Mereological Sum Research Articles

From slot mereology to a mereology of slots

In 2013, Bennett proposed a mereological theory in which the parthood relation is defined on the basis of two primitive relations: a is a part of b iff a fills a slot owned by b. However, this theory has issues counting how many parts an entity has. We explore the various counting problems and propose a new theory to solve them. Keeping the core idea of Bennett’s slots, this theory introduces mereological relations between slots. This theory enables us to solve all known counting problems and to go beyond the limits of Bennett’s theory by theorising expected features of mereological theories: supplementation principles and mereological sum and fusion. The theory is illustrated on ontological issues on the nature of structural universals and informational entities.

Atoms, combs, syllables and organisms

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts without proper parts. Typically, this thesis is characterized by an axiom stating that everything has atomic parts. The present paper argues that the success of this standard characterization depends on how the notions of sum and composition are defined. In particular, we put forward a novel definition of mereological sum that: (i) is not equivalent to existing definitions in the literature, if no strong decomposition principle is assumed; (ii) can be used to argue that the standard characterization of atomism fails, because having atomic parts is not sufficient to be a sum of atoms; and (iii) provides a purely mereological distinction between structured and unstructured wholes, contributing to the ongoing debate on this crucial topic.

Universalism and extensionalism revisited

We present a new notion of mereological sum that is inequivalent to extant ones in the literature and does not fall prey to reasonable complaints that can be raised against some such notions. In light of this notion, we then revisit the relation between mereological universalism and extensionalism. In particular we argue that Varzi’s claim to the point that universalism entails extensionalism is justified only insofar as one sticks to Varzi’s notion of sum. In effect, we distinguish different versions of extensionalism and argue that universalism—when cashed out in terms of our new notion of sum—entails some versions but not others. Most significantly it does not entail extensionality of proper parthood. In the light of the above we set forth a new mereological system, Universalist Quasi-Supplemented Mereology, that can be considered a worthy alternative to different mereological systems in the literature.

Buddhism and no-Self Theory: Examining the Relation between Human Actions and Moral Responsibility

Buddhists endorse the concept of human actions and their consequences as they uphold the doctrine of karma. However, they deny the existence of a ‘permanent self’. Few questions arise in this regard. If a permanent self does not exist then who guides a person to decide the course of an action? How does a person choose to perform an action of the many alternatives in a situation? Who takes responsibility for the consequences of an action? This paper attempts to answer these questions by reinterpreting the Buddhist’s ‘no-self’ theory from epistemological and logical perspectives. This paper argues that Buddhists while rejecting the existence of a ‘permanent self’ affirm the existence of impermanent psychophysical entities (five skandhas). The mereological sum of these psychophysical entities is known as a ‘person’ who performs actions. A person becomes morally responsible for the consequences of an action justifying the Buddhist doctrine of karma.

The concreteness of objects: an argument against mereological bundle theory

In a series of publications, L. A. Paul has defended a version of the bundle theory according to which material objects are nothing but mereological sums of ‘their’ properties. This ‘mereological’ bundle theory improves in important ways on earlier bundle theories, but here I present a new argument against it. The argument is roughly this: (1) Material objects occupy space; (2) even if properties have spatial characteristics, they do not quite occupy space; (3) on no plausible construal of mereological composition does a mereological sum of non-space-occupying entities occupy space; therefore, (4) material objects are not mereological sums of properties.

Parts of Falling Objects: Galileo’s Thought Experiment in Mereological Setting

This paper aims to formalize Galileo’s argument (and its variations) against the Aristotelian view that the weight of free-falling bodies influences their speed. I obtain this via the application of concepts of parthood and of mereological sum, and via recognition of a principle which is not explicitly formulated by the Italian thinker but seems to be natural and helpful in understanding the logical mechanism behind Galileo’s train of thought. I also compare my reconstruction to one of those put forward by Atkinson and Peijnenburg (Stud Hist Philos Sci 35(1):115–136, 2004), and propose a formalization which is based on a principle introduced by them, which I shall call the speed is mediative principle.

Reinterpreting Buddhist's No-self Theory: A Philosophical Study on Human Actions and Moral Responsibilities

The relation between human actions and moral responsibility for the consequences of the actions is a debatable topic in contemporary Buddhism. The reason is each action has either good or bad consequence(s). If consequence(s) of an action are good, the action is praiseworthy and rewarding. But if consequence(s) of an action are disastrous then the action is blameworthy. Buddhists endorse the concept of human actions and their consequences as they uphold the doctrine of karma. However, they deny the existence of a ‘permanent self’. Few questions arise in this regard. If a permanent self does not exist then who guides a person to decide the course of an action? How does a person choose to perform an action of the many alternatives in a situation? Who takes responsibility for the consequences of an action? This paper attempts to answer these questions by reinterpreting the Buddhist’s ‘no-self’ theory from epistemological and logical perspectives. While answering these questions, the paper discusses libertarianism, paleo-compatibilism, hard-determinism, and soft-compatibilism theories. It finds out which theory supports Buddhist’s claim on human actions and moral responsibility for consequences of the actions. This paper argues that Buddhists while rejecting the existence of a ‘permanent self’ affirm the existence of impermanent psychophysical entities (five skandhas). The mereological sum of these psychophysical entities is known as a ‘person’ who performs an action. A person becomes morally responsible for the consequences of an action for the reason that it justifies the Buddhist’s doctrine of karma.

Agreement Mismatch in Partitive Relatives

Agreement Mismatch in Partitive Relatives

ON CHRISTIAN THEISM AND UNRESTRICTED COMPOSITION

AbstractOur aim in this paper is to bring to light two sources of tension for Christian theists who endorse the principle of unrestricted composition (UC), that necessarily, for any objects, the xs, there exists an object, y, such that the xs compose y. In Value, we argue that a (concrete) composite object made of wholly valuable parts is at least as valuable as its most valuable part, and so the mereological sum of God and a wholly valuable part would be at least as valuable as God; but Christian theism arguably demands that no concrete object other than God can be as valuable as God. And in Creation, we argue that the conjunction of theism and unrestricted composition, together with the claim that every concrete entity that is numerically distinct from God is created by God, implies that God is created by God. We conclude by examining the prospects of restricting the thesis of unrestricted composition to the domain of material or spatiotemporal objects as a way to sidestep the above arguments against the conjunction of Christian theism and unrestricted composition.

The Lump Sum: A Theory of Modal Parts

A lump theorist claims that ordinary objects are spread out across possible worlds, much like many of us think that tables are spread out across space. We are not wholly located in any one particular world, the lump theorist claims, just as we are not wholly spatially located where one’s hand is. We are modally spread out, a trans-world mereological sum of world-bound parts. We are lump sums of modal parts. And so are all other ordinary objects. In this paper, I explore lump theory and investigate five arguments against it. These arguments may be the primary reasons why lump theory (as envisioned here) has not been widely accepted––or extensively explored––until now. I maintain that these arguments can be answered, and moreover, that accepting lump theory has distinct advantages, making it a competitive view in its own right.

A Unified Account of Three Uses of Dou

This paper gives a unified account of the distributive, occasion andcumulative readings of dou in the framework of event semantics, the last of whichis rarely discussed in the literature. Previous analyses on dou will be shown tohave difficulties capturing the cumulative reading (Lin 1998; Liu 2017). FollowingChampollion’s analysis of distance distributive items, I analyze dou as a distributorover events. What’s inside the scope of dou is the description of the subevents andwhat’s outside the scope of dou is the description of the mereological sum event.This analysis can capture the three uses of dou and adds dou to the category ofdistance distributive items surveyed in Champollion (2016).

Is composition identity?

Say that some things compose something, if the latter is a whole, fusion, or mereological sum of the former. Then the thesis that composition is identity holds that the composition relation is a kind of identity relation, a plural cousin of singular identity. On this thesis, any things that compose a whole (taken together) are identical with the whole. This article argues that the thesis is incoherent. To do so, the article formulates the thesis in a plural language, a symbolic language that includes counterparts of plural constructions of natural languages, and shows that it implies that nothing has a proper part. Then the article argues that the thesis, as its proponents take it, is incoherent because they take it to imply or presuppose that some things have proper parts.

A SPECULATIVE SOLUTION TO THE INSTANTIATION AND STRUCTURE PROBLEMS FOR UNIVERSALS

Abstract Typical structural universals are not just the mereological sum of their constituents. Hence, there is the Structure Problem of explaining this non-mereological structure. The Instantiation Problem is that the predicate "U is instantiated by x, y, etc., in that order" is ill-suited to be a primitive, unanalyzed predicate. The proposed solution to these problems is based on the observation that if universal U is said to supervene upon universals V, W, etc., then it is the instantiation of U that supervenes on the instantiation of V, W, etc. Assuming there are few subvenient universals, which is admittedly a speculation, their instantiation may be explained in ways that would be uneconomic if there were too many.

Empty Negations and Existential Import in Aristotle

AbstractAristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics.

Sums and Grounding

ABSTRACTAs I will use the term, an object is a mereological sum of some things just in case those things compose it simply in virtue of existing. In the first half of this paper, I argue that there are no sums. The key premise for this conclusion relies on a constraint on what, in certain cases, it takes for something to ground, or metaphysically explain, something else. In the second half, I argue that in light of my argument against sums, Universalism, which is perhaps the most widely accepted answer to the Special Composition Question, is false.

The Importance of "My" Being Single: A Response to Jiri Benovsky

The Importance of "My" Being Single:A Response to Jiri Benovsky Mark Siderits (bio) Given how much the issue of the self and diachronic personal identity has been discussed in recent decades, one might wonder why something like Benovsky's pluralist-self view has not already been proposed and critically examined. It does, after all, look promising as a way to negotiate a settlement between the partisans of self and of nonself. For it gives the first party what it says it wants—ontological commitment to selves—while also granting the nonself theorists their core claim that there is no single entity that is the referent of "I." But I doubt that any such settlement can last. Benovsky claims to have some sympathy for the view that I call Buddhist Reductionism, and his pluralist-self view does at first glance look like a near neighbor of [End Page 553] the view that these Buddhists hold. Their position can be described as claiming that(1) the self is simply unreal, and that (2) the person is merely conventionally but not ultimately real. Here the terms "self" and "person" are clearly being used to mean different things. By "self" they mean a soul-pellet or Cartesian ego, the one entity among the many psychophysical elements that is one's essence. By "person," on the other hand, is meant the mereological sum of some or all of the many causally connected psychophysical elements. An element and a mereological sum of elements are clearly different things. But instead of talking about "self" or "person," I propose to couch the discussion in terms of the meaning of the first-person pronoun "I." This is where Buddhist nonself theorists start: with the claim that the sense of an "I" is illusory and the source of existential suffering. Those who espouse Buddhist Reductionism do so as part of a strategy to extirpate the "I"-sense. Framing the discussion in terms of the first-person "I" may help us see why the pluralist-self view will not work. According to that view, "I" could be replaced by "we." Since "I" and "myself" are interchangeable, and the view has it that my self is a plurality, the first-person pronoun would always be a plural. Now there are cases where "we" is allowed in place of "I." But the parental "we" (every child quickly learns) is really just a way for the parent to refer to themselves, and so is a disguised singular. The royal "we" is another matter. There the idea is that since the monarch supposedly represents the nation in its entirety, what we take to be the pronouncement of a single entity actually speaks for a many. There is a difficulty, though: for these pronouncements to do their job, they seem to need the assistance of the idea of the state as a single transcendent entity to the interests of which the monarch is answerable. This is, in any event, how the monarch's subjects typically see things when the monarchy runs smoothly. It is not clear how the affairs of state would go if "the state" were understood to be just an enumerative term (like "gross" or "multitude"), a way of denoting some unspecified number of people occupying a certain territory and standing in certain complex spatio-temporal relations. How does one fire up the troops to make war against Prussia if one cannot invoke past wrongs to an entity with which the subjects identify? Motivating emotions such as loyalty or resentment at injustice seem to need a single object. The Buddha's account of the origin of suffering has something called "appropriation" (upādāna) as a crucial causal link. To appropriate is to take some event or state as "me" or "mine." Consider human socialization as a process of instilling a certain way of organizing the system that is a human organism. Gaining the ability to appropriate—to identify—represents a key stage in the progression from a desire-satisfaction model of system organization to the very different model of a system organized around principles of delayed gratification, responsibility-taking, and happiness-seeking. As we would now put it, appropriation is a key...

Truth and Truthmakers in Early Modern Scholasticism

ABSTRACT:Seventeenth-century Iberian and Italian Scholastics had a concept of a truthmaker (verificativum) similar to that found in contemporary metaphysical debates. I argue that the seventeenth-century notion of a truthmaker can be illuminated by a prevalent seventeenth-century theory of truth according to which the truth of a proposition is the mereological sum of that proposition and its intentional object. I explain this theory of truth and then spell out the account of truthmaking it entails.

A General Concept of Being a Part of a Whole

The transitivity of the relation of part to whole is often questioned. But it is among the most basic principles of mereology. In this paper we present a general solution to the problem of transitivity of parthood which may be satisfactory for both its advocates and its opponents. We will show that even without the transitivity of parthood one can define—basic in mereology—the notion of being a mereological sum of some objects. We formulate several proposals of general approaches to the concept of being a part of a whole, none of which contains any existential assumptions. By adding the transitivity of parthood we obtain an axiomatization of “existentially neutral” (or “nonexistential”) mereology.

Aristotle on Predication

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals.

“The king of France is bald” reconsidered: a case against Yablo

Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to refer to an entity whose existence or non-existence is a factual matter, e.g. ‘the king of France’: the failure of the presupposition that there is a unique French king makes some sentences with the term ‘the king of France’, in particular “The king of France is bald”, gappy. In this paper I will show that the sentence “The king of France is bald” must be false, and not gappy, according to Yablo’s own criteria and that, furthermore, the presupposition that the term ‘the king of France’ refers presents a fail-safe mechanism in the same way Yablo thinks abstract presuppositions do—this undermines his argument for metaontological antirealism.