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Both extended simples and unextended complexes have been extensively discussed and widely used in metaphysics and philosophy of physics. However, the characterizations of such notions are not entirely satisfactory inasmuch as they rely on a mereological notion of extension that is too simplistic. According to such a mereological notion, being extended boils down to having a mereologically complex exact location. In this paper, I make a detailed plea to supplement this notion of extension with a different one that is phrased (...) |
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Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, (...) |
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All parts of mereologically ‘gunky’ entities have proper parts. All parts relevant to mereologically ‘junky’ entities *are* proper parts. This essay explores the application of gunk and junk beyond the standard category of material object. One such application yields what is here dubbed ‘deep’ gunk and junk: a material entity x all of whose intrinsic elements from any fundamental ontological category C either have proper parts from C that also are intrinsic elements of x, or are proper parts of entities (...) |
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According to Lewis, mereology is the general and exhaustive theory of ontological composition, and every contingent feature of the world supervenes upon some fundamental properties instantiated by minimal entities. A profound analogy can be drawn between these two basic contentions of his metaphysics, namely that both can be intended as a denial of emergentism. In this essay, we study the relationships between Humean supervenience and two philosophical spin-offs of mereological monism: the possibility of gunk and the thesis of composition as (...) |
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In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson’s nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius and Russell, which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors (...) |
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Most of our best scientific descriptions of the world employ rates of change of some continuous quantity with respect to some other continuous quantity. For instance, in classical physics we arrive at a particle’s velocity by taking the time-derivative of its position, and we arrive at a particle’s acceleration by taking the time-derivative of its velocity. Because rates of change are defined in terms of other continuous quantities, most think that facts about some rate of change obtain in virtue of (...) |
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In this paper, I develop an original view of the structure of space—called infinitesimal atomism—as a reply to Zeno’s paradox of measure. According to this view, space is composed of ultimate parts with infinitesimal size, where infinitesimals are understood within the framework of Robinson’s nonstandard analysis. Notably, this view satisfies a version of additivity: for every region that has a size, its size is the sum of the sizes of its disjoint parts. In particular, the size of a finite region (...) |
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On a view implicitly endorsed by many, a concept is epistemically better than another if and because it does a better job at ‘carving at the joints', or if the property corresponding to it is ‘more natural' than the one corresponding to another. This chapter offers an argument against this seemingly plausible thought, starting from three key observations about the way we use and evaluate concepts from en epistemic perspective: that we look for concepts that play a role in explanations (...) |
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Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) |
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Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It (...) |
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This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) |
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The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic. |
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In this paper I argue against grounding being necessarily well-founded, and provide some reasons to think it's actually not well-founded. |
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Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) |
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It is widely accepted that continuity is the most essential characteristic of motion; the motion of macroscopic objects is apparently continuous, and classical mechanics, which describes such motion, is also based on the assumption of continuous motion. But is motion really continuous in reality? In this paper, I will try to answer this question through a new analysis of the cause of motion. It has been argued that the standard velocity in classical mechanics cannot fulfill the causal role required for (...) |
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Fundamental concrete particulars are needed to explain facts about non-fundamental concrete particulars. However, the former can only play this explanatory role if they are properly discernible from the latter. Extant theories of how to discern fundamental concreta primarily concern mereological structure. Those according to which fundamental concreta can bear, but not be, proper parts are motivated by the possibilities that all concreta bear proper parts and that some properties of wholes are not fixed by the properties of their proper parts. (...) |
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Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead. |
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I explore some ways in which one might base an account of the fundamental metaphysics of geometry on the mathematical theory of Linear Structures recently developed by Tim Maudlin (2010). Having considered some of the challenges facing this approach, Idevelop an alternative approach, according to which the fundamental ontology includes concrete entities structurally isomorphic to functions from space-time points to real numbers. |
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I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...) |
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Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response. |
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We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of (...) |
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This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...) |
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Say that space is ‘gunky’ if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius and Russell : Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated (...) |
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Logics of part/whole relations frequently take parthood or proper parthood as primitive, defining the remaining mereological properties and relations in terms of them. I argue from considerations involving Weak Supplementation for the conclusion that we should take fusion as our mereological primitive. I point out that the intuitions supporting Weak Supplementation also support a stronger principle, Weak Supplementation of Pluralities, and that the principle can only do the work demanded by our intuitions when formulated in terms of a notion of (...) |
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I argue in this paper that the debate over composition is factually empty; in other words, I argue that there’s no fact of the matter whether there are any composite objects like tables and rocks and cats. Moreover, at the end of the paper, I explain how my argument is suggestive of a much more general conclusion, namely, that there’s no fact of the matter whether there are any material objects at all. Roughly speaking, the paper proceeds by arguing that (...) |
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In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems that have to be added as axioms. Building on some work by Linnebo, we then show how to take the ‘potential’ nature of the usual operations seriously, by using a modal language, (...) |
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This paper describes a plausible view of the nature of physical objects, their mereological connections to each other, and their relation to spacetime. As well as being parsimonious, the view provides a plausible context for denying all of the following: (1) A theory that objects endure through time (and do not have temporal parts, as normally conceived) cannot claim that material objects are identical to space-time regions they occupy. (2) At least one of the family of mereological connections (part-whole, overlap (...) |
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How is the debate between endurantism and perdurantism affected by the transition from pre-relativistic spacetimes to relativistic ones? After suggesting that the endurance vs. perdurance distinction may run together a pair of cross-cutting distinctions, I discuss two recent attempts to show that the transition in question does serious damage to endurantism. |
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This paper examines the logical and metaphysical consequences of denying Leibniz's Law, the principle that if t1= t2, then φ(t1) if and only if φ(t2). Recently, Caie, Goodman, and Lederman (2020) and Bacon and Russell (2019) have proposed sophisticated logical systems permitting violations of Leibniz's Law. We show that their systems conflict with widely held, attractive principles concerning the metaphysics of individuals. Only by adopting a highly revisionary picture, on which there is no finest-grained equivalence relation, can a well-motivated metaphysics (...) |
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According to one of the more popular endurantist packages on the market, a package I will call multilocational endurantism, enduring objects are exactly located at multiple instantaneous regions of spacetime. However, for all we know, the world might turn out to be spatiotemporally gunky and spatiotemporal gunk entails that this package is false. The goal of this paper is to sketch a view which retains the spirit of multilocational endurantism while also recognizing the possibility of certain types of objects which (...) |
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This article provides a new context for an established metaphysical debate regarding the problem of persistence. I contend that perdurance, a popular view about persistence which maintains that objects persist by having temporal parts, can be formulated in quantum mechanics due to the existence of a formal analogy between temporal and spatial location. However, this analogy fails due to a ‘no-go’ result which demonstrates that quantum systems cannot be said to have temporal parts in the same way that they have (...) |
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Persistence in Time No person ever steps into the same river twice—or so goes the Heraclitean maxim. Obscure as it is, the maxim is often taken to express two ideas. The first is that everything always changes, and nothing remains perfectly similar to how it was just one instant before. The second is that nothing … Continue reading Persistence in Time →. |
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It’s widely accepted that we have most reason to accept theories that best fulfill the following naturalistically respectable criteria: (1) internal consistency, (2) consistency with the facts, and (3) exemplification of the theoretical virtues. It’s also widely accepted that metaphysical theories are necessarily true. I argue that if you accept the aforementioned criteria, you have most reason to reject that metaphysical theories are necessarily true. By applying the criteria to worlds that are all prima facie possible, I show that contingent (...) |
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We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research. |
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Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. Second, I argue that, for the nominalist, mathematical language is used to express physical facts about the world. In endorsing this line I follow moves (...) |
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It’s widely accepted that we have most reason to accept theories that best fulfill the following naturalistically respectable criteria: internal consistency, consistency with the facts, and exemplification of the theoretical virtues. It’s also widely accepted that metaphysical theories are necessarily true. I argue that if you accept the aforementioned criteria, you have most reason to reject that metaphysical theories are necessarily true. By applying the criteria to worlds that are all prima facie possible, I show that contingent local matters of (...) |
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The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilizing the formal procedure of quantization as a guide to ontic structure of modern physical theory. The example of (...) |
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