The mass-count distinction is a morpho-syntactic distinction among nouns that is generally taken to have semantic content. This content is generally taken to reflect a conceptual, cognitive, or ontological distinction and relates to philosophical and cognitive notions of unity, identity, and counting. The mass-count distinction is certainly one of the most interesting and puzzling topics in syntax and semantics that bears on ontology and cognitive science. This volume aims to contribute to some of the gaps in the research (...) on the topic, in particular the relation between the syntactic mass-count distinction and semantic and cognitive distinctions, diagnostics for mass and count, the distribution and role of numeral classifiers, abstract mass nouns, and object mass nouns (furniture, police force, clothing). (shrink)

The notions of part and whole play an important role for ontology and in many areas of the semantics of natural language. Both in philosophy and linguistic semantics, usually a particular notion of part structure is used, that of extensional mereology. This paper argues that such a notion is insufficient for ontology and, especially, for the semantic analysis of the relevant constructions of natural language. What is needed for the notion of part structure, in addition to an ordering among parts, (...) is the notion of integrated whole. In the context of semantics, the notion of an integrated whole needs to be relativized to a situation, or so it is argued. (shrink)

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers (...) such as 'whole', 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the (...) semantic differences between nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

It is common in contemporary metaphysics to distinguish two levels of ontology: the ontology of ordinary objects and the ontology of fundamental reality. This papers argues that natural language reflects not only the ontology of ordinary objects, but also a language-driven ontology, which is involved in the mass-count distinction and part-structure-sensitive semantic selection, as well as perhaps the light ontology of pleonastic entities. The paper recasts my older theory of situated part structures without situations, making use of a primitive (...) notion of unity. (shrink)

How do plurals and mass nouns refer? What kind of logic should be used in order to account for the truth-conditions of the sentences they appear in? For linguists, first-order predicate logic is adequate, provided it is supplemented by a notion of mereological sum for plurals and for mass nouns. On the contrary, according to some philosophers, new logics must be used, plural logic for plurals and mass logic for mass nouns. We survey (...) these debates in this entry. (shrink)

I present a high-level account of the semantical distinction between count nouns and non-count nouns. The basic idea is that count nouns are semantically either singular or plural and non-count nouns are neither.

Here is a common view. There exist things, and there exists stuff, where roughly, ‘thing’ is a count noun, and ‘stuff’ is a mass noun. Syntactically, ‘thing’ functions as a singular referring term that takes ‘a’ and ‘every’ and is subject to pluralisation, while ‘stuff’ functions as a plural referring term that takes ‘some’ and is not subject to pluralisation. Hence there exists a thing, and some stuff. Usual versions of the common view endorse two principles about portions of (...) stuff. The first principle is that (temporal) mereological essentialism is true of portions (parcels, masses, quantities) of stuff, where mereological essentialism is the thesis that for any persisting object or portion of stuff, that object or stuff has the same parts at every time at which it exists. The second principle is that portions of stuff obey a principle of stuff composition: for any two portions of stuff P1 and P2, there exists a portion of stuff that is the fusion of P1 and P2. I argue that these two principles are inconsistent. In particular, since I am sympathetic to PSC, I argue that mereological essentialism is false of portions of stuff. (shrink)

Mereological entities often seem to violate ‘ordinary’ ideas of what a concrete object can be like, behaving more like sets than like Aristotelian substances. However, the mereological notions of ‘part’, ‘composition’, and ‘sum’ or ‘fusion’ appear to find concrete realisation in the actual semantics of mass nouns. Quine notes that ‘any sum of parts which are water is water’; and the wine from a single barrel can be distributed around the globe without affecting its identity. Is there here, as (...) some have claimed, a ‘natural’ or ‘innocent’ form of mereology? The claim rests on the assumption that what a mass noun such as ‘wine’ denotes — the wine from a single barrel, for example — is indeed a unit of a special type, the sum or fusion of its many ‘parts’. The assumption is, however, open to question on semantic grounds. (shrink)

Proper names are generally taken to be count nouns. This paper argues that this is mistaken and that at least in some languages, for example German, names divide into mass and count. Making use of Kayne's (2005, 2010) theory of light nouns, this paper argues that light nouns are part of (simple) names and that a mass-count distinction among light nouns explains the behavior of certain types of names in German as mass rather than count. The paper (...) elaborates the role of light nouns with new generalizations regarding their linguistic behavior in quantificational and pronominal NPs, their selection of relative pronouns in German, and a general difference in the support of plural anaphora between English and German. (shrink)

Survey of issues pertaining to the semantics of mass and plural nouns.

There is an emerging view according to which countability is not an integral part of the lexical meaning of singular count nouns, but is ‘added on’ or ‘made available’, whether syntactically, semantically or both. This view has been pursued by Borer and Rothstein among others in order to deal with classifier languages such as Chinese as well as challenges to standard views of the mass-count distinction such as object mass nouns such as furniture. I will discuss a range (...) of data, partly from German, that such a grammar-based view of countability receives support when applied to verbs with respect to the event argument position. Verbs themselves fail to specify events as countable in English and related languages; instead countability is made available only by the use of the event classifier time or else particular lexical items, such as frequency expressions, German beides ‘both’, or the nominalizing light noun -thing. The paper will not adopt or elaborate a particular version of the grammar-based view of countability, but rather critically discuss existing versions and present two semantic options of elaborating the view. (shrink)

So-called mass nouns, however precisely they are defined, are in any case a subset of non-count nouns. Count nouns are either singular or plural; to be non-count is hence to be neither singular nor plural. This is not, as such, a metaphysically significant contrast: 'pieces of furniture' is plural whereas 'furniture' itself is non-count. This contrast is simply between 'the many / few' and 'the much / little' - between counting and measuring. However not all non-count nouns are, like (...) 'furniture', semantically atomic - 'wine' and 'water' are not. And here there are serious difficulties in the assignment of a range of values for variables, in a formal representation of quantified sentences involving such non-atomic non-count nouns. (shrink)

Othering is the construction and identification of the self or in-group and the other or out-group in mutual, unequal opposition by attributing relative inferiority and/or radical alienness to the other/out-group. Othering can be “crude” or “sophisticated”, the defining difference being that in the latter case othering depends on the interpretation of the other/out-group in terms that are applicable only to the self/in-group but that are unconsciously assumed to be universal. The Mass Noun Thesis, the idea that all nouns in (...) certain languages are grammatically and folk-ontologically similar to mass nouns in English, is an example of such sophisticated othering. According to this Thesis, (a) count nouns refer to discrete objects and mass nouns to stuffs; (b) the other’s language has only mass nouns and thus no count nouns; and therefore, (c) the other’s folk-ontology is an ontology of mass stuffs only. There is much evidence, however, that folk-ontology is independent from language. This paper argues that the Mass Noun Thesis is a case of sophisticated othering rooted in a conflation of grammatical and ontological conceptions of mass and count nouns that is applicable to the language of the interpreter/self but not to the languages of the relevant others, and that othering in this case is driven by a need to create some radically alien other to support a scientific or philosophical theory. (shrink)

The mass-count distinction is a morpho-syntactic distinction among nouns that is generally taken to have semantic content. This content is generally taken to reflect a conceptual, cognitive, or ontological distinction and relates to philosophical and cognitive notions of unity, identity, and counting. The mass-count distinction is certainly one of the most interesting and puzzling topics in syntax and semantics that bears on ontology and cognitive science. In many ways, the topic remains under-researched, though, across languages and with respect (...) to particular phenomena within a given language, with respect to its connection to cognition, and with respect to the way it may be understood ontologically. This volume aims to contribute to some of the gaps in the research on the topic, in particular the relation between the syntactic mass-count distinction and semantic and cognitive distinctions, diagnostics for mass and count, the distribution and role of numeral classifiers, abstract mass nouns, and object mass nouns.The mass-count distinction is a morpho-syntactic distinction among nouns that is generally taken to have semantic content. This content is generally taken to reflect a conceptual, cognitive, or ontological distinction and relates to philosophical and cognitive notions of unity, identity, and counting. The mass-count distinction is certainly one of the most interesting and puzzling topics in syntax and semantics that bears on ontology and cognitive science. In many ways, the topic remains under-researched, though, across languages and with respect to particular phenomena within a given language, with respect to its connection to cognition, and with respect to the way it may be understood ontologically. This volume aims to contribute to some of the gaps in the research on the topic, in particular the relation between the syntactic mass-count distinction and semantic and cognitive distinctions, diagnostics for mass and count, the distribution and role of numeral classifiers, abstract mass nouns, and object mass nouns. (shrink)

The concept of universal in Aristotle’s philosophy has several aspects. 1) Universal and plurality Aristotle posits universal (καθόλου) versus particular (καθ᾿ ἕκαστον) each covering a range of elements: some elements are universal while others are particulars. Aristotle defines universal as ‘that which by nature is predicated (κατηγορεῖσθαι) of many subjects’ and particular as ‘that which is not’ so. (OI ., I, 7, 17a38-b1) The plurality of possible subjects of universal is what Aristotle insists on. The inclusion of the notion of (...) ‘plurality’ in the definition of universal might make us expect to have ‘singularity’ in the definition of particular. So, when Aristotle says that universal is that which is naturally predicable of many subjects, we expect him to define the particular as ‘that which is predicable of one subject only.’ Nonetheless, Aristotle does not and indeed cannot define it this way. We cannot find a text in which he defines particular as such simply because particulars are not predicable of any subject unless we regard their predication of themselves a predication, which Aristotle does not, at least in a genuine sense. Thus, he defines a particular only negatively. Hence, the capability of predication of a plurality is indeed the capability of predication itself because the particular cannot be predicated of anything. A particular is that which cannot be predicated of anything (or: of anything else, if saying of a thing of itself is to be considered as predication). It is ‘numerically one’ and what of which the universal is predicated (Met., B, 999b34-1000a1). Those that cannot be predicated of anything, or particulars, are of two kinds: primary substances and individual accidents. Besides Categories we can hardly find a text where Aristotle discusses individual accidents maybe because they are of much less importance for him compared with substances. However, substances are what he mentions repeatedly so that we can confine particulars to substances. In fact, it is substance that Aristotle considers so repeatedly as what cannot be predicated. As the main particulars and individuals, substances are posited as the main things that are not universal. The closeness of the two concepts of ‘substance’ and ‘unpredicability’ is to the extent that he ignores individual accidents and makes these concepts equal and as the opposite of universal: ‘what is not predicated of a subject is said a substance (οὐσία λέγετα τὸ μὴ καθ᾿ ὑποκειμένου) but what is always said of some subject is called a universal.’ (Met., Z, 1038b15-16. cf. Met., B, 1003a7-9) Therefore, since particulars cannot be predicated of any subject and, thus, every predication is necessarily a predication of a plurality of subjects, the inclusion of ‘plurality’ in the definition of universal is either i) in the sense of ‘representation’ or it must be regarded as ii) an unnecessary addition mentioned just for clarification or iii) only for avoiding cases where something is predicated of itself. By the first we mean this: though a substance is not said of anything, it represents some one thing and there is some one thing that is that substance. A universal, on the other hand, can represent a plurality of things. There is, however, a third possibility that has no essential difference with the sense of representation. Aristotle might have ‘arbitrary predication’ in mind when he suses ‘plurality’ in the definition of universal: while a particular can be the arbitrary predicate of just one thing, a universal can be predicated, both really and arbitrarily, of many things. Whatever Aristotle’s intention was, what is important for our investigation is this: Aristotle uses the notion of plurality in the definition of universal in spite of the fact that it is not necessary. What this implies is that this notion is so important for Aristotle that albeit every predictability is a predictability of a possible plurality, he adds the notion of plurality. What makes this notion important, I believe, is that he has something like a class in mind when he defines a universal because the notion of plurality is indistinguishable from a class. 2) Universal and whole; particular and part In Aristotle, the concepts of universal and whole are so close: ‘That which is true of a whole class and is said to hold good as a whole (which implies that it is a kind of whole) is true of a whole in the sense that it contains many things by being predicated of each, and that each and all of them, e.g. man, horse, god, are one because all are living things (τὸ μὲν γὰρ καθόλου καὶ τὸ ὃλως λεγόμενον ὡς πολλὰ περιέχον τῷ κατηγορεῖσθαι καθ’ ἑκάστου καὶ ἓν ἃπαντα εἶναι ὡς ἑκαστον, ...). Phil Corkum points to Aristotle’s distinction between quantitative and integral wholes in Met., 5, 26, 1023b26-33 where a quantitative whole is called homoiomerous, as the sum of animal while an integral whole, e.g. a house, is called heteromerous. He links the notion of homoiomerous to the notion of indivisibility of individuals (in 1b6-9 and 3b10-18) and indivisibility of universals. He believes that in PrA., I, 4, 25b32-26a2 it is the transitivity of mereological containment that is discussed. 3) Universal is common between instances Universal is common (κοινόν) between all the plurality of subjects it can be predicated of because what belongs to more than one thing must be common between them. (Met., Z, 1038b10-12) In the Same way, what is common cannot be a particular and, thus, a substance. (Met., Z, 1040b23-24) An individual or substance is a ‘this’ and a ‘this’ cannot be what common indicates simply because it is here in ‘this’ and can be nowhere else while common must be common between several things. In fact, what can be indicated by a common is indeed a ‘such.’ (Met., B, 1003a7-9) 4) Universal is the same in its instances We have a universal i) in all of its instances and ii) in the same way (ταὐτὸ ἐπὶ πὰντων). (Met, Γ, 1005a9-10) While the first point is evident (otherwise how could it be their universal?), the second point might seem not only ambiguous but the cause of many problems. For Aristotle, therefore, a universal must be ‘one’ in number and not many. This numerically one universal is the very universal for all its instances. It is the same universal that is predicated on each of its instances. This sameness is not, however, a mere homonymous sameness or the sameness of a homonymous word. All these three points, namely oneness, sameness and rejection of mere homonymous sameness are asserted in Aristotle’s own words τι ἕν καὶ τὸ αὐτὸ ἐπὶ πλειόνων μη ὁμώνυμον. (PsA., A, 11, 77a8-9) This non-homonymous unity is asserted also in PsA., A, 24, 85b15-16. 5) Universal as predicate Contrary to substance that cannot be a predicate, universal is what cannot be prevented from being in the place of predicate. Therefore, Aristotle distinguishes universal from subject because while the latter must necessarily be capable of being a predicate, though it might take the position of subject as well, the latter does not necessarily have such a capability especially when it is a this because it cannot be a predicate in such a case: ‘For the subject and universal differ in being or not being a ‘this’; like man and body and soul are the subject of accidents while the accident is something like musical or white.’ (Met., Θ, 1049a27-30) This indicates that a universal is basically different from subject and although it can be posited in the place of subject, it is the position of predicate that is its position as a universal. In Metaphysics, Z, 13, Aristotle asserts that ‘no universal can be substance.’ The same is asserted in Met., I, 1053b16-17 cf. 1060b21. As James H. Lesher points out, Aristotle’s position is that ‘nothing predicated universally is a substance.’ 6) Universal in substance In Met., 10388b8-9 Aristotle says that no universal is a substance. While a universal cannot be a substance in the way essence (to ti en einai) is, it is, Aristotle asserts, ‘in’ it (ἐν τούτῳ δὲ ἐνυπάρχειν) (Met., Ζ, 1038b16-18). Aristotle’s examples are: animal in man and horse. A universal is ‘in’ the thing it is its universal. But in what sense a universal can be in a thing? It cannot be in it as ‘in a subject’, which is denied in Categories for secondary substances. If we check the senses of being in, we can find some other senses of ‘being in’ some of which are compatible with this sense of ‘being in.’ Michael J. Loux believes that contrary to his earlier works like Peri Ideaon and Organon in which the immanence of universals signals a reproduction of the platonic two worlds picture, in his later works like Physics and Metaphysics, when Aristotle tells us that universals are in particulars he means that they are ‘components of or ingredients in sensible particulars.’ In Metaphysics (Δ, 1014b3-9) Aristotle compares elements with universals and call them ‘the most universal things because elements are present either in all or in many things. 7) Logos is of universal Not only universals have logos (Met., Z, 1038b18-19) but ‘Every logos and every science is of universals and not of particulars.’ (Met., K, 1059b25-26) The reason is that they are the same: the logos of the unjiversal ‘circle’ is nothing but ‘being circle’ and the logos of the universal ‘soul’ is ‘being soul.’ (Met., Z, 1035b33-1036a2) The same is said about definition. (Met, Z, 1036a27-29) 8) Universal: in the soul Contrasting individuals, universals are in the soul (So., 3, 5, 417b22-23; cf. PsA., B, 19, 100a6-7). Aristotle also says that the form, i.e. the essence, of the artwork is in the soul. (met., Z, 1032a32-b2) Moreover, as Michael J. Loux points out, ‘the Peri Ideon tells us that we need universals to serve as the objects of noetic acts.’ 9) Universal: not beside individual In spite of the fact that demonstration creates the opinion that demonstrating is based on the existence of universals as existing among the existing things, they do not have existence besides individuals (PsA., A, 24, 85a31-35; Met, Λ, 1071a19-23). Aristotle believes that universals of a P-series (B203, 71) are not παρὰ τὰ εἴδη: 999a6ff. Also check De Anima, II, 3, 414b20-25 10) Primary or commensurate universal Aristotle distinguishes ‘πρῶτον καθόλού’ (PsA., B, 17, 99a33-35) literally meaning ‘primary universal’ but mostly, and truly, translated as commensurate universal. While a universal merely ‘μὴ ἀντιςτρέφει,’ a primary universal ‘ᾧ ἓκαςτον μὲν μὴ ἀντιςτρέφει’ (PsA., B, 17, 99a33-35). Aristotle mentions three conditions for a commensurate universal. It is an attribute that i) belongs to every instance of its subject (without exception!!!), and this belonging is ii) essentially and iii) qua that subject itself (ᾗ αύτό). (PsA., A, 4, 73b26-28) However, he insists that the second and the third conditions are indeed the same. (PsA., A, 4, 73b28-30) The first condition he paraphrases as ‘to belong to any random instance of that subject’ and the second and the third as ‘when the subject is the first thing to which it can be shown to belong.’ (PsA., A, 4, 73b32-74a3) Aristotle’s example is ‘the equality of its angles to two right angles’. This attribute is not a commensurate universal of figure due to the first condition: it cannot be demonstrated of any figure. Nonetheless, though it can be demonstrated of every isosceles because every isosceles has angles equal to two right angles, it is not a commensurate universal of isosceles due to the other conditions: it is not predicated of isosceles qua isosceles but qua triangle. These conditions seem to be like regulators: they organize everything to match to the right group. The method of finding commensurate universal is like test and error method based on elimination: you must eliminate each of the higher or lower universals and check if the attribute remains or not. The commensurate universal is that which remains in between eliminated universals. (cf. PsA., A, 5, 74a37-b4) Brad Inwoodpresents an understanding of commensurate universal that is different from what I have understood and, thus, must be checked: ‘These universals are propositions in which, for example, ‘all A are B’ is true and which are still true universal statements if converted: ‘all B are A’ is also true.’ -/- . (shrink)

This introduction to 'Mass and Count...' gives an overview of different views of the mass-count distinction as well as an introduction to the papers in the edited volume.

Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens under no or all conditions. In this paper, we provide a self-contained introduction to the integrated information theory of (...) consciousness (IIT). We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT-restriction to existing proposals and argue that the IIT-restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system. (shrink)

It is well-known that in the fifth of his Cartesian Meditations, Husserl puts forth a theory of intersubjectivity. Most commentators of Husserl have read his Cartesian Meditations as presenting a theory of intersubjectivity whose basis is empathy, in the form of a process of constituting the sense of “other” in one’s own experience, as the primary origin of the intersubjective layer of experience. In this paper, I claim that the structure of intersubjectivity as Husserl presents it in the Cartesian Meditations (...) is articulated as being governed by a logic of parts and wholes rather than that of a phenomenology of empathy, and that the articulation of this logic demonstrates that the transcendental ego is intrinsically intersubjective. My main philosophical claim in this regard is that the way Husserl’s account of transcendental empathy unfolds in the Cartesian Meditations implies a prior fundamental mereological structure of which the individual transcendental ego is only a part. That is, the transcendental ego has an eidetic a-priori intersubjective structure, in the sense of being a moment of an intersubjectively structured transcendental whole. In this sense, rather than being a singulare tantum, it is more fitting to say that transcendental subjectivity is actually a plurale tantum. (shrink)

This my 3am interview with Richard Marshall about my work and its inspirations. It focuses on my research on parst and wholes, tropes, and abstract objects.

It is well-known that the entangled quantum state of a composite object cannot be reduced to the states of its parts. This quantum holism provides a peculiar challenge to formulate an appropriate mereological model: When a system is in an entangled state, which objects are there on the micro and macro level, and which of the objects carries which properties? This paper chooses a modeling approach to answer these questions: It proceeds from a systematic overview of consistent mereological models for (...) entangled systems and discusses which of them is compatible with the quantum mechanical evidence (where quantum states are understood realistically). It reveals that entangled quantum systems neither describe undivided wholes nor objects that stand in irreducible relations. The appropriate model assumes that the entangled property is an irreducible non-relational plural property carried collectively by the micro objects, while there is no macro object. In this sense, quantum holism is an instance of property holism, not of object holism. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Academic discussions of the count/mass distinction in Chinese feature three general problems, upon which this essay critically reflects: 1) Most studies focus either on modern or on classical Chinese thus representing parallel discussions that never intersect; 2) studies on count/mass grammar are often detached from reflections on count/mass semantics, which results in serious theoretical and terminological flaws; 3) approaches to Chinese often crucially depend on observations of English grammar and semantics, as, e.g., many/much vs. few/little patterns, the (...) use of plural inflections, etc., which is seldom justified. The article investigates the relevant discourse on the count/mass issue in classical and modern Chinese and concludes with exploring two distinct areas related to countability: the semantics of singular in contexts in which objects are introduced as referential-indefinite and the semantics of number and countability as revealed in diangu. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency and distinctness. (...) The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (shrink)

This paper explores various subtleties in our ordinary thought and talk about normative reasons—subtleties which, if taken seriously, have various upshots, both substantive and methodological. I focus on two subtleties in particular. The first concerns the use of reason (in its normative sense) as both a count noun and as a mass noun, and the second concerns the context-sensitivity of normative reasons-claims. The more carefully we look at the language of reasons, I argue, the clearer its limitations and liabilities (...) become. The cumulative upshot is that although talk of reasons is intelligible and useful for the purposes of communication, we should be wary of placing much weight on it when engaging in substantive normative inquiry. By way of illustration, I consider some potential pitfalls of taking our talk of reasons too seriously, explaining how careful attention to the language of reasons undermines the main argument for moral particularism, Mark Schroeder’s recent defense of Humeanism about practical reasons, and the “reasons-first” program in metanormativity. (shrink)

In this article, I show that the semantics one adopts for mass terms constrains the metaphysical claims one can make about mixtures. I first expose why mixtures challenge a singularist approach based on mereological sums. After discussing an alternative, non-singularist approach, I take chemistry into account and explain how it changes our perspective on these issues.

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative (...) counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreover - even provided that the problem with coreferentiality can be fixed - the resulting analysis of cardinality ascriptions meets several difficulties. (shrink)

Most philosophers are familiar with the metaphysical puzzle of the statue and the clay. A sculptor begins with some clay, eventually sculpting a statue from it. Are the clay and the statue one and the same thing? Apparently not, since they have different properties. For example, the clay could survive being squashed, but the statue could not. The statue is recently formed, though the clay is not, etc. Godehart Link 1983’s highly influential analysis of the count/mass distinction recommends that (...) English draws a distinction between uncountable “stuff” and countable “things”. There are two mereological relations, related in specific ways. Our primary question here is whether an empirically adequate account of the mass/count distinction really does require distinguishing “things” from “stuff”, and thus postulating two corresponding mereological relations, or if instead positing only one sort of entity and corresponding mereological relation is sufficient, as other semantic theories would have it. This question is meant to be one of what we call natural language mereology. We are asking about the mereological commitments of English, or perhaps competent speakers of English, and not about ultimate reality as such. There is no pretense that we will definitively solve the metaphysical puzzle of the statue and clay. (shrink)

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

My bedroom window is a part of my house, but it is not a partial house. A half-built house is a partial house, but there is no house it is a part of. Being a part of something—parthood—is a familiar topic of philosophical inquiry. Being a partial something—partialhood—is not. The neglect of partialhood is a shame because it is intrinsically interesting as well as metaphysically and semantically important. After using fractions and counting constructions to identify partialhood in §1, I give (...) a theory of the relation in §2-§4. Armed with this theory I turn to applications both in the domain of objects and object-related constructions as well as the domain of events and event-related constructions. In §5 I argue that partialhood allows us to identify a notion of distributivity that helps pinpoint the metaphysical basis of the mass/count distinction. In §6 I argue that the progressive morpheme expresses partialhood; in metaphysical terms, what it is for something to be happening is for there to be a partial event. (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive (...) to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

The notion of existence is a very puzzling one philosophically. Often philosophers have appealed to linguistic properties of sentences stating existence. However, the appeal to linguistic intuitions has generally not been systematic and without serious regard of relevant issues in linguistic semantics. This paper has two aims. On the one hand, it will look at statements of existence from a systematic linguistic point of view, in order to try to clarify what the actual semantics of such statements in fact is. (...) On the other hand, it will explore what sort of ontology such statements reflect. The first aim is one of linguistic semantics; the second aim is one of descriptive metaphysics. Philosophically, existence statements appear to reflect the distinction between endurance and perdurance as well as particular notions of abstract states and of kinds. Linguistically, statements of existence involve a particular way of drawing the distinction between eventive and stative verbs and between individual-level and stage-level predicates as well as a particular approach to the semantics of bare plurals and mass nouns. (shrink)

Karl Pfeifer attempts to present a coherent view of panentheism that eschews Pickwickian senses of “in” and aligns itself with, and builds upon, familiar diagrammed portrayals of panentheism. The account is accordingly spatial-locative and moreover accepts the proposal of R.T. Mullins that absolute space and time be regarded as attributes of God. In addition, however, it argues that a substantive parthood relation between the world and God is required. Pfeifer’s preferred version of panpsychism, viz. panintentionalism, is thrown into the mix (...) as an optional add-on. On this account, God is conceived of as a “spiritual field” whose nature can be made more intelligible by regarding “God” as having a mass-noun sense in some contexts. Pfeifer closes with the suggestion that we look to topology and mereology for further development of the position outlined in his paper. (shrink)

Arguing first that the best way to understand what a continuant is is as something that primarily has its properties at a time rather than atemporally, the paper then defends the idea that there are occurrent continuants. These are things that were, are, or will be happening—like the ongoing process of someone reading or my writing this paper, for instance. A recently popular philosophical view of process is as something that is referred to with mass nouns and not count (...) nouns. This has mistakenly encouraged the view that the only way to think of process is as the stuff of events, and has obscured the possibility of thinking of processes as individual continuants. (shrink)

This paper will first give an overview of the role of events in semantics against the background of Davidsonian semantics and its Neo-Davidsonian variant. Second, it will discuss some serious issues for standard views of events in contemporary semantics and present novel proposals of how to address them. These are [1] the semantic role of abstract (or Kimean) states, [2] wide scope adverbials, and [3] the status of verbs as event predicates with respect to the mass-count distinction. The paper (...) will show that abstract states as the entities described by (most) stative verbs are incompatible with Neo-Davidsonian event semantics and proposes a decompositional analysis of stative verbs that may be able to overcome the difficulty. The paper will argue that in addition to Davidsonian events, the semantics of adverbials requires events as truthmakers as well as actions as more complex entities sharply distinguished from events. The paper will also argue that the verbal domain of events sides with mass nouns rather than dividing into mass and count, unlike event nouns. (shrink)

Terms for consciousness, used with a cognitive meaning, emerged as count nouns in the 17th century. This transformation repeats an evolution that had taken place in late antiquity, when related vocabulary, used in the sense of conscience, went from being mass nouns designating states to count nouns designating faculties possessed by every individual. The reified concept of consciousness resulted from the rejection of the Scholastic-Aristotelian theory of mind according to which the mind is not a countable thing, but a (...) pure potentiality. This rejection was motivated by an acute sense of the mind’s fallible subjectivity. While conditioned by recent historical events, the 17th century’s pervasive sense of subjectivity also reveals a heavy debt to Hellenistic philosophy, which had been recently rediscovered. But whereas Hellenistic thought, mistrustful of theoria, only reifies conscience, early modern thinking, more mistrustful of praxis and seeking its grounding in theoria, goes a step further and reifies consciousness. Partly modeled on theological ideas, the resulting concept of consciousness is plagued by paradoxes that have becomes notorious for their intractability. But essentially the same model of consciousness underwrites contemporary theory, embroiling contemporary debates in the same controversies that dominated the 17th century. Sidestepping these difficulties by returning to the Scholastic-Aristotelian theory of mind would be a tall order, but it is not impossible. Alfred North Whitehead's theory of consciousness offers an example. His novel theory of time enables Whitehead to rehabilitate the Aristotelian concept of passive mind in a wholly naturalistic way. (shrink)

The need for the definite article to express a singular kind ("the cat") in the Germanic languages is predicted by Borer's (2005) structural approach to the mass-count distinction. Chierchia's (1998) "down" operator can apply to nPs to derive mass kinds ("rice") and to DivPs to derive plural kinds ("cats"), but there is no determinerless structure that exclusively denotes properties of atomic individuals to which this same operator can apply to derive singular kinds. The only alternative is the process (...) that Chierchia proposes for plural kinds in Romance, where the definite article returns a maximal individual that can be intensionalized into a kind. In articleless languages like Mandarin, this account allows for a universal property-denoting denotation of nP and simultaneously captures the fact that singular kinds have the same distribution as mass kinds. (shrink)

Studies of visual event individuation often consider people's representations of activities involving agents performing complex tasks. Concomitantly, theories of event individuation emphasize predictions about agents' intentions. Studies that have examined simple, non-agential occurrences leave open the possiblity that principles of visual object individuation play a role in visual event individuation. Unearthing principles that may be sufficient for event individuation which are distinct both from predictions about agents' intentions and from visual object individuation, we draw on and extend studies that reveal (...) object and event representation to be deeply analogous in our cognitive economy. We provide evidence that ‘temporal shaping' is a sufficient low-level perceptual criterion for the visual individuation of events. In our study, temporal shaping is effected by the introduction of pauses into an otherwise continuous process. Future studies should address other visual mechanisms for introducing temporal shaping (e.g., color changes). (shrink)

I relate plural quantification, and predicate logic where predicates do not need a fixed number of argument places, to the part-whole relation. For more on these themes see later work by Boolos, Lewis, and Oliver & Smiley.

According to Composition is Identity, a whole is literally identical to the plurality of its parts. According to Mereological Nihilism, nothing has proper parts. In this note, it is argued that Composition is Identity can be shown to entail Mereological Nihilism in a much more simple and direct way than the one recently proposed by Claudio Calosi.

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity (...) to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial. (shrink)

This paper provides a critical examination of three related attempts to defend Composition as Identity (CI), namely the thesis that if some things compose something, then they are it. First, it will be argued against Donald Baxter’s view of composition as ‘loose identity’ that by construing composition as strictly a many-many relation, the view trivializes CI, and cannot be an option for the advocate of CI who takes composition as a genuine many-one relation. Second, it is argued against Baxter’s modified (...) view of composition as ‘cross-count identity’ that the ‘are’ in ‘they are it’ cannot be viewed as expressing cross-count identity. Lastly, it is argued against Aaron Cotnoir’s view of composition as ‘general identity’ that it amounts to resorting back to Baxter’s old view of composition as a many-many relation. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify (...) four main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

We live in times of an increasing polarization in which the margins of the political spectrum begin to dominate our social imagination again. While the neoliberal iteration of the capitalist project suggests an extreme individualism as the normative default position, the devastating impact of the globalized economy on many has reignited the pursuit of socialist alternatives. In this constellation, Simmel’s social theory of modernity can be a useful resource to undercut the return of the old battle between opposite economic systems. (...) This paper argues that two kinds of pluralism can be derived from his conceptualization of the social effects of the money economy. In contrast to one-size-fits-all concepts of freedom, Simmel embraces a social pluralism which acknowledges a plurality of cultural spheres as relevant for the self-actualization of modern individuals, attributing different combinations of independence and embeddedness to them. Moreover, he rejects the social extremes of socialism and individualism, since they fail to properly integrate individual freedom into the social whole without undermining it. Instead Simmel gives us the vision of a pluralist economy in which democratic worker’s cooperatives are combined with an overall liberal market to satisfy both the longing for community and the strive for individual distinction. (shrink)

The following are the characteristics of a genus: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (...) (Met., I, 1057a18-30; 1057b31-34) 5. Not every predicate is a genus of what it is predicated on; for this would equate a genus with one of its own species. (PsA., A, 22, 83b7-10) 6. The opposite of the genus should always be the genus of the opposite. (To., Δ, 4, ^125a27-29) 7. A genus divides the object from other things. (To., Z, 3, 140a^24) 8. None of unity and being is a genus. (Met., B, 998b22-27; Met., K, 1059b31-34; PsA., B, 7, 92b12-14) 9. There is no necessity or even no possibility that things that are the same specifically or generically should be numerically the same. (To., H, I, 152b30-) 10. To be called one due to having one genus is in a way similar to be one due to having the same matter. (Met., Δ, 1016a24-28) 11. The substance of a thing involves its genus, and thereby all the higher genera are predicated of the lower. (To., Z, 5, 143a^20- ) 12. Being falls immediately into genera. (Met., Γ, 1004a4-6) A. Characteristics of relations between genera The characteristics of relations between genera, the relations between genera and species excluded, are as follows: 1. Genus is not an element in the composition of things. (Met., I, 1057b20-22) 2. Things resulting from the same division of the same genus are simultaneous by nature. (Cat., 13, 15a3-4) 3. Processes of proof cannot pass from one genus to another. (PsA., A, 23, 84b14-18) 4. It is not necessary for subordinate genera to have different accounts. (To., I, 15, ^107a19-) E.g. when we say a raven is a bird, we also say it is a certain kind of animal. 5. It is necessary for genera that are not subordinate one to the other to have different accounts. (To., I, 15, ^107a27-30) E.g. whenever we call a thing an engine, we do not call it an animal, nor vice versa. 6. If one of the genera is predicated in what it is, all of them, both higher and lower than this one, if predicated at all of the species, will be predicated of it in what it is; so that what has been given as genus is also predicated in what it is. (To., Δ, 2, ^122a10) 7. The same object cannot occur in two genera of which neither contains the other. (To., Z, 139b32-140a2) 8. Those to which the same figure (σχῆμα) of predication applies, are the same in genus. (Met., Δ, 1016b32-35) 9. Attributes that inhere always in each several things can be divided to two groups: those that are wider in extent but not wider than its genus and those wider than its genus. (PsA., B, 13, 96a24-27) 10. The relation between A and B must be extendable in respect of all the genera of A. Thus, if A is double of B, it must also be in excess, the genus of double, to B. Aristotle accepts, however, that this may be objectable in some cases: while knowledge is called knowledge of an object of knowledge, it cannot be called a state and disposition (which is the genus of knowledge) of an object of knowledge. In fact, it is a state and disposition of the soul. (To., Δ, 4, 124b28-34) B. Characteristics of species The following are the characteristics of species: 1. Things are said to be other in species if they are of the same genus but are not subordinate the one to the other. (Met., Δ, 1018a38-b2; Met., I, 1057b35-37) 2. Contraries are other than one another in species. (Met., Δ, 1018b5-7; Met., I, 1058b26-) 3. It is not sufficient for a difference to be the basis of distinguishing species in a genus because it belongs to the genus in virtue of its nature as, e.g., the difference between men and women belongs to animal in virtue of its nature. It must also be a modification peculiar to the genus (οἰκεῖα πάθη τοῦ γένους) in the strongest sense. (Met., I, 1058a29-37) Thus, contraries which are in the formula (ἐν τῷ λόγῳ) make a difference in species, but those which are in the compound material thing do not make one as e.g. being male and female is a difference in matter. (Met., I, 1058a37-b23) 4. Some things are peculiar to the species as distinct from genus: there are attributes peculiar to each distinct species. (PrA., A, 27, 43b27-29) 5. There is no necessity or even no possibility that things that are the same specifically should be the same numerically. (To., H, I, 155b30-) C. Characteristics of relations between genera and species The following are the characteristics of relations between genera and their species: 1. Although species predicated of individuals seem to be principles rather than the genera, it is hard to say, Aristotle asserts, in what sense species are to be taken as principles. (Met., B, 999a14-21) 2. Things that are one in species are all one in genus, while things that are one in genus are not all one in species. (Met., Δ, 1016b35a1) 3. The relation of a species to its genus is like the relation of primary substance to all others: the species is a subject for the genus (ὑπόκειται γὰρ τὸ εἴδος τῷ γένει) and the genera are predicated of the species but the species are not predicated of them. (Cat., 5, 2b17-22) 4. Of the species themselves- those which are not genera- one is no more a substance than another: a certain horse is no more a substance than another horse. (Cat., 5, 2b22-26) 5. Genera are prior to species since they do not reciprocate as to implication of existence (κατὰ τὴν τοῦ εἶναι ἀκολούθησιν). For example, if there is a fish there is an animal, but if there is an animal there is not necessarily a fish. (Cat., 13, 15a4-7) 6. What belongs both to a species and to its genus, it belongs to the species more properly indeed than to the genus. (PrA., A, 27, 43b29-32) 7. A predicate drawn from the genus is never ascribed to the species in a derived form and as its genus. Thus, e.g. coloured cannot be a genus of ‘white’ when we say ‘white is coloured.’ (To., B, I, ^109b1-5) 8. Genera are predicated of their species synonymously because the species take on both the name and the account of their genera. (To., B, I, ^109b3-6) 9. All the attributes that belong to the species belong to the genus as well but there is no necessity that all the attributes that belong to the genus should belong also to the species. (To., B, 4, 111a20-32) 10. Those things of which the genus is predicated must also of necessity have one of its species predicated of them. (To., B, 4, 111a33-) 11. The higher genus should be predicated of the species in what it is. (To., Δ, 2, ^122a6) 12. The species, or any of the things which are under the species, is not predicated of the genus because the genus is the term with the widest range of all. (To., Z, 6, 144a27f.) 13. The same species cannot be in two genera neither of which contains the other. (To., Z, 6, 144b14f.) 14. None of the species of a genus is prior or posterior to other species but they are thought to be simultaneous by nature. (Cat., 13, 14b38-15a1) 15. Daniel W. Graham points that sometimes Aristotle speaks of species as classes (Cat., 5, 2a14-17) and sometimes as properties or a certain character (ποιόν τι) of substances, which is difficult to be distinguished from the category of quality. (Cat., 3b13-22) D. Characteristics of differentia 1. The last differentia will be the substance, the definition and the form of the thing. (Met., Z, 1038a18-28) 2. If we divide according to accidental qualities, there will be as many differentiae as there are processes of division. (Met., Z, 1038a25-28) 3. The differentia divides the object from any of the things contained in the same genus. (To., Z, 3, 140a24-) 4. A. C. Lloyd argues that Aristotle’s logic of classification contains a vicious circle because: ‘For a genus to be predicated unequivocally and essentially of a species the specific differentiae have to be ‘appropriate’; but in order to know whether a proposed differentia is appropriate we have to know whether the genus is predicable essentially of the species thus defined.’ The predication of differentia on primary substance seems to make difficulties in Aristotle’s system, as Terence Irwin points out. It seems to violate the distinction of strong predication and inherence, a distinction between predication of count-nouns and predication of characterizing adjectives. Irwin says that this violation is only apparent because although the differentia-term is an adjective, its gender agrees with the gender of the understood genus-term and not with that of the subject term. ‘Man is biped’ is indeed ‘Man is a biped animal.’ This shows, Irwin asserts, ‘why Aristotle can still mention that strong predication is nominal and inherence is adjectival.’ Differentiae are not, however, secondary substances, as Aristotle himself insists. A differentia does not say what the thing is, as secondary substances do, but only what it is like or what sort it is. (ποιον: To., 122b12-17; 128a20-29; 139a28-31; 142b25-29) Nonetheless, differentiae are not qualities because they are not inherent. Thus, they cannot be regarded in any of the ten categories. Irwin thinks that this anomaly is unnecessary because Aristotle could give good reasons for taking differentiae to be second substances. E. Characteristics of relations between differentia and genera or species 1. It is not possible for the genus to be predicated of the differentia taken apart from the species. (Met., B, 998b23-25; Met., K, 1059b31-33; To., VI, 6, 144a32-b1) 2. It is not possible for the species of the genus to be predicated of the proper differentiae of the genus. (Met., B, 998b24-26) 3. Where the differentia is present, the genus accompanies it, but where the genus is, the differentia is not always present. (Met., Δ, 1014b12-14) 4. The number of species are equal to the number of differentiae. (Met., Z, 1038a15-18) 5. The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. (Cat., 3, 1b16-20; To., I, 15, ^107b19-) 6. There is nothing to prevent genera subordinate one to the other from having the same differentia. (Cat., 3, 1b20-22) 7. Since the higher genera are predicated of the genera below them, all differentiae of the predicated genus will be differentia of the subject also. (Cat., 3, 1b21-24) 8. The definition of the differentia is predicated of that of which the differentia is said. (Cat., 5, 3a25-28) 9. In giving what a thing is it is more fitting to state the genus than the differentia. For example, anyone who says that man is an animal shows what man is better than who describes him as terrestrial. (To., Δ, 6, ^128a24-27) 10. The differentia always signifies a quality of the genus, but the genus does not do this of the differentia. (To., Δ, 6, 128a27-29; To., Z, 6, 144a20-23) 11. A specific differentia, along with the genus, always makes a species. (To., Z, 6, 143b^1-) 12. A genus is always divided by the differentiae that are co-ordinate with it in a division and the differentiae that are co-ordinate in a division are all true of the genus. (To., Z, 6, 143b^1-) 13. Differentia cannot be predicated of the genus because genus is the term with the wider range. (To., Z, 6, 144a27-) In fact, genus is predicated, not of the differentia, but of the object of which the differentia is predicated. (To., Z, 6, 144a^31-b3) 14. Neither species nor the objects under it can be predicated of the differentia because the differentia is a term with a wider range than the species. (To., Z, 6, 144b4-) 15. The differentia is posterior to genus but prior to the species. (To., Z, 6, 144b^9-) 16. The same differentia cannot be used of two genera neither of which contains the other and if they do not both fall under the same genus. Otherwise, the same species will be in two genera neither of which contains the other, which is impossible. (To., Z, 6, 144b14-) 17. Genus and differentia are prior to and more familiar than the species: ‘For annul the genus and the differentia; and the species too is annulled, so that they are prior to the species. They are also more familiar; for if the species is known, the genus and differentia must of necessity be known as well (for anyone who knows what a man is knows also what animal and terrestrial are), whereas if the genus or the differentia is known it does not follow of necessity that the species is known as well; thus the species is less intelligible.’ (To., Z, 4, 141b15-) F. Characteristics of relations in series of classes 1. Mutually exclusive series. If no term in the series ACD… is predicable of any term in the series BEF…, and if G- a term in the former series- is the genus of A, clearly G will not be the genus of B; since, if it were, the series would not be mutually exclusive. (PsA., A, 15, 79b6-11) 2. Atomic disconnection of series. Of two mutually exclusive series ACD and BEF, if neither A nor B has a genus and A does not inhere in B, this disconnection must be atomic. (PsA., A, 15, 79b6-14) G. Characteristics of relations of individuals 1. No individual in a species is more substance than another individual in another species. (Cat., 5, 2b26-28) An individual man, for instance, is no more a substance than an individual ox. 2. Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 3. Not distinguishing between class membership and class inclusion? Some commentators like Vlastos and Ackrill (1963, 76) criticized Aristotle because he, they believe, did not distinguish between class membership (between species and particulars) and class inclusion (between genera and their species). Having accepted this point, Daniel W. Graham believes it is ‘question-begging in a curious way.’ Phil Corkum thinks that Aristotle employs mereological notions. (This criticism seems so strange because all the Aristotle’s point in distinguishing species 2 from genera is strictly the distinction of class membership and class inclusion as they call them so. (shrink)

In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification (...) are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)

ABSTRACT The individual-community relationship has always been one of the most fundamental topics of social sciences. In sociology, this is known as the micro-macro relationship while in economics it refers to the processes, through which, individual actions lead to macroeconomic phenomena. Based on philosophical discourse and systems theory, many sociologists even use the term "emergence" in their understanding of micro-macro relationship, which refers to collective phenomena that are created by the cooperation of individuals, but cannot be reduced to individual actions. (...) "Emergence" theories attempt to explain the nature of society as a complex system by examining how individuals and their relationships lead to the creation of integrated and macro-social phenomena such as markets, educational systems, cultural beliefs, and shared social practices. As a prelude to activity, every researcher has to answer the question from the methodological point of view, how is it possible to study the behavior of social groups and how can we gain knowledge about the laws related to social groups? Anyone who deals with humanities and social sciences or any reality and phenomenon that affects human beings, inevitably deals with the reality that is emerging. In fact, emergence occurs when one level of reality emerges radically from another level. Examples of emergent levels of reality include how the mind emerges from the body; or the way society emerges from human beings. Therefore, when there is an emerging factor, different scientific disciplines should be used, because it is inevitable to talk about social affairs, psychology and neurobiology, as well as physical and even chemical. -/- INTRODUCTION Since its beginning in the 19th century, sociology has faced the fundamental question of what a social phenomena stands for? At a glance, sociologists deal with the study of social groups, collective behavior, institutions, social structures, social networks, and social dynamics, and ultimately all such phenomena are composed of individuals. Therefore, social phenomena seem to have no independent ontological status, and in this case, sociology is ultimately about reducible individuals. Different approaches about the micro-macro relationship, using the concept of "emergence", argue that although collective phenomena are created by individuals, they cannot be reduced to individual action. The term "emergence" is used to distinguish "emergent results" from " Procedural results". Results are called Procedural that can only be calculated by adding or subtracting the causes that act together. On the contrary, they are emergent outcomes that are qualitatively novel compared to the causes from which they originate. An example of such emergent results is mental characteristics that emerge from neural processes, but are not considered among the characteristics of neural processes of components - which are their origin. Philosophical debates about emergentism and reductionism focus on the mind-brain relationship, but as many philosophers have noted, they can be generalized to apply to any hierarchical set of features. The cognitive revolution reactivated a 19th century controversy between theorists of Identity and dualism. The theorists of Identity believe in reductionist materialism and elimination of metaphysics, according to which the mind is nothing more than the biological, while the dualists believe that the mind and the brain are distinct from each other. Emergence has been considered as a third way between the theories of Identity and dualism. -/- METHODOLOGY Interdisciplinarity Is fundamentally indicated by the dominance of open systems as well as social and emerging systems at different levels. Therefore, as long as we are facing a new emergentism, there will necessarily be different fields and an interdisciplinary method. The commonality of social sciences and cognitive sciences on the issue of emergence provides the possibility of interaction and exchange of concepts between these two for deeper research. Therefore, in this research, apart from the concepts of Subvenience and downward causation, we have used multiple realization and wildly disjunctive, which are used to explain the emerging concept in cognitive sciences, including neurobiology, psychology, and philosophy. For analytical and interdisciplinary approaches, after examining the concepts of subvenience, and wildly disjunctive, Individualistic and collectivist emergentism have been reviewed. And then their adequacy is criticized and evaluated in meeting strong emergence conditions. -/- FINDINGS Philosophers of the mind have been able to define the conditions of irreducibility and downward causation, which are essential for strong emergence, by using the principle of subvenience with the help of multiple realization and wildly disjunctive principles. Therefore, by definition, emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and emergentist collectivism faces the challenge of reification. The analysis of the challenges facing the two methodological approaches of individualism and collectivism leads us to three unresolved issues about the emerging phenomenon, which are realism, downward causality, and mechanism. Despite the differences in the stances of these two approaches regarding the aforementioned triple problems, individualists and collectivists both agree that some social characteristics are reducible; and some others are irreducible due to their complexity, the determination of which, depends on the case study of the mechanism of emergence of each social characteristic. -/- CONCLUSION An emergence that is consistent with reductionism is called a weak emergence. And strong emergence includes the principle of irreducibility and downward causality. According to strong emergence, the characteristics of social phenomena have downward causal power, which cannot be reduced to the causal forces. The principle of subvenience, together with multiple realization and wildly disjunctive, can provide the conditions of irreducibility and downward causality, which are essential conditions of strong emergence. Based on the philosophical analysis of two methodological approaches, individualist and collectivist, it can be concluded that emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and reification collectivism faces the challenge of reification. The analysis of the problems faced by these two approaches leads us to three unresolved issues, which are realism, downward causality, and mechanism. individualist emergentists acknowledge the existence of emergent social characteristics, but despite this, they believe that these characteristics are not real but merely analytical constructs that require explanation based on individuals and their mutual actions. But collectivists argue that emergentism yields a categorical ontology and supports social realism. They accept the dependence of social characteristics on individuals, but claim that social entities and structures are ontologically independent. Individualists and collectivists both agree that some social characteristics are reducible; and others are irreducible due to their complexity; and the only way to recognize this is to engage in empirical studies of the mechanisms and temporal processes of "emergence" that create social characteristics. -/- NOVELTY The newness of this compact article is as follows: a) Presenting an interdisciplinary approach using the analysis of philosophy of cognitive sciences, including the philosophy of mind, neurobiology and psychology to formulate the issue of social emergence; b) Criticizing individualist and collectivist methodological approaches to the issue of social emergence and explaining the sufficiency and shortcomings of both in providing weak and strong emerging conditions; c) Explaining and categorizing the challenges facing methodological approaches in explaining the phenomenon of social emergence, in three categories: realism, downward causality, and mechanism. 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The notion of suffering carries with it aspects which are private and individual on the one hand and social and lingual on the other. I would pay attention to the latter part of the suffering notion, where the notion of suffering is recognized to be primitive by almost all the theories of human values. This primitive character allows a commensurable basis on the basis of which most plural theories share something in common to talk objectively to each other. In this (...) paper I would like to offer three arguments in order to advance a thesis that one’s suffering is redemptive of others First, the conservation law of mass says that matter of a closed system can neither be created nor destroyed, although it may be differently rearranged. This may be applied to the experience of suffering, to allow the conservation law of suffering: my unjust self-interest costs pains in others to the level of the same amount but if I voluntarily suffer a sacrifice others will have their pains lightened to the analogous level. Second, notion of yin-yang helps to support the redemptive thesis of suffering. The notion says that all things in the reality consist of two complementary opposite capacities that interact within a greater whole, as part of a dynamic system. Then, my acceptance of suffering and the decrease of other’s pain are two complementary capacities of one reality. Third, any person is responsible for his own act, so is a society as a whole. Then, as an individual restores his damaged person, when he commits a crime, by being suffered or punished, a society restores itself to its own proper state, when any member of the society is wronged, by suffering communally in one way or other. (shrink)