 1994, p.130; Koslicki, 2006, p.717). Proper parts are those parts of the object that are not identical to the whole (Varzi, 2008, p.108). Mereological hylomorphism obeys the principle of extensionality of parthood, i.e. two composite objects are identical if and if they have the same (proper) parts (Varzi 2008, p. 108). Thus, according to this reading of hylomorphism, objects are identical to the sum of its parts. Non-mereological hylomorphism denies that form and matter are parts of the objects (e.g., Johnston, 2006; Marmodoro 2013). There is also a version of permissivist hylomorphism that does not denies that form and matter are parts of objects, while not endorsing the principle of extensionality of parthood (e.g., Baker, 2007; Fine 1999, 2003, 2008) According to the latter, matter and form coincide with the object, although they are not identical to it. In this thesis, I will exclusively take into account mereological hylomorphism. Both Sattig’s Q-hylomorphism and my interpretation of Aristotle’s hylomorphism assume a mereological reading of (quasi-)hylomorphism —that is ordinary objects are compounds that have a formal part and a material part. However, Sattig’s Q-hylomorphism diverges from my interpretation of Aristotle’s hylomorphism for what concerns the nature of form and matter. On

one hand, I endorse that, according to Aristotle, the object’s matter is the object’s material parts, while the object’s form is the relation in which the object’s material parts stand. On the other hand, Sattig claims that the object’s matter is a material object and the object’s form is a complex conjunctive fact about that material object. Now that I have made clear the broader context of this thesis, I shall move on to the discussion of perspectival hylomorphism, Aristotle’s hylomorphism and the comparison between them. What follows is a diagram that illustrates the philosophical context of this thesis.

6 Nihilism Countless microscopic objects arranged -wise

es Y

No No Existence Monism Are there many objects? Are they composite objects? Are they composite

es Y ?

at all

No Extreme Nihilism Are there objects Theory of structure Quasi-hylomorphism Hylomorphism

es es Y Y

Y es No Y (Hylomorphism) Is the form a proper part? Is the form a complex fact? Do they have a matter and a form?

es Y

es es es es Y No No Y Y Y than ordinary ordinary objects? ordinary (Eliminativism) (Permissivism) less (Hylomorphism) only their parts? Mereology) embodiment (Conservatism)

Is the form a relation?

form? (Classical Extensional objects? objects?

Is there Is there more than ordinary Is there more than Do they have a matter and a Are they composite objects? Theory of rigid and variable

Are they identical to the sum of Are there there Are

2 Perspectival Hylomorphism

To narrow down the scope of this thesis, let us see what it is at stake so far. First, there are such things as ordinary objects. Second, these ordinary objects have parts and for this reason, they are characterized by mereological relations, i.e the relations holding between parts and wholes. Third, as we have seen in the previous chapter, a mereological account of ordinary objects is hylomorphism. Although there are different versions of hylomorphism (Marmodoro, 2013; Koslicki, 2008; Johnston, 2006; Fine, 1999; Rea, 1998; Tahko, 2011), they all claim that ordinary objects are compounds of form and matter. In particular, according to mereological hylomorphism, ordinary objects are hylomorphic compounds taken as wholes, whose parts are matter and form (e.g., Haslanger, 1994, p.130; Koslicki, 2006, p.717). So far so good. I here narrowly consider a particular version of mereological hylomorphism, namely p erspectival hylomorphism. This relatively new account view on ordinary objects has been proposed by Thomas Sattig in his book The Double Life Of Objects (Sattig, 2015). As it is clear from the title, Sattig argues that ordinary objects have a double-layered life because they are compounds of matter and form (Sattig, 2015, p.1). Moreover, both form and matter of ordinary objects offer two different perspectives or ways in which it is possible to talk about the same ordinary object (ibid.). Perspectival hylomorphism has two parts: a metaphysical position, that is quasi-hylomorphism (hereafter Q-hylomorphism), and the semantic for this metaphysics, that is perspectivalism (Sattig, 2015, p. vii). My criticism of perspectival hylomorphism does not concern its semantics, but its metaphysics. Therefore, here Sattig’ s perspectivalism will be left aside, while I will discuss his quasi-hylomorphism. The metaphysical view that is endorsed by Sattig includes an arguable notion of form, as we shall see later (2.2). A detailed picture of q-hylomorphism will provide a useful background for the comparison between Sattig and Aristotle in the later chapters. This chapter is structured as follows. First, I discuss two philosophical views on which q-hylomorphism draws upon: Classical Mereology (2.1.1) and Aristotelian Hylomorphism (2.1.2). Then, I dedicate the rest of this chapter to the analysis of the notion of form that is proposed by Sattig, i.e. K-path (2.2). This latter notion is the point of my critique: this thesis is against K-paths.

2.1 Q-Hylomorphism

Q-hylomorphism and more broadly perspectival hylomorphism is an original metaphysical account that is built on two previous, and rather traditional, philosophical accounts, namely Classical Mereology, and Aristotelian hylomorphism (Sattig, 2015, p.1). Sattig takes full advantage of these previous philosophical traditions and, while avoiding some of their most debatable features

(Sattig, 2015, p. 27-29). In a nutshell, Sattig argues that ordinary objects are compounds of matter and form as suggested by Aristotelian Hylomorphism (Sattig, 2015, p.13). However, Sattig’s account differs from Aristotelian Hylomorphism when specifying the metaphysical nature of matter and form (ibid.). The matter of an ordinary object is a material object as described by Classical Mereology, while the form of an ordinary object is a complex fact about that material object, that is a K-path (ibid.). Now, let us have a closer look at the philosophical account on which q-hylomorphism relies.

2.1.1 Classical Mereology

Mereology is the study of parts and wholes: it investigates the relations of parthood among parts within a whole and between part and whole (Varzi, 2016). Mereology has always been a subject of interest for philosophers from ancient times1. Nonetheless, the first accurate formulation of mereology is ascribed to Leśniewski (1916 and 1927) 2. To be precise, Leśniewski called his own theory of part and whole ‘Mereology’ and then the use of the term ‘mereology’ was extended to different part-whole theories3 (Simon 1987, p. 6). Leśniewski’s mereology is a deductive system of axioms formulated in non-logical terms. The axioms of Mereology were to be assumed with a background logic, namely Ontology and Protothetics4 (Betti and Loeb 2012, p.234). However, Leśniewski’s logic remained quite unexplored by his contemporaries. In 194o, Leonard and Goodman developed a mereological theory, that is called the Calculus of Individuals (Leonard and Goodman 1940). The Calculus of Individuals is formulated in the language of first-order predicate logic, that was more familiar than Leśniewski’s background logic. The Calculus of Individuals and Mereology mainly differ in the logic they assume (Simons 1987, p.18). Although there is this difference, these theories employ similar principles on parthood relations5. For this reason, the Calculus of Individuals is said to be equivalent to Mereology. Both these theories are considered the foundations of contemporary mereology. In particular, together with other theories built from them, Mereology and the Calculus of Individuals form a formal mereological theory, that is called Classical Extensional Mereology (CEM)6. Before going deeper into CEM, I shall stress one point.

1As in Varzi (2016) points out that interest in the study of mereology can be historically traced from ancient times (Plato, Aristotle, etc.), throughout the Middle Ages (Aquinas, Scotus, Ockham, etc.) and modern times (Leibnitz, Kant, etc. ). Further readings on an historical approach to mereology see, e.g. Barnes (1988), Henry (1989), Arlig (2015), Burkhardt and Dufour (1991), ans Koslicki (2008). 2 Leśniewski formulated ‘Mereology’ in an informal way in Foundations of the General Theory of Sets ( 1916) and in a formal way in Foundations of Mathematics ( 1927) (Simons 1987, 2007). 3 For clarity, Mereology (with a capital ‘M’) refers to Leśniewski’s mereology. 4 For further readings see, e.g. Betti&Loeb (2012), Simons (1982, 1987, 2007). 5 The equivalence between Leśniewski’s and Leonard and Goodman’s is demonstrated in (Simons 1987, p.22ff). 6 Following Simons (1987), I abbreviate classical extensional mereology as CEM. Sattig refers to CEM as Classical Mereology.

During the last decades, it has been highly discussed whether mereology should be considered ontologically innocent (Bricker, 2016; Cotnoir, 2013; Feldbacher-Escamilla, 2019; Forrest, 1996b; Hawley, 2014; Smid, 2015; Varzi, 2000 and 2008). Claiming that mereology is ontologically innocent means that mereology is not committed to any particular domain of objects. Hence, mereology is to be conceived a part of formal ontology7 (Varzi 2008, p.115). Here, formal indicates an ontology that is given in terms of structure and not of content. A formal ontology is a sort of scheme structuring whatever there is, independently of what there is (ibid.). Therefore, a formal ontology determines certain formal structures that can be instantiated by anything that there is. However, a formal ontology is not committed to those things that instantiate its structure. In this sense, a formal ontology does not require a content or a specific domain of entities to be applied to: it is metaphysically neutral (ibid.). The formal structure provided by mereology is that of the relation of parthood, regardless of any specific domain of entities. The relations between parts and wholes are not proper only of a particular kind of entities, it is quite the opposite. For example, we can think about parthood relations of concrete objects (e.g., the petal is part of the flower), of abstract objects (e.g., Nessun dorma is part of Turandot by Puccini), of nonexistent object (e.g., the square is part of the round square), of events (e.g., Bloody Sunday is part of the Irish War of Independence), and so on. It is clear that these examples are assuming different kinds of entities and distinct types of metaphysics. Still, mereology is able to describe the part-whole relations in each case. Mereology is a deductive and axiomatic theory of parts and wholes that can be used for any domain of entities, while metaphysics establishes what is the domain of entities. Conversely, if mereology is to be dependent on a certain metaphysics, then it would turn into a part of it (ibid.). If this was the case, each of the above-mentioned examples would imply a distinct mereology according to their own metaphysical accounts. As a consequence, each metaphysics would enclose its own mereology. Additionally, if mereology was dependent on metaphysics, then the sense in which something is part of something else would vary according to the background metaphysics. For example, assume that mereology, i.e. parthood relations, depends restrively on a given metaphysics, i.e. a certain domain of entities. Let us also assume that this metaphysics includes only existent objects. Given these assumptions, it is not accurate to say that the square is part of the round square because in the assumed metaphysics there are no nonexistent objects. Therefore, since these objects are not contained in the assumed metaphysics, it is not possible to claim that they have parts and to describe their mereological relations. In this sense, mereology would be committed a particular domain of entities and, for this reason, it would not be ontologically innocent. Whether mereology is ontologically innocent or not is an ongoing debate. In this work, I assume that mereology is conceived as a formal ontology, that is

7 For further readings on mereology as formal ontology see also Gruszczyński and Varzi (2015). Notice that the reading of mereology as formal ontological is not the only sense in which mereology can be said to ontologically innocent. See, e.g. Lewis (1991).

metaphysically neutral, and ontologically innocent (Varzi 2008). Nevertheless, the reasons for my position goes beyond the scope of this work and I will not discuss them8. I shall move on to the main notions and principles of CEM. Broadly speaking, mereology can be formulated in different ways according to the kind of logic and the primitive terms it assumes. As for the former, I give mereology formulation in first-order predicate logic with identity as in Varzi (2016, Sec. 2)9. As for the latter, I will adopt as primitive term, again as in Varzi (2016, Sec. 2.1), the notion of (improper) part and derive from it the other mereological notions10. ‘Part’ is a relational predicate that stand for a relation that is reflexive, transitive and antisymmetric11 (Varzi 2016, p.8). The basic axioms of mereology as follows (ibid.).

Reflexivity Everything is part of itself.

Transitivity A ny part of any part of a thing is itself part of that thing.

Antisymmetry Two distinct things cannot be part of each other.

Other mereological notions derive from these axioms12. Here, I list those significant to consider Sattig’s use of Classical Mereology.

Equality x i s equal to y i ff x is part of y and y is part of x

Proper part x is a proper part of y iff x is a part of y and x is not identical with y

Proper extension x is a proper extension of y iff y is a part of x and x is not identical with y

Overlap x overlaps y iff there is a z that is part of x and that is part of y

8 The justifications of my view on the ontological innocence of mereology may be the subject for future works. 9 There are other versions of CEM using, for example, plural quantification, as in Lewis (1991). Also, Leśniewski’s mereology (1916, 1927) was developed in his own logic, i.e. Ontology. 10 There are formulations of CEM using different primitive terms, among them proper part (Simon 1987), p roper extension (Whitehead 1919), and s ummation (Fine, 2010). 11 The relation of parthood can be given in terms of a binary predicate ‘P’ such that we have the following axioms: Reflexivity (Pxx), Transitivity ((Pxy ∧ Py z) → Pxz), and Antisymmetry ((Pxy ∧ Pyx) → x= y. ) ( Varzi 2016, Sec.2.1) 12 The formal definitions are given in Varzi (2016) as follows: E quality ( EQxy =df Pxy ∧ Py x)

Proper Parthood (PPxy =d f Pxy ∧ ¬x= y) , Proper Extension (PExy =d f Py x ∧ ¬x = y), and Overlap

(Oxy =d f ∃z(Pz x ∧ Pz y)).

The above-mentioned axioms and definitions (plus the definition of underlap 13) are the basis of all the standard mereological theories (Varzi 2016, Sec.2.2). CEM is a mereology erected from those axioms and definitions together with the notion of mereological sum and two (or more, as we shall see in the following paragraphs) composition principles, i.e principles determining how the parts form the whole (ibid.). The notion of mereological sum describes how the parts relate to the whole. For something x to be a sum of its parts zs , there are two conditions to be satisfied. First, the parts, zs , are all the parts of the whole, x. Second, every part of the whole, x, has a part in common with at least one of the zs 14 (Varzi 2008, p.109). Therefore, if a whole is the sum of a plurality of things15, not only the whole have this plurality as its parts, but also each part of the whole overlaps with one of these things. For example, consider the piece of marble M of which the Venus de Milo is made. Consider also the smaller pieces of marble, m1,m2, m3 , …mn , that are the parts of M. M is the sum of m1, m 2, m3, …mn, because m1,m2, m3, …mn, are all the parts of M and each part of M shares a part with at least one of m1,m2, m3 , …mn .

Therefore, we can say that M is the mereological sum of m1 + m2, + … mn . So far, I have introduced the operation of mereological summation. Now, I move on to the principles16 that CEM uses to characterize mereological sums17. First, let us consider the existence of mereological sums. As we have seen in the previous paragraph, a mereological sum explains how a plurality of parts form a whole. Now the question is: when can we say that a mereological sum exist? According to the principle of unrestricted composition, the answer to this question is: whenever there is a plurality of things, then there exists a thing that is a mereological sum of that plurality of things (Lewis 1991, p.7). So, a mereological

13 The definition of underlap is ‘ x undelaps y iff there is a z such that x is part of z and that y is part of z’. The formal definition of underlap as in Varzi (2016) is Underlap (Uxy =d f ∃z(Px z ∧ Pyz) ). 14 This definition of sum is not given in terms of set-theory. It does not assume the existence of sets and therefore it is not ontologically committed to sets. This definition, using plural variables, was originally given by Van Inwagen (1990, p.29). 15 I use the term ‘things’ in a very broad sense. I am not distinguishing between atomic or atomless entities. For further readings on the debate between atomicity and atomlessness see Simons (1987, p. 41ff), Varzi (2016, p.36ff). 16 There are different formulations of the axioms and principles of CEM(Leśniewski 1916 and 1927, Tarski 1937, Leonard and Goodman 1940, Van Inwagen 1990, Lewis 1987 and 1991, etc. ). In particular, from Lewis (1986, 1991), CEM principles are standardly considered to be the principle of unrestricted composition and the principle of uniqueness of composition (see Sattig 2015, van Cleve 2008, Koslicki 2008). However, especially the latter principle often assumes another principle, that is the principle of extensionality of parthood (Varzi, 2008). From the extensionality of parthood principle is possible to derive the principle of extensionality of composition and then the principle of uniqueness of composition. For a more detailed discussion on the different aspects of the principles of CEM, see Varzi (2008). 17 My presentation of the principles of CEM follows Lewis (1991) and Varzi (2008 and 2015).

sum is a whole whose parts are the plurality of things composing it18. It follows that existence of a mereological sum, that is a whole, solely depends on the existence of a plurality of things, which are the whole’s parts19. Does the plurality of things have to be arranged in a certain way to form a whole and, in turn, to be considered as the whole’s parts? No. The principle of unrestricted composition claims that any plurality of things form a mereological sum, no matter how the plurality of things is arranged (Varzi 2015, p.412). In this sense, the existence of mereological sums is not restricted to any particular kind of composition of the parts. The principle of unrestricted composition is also called mereological universalism as whenever there is a plurality of things, there is always an object which is composed of them. (Van Inwagen, 1990, p. 74). Consider again the piece of marble M of which the Venus de Milo is made and the smaller pieces of marble m1, m2, … mn. The plurality of m1, m2, … mn can form a mereological sum, that is M, such that M = m1 + m2 + … mn. Now, consider also the Mona Lisa (M L) and the smaller material pieces composing it, ml1 , ml2 , … mln , such that ML = ml1 + ml2 + … mln. According to the unrestricted composition principle, the plurality of m1,m2 , … mn together with the plurality of ml1 ,ml2 , … mln can form a mereological sum (call it MML) such that MML = (m 1 + m2 + … mn) + ( ml1 + ml2 + … mln ) . Moreover, all the parts of the works of art in the Louvre Museum can be summed together and form a mereological sum. To push it further, we can also add the parts of the Vatican Museum’s works of art and form other mereological sums and so on ad infinitum. In a nutshell, the unrestricted composition principle states that literally any plurality of things can form an object, that is mereological sum of those things 20. There is another principle characterizing mereological sums according to CEM, namely the principle of uniqueness of composition. It claims that if x and y are the mereological sums of the same things, then x and y are exactly one and the same thing ( Varzi 2008, p.109). A thing considered as a whole is the mereological sum of its parts, therefore x and y are identical if they are mereological sums of the same (proper) parts (Smid 2017, p.8). This principle is related to (and sometimes

18 The notion of composition has been highly debated in mereology, especially after Van Inwagen’s “Special Composition Question” (1990, Ch.12). This question asks which are the conditions under which a plurality of things composes one thing. 19 The existence of a whole is derived, and not independent, from the existence of the parts. For this reason, Lewis (1991) argues that the ontological commitment to the parts of a whole is the same as the ontological commitment to the whole. To put it differently, the existence of the whole does not result in an (additional) ontological commitment. In this sense, Lewis claims that mereology is ontologically innocent. Note that this sense differs significantly from the way in which the ontological innocence of mereology is presented in Varzi (2008) . 20 It is important to notice that the unrestricted composition principle is the strongest formulation among the composition principles (e.g. bounds, sums, products, etc.). For a detailed discussion about all composition principles and about the pros and cons of the unrestricted composition principle, see Varzi (2016, Sec.4).

even identified with21) two other principles of CEM, namely the principle of the extensionality of parthood and the one of the extensionality of composition ( Varzi 2008). One of the main traits of CEM, if not the main, is that it is extensional. In particular, extensionality concerns the proper parts of composite objects. These objects, in contrast to simple objects22, have proper parts, i.e. parts that are not identical to the whole of which they are parts (Varzi 2008, p. 108). The extensionality of proper parts has a crucial role in determining the identity of composite objects. Let us look at this issue step by step. Following Varzi, the extensionality of parthood principle states that x and y are identical if and only if they are composite objects sharing the same proper parts (ibid.). Now, remember that, according to CEM, a plurality of things can form a whole through the operation of mereological summation. Wholes, i.e. composite objects, are mereological sums of a plurality of things, that are the object’s parts. Moreover, the parts of a whole are the plurality of things that form the mereological sum, that is precisely that whole. Again, the extensionality of parthood principle claims that x and y are identical only if they have the same parts. It follows that if x and y have the same parts, they have to be formed by the same plurality of things, that means that x and y mereological sums of the same things. However, can there be two composite objects sharing the same parts and thus being mereological parts of the same things? No. At this point, the uniqueness of composition principles tells us that when x and y are the mereological sums of the same things (given that they have the same (proper) parts, they are identical, i.e. there is one and only one object (Varzi 2008, p.109). To put it differently, two objects are distinct if and only if they are not the mereological sum of the same things, given that they do not have the same (proper) parts (Varzi 2008, p.108). So, a composite object is a unique mereological sum of its proper parts. Therefore, the identity of composite objects strictly relies on their parts and, consequently, on their being unique mereological sums. Finally, the principle of extensionality of composition states that x and y are identical if and only if they are composed of the same things (Varzi 2008, p.209). This principle is entailed by the uniqueness of composition principle, saying that x and y are identical when they are mereological sums of the same things (Varzi 2008, p.110). Let us see the relation between these two principles. Mereological summation is CEM’s kind of composition23 as it defines how parts

21 The principle of uniqueness of composition is explicitly identified with extensionality in Sattig (2015, p. 2). Nevertheless, as Varzi (2008) shows the principle of uniqueness of composition can be derived from, but it is not exactly the same as the principle of the extensionality of parthood and the one of the extensionality of composition. 22 For further readings on simple objects, i.e. things with no proper parts, see Varzi (2016, Sec. 3.4). The principle of extensionality of parthood is restricted to composite objects and the explanation of this can be found in Varzi (2008, p.108). Here, I refer to proper parts simply as “part/parts”. 23 Mereological summation is the kind of composition used by CEM. Therefore, following CEM, all the composite objects that exist are mereological sums. In addition, this composition is not restricted to particular kinds of composite objects, but it characterizes all mereological sums (see, e.g. Lewis 1991, Sider 2001, van Cleve 2008, Rea 1998).

can form wholes24 and the way in which wholes are composed by their parts. According to CEM, a mereological sum is a whole whose parts are the plurality of things of which the whole is composed. Thus, in CEM a whole is composed of some things as it is the mereological sum of those things, that are its parts25. If mereological sum is taken as the only kind of composition, the extensionality of composition principle follows from the uniqueness of composition principle. Therefore, x and y are identical when they are composed of the same things, where being composed of can be explained as being the mereological sum of. What follows is a table of the mereological notion and principles that I have discussed so far.

Mereological Sum x is a sum of the zs =d f the zs are all parts of x and every part of x has a part in common with at least one of the z s.

Unrestricted If there is at least one zs, then there exists an x that is a sum of Composition all zs.

Uniqueness of If x and y are sums of the same things, then x =y. Composition

Extensionality of If x and y are composite objects with the same proper parts, Parthood then x =y .

Extensionality of If x and y are composed of the same things, then x =y. Composition

Composition x is composed of the zs =df x is a sum of the zs and the zs are pairwise disjoint (i.e., no two of them have any parts in common).

I have introduced the main traits of CEM in order to draw a comparison with Sattig’s q-hylomorphism. Q-hylomorphism claims that ordinary objects are compounds of form and matter. The form of an ordinary object is a K-Path. The

However, opponents of this view maintain that only some mereological sums exist as composite objects (Van Inwagen 1990, Thomson 1977, Sattig 2015). 24 CEM uses the notion of mereological sum according to the principles discussed in this section. However, there are other mereology using notions of mereological sum according to weaker principles of composition, e.g. Minimal Mereology, Atomistic Mereology, etc. For further readings of different kinds of mereology, see Varzi (2016). 25 The notion of composition, in general and considered in terms of mereological sum, is part of a huge debate concerning the identity of composite objects. In particular, it is highly discussed whether composition can be considered as identity or not (see, e.g. Merricks, 1992; Van Inwagen, 1994; Lewis, 1991; McDaniel, 2008; Cotnoir and Baxter, 2014; Wallace, 2011; Hawley 2006 and 2013). I will not discuss this debate here for it goes beyond the aim of this thesis. However, this issue may be a topic for future works.

matter of an ordinary object is a composite material26 object as described by CEM. As we have already seen in the previous paragraphs, CEM states that a composite object is an object that has proper parts, i.e. parts that are not identical to the whole (Varzi 2008, p.108). Sattig argues that according to CEM mereological sums are the only kind of whole that there is, namely the only way in which composite objects exist (Sattig 2015, p.1). Thus, in Sattig’s view, CEM identifies composite objects and mereological sums27. Q-hylomorphism is partly, but not entirely committed to CEM. On the one hand, q-hylomorphism makes use of CEM’s notion of composite object in order to describe the matter of an ordinary object. The latter is a composite material object, being the mereological sum of smaller material objects (Sattig, 2015, p.13). On the other hand, Sattig distinguishes between composite material objects and ordinary objects (Sattig, 2015, p. 14). While all ordinary objects are composed by a composite material object, not all composite material objects are ordinary objects (ibid.). To put it differently, all composite material objects are mereological sums, but only some of these mereological sums are ordinary objects. More precisely, composite material objects (partly) compose ordinary objects when they instantiate some properties (and relations) that mark them as belonging to a certain kind (Sattig, 2015, p.4). For example, the piece of marble M is a composite material object, namely the mereological sum of its smaller material parts m1 , m2, m3 , …mn . M composes the ordinary object, namely the Venus de Milo, because it instantiates some properties and relations making the Venus an instance of the kind statue. Note that in this way Sattig applies the unrestricted composition principle only to composite material objects and not to ordinary objects. As a result, the composition of ordinary objects is restricted because only some composite material objects fulfill the role of the matter of ordinary objects. Moreover, Sattig argues that extensionality, or what he calls the uniqueness composition principle28, concerns restrictively composite material object and not ordinary objects (Sattig 2015, p. 14). For what concerns composite material

26 By material object, Sattig means an object that has a location in space and time, and that is characterized by physical properties (Sattig 2015, p.1). 27 The existence of mereological sums and the relative identification with certain kinds of objects strictly depends on the acceptance of unrestricted composition principle or universalism. The account that Sattig takes into account that of Lewis (1991). 28 I shall make clear that Sattig defines the uniqueness of composition principle in terms of extensionality (Sattig 2015, p.4). In particular, his uniqueness of composition principle corresponds to what Varzi calls the extensionality of composition principle (Varzi 2008) However, as we have seen in the previous paragraphs these principles are different (Varzi 2008). Although these principles are very interconnected, they claim different things. Therefore, Sattig reduces the uniqueness of composition principle to that of the extensionality of composition. However, this implication fails as proven by Varzi (2008, p.110). Additionally, Sattig’s notion of composition is arguable too as it corresponds to Varzi’s notion of mereological sum (Sattig 2015, p.4; Varzi 2008, p.109). Again, it seems that the notion of mereological sum is reduced to that of composition, while they are different (one includes the notion of overlaps, while the other that of disjoint; see the definition in the table above).

objects, CEM provides an account of composition, namely mereological summation, that indicates which parts compose a whole, but not how they do so (Sattig 2015, p.2). Conversely, for what concerns ordinary objects, it is also relevant how the parts compose a whole, i.e. the arrangement of the parts and to which kind of object the whole belongs to (Sattig 2015, p.10). So far, I have considered the matter of an ordinary object that, as Sattig argues, follows CEM’s notion of composite object. I will discuss the form of ordinary objects in 2.2. In the next subsection, I focus on Sattig’s interpretation of Aristotelian hylomorphism.

2.1.2 Aristotelian Hylomorphism

Aristotelian hylomorphism is a metaphysical account that originally theorized by in Aristotle’s more than 2000 years ago. In contemporary metaphysics, there are several hylomorphic approaches that draw on it (e.g., Marmodoro, 2013; Koslicki, 2008; Johnston, 2006; Fine, 1999; Rea, 1998; Tahko, 2011). In this subsection, I present Aristotelian hylomorphism (hereafter, AH for brevity) restrictively to the account given by Sattig (2015, p.5-13). By contrast, in the next chapter, I will offer my interpretation of Aristotle’s hylomorphism. As it will be clear in the last chapter, I disagree with Sattig’s account because it overlooks some important features of Aristotle’s hylomorphism. According to Sattig, AH claims that objects are compounds of matter and form (Sattig, 2015, p.6). Sattig argues that AH is a kind of composition that is very different from the one of CEM (Sattig, 2015, p.5). Following Sattig, AH describe objects as structured wholes as their parts are arranged according to a given kind (Sattig, 2015, p.6). Ordinary objects, as Sattig points out, come into existence when a plurality of objects is unified according to a certain principle (ibid.). While the plurality of the object's parts corresponds to the object's matter, the principle of unity is the object's form (ibid.). Forms are conceived as slots29 to be filled by the matter according to a certain kind and arranged in a specific way (ibid.). Thus, an object comes into existence when its form, that establishes the object’s kind and the arrangements of its material parts, is filled by the matter (ibid.). For example, take again the Venus de Milo. Following Sattig’s account of AH, the Venus is the compound of the form statue and the matter marble. The Venus is generated when the matter marble fills the form statue, that is the principle of unity that determines the arrangement of the object’s material parts. So, according to Sattig, the form is responsible for the object’s generation and condition of existence (Sattig, 2015, p.6 and p. 28). Moreover, Sattig maintains that the form dictates also the object’s identity because it accounts for the structure of the object, namely being arranged according to a certain kind (ibid.). In contrast to CEM, where the parts of mereological sums (i.e. objects considered as wholes) are all on the same level, AH states that the object’s parts are hierarchically arranged. What establishes this arrangement and determines ordinary objects structure is the form (Sattig, 2015,

29 Sattig interprets the notion of form as s lots as in Harte (2002) and Koslicki (2009).

p.6) The parts of the objects, namely the matter and the form, are not on the same level. For example, in our case of the Venus, its identity relies on its form statue for it establishes the arrangement of its matter, the marble. To sum up, according to AH objects are structured wholes that are compounds of form and matter. The form is responsible for the object’s generation and structure as the form is what defines the object’s condition of existence and identity (Sattig, 2015, p.28). Q-hylomorphism draws on AH as it claims that ordinary objects are compounds of matter and form (Sattig, 2015, p.13). However, Q-hylomorphism describes the form in a completely different way compared to AH (ibid.). According to Q-hylomorphism, the form of an ordinary object is a K-path, namely a complex fact about a material object (Sattig, 2015, p. viii and p.19). In addition, Q-hylomorphism differs from AH as it analyzes ordinary objects as unstructured wholes, and not as structured ones like in AH. Sattig contends that ordinary objects as compounds of matter and form are characterized by a kind of composition that follows CEM, namely compounding (Sattig, 2015, p.23). The latter is a mereological operation that combines the operation of summation as in CEM and the relation of subjecthood, that obtains between the object’s matter, i.e. a material object, and the object’s form, i.e. K.path (ibid.). For example, consider again the Venus de Milo. It is an unstructured compound of the statue- path and a material object, that is the mereological sum of its smaller material parts, (in this case p iece of marble) such that the piece of marble is the subject of the s tatue-path.

2.2 K-paths and Complex facts

Q-hylomorphism analyses ordinary objects as a compound of form and matter (Sattig, 2015, p.13). I here focus on the notion of the form of ordinary objects, that of K-path. Before explaining what a K-path is, we need to introduce another notion on which it is built: kinds, or sortals. Sortals are concepts that indicate how to count things that belong to a certain kind (Grandy, 2016). Sortals are usually expressed by count names30 that refer to ordinary objects (Sattig, 2015, p.15; Grandy, 2016, Sec.2) Sortals are able to identify ordinary objects as instances of a certain kind according to their qualitative aspect (Sattig, 2015, p.15). In particular, they individuate instances of a given kind in space and time (ibid.). For example, take the Venus de Milo. It is an instance of the kind statue in Louvre Museum at a certain time, t. Moreover, sortals are able to trace the qualitative change of their instances over time, e.g. having been torn apart, the Venus de Milo is not anymore a statue as it has lost the properties that were making it an instance of the kind statue (e.g., being a work of art, having a certain shape, being recognizable by the public, etc.). In general, sortals are useful to pinpoint ordinary

30 Count names have singular and plural construction, while mass names have only singular construction. The former answers to the question ‘How many..?’, while the latter answers to the question ‘How much…?’ (Grandy, 2016, Sec.2). For an overview of sortals, see Grandy (2016).

objects in our ordinary world according to their qualitative aspect, namely being an instance of a certain kind. K-paths relies on the notion of sortal as they likewise describe the qualitative aspect of ordinary objects (Sattig, 2015, p.25). K-paths denote ordinary objects as instances of a certain kind K (Sattig, 2015, p.16). The notion of K-paths is built on three notions: (1) the notion of property that realizes a kind, or sortal, K, (2) the notion of property in the sphere of discourse of K, (3) the notion of a K-state of a material object (ibid.). We start from (1). Every kind K has (1a) qualitative content consisting of the properties that the instances of K, the Ks, have in common, such that they are the specific qualitative properties of the Ks (ibid.). For every kind K, there are (1b) specific properties realizing the kind K, the K-realizers (Sattig, 2015, p.17). The K-realization is explained in terms of (1a) and of grounding (ibid.). Here 31 grounding is conceived as the relation with the stronger explanatory power holding among facts or propositions:

‘when a fact or proposition p grounds a fact or proposition q, then the holding of q consists in the holding of p; q holds in virtue of p’ s holding; the holding of p explains the holding of q. [...] When a plurality of facts or

propositions p1 , p2 ,... ground a fact or proposition q, then each of p1 , p2 , ... p artly ground q .’ (ibid., Sattig ’s emphasis)

Now, material objects instantiate (1a), namely the qualitative content of a kind K (Sattig calls it ΦK ) (ibid.). The instantiation of ΦK is partly grounded by the instantiation of the specific properties, K-realizers (1b) (ibid.).

‘If a material object a instantiates ΦK, then a property ϕ partly realizes K if a’ s being ϕ partly grounds a’s being ΦK . Moreover, if a instantiates ΦK,

then a set or plurality of properties ϕ1, ϕ2, ..., ϕn, completely realizes K if K a’ s being ϕ1 , a’s being ϕ2 ,... and a’s being ϕn jointly ground a’s being Φ .’ (ibid.)

Therefore, when an object instantiates a qualitative profile of a kind (1a), it means that there is a (1b) property that partly realizes that kind if the object’s having that property partly grounds the objects having the qualitative profile of that kind. In our example, if the Venus de Milo instantiates the qualitative profile of the kind statue, then a property, such as being a work of art, partly realizes the kind statue if the Venus’ being a work of art partly grounds the Venus’ being a statue. Moreover, let us move on to the notion of property in the sphere of discourse of K (2). For every kind K, there is a manifold of properties, the K-meaningful properties that, in virtue of their meaning, can be attributed to the Ks, i.e. the properties of the qualitative content (1a) (Sattig, 2015, p.17). The K-meaningful properties are the sphere of discourse K (2) (Sattig, 2015, p.18). Again in the case of the Venus de Milo, for the kind statue, there is a series of properties that can be meaningfully applied to this kind, e.g. being made of marble, having a certain location, etc. Thus, there is a selection of properties that can be meaningfully

31 Sattig’s definition of grounding follows Fine (2001).

applied to the object belonging to a certain kind. The properties realizing a kind K, the K-realizers, are lower in number than the K-meaningful properties (ibid.). We can meaningfully talk of a kind K in several ways and not just relative to the properties realized by its instances. Finally, let us examine the notion of a K-state of a material object (3). For every kind K,

‘K-s tate of a material object is a complex, conjunctive fact, or state of affairs, about the object that obtains at a particular time.’ (ibid.)

In footnote 29, Sattig claims that facts are a sui generis ontological category (Sattig, 2015, p.18, fn.29). They are complex entities whose parts are arranged in a particular way (ibid.). Sattig insists that among different kinds of facts, there are conjunctive facts (ibid.). I focus more deeply on complex conjunctive facts in 4.3. Sattig argues that K-states provide ordinary objects with two types of qualitative profile: (3a) the object’s K-meaningful intrinsic profile at t and (3b) the object’s K-realization profile at t ( Sattig, 2015, p.18). (3a) consists of:

‘the maximal conjunction of the facts that a exists at t, that a has ϕ1 at t,

that a has ϕ2 at t, ..., that a has ϕ n at t , such that

(i) each ϕ i is an intrinsic qualitative property of a , and

(ii) each ϕ i falls in the sphere of discourse of K’ (ibid.)

For example, taking the Venus de Milo again. The Venus’ statue- meaningful intrinsic profile is the maximal conjunction of the facts that Venus exists at t, that Venus is work of art at t, that Venus is made of marble at t, etc., such that every property is an intrinsic qualitative property of Venus and that every property falls in the sphere of discourse of s tatue.

Moreover, (3b) contains two types of fact:

‘the maximal conjunction of the facts that a has ψ1 at t, that a has ψ2 at t, .

. . , that a has ψn at t, such that ψ1 , ψ2 , . . . , ψn together completely realize K—that is, the maximal conjunction of the facts about a that jointly ground a ’ s being ΦK , where ΦK is the qualitative content of K. &

[...] the maximal conjunction of the facts that ψ1 partly realizes K, that ψ2

partly realizes K, . . ., that ψn partly realizes K.’ (ibid., I added the ‘&’, for clarity)

Think again of the Venus. The Venus’ statue realization profile is the maximal conjunction of the facts that Venus is work of art at t, that Venus is made of marble at t, etc. such that all the properties together realize the kind statue, namely the maximal conjunction of facts about the Venus that jointly ground Venus’ having the qualitative content of the kind statue. A similar example can be given when a property only partly realizes the kind.

Sattig stresses that the inclusion of facts indicating which kind are realized by which properties is a relevant part of the notion of K-state. In this way, these facts have an ‘individuative force’ (Sattig, 2015, p.19). In particular, the facts involved in a K-state imprint the kind to which a material object belongs to at a given time (ibid.). The notion of K-state identifies the kind of a given object at a certain time t. By contrast, a K-path is a series of K-states and therefore indicates that an object is an instance of the kind K across time (ibid.). K-paths are described as collections of K-states, whose unity is characterized by the following properties (Sattig, 2015, p.20-21).

K-continuity The K-realizers of any two K-states spatially and temporally c lose in a K-path are extremely similar.

K-connectedness Although the K-realizers of any two K-states in a K-path can be far away from each other, they are connected in some way that is they have a minimum amount of similarity.

Lawful causal Any present K-state causally depends on the previous dependence K-state included in the same K-path (Immanent causation). Maximality A K-path is exclusively the largest conjunction of K-states unified according to K-continuity, K-connectedness, and lawful causal dependence.

It is important to point out that K-paths, material objects and ordinary objects work in very distinct ways (Sattig, 2015, p.21). Ordinary objects are compounds of matter and form, namely the material object and the K-path. The matter, i.e. the material object, is the subject of the K-path in the sense that is the subject of some facts in the K-path. For example, using again the Venus de Milo, the material objects, e.g. the piece of marble M, is the subject of statue- path. However, the same material object, piece of marble M, may be the subject of several K-paths, e.g. statue- path, work-of-art- path, etc. At the same time, the K-path, statue- path, can characterize more than one material object, e.g. the Venus de Milo, the David of Michelangelo, the Statue of Liberty, etc. I further develop this point in Chapter 4. I conclude this chapter reporting ordinary objects’ existence and identity conditions. When there is a material object a and a K-path i, being a is a subject of i, then there exists a compound, or an ordinary object, Σc (a, i) (Sattig, 20015, p.23).

Moreover, the compound Σc (a, i1) is identical to the compound Σc (b, i2 ) if and only if a is identical to b and i1 is identical to i2 (ibid.). To sum up, K-paths are (very!) complex facts, leaving aside whatever facts really exist. I hope the following schema may highlight the complexity of K-paths while triggering questions about their explanatory power. In the following chapter, I illustrate my interpretation of Aristotle’s hylomorphism. Finally, in the

last chapter, I contend that Aristotelian forms are the best candidate to be the formal part of ordinary object, without bringing into play K-paths.

3 Aristotle’s Hylomorphism

In this chapter, I offer my own interpretation of Aristotle’s hylomorphism32. Since it is a metaphysical position developed more than 2000 years ago, it has been discussed, endorsed, and modified by many authors (see e.g., Alexander of Aphrodisias (trans.1990), Aquinas (trans. 1949), Ockham (trans.1991), Buridan (trans. 1989), Scotus (trans. 1968)) . In this work, I will not consider the several evolutions of this theory through the history of philosophy (Ainsworth, 2016; Manning, 2012 and 2013; Pasnau, 2010 and 2011; Spade, 2008). It is needless to say that I will mention commentaries and secondary literature on Aristotle. What I mean by ‘my own interpretation’ is that my account of hylomorphism is not 33 committed to any specific kind of (Neo-) Aristotelian hylomorphism . What I will present here is my own account of hylomorphism and I follow as closely as possible Aristotle’s original texts. To be clear, my interpretation of hylomorphism draws on the well-known one of Frede and Patzig34 (Frede&Patzig, trans. 2001). The latter defends the individuality of Aristotelian forms, and so do I (see, e.g. Frede, Patzig&Reale, 2001, p.28, 54, 58 and the whole book in general). However, my account of hylomorphism assumes a mereological approach that is not present in Frede and Patzig (2001). I endorse mereological 35 hylomorphism because I interpret hylomorphism as a kind of mereological composition (Koslicki, 2006, p. 717). According to this view, hylomorphism can be examined in terms of parthood relations where form and matter are (proper) parts of the compound, that is the object considered as a whole. The notion of proper parts is to be understood in CEM’s terms, i.e. parts that are not identical to the whole (Varzi, 2008, p.108). In addition, the novelty of my account of hylomorphism is that the form is explained in terms of relations. I claim that the form is the (sum of) relation(s) in which the material parts of the object stand. I will further develop this position in

32 In the whole chapter, unless otherwise specified, I use h ylomorphism to refer to Aristotle’s hylomorphism. 33 For contemporary versions of hylomorphism see, e.g. Evnine (2016), Fine (1992, 1994, 1999, 2008), Jaworski (2014), Johnston (2006), Koslicki (2007, 2008), Marmodoro (2013), Pruss (2013),Sattig (2015), Rea (1998, 2011). For collections of papers about contemporary hylomorphism see, e.g. Bailey & Wilkins (2018), Novotný & Novák (2014), Oderberg (1999), and Tahko (2011). 34 For the original edition, see Frede, M., & Patzig, G. (1988). Aristoteles," Metaphysik Z": Text, Übersetzung und Kommentar. CH Beck. The page number refers to Frede, M., Patzig, G., & Reale, G. (2001). I l libro Z della Metafisica di Aristotele (Vol. 86). Vita e pensiero. 35 On mereological hylomorphism, see Haslanger (1994), Koslicki (2006, 2007, 2008, 2015). For further readings against mereological hylomorphism, see Johnston (2006), Marmodoro (2013).

this chapter and in the next one. In my analysis, I will mainly draw on Metaphysics, 36 Physics, Topics, and Categories. Not only these books contain a clear picture of Aristotle’s hylomorphism—they are also extremely relevant for the aim of this research as they validate my account of Aristotle’s form. A closer examination of Aristotle’s texts will provide the philosophical background needed to grasp the next (and final) chapter. The structure of this chapter is as follows. First, I focus on Aristotle’s hylomorphism (3.1): I give an account of the notion of form and matter (3.1.1), and the one of compound (3.1.2). Then, I further examine Aristotle’s mereology (3.2) and, especially, the notion of p art ( 3.2.1) and the one of whole (3.2.2).

3.1 Form, Matter, and Compound

Aristotle’s hylomorphism is widely known as the metaphysical view that takes objects to be compounds of form (εἶδος or μορφὴ) and matter (ὕλη). In his examples, Aristotle usually refers to a specific kind of objects, namely sensible objects (Frede, Patzig&Reale, 2001, p. 45). These objects are characterized by being something concrete and particular (Met. Z.15, 1039b 28, Frede, Patzig&Reale, 2001, p. 175ff. and p.432). In other words, Aristotle is talking about ordinary objects, such as human beings, statues, houses, horses, trees, etc. (Shields, 2008, Sec.8). In more modern and technical vocabulary, those objects are called concrete particulars (Ainsworth 2016, Sec.1; Rettler 2016, Sec. 1.2.2 and Sec. 1.2.4) . Concrete particulars are objects with specific characteristics. First, they are concrete because they have physical parts in the sense that they are at least partially made of matter (Loux, 2006, p.85). Accordingly, concrete particulars are material objects with a number of physical properties (Koslicki, 2008, p.9). Secondly, they are particulars because they have a determined and unique location in space at each time of their existence. This entails that concrete particulars occupy one single region of space at a given time (Loux, 2006, p.85). Third, concrete particulars are subject to generation and corruption (ibid). Consider the Venus de Milo, for example. It is concrete for it has a physical/material part, namely the marble. Furthermore, it has physical properties, such as being 203 cm high, being approximately white, having the shape of an S curve, etc. The Venus is also a particular as it can occupy one single region of space at a time, namely 48.859958°N 2.337269°E in the Louvre Museum, in Paris,

36 My English primary sources are in Categories, Topics, Physics, Metaphysics in Barnes (1984). The page numbers refer to The Complete Works of Aristotle: The Revised Oxford Translation, One-Volume Digital Edition (2014).

France, at a time t. Additionally, the Venus has a temporally limited existence that lasts from its creation to its destruction. Aristotle’s hylomorphism provides an explanation for the metaphysics, i.e. nature of concrete particulars, and more in general of ordinary objects. It claims that ordinary objects are compounds of matter and form in the sense that they have a material and a formal component, or part (Shields, 2008, Sec.8). Insofar as they are composed by matter and form, ordinary objects are not 37 mereologically simple , i.e. objects with no (proper) parts. According to hylomorphism, ordinary objects are mereologically complex because they have (proper) parts, namely form and matter (Haslanger, 1994, p.130; Koslicki, 2006, p.717). Therefore, Aristotle’s hylomorphism is a metaphysical view that deeply makes use of mereological notions. Briefly, this is the scenario. Ordinary objects are compounds of form and matter, such that form and matter are parts of the compound and the compound is the object considered as a whole. In the next subsection, I focus more deeply on the notions of form and matter.

3.1.1 Form and Matter

Hylomorphism was originally conceived to explain how ordinary objects change, i.e. they can lose or gain certain properties while remaining the same objects. (Shields, 2008, Sec.8). Then, it was endorsed to illustrate the existence of ordinary objects (Cohen, 2016, Sec.6). In this subsection, I examine Physics, Categories and Metaphysics ZHΘ as they are extremely relevant for Aristotle’s theory of change and ontology. In Physics I.7, Aristotle claims that every change implies two things, 38 namely something that remains the same and something that it is gained or lost (P hys. I.7, 190a 14ff., 190b 9-10). More precisely, the matter is what persists through the change — literally translated, the matter is what stays under (τ ὸ ὑποκείμενον ) the process of change (Phys. I.7, 190a 21-b5, 191a 9-11). The form is what is gained or lost as it informs or ceases to be in the matter (Phys. I.7, 190b 10-15, 191a 11-15). Recall my account of the form as the (sum of) relation(s) in which the material parts of the object stand. Accordingly, when the form informs a matter, the object’s material parts relate among each other in a certain way. Therefore, gaining or losing a certain form entails a change in the relation among the object’s material parts. Consequently, if this relation, i.e. the form, is different (for it is either no longer the same or it is a new one), then the object changes. For example, think of a leaf that changes its color and becomes red in fall. The organic matter of the leaf undergoes the change: it loses the (accidental) form of this not-red leaf and it gains the (accidental) form of this red leaf. In this example, the

37 Since I endorse mereological hylomorphism, I am using mereological notions, such as simplex, complex, proper parts i n the sense of CEM (see Ch.2). 38 Notice that Aristotle’s theory of change involves the other notions, e.g. motion, opposition, and privation. The discussion of these notions requires a deeper analysis of Aristotle’s theory of change that goes beyond the scope of this thesis. On this topic, see Charlton (1983), Bogen (1991, 1992), Kosman (1969).

relation that obtains among the object’s material parts is different. First, the relation among the material parts is such that they instantiate the property of being not-red. Then, the material parts relate among each other such that they instantiate the property of being red. Every kind of change works according to this process and matter and form play an essential role in it. In Phys.I .7, Aristotle explains that there are two main kinds of change: substantial change and accidental (or non-substantial) change. The first kind of change concerns generation (γένεσις) and corruption (φθορά) of objects (P hys. I.7, 190b 25). A substantial change results in the coming into or going out of existence of an object (P hys. I.7, 190b 30-32). As all changes, also in these cases what remains the matter, while what is gained or lost is the form. Nonetheless, substantial changes involve exclusively substantial forms, that characterize objects from their generation to their corruption (ibid.). According to my view, a substantial form is the sum of all relations obtaining among the object’s material parts during its entire existence. For example, consider the Venus de Milo. The Venus came into existence when its material parts started to stand in a certain relation, that it the substantial form this particular statue. In addition, the Venus is the same existing object as its material parts still stand in that very relation. The second kind of change is accidental change and it indicates the change of a property in an already existing object (Phys. I.7, 190b 23-28, 32-36). This change does not involve the coming into or going out of existence of objects, but simply, the object’s coming into being something (Phys. I.7, 190b 30-32). The form that is gained or lost in an accidental change is an accidental form (Phys. I.7, 190b 26-27). The latter is the form that denotes the object’s properties (ibid.). Following my reading, an accidental form is one single temporary relation obtaining amon the object’s material parts. Again, take the Venus de Milo. The Venus has the accidental form this particular statue being white because its material parts are related such that they instantiate the property of being white. The Venus would lose that accidental form, if its material parts of Venus were no longer in that relation. Distinctions like substantial/accidental change and substantial/accidental forms rely on a broader Aristotelian distinction, namely the one between substance and accidents. I will examine more deeply this distinction in the next subsection. For now, it is enough to point out that the notion of substance refers to either the form or the compound of form and matter, i.e. the object (C at. V 2a 13-16, 19-26; Met. H. 3, 1043a 28-30; Frede, Patzig&Reale, 2001, p. 178). By contrast, accidents are temporary qualifications of objects, (Cohen, 2016, Sec. 7). On a predicative level, a substance is the subject of the predication, while the accidents are the predicates (C at.V, 2a 13- 2b 5). Similarly, in Metaphysics H and Θ, matter and form clarify how ordinary 39 objects change through time, i.e. diachronic change . In these texts, Aristotle 40 explains matter and form in terms of potentiality and actuality (M et. H. 1, 1045a

39 For further reading on this topic, see Cook (1989), Coope (2009), Falcon (2013), Gill (1991), Makin (2006), Haslanger (1994), Frede (1994), Witt (1987). 40 See also Met. ∆.5, 1017b 1-9; M et. N.1, 1088b 1.

25-32). On one hand, the matter expresses the potentiality of an object to come into being or to come into existence and it can potentially be informed by the form (M et. H.6, 1050a 23-25; Met. Θ. 8, 1050a 15-16). On the other hand, the form indicates actuality as it makes actual what the matter was only potentially (ibid.). According to my account of the form, potentiality denotes the relation that can potentially obtain among the object’s material parts, while actuality indicates the relation in which the object’s material parts actually stand. Consider the Venus de Milo. Before coming into existence, the matter marble was only potentially a statue. When its material parts started to relate among each other according to the form this particular statue, the Venus came into existence. Moreover, the notion of matter and form are famously discussed by 41 Aristotle in Metaphysics Z .The aim of Metaphysics Z is to investigate the nature of substances. The form is what determines the nature of ordinary objects and it analysed in two distinct ways. This distinction is due to an explanatory gap between Met. Z.3 (and Categories) and Met. Z.4. In Met. Z.3 (and Categories), Aristotle explains that the form (i) is what makes an object something that is determined (τ όδε τι) and different from anything else (M et. Z.8, 1028a 26-28; Frede, Patzig&Reale, 2001, p. 178). In Met. Z.4, Aristotle argues that the form (ii) is the definition of an object, that is the way in which an object is known (Frede, Patzig&Reale, 2001, p. 433). I will restrictively focus on the notion of form as in (i) because it is more relevant for my ontological and mereological analysis. Therefore, I am assuming that the object’s form is particular and that it specifies the individuality of a given object. Following my view, the form is particular because the (sum of) relation(s) among the object’s material parts is unique. Ordinary objects are particulars because they have a unique substantial form that indicates the determined relation in which the object’s material parts stand. For example, the Venus de Milo is something determined in virtue of its substantial form this particular statue, that characterizes the relation among it material parts. Moreover, in Met. Z.13 Aristotle argues that the form cannot be universal because the form belongs exclusively to the object of which it is part, while universals belong to many things (M et. Z.13, 1038b 9-13). This does not imply that either Aristotle or my interpretation of it radically excludes universals from the ontology, as we shall see in the next subsection. In Categories V, Aristotle describes particulars, or individual objects, as the entities that exist in the primary and highest way of being, namely as primary substances (Cat. V. 3a 10-15). By contrast, universals are identified with secondary substances, that are the universals exemplified by the properties of primary substances (Cat. V. 3a 16-20). Secondary substances exist and are present in the ontology, but they are ontologically dependent on primary substances. Consider again the Venus de Milo. It is a

41 The literature about Metaphysics Z is incredibly vast and variegate. Here, I restrictively indicate readings that interpret (or that sympathize with the interpretation of ) forms as individuals, see Albritton (1957), Burnyeat (1975) Frede (1987, 1990), Frede & Patzig (1988), Furth (1990), Harter (1975), Heinaman (1979), Lloyd (1981),Sellars (1957), Whiting (1984, 1986), Witt (1989).

particular object whose properties exemplifies universals, e.g. the property of being white exemplifies w hiteness. It is important to understand that there is a strict relation of interdependence between form and matter. On one hand, the matter needs the form in order to be something determined, namely an existing object. It is only by being in a determined relation,i.e.the form, that the material parts of an object are a determined and particular object (Met. Z.11, 1037a29). On the other hand, the form needs a material anchorage, which is the condition of possibility of existence in the (physical) world. To return to the Venus: it requires both the form this particular statue and the matter marble to have the concrete and material possibility to become this particular statue. Now that we have a clearer picture of matter and form and their role, let us move to their combination: the compound.

3.1.2 Compound

The compound is the union of matter and form. The ancient Greek term for compound is σύνολον and it literally means with all. This term perfectly indicates that compounds are objects considered as wholes. As it will be clearer in 3.2.2, Aristotle describes wholes as those things that do not lack any of their parts. It is in virtue of having both form and matter, i.e. of being compounds, that ordinary objects are identified by Aristotle as existing objects (Met. Z.8, 1033b 17-19). According to Aristotle, what exists in a strict ontological sense it is only the compound of form and matter. When we speak about form and matter as separate from the compound, namely as entities per se, the level of analysis is conceptual, and not ontological42. Aristotle uses the terms λογικῶς to indicate a purely abstract reasoning without any specific ontological and metaphysical implication (M et. Z.4, 1029b 13, Angioni, 2012, p.41). Form and matter are conceptual tools that explain the metaphysics of ordinary objects. 43 In Categories , Aristotle refers to ordinary objects as primary substances44. These entities are what exist in the highest and most fundamental degree on being. It is extremely interesting to notice that primary substances have exactly the same features of concrete particulars. First, a substance is something determined45, namely a certain this, meaning that it is individual (ἄτομον) and numerically one (ἓν ἀριθμῷ) (Cat. V. 3a 10-15). It is individual in the sense that it occupies one determined region of space at each time of its existence46 (Met. Z.16, 1040b 23-27). Moreover, a substance is numerically one as it exists only as an

42 On the distinction between the logical and ontological level see also Burnyeat (2001), Frede & Patzig (1988), Scaltsas (1994). 43 For further reading on Categories, see Ackrill (1994), Haaparanta & Koskinen (2012), Irwin (1989), Moravcsik (1967), Shields (2012), Thorp (1974). 44 In this passage, for brevity, I refer to primary substances simply as substances. Moreover, I am using the terms s ubstance, c ompound, and ordinary objects i nterchangeably. 45 See also (M et. Z.1, 1028a 25-28; Frede, Patzig&Reale, 2001, p. 54 and p.173ff.) 46 As the ancient Greek terms suggest, a substance is not divisible because its physical parts cannot be scattered across space.

irreducible unity of form and matter (Met. B. 3, 998b 20-22). According to my account of form, a substance comes into existence exclusively when its material parts stand in determined relation among each other, and this relation is the form. Therefore, the unity of form and matter is what accounts for the object’s existence. Second, a substance is able to have incompatible properties at different times and this entails that they change (C at.V. 4a 9-20). At this point, it is useful to illustrate the distinction between primary and secondary substances47. As already pointed out in the previous subsection, primary substances are individual objects, like the individual man or the individual horse (C at. V. 2a 10-15). Secondary substances are the qualifications of primary substance and, in contrast to primary substances, secondary substances are universals because they are instantiated by more than one individual object (C at. V. 2a 16-20). According to Aristotle, universals belongs to many objects at the same time (Met. Z.13, 1038b 11-13). Consider again the Venus de Milo. It is an individual object whose properties exemplifies universals, e.g. the property of being white exemplifies whiteness. Universals and the properties that instantiate them exists only in a derivative sense because their existence depends on individual objects (Cat. V. 2b 5-6). The difference between primary and secondary substances ensures that the individual object remains numerically the same object, while the properties (that instantiate universals) change. Third, substances are composite objects, i.e. objects with parts that are distinct from the object considered as a whole, because they have a formal and a material part. According to my interpretation of Aristotle’s hylomorphism, substances are identical to the sum of their parts, namely to the sum of form and matter. This entails that the sum of the object’s material parts and the relation obtaining among the object’s material parts is identical to the object itself. Since the form characterizes the relation holding among the object’s material parts, it is an internal relation of those material parts. By internal relation, I mean a relation that is determined by the things it relates (Betti, 2015, p. 89; MacBride, 2016, Sec. 3). The form is not something additional to the object’s material parts for it depends on those parts. For example, take the Venus the Milo. The Venus is a mereologically composite object as it is a compound of the form this particular statue and the matter marble. Now, the form this particular statue portrays the relation in which the marble parts of the Venus stand. Since that relation, i.e. the form, relies on the marble parts, there is nothing further to those m arble p arts. After having examined Aristotle’s hylomorphism, let us analyze Aristotle’s mereology, namely its notion of part and w hole.

47 On this difference, see also Met. Z.1, 1028a 10-13. For further reading on this distinction primary/secondary substances, see Annas (1974), Cresswell (1975), Engmann (1973), Jones (1972), Scaltsas (1994), Loux (1991), Wedin (1993).

3.2 Part and Whole

Aristotle does not dedicate a specific work or a part of it to mereology. Aristotle’s mereology is scattered across several of his texts and, for this reason, it always requires some sort of interpretative work. In contemporary literature, there are different sorts of Aristotelian mereologies according to specific interpretations of Aristotle’s work. For example, Ackrill (1994), Haslanger (1994), Koslicki (2006, 2007, 2008), Kosman (1969), Evnine (2016), Lewis (1982), Gill (1991, 2005), Galluzzo (2018), Fine (1999). In particular, different interpretations of the notion of form 48 have influenced the approach to Aristotle’s mereology in several ways. In this section, I prefer to avoid any specific commitment to these interpretations of Aristotle. I will rather discuss Aristotle’s work assuming the notion of form I have presented in (3.1.1), namely the relation obtaining among the object’s material parts. I here outline Aristotle’s mereology by considering the several senses of part 49 and whole as they are introduced in Metaphysics ∆.25 and ∆.26 . Broadly speaking, the book ∆ of Metaphysics is a dictionary of the most fundamental philosophical notions used by Aristotle. Therefore, we can suppose beforehand that the mereological notions of part and whole have a crucial role in Aristotle’s metaphysics (Koslicki, 2007,p.132).

3.2.1 Part

In Metaphysics ∆.25, Aristotle explains four senses (1-4) in which the notion of part (μέρος) can be thought of (Met. ∆.25, 1023b 12-25). Two of them, namely (1) and (3), are the most relevant for this research, as we shall see in this section. First, part (1) is interpreted in terms of quantity (ποσὸν). Part means that into which a quantity can be divided. More precisely, there are two ways in which to be part of a quantity can be interpreted: (1a) to be a part of a given quantity where quantity is an arbitrarily established quantity and (1b) to be a part of a given quantity where quantity is considered as a whole. On one hand, (1a) a quantity is merely the measure of a given quantity and it can be divided into its parts in this sense. For example, as Aristotle explains, the number 2 is part of the number 3. Consider 3 to be a given quantity: it can arbitrarily be divided into three parts, of which two parts quantify the number 2 (Koslicki, 2007, p.134). Therefore, 2 is in or is part of 3

48 The debate about Aristotle’s mereology is an ongoing one. It concerns questions that go beyond the mereological relation holding among the form, the matter and the compound. For example, scholars’ interpretation of form as a proper part lead to a certain account of Aristotle’s mereology see Haslanger (1994), Koslicki (2008). Other interpretations, e.g. form as definition, prompt different mereological approaches, see Galluzzo (2018). Moreover, additional issues such as the priority of the form (Haslanger, 1994; Koslicki, 2014; Peramatzis, 2011), the individuality of the form (Frede, 1987), the grounding problem (Koslicki, 2018; Sirkel & Tahko, 2014, Corkum, 2016), etc. are all relevant to this topic. I will not address these issues here as they are not essential to the scope of this work. 49 In the text, I use my own translation of the ancient Greek version of Metaphysics edited by Ross (1924).

in this sense. On the other hand, (1b) quantity measures a whole, and it is not just an arbitrarily given quantity. Thus, in this sense, being a part means to be part into which a whole can be divided. As Aristotle points out, in the latter sense 2 is not part of 3. The number 3 as a whole cannot be divided by 2. Conversely, in the former sense, one can say that the number 2 is part of the number 4, as the latter as a whole can be divided by 2. The distinction between (1a) and (1b) is mereologically fundamental. For example, consider the Venus de Milo: it is a compound of the form this particular statue (S ) and the marble (M) of which it is made, such that Venus is M + S. Moreover, the marble M is the matter of Venus and it is the sum of all the material parts (m1,m2, … mn ) of the Venus, such that M = m1 + m2 + … mn. The form S, as already pointed out in 3.1.1, is the (sum of) relation(s) holding between the (material) parts and the whole, namely Venus. Now, it is only when m1, m 2, … mn stand in a particular relation — that is the form — that we can look at them as parts in the sense of (1b), i.e. part of a given quantity where quantity is considered as a whole. M1, m2, … mn are the (material) parts of the Venus because they relate to the whole according to the form S. When m1 , m2, … mn are parts as in (1a), i.e. part of a given quantity where quantity is an arbitrarily established quantity, they are not parts of a whole, but only parts of a given quantity, e.g. a given quantity of marble. So, according to (1a), m1 ,m2, … mn are parts of the quantity of matter, M, but not of the Venus de Milo, i.e. the whole.

Therefore, m1 + m2 + … mn are parts in two different ways, (1a) and (1b). When they are parts as in (1a) they are narrowly parts of a certain quantity (of matter), whereas when they are parts as in (1b) they are parts of a whole. This point will be further discussed in 3.2.2. Second, parts (2) are those divisions into which the form can be divided. To be clear, here Aristotle refers to the form in terms of definition. At a purely logical level the form provides the definition of a substance or of a compound. At this level of analysis, that is distinct from the ontological level, the form is a 50 definition consisting of two parts: the genus and the differentia . The genus is the generic kind under which a given substance falls. The differentia represents the differences of species within the same genus. For example, human beings are defined according to their genus, animal, and their specific difference, rational. Many different species belong to the same genus such that they are parts of the same genus. Therefore, this second sense of part defines the way in which distinct species are parts of the same genus. In other words, the notion of part in this sense shows how the parts, i.e. genus and differentia, of the form considered as definition relate one to each other. Third, part (3) means that into which the whole (τὸ ὅλον) can be divided or 51 that of which it is composed. The whole has as its parts the matter and the form. This sense of part is strictly mereological because it explains the relation of parthood between form, matter, and compound, i.e. whole. Nevertheless, in this

50 The differentia is the specific difference characterizing a particular species. It is often referred to only as s pecies. Here, I call it d ifferentia. 51 The matter is referred to as ‘that into which the form is’ (‘τοῦτο δ᾽ ἐστὶν ἡ ὕλη ἐν ᾗ τὸ εἶδος).

passage, Aristotle uses the term whole to refer either to the form (τὸ εἶδος) or to what has the form (τὸ ἔχον τὸ εἶδος), that is the compound. So, it seems that not only the compound but also the form is to be considered as a whole. Compounds or substances exist in the highest and most concrete way of being. In other words, they are the only things that exist in a primary sense. Conversely, the form per se does not exist and it is not an ontological notion. The form, as separate from the compound, is considered on a purely logical level. It is obscure why Aristotle refers to the form as a whole here. As suggested by Koslicki (2007,p.137-138), the form may be plausibly interpreted as a whole, if the form is conceived as the definition. In this way, it is possible to say that the form is a whole and that it has parts, namely genus and differentia. A piece of evidence in favor of this interpretation is the fourth (and last) sense in which part can be described. Finally, parts (4) of the whole are the elements in the definition of each compound or substance. These parts in the definition are the genus and the differentia. If the whole is considered to be the form, as in a certain sense in (3), then the genus and the differentia are the parts of the form. One may object that this fourth sense of part is the same as (2). However, in (2) the differentia is said to be part of the genus as there are many species of the same genus. Therefore, in (2) the relation of parthood holds between one part, i.e. the differentia, and another part, i.e. the genus, of the definition. In this last sense, instead, the relation of parthood holds between the parts, i.e. the genus and the differentia, and the whole, i.e. the definition. It may be useful to remark that Aristotle characterizes the distinct relations of parthood in (2) and in (4) in exactly the same way he distinguishes (1a) and (1b). The relation of parthood among parts, whether they are given quantities or genus and differentia, is deeply different from the relation of parthood occurring between the parts and a given whole. Let us now move on to the senses of ‘whole’.

3.2.2 Whole

In Met. ∆.26, Aristotle points out the different meanings of whole (ὅλον) (M et. ∆.26, 1023b 26 - 1024a 10 ). First, a whole (1) is that from which none of the 52 parts of which it is said to be naturally a whole are missing. In this sense, a whole

52 There is an issue that is worthy to mention concerning the translations of this passage. Following Ross (in Barnes, 1984) and also (Koslicki, 2006), I opted for a very literal translation not only because this is the most faithful to the text, but also, and especially, because it is mereologically neutral. By mereologically neutral, I mean that this translation does not entail any specific interpretation of Aristotle’s mereology. In this sense, there are other translations that are not mereologically impartial as they add details on mereological relations that are not in the text. For example, Tredennick (1933) translates “[...] that from which no part is lacking those things as composed of which it is called a natural whole” (Tredennick, 1933, p. 281, my emphasis). Another example is the translation of Reale (2000), “[...] that from which is lacking none of the parts of which the whole is said to be naturally constituted” (trans. Reale, 2000, p.255, my translation from Italian and my emphasis). The terms composed and constituted refer to different, albeit very related,

is explained in terms of its parts. In particular, this passage claims that a whole cannot lack the parts according to which it is called a whole by nature. Positively stated, a whole must have all the parts for which it is called a whole by nature. Here, “by nature” (φύσει) suggests that the notion of whole ordinarily relies on the presence of the parts. Therefore, all of the parts of a whole have to be present, either potentially or actually, for the whole to be called such. Substances are wholes in this sense as they are complete entities, lacking none of their parts. Secondly, a whole (2) is that which so encompasses the things that it 53 encompasses that are a unity (ἕν τι, which literally means something that is one ). This definition of whole considers again the whole in terms of its parts similarly to (1). However, this time both the parts and the whole are considered for their being a unity. Aristotle specifies two senses in which a whole can be a unity. On one hand, a whole (2a) is a unity because each and all of its parts is a unity; on the other hand, a whole (2b) is a unity because it is composed by its parts. (2a) indicates how all the parts, each of them taken individually, relate to the whole. Each of the parts of the whole is itself a unity, e.g. a man is a living being, a horse is a living being, god is a living being, such that also all the parts of the whole are a unity, e.g. all of them are living beings. Note that unity in this sense differs from the case in which unity results from all the parts taken together (Kirwan, 1993, p.175). For example, consider an airplane and its parts: the unity of the airplane is given collectively by 54 all its parts, and not by the fact that each of the parts is individually an airplane . This other sense of unity is the one of (2b): a whole is a unity as it is (collectively) composed by its parts. According to this sense, a whole is the continuous and the 55 limited , when there is a unity (resulting) from many things, especially if these things are present in the unity potentially, and if not, also if they are actually present in it. This notion of whole denotes a compositional unity, namely the unity deriving from the composition of parts. According to Aristotle, the parts can be present in the whole either potentially or actually. As we have seen in 3.1.1, potentiality and actuality are paired with matter and form to justify the change in substances. Matter and form, which are the parts that can be present potentially or actually, are responsible for continuity and change in substances. . If things are wholes, then their parts form a unity such that the whole is one and only one mereological relations, namely composition and constitution. The first one is the relation between an object and its parts, the second is the relation between an object and what it is made of (Evnine, 2011, p.1). My point is that these kinds of translation may influence different readings of Aristotle’s mereology. For an interesting overview of the relation between constitution and composition, see Evnine, (2011). 53 A more detailed discussion on unity and oneness is the topic of 4.1.1 and 4.1.2. 54 Cf. Kirwan, 1993, p.175. 55 Aristotle defines wholes as the continuous and the limited. The continuous (συνεχὲς) literally means what it is held together, and it indicates a whole whose unity exists from the joining of its parts. Moreover, the limited (πεπερασμένον), literally means what is finished or accomplished and it suggests that a whole is something complete, namely something that does not lack any of its parts. Note that also the notion of whole as in (1) involves completeness in this sense.

thing. For this reason, Aristotle claims that wholeness (ὁλότητος) is a kind of 56 oneness (ἑνότητός) . Thirdly, as for the notion of part, the notion of whole (3) is analyzed in terms of quantity. Things that are referred to as quantities have a beginning, a middle and an end. This mainly entails that quantities are limited continuities (see note 40 and Kirwan 1993, p. 176) There are two (or better three) ways in which quantities are characterized depending on the position of their parts. On one hand, a quantity, whose position of its parts does not make any difference to it, is 57 called totals (πᾶν) (3a). On the other hand, a quantity, whose position of its parts makes a difference, is called a whole (ὅλον) (3b). Moreover, there are also quantities which are both, and therefore they are both totals and wholes (καὶ ὅλα καὶ πάντα) (3ab). Within the latter, there are quantities whose position of their parts makes a difference to their shape, but not to their nature, and also those on which the 58 position of their parts makes a difference to their nature . Few examples here can help. For what concerns (3a), Aristotle takes as examples liquids. He argues that they are not wholes, but only totals. Consider some water, the position of its parts does not affect it in any way. This is because mass terms refer to things that are not considered as a unity per se, but only derivatively, e.g. a glass of water, a liter of water, etc. Thus, liquids are not intrinsically quantities whose positions of parts makes a difference to them. An example of (3ab) is the wax because a change in the position of its parts, e.g. when it melts, affects only its shape, but not its nature, i.e. it is still the same wax. Finally, Aristotle does not make explicitly an example of a whole (3b), but we can think of the Venus de Milo. As a statue, the Venus cannot survive a rearrangement of its parts, therefore the position of its parts makes a difference to it. For example, if someone tears apart the Venus, then the Venus ceases to exist. Now that I have explained all the meanings of part and whole according to Metaphysics ∆25 and ∆26, we have a clearer picture of both Aristotle’s hylomorphism and Aristotle’s mereology. In the last chapter, I will compare Aristotle’s notion of form and Sattig’s notion of form. My aim is to show that Aristotle’s notion of form can perform the same role as Sattig’s, without appealing to complex facts.

4 Aristotle’s Forms versus K-Paths

56 The notion of oneness has different senses in Aristotle. It relates to being in general, to unity, and to sameness. I further discuss oneness in the next section. 57 Koslicki suggests that Aristotle’s totals are very close to CEM’s mereological sums (Koslicki, 2007, p.136). 58 This passage is very unclear and highly debated. I give some examples of (3a), (3b), (3ab), two of them are directly from Aristotle’s text. For some interesting issues concerning the translation from ancient Greek to English of this passage see Kirwan (1993, p. 176ff).

In this chapter, I compare Aristotelian forms and K-paths. As discussed in 3.1.1 and in 2.2., both Aristotle’s hylomorphism and Perspectival Hylomorphism agree that ordinary objects are compounds of form and matter, and, for this reason, they are hylomorphic approaches. Nonetheless, Perspectival Hylomorphism (hereafter, PH) and Aristotle’s hylomorphism provide two different accounts of form and matter. Here, I narrowly focus on the accounts of form, namely 59 Aristotelian forms and K-paths. I briefly summarize them as follows . 60 First, an Aristotelian form (hereafter, A-form) is a component of ordinary objects, that are compounds of matter and form. Following a mereological reading of Aristotle hylomorphism, I claim that form and matter are parts of ordinary objects. According to my interpretation of Aristotle’s form (see Ch. 3), the A-form is the (sum of) relation(s) in which the material parts of an object stand. The unity of A-form and matter characterizes the existence and the identity of ordinary objects. Both of these aspects will be addressed in this chapter. Secondly, a K-path is the individual form of ordinary objects, where the object is a compound of form and matter. Given PH’s mereological stance, PH (see Chapter 2) takes both the formal and the material component of the object to be the object’s parts (Sattig, 2015, p.13 and p. 22-23). An ordinary object has a formal part, i.e. the K-path, and a material part, i.e. a material object (ibid.). A K-path, for some kind K, is the conjunction of complex facts ‘imprinting a kind’ on one (or more) material object(s) over time (Sattig, 2015, p.19). More precisely, a K-path is the conjunction of K-states unified according to the following criteria: continuity, connectedness, lawful causal dependence, maximality. (Sattig, 2015, p. 20-21). A K-states is, in turn, a conjunction of facts that provides a material object with a 61 K-meaningful intrinsic profile and K-realization profile (Sattig, 2015, p.18). Briefly, K-paths and K-states are conjunctive complex facts that individuate ordinary objects as belonging to/being instances of a certain kind, or sortal (Sattig, 2015, p.19). The following table elucidates the account of ordinary objects according to Aristotle’s hylomorphism and Perspectival Hylomorphism.

Ordinary Objects

Form Matter

59 For an extensive discussion of Perspectival hylomorphism and Aristotelian hylomorphism, see Chap. 2 and Chap. 3. In the present chapter, I am assuming and referring to these theories as background. 60 For brevity, I refer to Aristotelian form(s) as A -form. 61 For further details, see 2.2.

Aristotle’s hylomorphism The (sum of) relation(s) obtaining The material among the (proper) part of an object parts of the object Perspectival hylomorphism K-path, complex fact about a material A material object object(s)

In general, the form is the formal part of ordinary objects. However, according to Aristotle’s hylomorphism, the form is a (sum of) relation(s), while according to Perspectival Hylomorphism the form is a complex fact, namely a K-path. Sattig addresses the difference between these two notions in the following passage:

‘[…]Correspondingly, it is central to the Aristotelian conception that forms play an object-generating and object-structuring role. […]K-paths are just complex facts that play no deep unifying and structuring role. The identity of an ordinary object depends on the component K-path simply because the latter is another part of the object.’ (p. 28, my emphasis)

This chapter is divided into three parts. I will start my argument from Sattig’s rejection of A-forms. In the first part, my aim is to demonstrate that A-forms alone are not entirely responsible for the generation and the structure of ordinary objects (4.1). Moreover, I will stress that A-forms can account for the main features of K-paths (4.2). In the last part, I question what kind of entity a K-path is and I suggest an argument against them, following Betti (2015)(4.3).

4.1 Horizontal and Vertical Unity

62 According to Sattig, forms determine the existence and the identity of objects (Sattig, 2015, p. 6). On one hand, the form has an object-generating role as it dictates both how objects come into existence, exist, and go out of existence (Sattig, 2015, p.6 and p.28). On the other hand, the form has an object-structuring role because it determines the identity of objects as structured wholes (ibid.). I do not argue that the form does not have this role. What I analyze is rather how the form regulates the generation and the structure of ordinary objects. I claim that forms alone cannot play either of an object-generating or an object-structuring role. Forms have a crucial role in the generation and the structure of ordinary objects and, so, also in their existence and identity. So far, so good. However, let us take a step back and reflect on how ordinary objects are generated and how

62 In this subsection, I am only referring to Aristotelian forms, therefore I drop the prefix A-.

they are structured. Broadly speaking, Aristotle describes generation as a peculiar (and fundamental) kind of change, namely substantial change. Like every change, substantial change, i.e. generation/corruption, requires two elements (Phys. I.7, 1090a 14ff.). First, there has to be something that it is gained or lost through the change. Second, there has to be something that continues to be the same, or persist, through the change. The first element corresponds to form, while the second one corresponds to matter. The matter continues to be the same in the sense that it underlies the substantial change. The form is what is gained in the sense that there is a new relation among the material parts of the object. In this way, the matter is informed by the form and the ordinary object comes into 63 existence . Form and matter are so deeply connected, that it is debatable to identify the form as the element responsible for the existence of the object (as in Sattig, 2015, p. 6). The form alone cannot account for the object’s coming into existence. The ‘object-generating’ role, that Sattig refers to (Sattig, 2015, p. 28), is equally perform by form and matter. Let me focus on how Sattig uses the term object. On one hand, if he refers to the material object, it is trivial that the form cannot generate it. For example, in the case of the Venus de Milo, the marble is already there and it is not generated by the form. On the other hand, if Sattig uses the term object to refer to ordinary objects, one might agree that the form is responsible for the object’s generation. According to this view, in the case of the Venus de Milo, the form would be responsible for the marble’s becoming the Venus de Milo. However, the form alone cannot play an object-generating role because it does not exist separately from the matter that it informs. Consider the Venus de Milo, the form unifies the marble parts (to use Sattig’s terms), but it is not ontologically independent from those parts. Form and matter are ontologically interdependent so that what can account for the object’s generation and existence is exclusively their unity. According to my account of Aristotle’s form, this is evident as the form is the (sum of) internal relation(s) among the material parts of an object, while the matter corresponds to the relata of that relation. The reason for this is that the matter is what makes the object concrete and physical. The form, that is what makes the object something determined, needs a material anchorage anyway. An ordinary object, that is material and determined only comes into existence in this way, i.e. when the form informs the matter. For example, take the Venus de Milo: its form alone, this particular statue, would not have been able to generate the Venus. What, together with the form, made the generation of the Venus possible was the matter, marble. It is clear that the marble is essential for the Venus to come into existence. For if the marble was not there, there could not have been a

63 Recall that neither the form nor the matter is subjected to generation and corruption (M et. Z .8, 1033b 17-19).

relation among the material parts of the object. Form and matter are unified in such a way that they ensure the unity of the object over time, i.e. diachronic unity. Following Gill (1991), I refer to this unity as horizontal unity. It is horizontal because it indicates the unity of the object over time, namely its generation, existence, and 64 corruption . Within this unity, the matter provides the object with ‘material continuity’ over time (Gill, 1991, p. 108). Moreover, the form ensures continuity as it is the sum of all the relations in which the parts of the object stand throughout the object’s existence. The relevance of form and matter is likewise important for the structure of objects. Sattig points out that, according to Aristotelian hylomorphism, the 65 identity depends on the form because ordinary objects are structured entities (Sattig, 2015, p. 6). By contrast, I argue that not only the form but also the matter plays a role in establishing the identity of ordinary objects. This point is clear especially when Aristotle combines form and matter respectively with actuality 66 and potentiality. To be actual and to be potential are two senses of being that can explain both the generation and the structure of an object. First, the matter denotes the potentiality that a (not yet existing) object has to come into existence. I am not claiming that matter exists without a form. In this case, I am referring to objects, i.e. compound of form and matter, that have potentially another substantial form such that they can potentially exist as other objects. In particular, 67 this potentiality consists in the ability of the matter to receive a certain form , i.e the material parts of the object can potentially stand in a certain relation. However, the potentiality of the matter is not yet restricted to a determined way in which the object has to come into existence. The matter rather indicates a range of things that can come into existence potentially. For example, the marble is a

64 The notion of horizontal unity is also useful to explain accidental change. I will give an account of accidental change in 4.2. 65 The notion of identity is one of the most debated notions of Aristotle’s philosophy (Angioni, 2012; Bowin, 2008; Gill, 1991; Hartman, 1976; Maurin, 2011; Lewis, 1982; Scaltsas, Charles, & Gill, 2001; Rea, 1998; White, 1971; and many others). I will not present all the different views and theories behind this notion. This research cannot possibly take all these positions into account, but I reserve this topic for future works. It is enough to say that identity has not a univocal meaning for Aristotle, as many of his notion. As a result, identity expresses several kinds of sameness (see Top. I.7, 103a 6-14; Top. I.7, 103a 23-31; Met. Δ.9,1018a 7-9; Lewis, 1982; Smith, 1997; Rea, 1998; White, 197). Among these kinds of sameness, there is a sense in which objects are the same according to the form and another into which objects are the same according to matter. 66 See Met. ∆.8. 67 Notice that potentiality is not identical to possibility. Potentiality represents the possibility that an object has to exist in a concrete way, that it is with material parts and physical properties (Shields, 2016, Sec. 8). As a consequence, not every matter can be informed by every form. For example, the matter water cannot receive the form this particular statue.

potential statue, a potential column, a potential vase, etc. The potentiality becomes actuality when the form informs the matter so that the matter becomes something determined. This transition corresponds to the fact that the material parts of an object actually stand in a certain relation, that is the actual form. In this way, the form makes actual what the matter potentially was. Therefore, being a determined relation among the material parts of an object, the form realizes one thing out the range of potential things that the matter could have been. Consider the previous example, the form this particular statue makes the matter marble, that was potentially also other objects, something determined and actual, i.e. the Venus de Milo. Without the potentiality of the matter, the form cannot be anything concrete i.e. physical and material. Vice versa, without the actuality of the form, the matter cannot be something determined. Ordinary objects are concrete and determined only as compounds of form and matter. Actuality and potentiality illustrate how ordinary objects are structured. They exist as irreducible unities of their components, i.e. as composite unities. Form and matter determine two ways in which ordinary objects can be described as unities. First, the unity of form and matter characterizes the existence of objects over time, i.e. horizontal unity, as I discussed in the previous paragraphs. The latter explains how objects come into existence, exist and go out of existence. Second, the unity of form and matter dictates how objects are structured qua existing objects. This other kind of unity is called vertical unity (Gill, 1991, p.138). It establishes that if there is a unity of (substantial) form and matter, then there is an object which is the compound of that (substantial) form and that matter. Since ordinary objects exist as unities of form and matter, the identity of the object relies on both form and matter. Consequently, if form and matter are not unified, there is no object at all. Therefore, the unity of form and matter is the foundation of the existence and identity of ordinary objects. Aristotle argues that form and matter are one and the same reality because their unity accounts for the existence of the same object (Met. H. 6 1045b 17). Ordinary objects are unities whose components show two ways of being of the same object. The matter exhibits the potentiality of the object, while the form denotes the object’s actuality (Met. H. 6 1045b 18-22). What follows is a diagram that shows how horizontal and vertical unity work.

My point is that the form alone cannot perform an object-generating and an object-structuring role. The arguments above demonstrate that it is the unity of form and matter that answers for the existence and the identity of ordinary objects.

4.2 Forms and K-Paths

According to Perspectival Hylomorphism, a K-path is the form of ordinary objects. However, it seems to be very complex notion including a significant number of elements, e.g. qualitative content, realizers, meaningful properties, conjunctive complex facts, etc. (see here 2.2.2, and Sattig, 2015, p.16ff). Therefore, one might wonder whether there is a notion able to perform the same role of K-path while avoiding its complexity. I believe that A-form is a valid candidate for this role. Since K-paths are facts and A-forms are relations, what will result is not that the K-paths are A-forms, but rather that A-forms can account for K-paths’ main features. Before examining the details, I shall make a general point. If K-paths are forms because they provide ordinary objects with a qualitative profile, then A-forms also can be forms in this sense. As previously discussed in 3.1.1, the A-form is the (sum of) relation(s) obtaining among the material parts of an object objects. For example, among many things, the A-form makes an object unique as the (sum of) relation(s) in which material parts of the object stand is uniquely spatiotemporally located. Moreover, the A-form indicates when objects belong to a certain kind because the material parts relate to each other in a way that exemplifies a certain kind. For example, the Venus de Milo belongs to the kind statue because there is a relation among material parts such that Venus is an instance of the kind s tatue.

Now I take into account the main features of K-paths and how forms have similar traits. K-paths are described as a series of K-states, whose unity is characterized by the following properties (Sattig, 2015, p.20-21).

K-continuity The K-realizers of any two K-states spatially and temporally c lose in a K-path are extremely similar.

K-connectedness Although the K-realizers of any two K-states in a K-path can be far away from each other, they are connected in some way that is they have a minimum amount of similarity.

Lawful causal Any present K-state causally depends on the previous dependence K-state included in the same K-path (Immanent causation).

Maximality A K-path is exclusively the largest conjunction of K-states unified according to K-continuity, K-connectedness, and lawful causal dependence.

First, K-paths express continuity for two K-states, that are spatiotemporally close in a K-path, are very similar. For example, consider the Venus the Milo: it is a compound of the material object piece of marble and the statue-path. Any temporally and spatially close statue-states in a statue- path are continuous because they contain extremely similar facts. In a statue- path, a statue-state, that contains the fact that the piece of marble has the property of being white at a time t, is extremely similar to the statue- state, that contains the fact that the piece of marble has the property of being white at a time t1 , where t and t1 are temporally contiguous times. Second, in the same K-path, K-states are always connected by a minimum degree of similarity, no matter their distance in space and time. The connectedness of a K-path is complementary to its continuity. The latter points out a high level of similarity due to the closeness of K-states, while the former requires a minimal level of similarity depending on the remoteness of K-states. Let us consider again the Venus de Milo. Statue-states included in the statue- path can be distant in space and time, and yet they are similar to a minimum extent. This similarity implies that statue- states are always somehow connected in virtue of containing facts that are very similar. The statue- state, that contains the fact that the piece of marble has the property of having a certain shape at a time t, has to be similar to the statue-state, that contains the fact that the piece of marble has the property of having a certain shape at a time t1 , where t and t1 are distant in time. Only by having this similarity, two K-states are connected and included in the same K-path.

Third, K-paths imply causal dependence of K-states, that are close in time, because a K-state depends on the previous K-state. Think of the Venus de Milo again. In a statue-path, a statue- state causally depends on the statue- state before it because the latter contains facts that influence the facts contained in the former. If a statue- state contains the fact that the material object piece of marble has the property of being at the Louvre at a time t, then this fact affects the statue- state of the piece of marble at a later (contiguous) time. As a result, the statue- state will also contain the fact that the material object piece of marble has the property of being at the Louvre. The causal dependence of temporally close K-states implies also their similarity as in the case of continuity and connectedness. Finally, a K-path is maximal as it is restrictively the largest conjunction of K-states unified by continuity, connectedness, and causal dependence. For example, the statue- path is the maximal conjunction of all and only the statue-states connected according to the features above-mentioned. In what follows, I demonstrate that the features of K-paths, i.e. continuity, connectedness, lawful dependence, and maximality, in terms of A-forms, i.e. the relation obtaining among the object’s material parts. First, similarly to K-paths, the A-form is also an element of continuity. When the relation obtaining among material parts of an object is examined at times and in regions of space, that are close, then the relation will be very similar. For example, think of Venus de Milo again: its material parts occupy in a region of space R at a certain time t. The form of the Venus is the relation in which the Venus’ material parts stand in R at t. If we look at that relation one second after t, call it t1 , we will notice that the relation among Venus’ material parts has not changed that much. Thus, the form remains very similar when it is analyzed at two close times. The same explanation works for the regions of space. If the form of an object is thought about in two close regions of space, the relation denoted by the form will be similar. From this similarity, it follows that the form is characterized by continuity across space and time. This continuity of the form can be explained through the difference between substantial and accidental forms. The first one is the maximal sum of the relations among the material parts of the object. A substantial form accounts for the existence and the identity of an object from its generation to its corruption. Accidental forms are instead single temporary relations in which the material parts of an object stand. While the latter characterizes the object for a limited time and change, the substantial form ensures continuity during the whole existence of the object. When the object goes out of existence, the material parts no longer relate among each other in the same way – that is the object has lost its substantial form. The following diagram shows the distinction between substantial and accidental form.

Second, let us examine how the connectedness of K-paths can be explained in terms of A-forms. Again, the distinction between substantial and accidental form is helpful. As discussed in the previous paragraph, the substantial form is the maximal sum of all the relations obtaining among the material parts of the object throughout its existence. Apart from being an element of continuity, the substantial form is also an element of connectedness because it connects the object’s accidental forms. During its existence, an ordinary object is characterized by several accidental forms. To be precise, accidental forms show different ways in which the material parts of the object relate to each other. For example, I am sitting on my chair right now: the relation among my material parts is the accidental form of this particular human being seated (hereafter seated) . When I will stand up, my material parts will no longer relate according to that accidental form, i.e. seated. This entails that there is a new relation in which my material parts stand, namely the accidental form this particular human being standing up (hereafter standing up). Let us focus on the accidental forms, seated and standing up. Think about the case in which the accidental forms are not spatiotemporally contiguous, but they are far away from each other. Let us examine seated and standing up*, where the latter is the accidental form that I will have in twenty years. These accidental forms are distant in space and time and they may describe the relation obtaining among my material parts in very different ways. Seated and standing up* may not be very similar accidental forms, yet they are connected by a minimal similarity. All accidental forms are similar to a minimum extent, regardless of their spatiotemporal locations. This similarity is ensured by the substantial form, that connects all the relations in which the material parts of the object stand for its entire existence. In the example above, seated, standing up, and standing up* are connected by being parts of the sum of relations, i.e. the substantial form t his particular human being.

Third, the feature of causal dependence of K-paths can also be explained in terms of A-forms. In chapter 3, I have pointed out the form is an internal relation in which the object’s material parts stand. The form is an internal relation as it is determined by the things that stand in the relation, i.e the material parts of the object. The latter are physical parts of the object in the sense that they are material and that they occupy a certain region of space at a given time. Consequently, also the relation obtaining among these material parts is located in space and time. The fact that the object’s material parts stand in a certain relation at a time t — note that this is my account of Aristotle’s accidental form — deeply affects at a later time. To put it differently, the relation obtaining among the object’s material parts causally depends on their previous relation. For example, recall the example of the Venus de Milo: its accident form this particular statue being at the Louvre Museum indicates the relation among the Venus’ marble parts at a certain time t. The relation in which the marble parts of Venus will stay at a later time causally depends on the way in which they related to each other at t. Since the form is an internal relation among the material parts, how these parts relate at a given time causally depends on how they related to each other previously. As a result, A-forms are characterized by causal dependence in that the relation among the object’s material parts at a given time causally affects that that relation at a later time. Finally, let us analyze maximality. It is possible to compare K-path’s being the maximal conjunction of complex facts to the substantial form’s being the maximal sum of relations among the object’s material parts. Both K-paths and forms are maximal in the sense that they are characterized by uniqueness. Maximality seems a sufficient condition for uniqueness in the sense that what is maximal is always unique. What is maximal contains/includes all and only its parts, what is unique is identical to the sum of its parts. Therefore, every time that something is maximal, it is also unique because it is identical to the parts it includes. However, maximality seems not to be a necessary condition for uniqueness, namely something can be unique without being maximal. Let us go back to K-paths and A-forms. A K-path is exclusively the maximal conjunction of K-states combined a certain way such that there is identical to the K-states it includes, and so it is unique. (Sattig, 2015, p.24). Moreover, a (substantial) A-form is the maximal sum of all and only the relations obtaining among the object’s material parts such that it is identical to those relations it includes, and therefore it is unique. By including all these relations, a substantial form denotes how the object’s material parts relate among each other over the object’s existence. Not only the single relations, i.e. accidental forms, but also the sums of these relations, i.e. substantial forms, are numerically distinct for every object. There

are no two substantial forms that are identical, and each substantial form is unique. To summarise, A-forms can account for the main feature of K-paths, although in terms of relations. This comparison suggests that Aristotelian form can play the same role as K-paths without claiming for complex facts. In the following subsection, I address some questionable features of K-paths.

4.3 What is a K-path?

The notion of K-path is the core of Perspectival Hylomorphism (Sattig, 2015, p. 19). In section 2.2, I have presented this notion, what it contains, and what are its features. In the previous section, I have shown that A-forms are able to play the role of K-path as K-path’s main feature can be explained in terms of A-form. What I will examine now is the kind of entity that K-path is. To be more precise, for any kind K, a K-path is the maximal conjunction of K-states, that are in turn facts providing a material object with a K-meaningful intrinsic profile and a K-realizing profile. In other words, a K-path is a complex conjunctive fact about a material object and the latter is the subject of a K-path. According to PH, ordinary objects are compounds of form and matter where the object’s form is a K-path and the object’s matter is a material object (Sattig, 2015, p.29). I now address problems that K-paths show. K-paths are a series of K-states, that in turn are complex conjunctive facts about a material object (Sattig, 2015, p. 18 and p.30). These K-states include facts that indicate the object’s properties that realize a certain kind in a K-state. These facts have an individuative force because they individuate the object in a K-state from its properties realizing a given kind (Sattig, 2015, p.19). Therefore, objects are individuated by K-state in K-path. Moreover, Sattig argues that a K-path is the individual form of ordinary objects. It is individual because it has a location in space and time (ibidem.). A K-path provides the material object with an individual qualitative profile that includes a K-meaningful intrinsic profile and a K-realizing profile. It does so in virtue of being “a distribution of facts across a particular four-dimensional region of space-time” (Sattig, 2015, p.29). In addition, one of the main features of a K-path is maximality. It is only the maximal conjunction of K-states unified according to continuity, connectedness and causal dependence that counts as K-path (Sattig, 2015, p. 21). A K-path is unique because there is only one maximal conjunction of K-states unified in this way (Sattig, 2015, p. 24). Therefore, each K-path corresponds to the maximal conjunction of K-states, for any kind K. These several aspects of K-path seem to be coherent, so far. However, other aspects of K-paths appear to be ambiguous.

According to Sattig, K-paths are different from A-forms as the latter justifies the existence and the identity of ordinary objects. I have already discussed this point in 4.1, but I shall focus now on what K-paths are. Sattig argues that K-paths are just complex facts. Moreover, these facts have neither unifying nor structuring function (Sattig, 2015, p.28). On one hand, K-paths do not unify the ordinary object in the sense that they do not account for the object’s existence. On the other hand, K-paths do not provide the structure of the object because they do not determine the identity of the object. My concerns about this description of K-paths are as follows. First, K-paths corresponds to a series of K-states unified according to some K-relevant aspects. The unity of K-state corresponds to the K-path. Nonetheless, one may claim that the K-path is a unity, but it does not provide unity to the ordinary object. This may be true as it is not the K-path that dictates when an ordinary object is a unity. However, the K-path is involved in the unity of an ordinary object as it is a part of it. More precisely, if ordinary objects are described as compounds, then their main characteristic is that they are unities of their parts. It is in virtue of being parts of the compound that both a K-path and a material object affect the unity of ordinary objects. Second, the same argument can be applied to the structuring role of the K-path. I am not claiming that the K-path is what determines the structure of ordinary objects tout court. I am rather pointing out that K-paths have (partly) this role because they are part of the compound. In the simplest case, the structure of a compound corresponds to the union of the components. This is also Sattig’s description of ordinary objects: they are compounds of two components, namely a K-path and a material object. Again, both K-paths and material objects have their role in the structure of ordinary objects as they are parts of the compound. They also b oth d etermine the identity of the objects (ibid.). Furthermore, Sattig claims that distinct material objects can be the subject of the same K-path and that the same material object can be the subject of distinct K-paths (Sattig, 2015, p.21). For example, consider the piece of marble of which the Venus de Milo is made and the piece of marble of which the David of Michelangelo is made. These material objects are subject of a K-state in the same statue-path. In addition, the same piece of marble of which the Venus is made can be the subject of the statue- path as well as furniture- path. Although this aspect of ordinary objects seems very intuitive, it raises some questions concerning the nature of K-path. As pointed out a few paragraphs above, a K-path is the individual form of an ordinary object because it is localized in space and in time. According to this account, it appears that a K-path is a conjunction of complex facts about68 a material object during a period of time and in a certain region of

68 Sattig does not specify whether K-paths are propositional or compositional facts. Sattig refers to ordinary objects interchangeably as ‘facts about’ and ‘ facts that include/contain’.

space. If distinct material objects can be the subject of the same K-path, the K-path does not really stand for an individual form, but rather for a universal one. Moreover, Sattig argues that K-paths provides the object with an individual qualitative profile and that this qualitative profile is kind-dependent (Sattig, 2015, p.26). As also Sattig points out (Sattig, 2015, p. 15), kinds are concepts under which many objects fall. Again, if many material objects can be the subject of the same K-path is not clear how the qualitative profile of the object could be individual. Conversely, if K-path were universal, then many material objects could the subject of the same K-paths in virtue of sharing the same qualitative profile, that depends on a given kind. Moreover, Sattig’s argues that a K-path is a complex conjunctive fact (Sattig, 2015, p. 139). Prima facie, it seems explicit that K-paths are conjunctions of facts, that consists of a conjunction—they are the maximal conjunction of K-states, that in turn are conjunctive facts. Nonetheless, when describing K-paths more deeply, Sattig ascribes to K-paths some features that are proper to structural universals. The latter are universal reticulated in particular objects that exemplify the structure of the universal (Menzel,2017, 2.3). In particular, Sattig argues that material objects instantiate the qualitative content of a kind, namely the properties that are shared by the instances of that kind (Sattig, 2015, p.16). In addition, K-paths are individuated by the qualitative content of a kind K. Therefore, when a material object is a subject of a K-path, it instantiates the qualitative content of a kind K that individuates the K-path. The qualitative content of a kind K are the properties that all the instances of a kind K have in common. Thus, when material objects instantiate the same qualitative content of a kind K, it means that K-path individuated by that qualitative content is likewise the same. This suggests that K-paths are structural universals whose structure is identified by a qualitative content, that it is exemplified by material objects. For example, think of the Venus de Milo. The piece of marble of which it is made instantiates the qualitative content of the kind statue, namely the properties shared by the instances of the kind statue, e.g. having a certain shape, being of a certain high, having a certain weight. The qualitative content of the kind statue individuates the statue- path. All the material objects, that are instances of the kind statue, instantiate the same qualitative content, that individuates the same statue-path. Therefore, although Sattig denies that K-paths have a structuring-role (Sattig, 2015, p.28), it seems that they have a universal structure that is exemplified by material objects. Additionally, it appears that K-paths are individual and concrete because they involve material objects or particulars. K-paths form a compound, i.e. an ordinary object, together with a material object. The material object, that is the matter of the ordinary object, is itself an unstructured whole (Sattig, 2015, p.28).

Moreover, the ordinary object is the material object plus a conjunctive fact about that very material object, namely a K-path. Now, if ordinary objects are the compounds of a material object and a K-path, then it seems that the very same object is taken twice. Let us see how. Consider again the Venus the Milo (V) . According to Sattig’s theory, it is a compound of a material object, piece of marble (M ) , and the K-path, statue -path (S) . S is the maximal conjunction of facts about M such that M has an individual qualitative profile according to the kind statue. To be precise, we shall refer to S as S(M), namely the statue- path about M. If we consider the material object M as already itself a whole, then we would count that object a first time. In addition, given that the M is also the matter of V, we would count that very same object M a second time when considering the ordinary object as a whole. Therefore, we would have that V= M + S(M). As a result, if ordinary objects are compounds of a material object and a K-path, they would include the same object counted twice. Moreover, there would be two kinds of wholes, namely the material object and the ordinary object. Finally, also the compositional structure of K-paths seems to be controversial. Here, I follow an objection against facts presented by Betti (2015). This objection points out that in an ontology that includes facts and adheres to basic principles of mereology, a fact with constituents always coincides with a sum with parts. Facts and sums usually refer to two different kinds of 69 composition, namely nonmereological and mereological . Betti claims that “For every fact Fa with constituents F, a, there exists a sum of a + F with parts a, F, coincident with the fact” (Betti, 2015, p.69). Therefore, there are two coincident objects: one is explained in terms of fact with constituents, the other is explained in terms of sum with parts. Let us examine whether K-paths also entails this coincidence. The composition of K-paths is very complex, and it is not totally explicit whether it is mereological or not. K-paths are the maximal conjunction of K-states, that in turn are maximal conjunctions of facts. Therefore, a K-state is a conjunctive fact for it is conjunct of the facts of which it is composed(Mulligan & Correia, 2017, Sec. 2.5). K-states includes K-meaningful and K-realizer properties of a certain material object. For example, the K-state about the piece of marble M includes the maximal conjunction of facts that M exists at t, that M has the property of being 203 cm high, that M has the property being approximately white, etc. Think about the material object M and one of its properties, say being 203 cm, such that M is 203 cm high. M and being 203 cm high can form two distinct, yet coincident objects. On one hand, according to a nonmereological composition, they can be the constituents of a fact, namely M’s being 203 cm high. On the other hand, according to mereological composition, they can be the parts of a mereological sum, namely M + being 203 cm. Therefore, for each fact with constituents included

69 Mereological composition is discussed in 2.1.

in K-states and in K-paths, there is a sum with parts that coincide with the fact. It is debatable whether we should accept this double kind of composition. More precisely, there are two points that make even more arguable that Perspectival Hylomorphism needs facts. First, Perspectival Hylomorphism applies mereological composition both to ordinary objects and to object’s matter, i.e. a material object. It is not clear why Sattig needs to bring into play complex facts that involve a totally different kind of composition. Second, the most plausible reason to involve complex facts, namely K-paths, is that they play a unifying role. However, Sattig denies that K-paths have a unifying role and so his motivation for invoking facts is uncertain. Let me summarize the questionable features of K-paths that I discussed above. First, K-paths are defined as the individual forms of ordinary objects, while they have features proper of universal forms, i.e. they belong to and are instantiated by more than one material object. Second, K-paths are conjunctive facts, but they have features proper of structural universals, i.e. material objects, that fall under the same K, instantiate and realize the same properties that in turn individuate a K-path. Third, ordinary objects as compounds of a material object and a K-path imply that the material object is taken twice, i.e. a first time the object is counted as a material object, plus a second time the very same objects (together with the K-path) is counted as an ordinary object. Fourth, the compositional structure of K-path remains unclear as it is not defined whether they have mereological or non-mereological composition, i.e. if K-path have a non-mereological composition, then there would be a sum with parts that coincide with the facts included in the K-path. To conclude, in this chapter I have discussed the role that A-form plays in the generation and in the structure of objects. Then, I have discussed the main feature of K-paths in terms of A-form to show that A-forms are a valid alternative to K-path and they avoid the commitment to complex facts. Finally, I have explained my doubts about K-paths considered as complex conjunctive facts.

Conclusion

The aim of this thesis was to show that Aristotle’s notion of form is deeply relevant to the contemporary debate about the metaphysics of ordinary objects. Aristotle’s hylomorphism, the metaphysical account that take ordinary objects to be compounds of form and matter, has been the inspiration for many contemporary versions of hylomorphism. For example, Evnine (2016), Fine (1992, 1994, 1999, 2008), Jaworski (2014), Johnston (2006), Koslicki (2007, 2008), Marmodoro (2013), Pruss (2013), Sattig (2015), Rea (1998, 2011). In particular, I focused on a contemporary metaphysical account, namely perspectival hylomorphism as proposed by Thomas Sattig in The Double Life of Objects (2015). The metaphysics of perspectival hylomorphism, i.e. q-hylomorphism, claims that ordinary objects are compounds of form and matter, as Aristotle’s hylomorphism. However, Q-hylomorphism diverges from Aristotle’s hylomorphism in that it ascribes a different nature to form and matter. According to it, the matter of an ordinary object is a material object, that in turn is the mereological sum of smaller material objects, while the form of an ordinary object is a K-paths, namely a complex conjunctive fact about that material object. Conversely, I interpreted Aristotle’s hylomorphism claiming that the matter of an ordinary object is its material parts, while the form of an ordinary object is the (sum of) relation(s) obtaining among the object’s material parts. I showed that my interpretation of Aristotle’s notion of form is able to perform the same role of K-paths without committing to complex conjunctive facts. Moreover, I suggested that the involvement of K-paths leads to more problems than it solves. In Chapter 1, I introduced the notion of ordinary object. Then, I specified two main assumptions I relied on this thesis, namely that ordinary objects exist and that they are to be conceived as concrete particulars. Moreover, I outlined the broader context of the metaphysics of ordinary objects in order to place the discussion of this thesis. In Chapter 2, I presented Sattig’s perspectival hylomorphism by focusing on the metaphysical account of q-hylomorphism. I discussed the two philosophical traditions on which q-hylomorphism draw upon, namely Classical Mereology and Aristotelian Hylomorpshim. Then, I examined the core notion of q-hylomorphism, that of K -path. In Chapter 3, I analyzed Aristotle’s hylomorphism. I examined its three fundamental notions, namely form, matter, and compound. Then, I reconstructed

Aristotle’s mereology by taking into account the notion of part and whole. The whole chapter is based on my own interpretation of Aristotle’s original texts. In Chapter 4, I compared the notion of Aristotle’s forms and the notion of K-paths. In contrast to Sattig’s reading of Aristotle’s hylomorphism, I claimed that both form and matter determine the object’s condition of existence and of identity. Then, I explained the main features of K-paths in terms of my interpretation of Aristotle’s to show that the latter is a valid alternative to the former. Moreover, I put the notion of K-path into question by raising issues concerning its nature. Therefore, this thesis shed light on the importance of Aristotle’s notion of form for contemporary theories of ordinary objects. Moreover, I proposed an alternative interpretation of Aristotle’s form that is not only more viable in the present discussion, but also opens up to further research.

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Chapter 4

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Menzel, Christopher, "Possible Worlds", The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.), URL = . Mulligan, Kevin and Correia, Fabrice, "Facts", The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.), URL = . Rea, M. C. (1998). Sameness without Identity: an Aristotelian Solution to the Problem of Material Constitution. Ratio, 11(3), 316–328. https://doi.org/10.1111/1467-9329.00073 Sattig, T. (2015). The double lives of objects: an essay in the metaphysics of the ordinary world (First edition). Oxford: Oxford University Press. Scaltsas, T., Charles, D., & Gill, M. L. (2001). Unity, identity, and explanation in Aristotle’s metaphysics. Oxford University Press.

Shields, Christopher, "Aristotle", T he Stanford Encyclopedia of Philosophy ( Winter 2016 Edition), Edward N. Zalta (ed.), URL = . Varzi, A. C. (2008). The Extensionality of Parthood and Composition. The Philosophical Quarterly (1950-), 58( 230), 108–133. Retrieved from JSTOR. White, N. P. (1971). Aristotle on Sameness and Oneness. The Philosophical Review, 80( 2), 177. https://doi.org/10.2307/2184029