On the Overlap Between Everything and Nothing

Graham Priest has recently proposed a solution to the problem of the One and the Many which involves inconsistent objects and a non-transitive identity relation. We show that his solution entails either that the object everything is identical with the object nothing or that they are mutual parts; depending on whether Priest goes for an extensional or a non-extensional mereology.

TAXONOMY OF PARTS AND ITS LOGICAL PRINCIPLES IN MEREOLOGY

Problem setting. One of the complex and controversial theoretical issues is the meteorological division and construction of the taxonomy of parts. After all, humanitarian and social subjects, due to their own specifics related to their existence, need other grounds for distribution. Thus, the study of the taxonomy of parts and its logical principles in meteorology will help to deepen the understanding of the specifics of the humanities and social sciences and the development of the logical basis of the methodology of the humanities. Recent research and publications analysis. Analysis of sources of origin, modern theoretical works on meteorology indicate unresolved issues regarding the taxonomy of parts, the possibility of involving mathematical set theory, doubts about the stability of the principles of part ratio, the problem of identity and more. Paper objective. The purpose of the study is to consider the problem of division of the whole into parts and the principles of construction of the taxonomy of parts, the reasons for their stability or doubt in meteorology. Paper main body. Mereological structure consists of a whole and parts. Parts can be constituent elements, components, ingredients, portions, aspects, parties, members, etc. Parts can be considered in the abstract (as a part in relation to any whole) or in relation (taking into account the function, ie as a component of the whole). Parts can be concrete or abstract. When analyzing the types of parts, there may be a problem of identity. The order of the parts, their distribution and relationship are determined by reflexivity, transitivity and antisymmetry. All three principles - reflexivity, transitivity and antisymmetry, together with taxonomy appear as the theoretical basis of classical meteorology. Conversely, in non-classical meteorology, arguments are developed regarding doubts about the stability of these principles. Additional principles are the principles of composition and decomposition. Extensional mereology demonstrates its limitations in relation to living objects. Conclusions of the research. The article analyzes the types of parts, the principles of their relationship, doubts about the stability of these principles and their assessment of the identity of parts and the whole. In our opinion, this opens the possibility of further distinguishing between extensional mereology and meteorological approach in hermeneutic logic, which determines the further success of building an authentic logic of humanitarian and social cognition.

Two notions of fusion and the landscape of extensionality

There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular on two specific sets of principles that appear to be of particular philosophical interest. The first way to make the two notions equivalent can be used to shed some interesting light on the kind of intuition both notions seem to articulate. The second shows the importance of a little-known mereological principle which I will call ‘Mild Supplementation’. As I will show, the mereology obtained by adding Mild Supplementation to Minimal Mereology occupies an interesting position in the landscape of theories that are stronger than Minimal Mereology but weaker than what Achille Varzi and Roberto Casati have labelled ‘Extensional Mereology’.

An Extensional Mereology for Structured Entities

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be accounted for by bringing together the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics.

The Limits of Classical Extensional Mereology for the Formalization of Whole–Parts Relations in Quantum Chemical Systems

This paper examines whether classical extensional mereology is adequate for formalizing the whole–parts relation in quantum chemical systems. Although other philosophers have argued that classical extensional and summative mereology does not adequately formalize whole–parts relation within organic wholes and social wholes, such critiques often assume that summative mereology is appropriate for formalizing the whole–parts relation in inorganic wholes such as atoms and molecules. However, my discussion of atoms and molecules as they are conceptualized in quantum chemistry will establish that standard mereology cannot adequately fulfill this task, since the properties and behavior of such wholes are context-dependent and cannot simply be reduced to the summative properties of their parts. To the extent that philosophers of chemistry have called for the development of an alternative mereology for quantum chemical systems, this paper ends by proposing behavioral mereology as a promising step in that direction. According to behavioral mereology, considerations of what constitutes a part of a whole is dependent upon the observable behavior displayed by these entities. Thus, relationality and context-dependence are stipulated from the outset and this makes behavioral mereology particularly well-suited as a mereology of quantum chemical wholes. The question of which mereology is appropriate for formalizing the whole–parts relation in quantum chemical systems is relevant to contemporary philosophy of chemistry, since this issue is related to the more general questions of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, which have been of central importance within the philosophy of chemistry for several decades. More generally, this paper puts contemporary discussions of mereology within the philosophy of chemistry into a broader historical and philosophical context. In doing so, this paper also bridges the gap between formal mereology, conceived as a branch of formal ontology, and “applied” mereology, conceived as a branch of philosophy of science.

The Limits of Classical Extensional Mereology for the Formalization of > Whole-Parts Relations in Quantum Chemical Systems

This paper examines whether classical extensional mereology is adequate for formalizing the whole-parts relation in quantum chemical systems. Although other philosophers have argued that classical extensional and summative mereology does not adequately formalize whole-parts relation within organic wholes and social wholes, such critiques often assume that summative mereology is appropriate for formalizing the whole-parts relation in inorganic wholes such as atoms and molecules. However, my discussion of atoms and molecules as they are conceptualized in quantum chemistry will establish that standard mereology cannot adequately fulfill this task, since the properties and behavior of such wholes are context-dependent and cannot simply be reduced to the summative properties of their parts. To the extent that philosophers of chemistry have called for the development of an alternative mereology for quantum chemical systems, this paper ends by proposing behavioral mereology as a promising step in that direction. According to behavioral mereology, considerations of what constitutes a part of a whole is dependent upon the observable behavior displayed by these entities. Thus, relationality and context-dependence are stipulated from the outset and this makes behavioral mereology particularly well-suited as a mereology of quantum chemical wholes. The question of which mereology is appropriate for formalizing the whole-parts relation in quantum chemical systems is relevant to contemporary philosophy of chemistry, since this issue is related to the more general question of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, which have been of central importance within the philosophy of chemistry for several decades. More generally, this paper puts contemporary discussions of mereology within the philosophy of chemistry into a broader historical and philosophical context. In doing so, this paper also bridges the gap between formal mereology, conceived as a branch of formal ontology, and ‘applied’ mereology, conceived as a branch of philosophy of science.

Between Atomism and Superatomism

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis.

Hylomorphic Offices

Neo-Aristotelian hylomorphism has struggled to arrive at anything approaching a consensus regarding the notion of form. Contending that no ‘right-minded modern’ could embrace anything akin to Aristotle's own preferred conception of a form as a causally efficacious entity capable of unifying material elements into a substantial whole, Fine (1994), for instance, has introduced a notion of form as a function yielding a ‘principle of unity’ capable of ‘variable embodiment’. Others, including Johnston (2006) , have opted for an account of form given in terms of ‘complex quantified relations’, and still others, including most prominently Koslicki (2008) and (2018), have championed a notion of forms as ‘structures’, where structures function as parts in line with the axioms of classical extensional mereology. Some have, though, simply despaired of the program of retrofitting the notion of form with some manner of acceptably modern ersatz replacement. Thus Evnine (2014) has developed a notion of ‘amorphic hylomorphism’, intended to salvage what is worth saving in hylomorphism shorn of anything reeking of the bad old notion of form. Each of these proposals has something to be said on its behalf. Unfortunately, none articulates a conception of form capable of discharging the task most wanted of form: unifying matter in such a way as to provide a privileged ontology, where that is understood as an ontology rejecting universal mereological aggregation without adverting to a notion of intention-dependence in the manner of ‘amorphic’ hylomorphism. A better way forward is to articulate the notion of form in terms of the apparatus of offices, introduced by Pavel Tichý (1987). This approach has, inter alia, the advantage of dissolving some of the puzzles that have developed around the notions of form and matter.

The stage

This chapter presents a distilled picture of the crucial issues in the theoretical background assumptions and develops the framework on which strata theory is built. This framework is essentially a synthesis of the work by Lønning (1987), Link (1998), Krifka (1998), Landman (2000), and others. Its mathematical foundation is classical extensional mereology, which is presented and discussed at length. The overview in this chapter is intended as a reference point for future researchers, and spells out the relevant background assumptions as explicitly as possible, especially in the case of points where the literature has not yet reached consensus on a preferred analysis. Issues discussed in this chapter include the meaning of the plural morpheme, the question whether the meanings of verbs are inherently pluralized, the formal properties of thematic roles, and the compositional process.