This article motivates and develops a reductive account of the structure of certain physical quantities in terms of their mereology. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. The resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and explain.

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...) well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...) options, including their accounts of what X is, the examples supporting each theory, and the reasons for identifying the science of X with (most or all of) mathematics. Some comparison of the options is undertaken, but the main aim is to display the spectrum of viable alternatives to Platonism and nominalism. It is explained how these views answer Frege’s widely accepted argument that arithmetic cannot be about real features of the physical world, and arguments that such mathematical objects as large infinities and perfect geometrical figures cannot be physically realized. (shrink)

Recently, there has been a revival in taking empirical magnitudes seriously. Weights, heights, velocities and the like have been accepted as abstract entities in their own right rather than just equivalence classes of objects. The aim of my paper is to show that this revival should include value magnitudes. If we posit such magnitudes, important value comparisons can be easily explained; it becomes easier to satisfy the axioms for measurement of value; goodness, badness, and neutrality can be given univocal definitions; (...) value aggregation can be given a non-mathematical understanding which allows for Moorean organic unities. Of course, this does not come for free. One has to accept a rich ontology of abstract value magnitudes, but, to quote David Lewis, ‘The price is right; the benefits in theoretical unity and economy are well worth the entities.’. (shrink)

2020 update of the entry "Properties".

Ted Sider has shown that my indeterminism argument for comparativist theories of quantity also applies to Mundy's absolutist theory. This is because Mundy's theory posits only "pure" relations, i.e. relations between values of the same quantity (between masses and other masses, or distances and other distances). It is straightforward to solve the problem by positing additional mixed relations.

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is (...) detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (shrink)

This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects (...) instantiate but also how they instantiate these properties and relations. I propose that objects are identical when they stand in certain qualitative relations in virtue of their existence. And concrete objects are distinct when they do not stand in the same kinds of relations to one another in virtue of their existence. (shrink)

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism --- the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. In this paper I will present a version (...) of substantivalism that respects Leibnizian theses about space-time symmetries, and argue that it is superior to both relationism and the more orthodox form of substantivalism. (shrink)

Scientific properties come in degrees: elephants are more massive than mice. Are facts like these fundamental or can they be explained in other terms? This article argues that the structure of physical quantities like mass reduces to facts about the role that mass plays in the laws of nature. On this view elephants are more massive than mice partly in virtue of the fact that elephants are harder to throw around.

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate (...) particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes. (shrink)

Do properties have intrinsic properties of their own? If so, which second-order properties are intrinsic? This paper introduces two competing views about second-order intrinsicality: generalism, according to which the intrinsic–extrinsic distinction cuts across all orders of properties and applies to the properties of properties as well as the properties of objects, and objectualism, according to which intrinsicality is a feature exclusive to the properties of objects. The case for generalism is then surveyed along with some proposals for distinguishing intrinsic second-order (...) properties from extrinsic ones. After addressing these broad questions about the nature of second-order intrinsicality, the Problem of Accidental Intrinsic Properties of Properties is introduced and put to work as a case study for the significance of second-order intrinsicality. The connection between this problem and the metaphysics of quantitative properties is then examined. (shrink)

According to comparativist theories of quantities, their intrinsic values are not fundamental. Instead, all the quantity facts are grounded in scale-independent relations like "twice as massive as" or "more massive than." I show that this sort of scale independence is best understood as a sort of metaphysical symmetry--a principle about which transformations of the non-fundamental ontology leave the fundamental ontology unchanged. Determinism--a core scientific concept easily formulated in absolutist terms--is more difficult for the comparativist to define. After settling on the (...) most plausible comparativist understanding of determinism, I offer some examples of physical systems that the comparativist must count as indeterministic although the relevant physical theory gives deterministic predictions. Several morals are drawn. In particular: comparativism is metaphysically contingent if true, and it is most natural for a comparativist to accept an at-at theory of motion. (shrink)

One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) as it is exercised by ordinary people. I do so by looking at the different theories that have been put forward in the recent debate, and showing for each of these that they are unable to account for the mathematical practices of ordinary people. In order to show that these practices do need to be accounted for, I also argue that ordinary people are doing mathematics, i.e. that they engage in properly mathematical practices. Because these practices are properly mathematical, they should be accounted for by any philosophy of mathematics. The conclusion of my thesis, then, is that current theories fail to do something that they should do, while remaining neutral on how well they perform when it comes to accounting for the practices of professional mathematicians. (shrink)

ABSTRACTThis paper presents a view of quantities as ‘adverbial’ entities of a certain kind—more specifically, determinate ways, or modes, of having length, mass, speed, and the like. In doing so, it will be argued that quantities as such should be distinguished from quantitative properties or relations, and are not universals but are particulars, although they are not objects, either. A main advantage of the adverbial view over its rivals will be found in its superior explanatory power with respect to both (...) certain fundamental principles of quantity and ordinary quantitative reasoning involving quantitative relations like three times as long as and 2 metres longer than. (shrink)

This article introduces and motivates the notion of a “properly extensive” quantity by means of a puzzle about the reliability of certain canonical length measurements. An account of these measurements’ success, I argue, requires a modally robust connection between quantitative structure and mereology that is not mediated by the dynamics and is stronger than the constraints imposed by “mere additivity.” I outline what it means to say that length is not just extensive but properly so and then briefly sketch an (...) application of proper extensiveness to the project of providing a reductive ground for metric quantitative structure. (shrink)

A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmaker (...) of such truths? It is argued that Aristotelianism can answer the question, but only a semi-Platonist form of it. (shrink)

The leading account of intrinsicality over the last thirty years has arguably been David Lewis's account in terms of perfect naturalness. Lewis's account, however, has three serious problems: i) it cannot allow necessarily coextensive properties to differ in whether they are intrinsic; ii) it falsely classifies non-qualitative properties like being Obama as non-intrinsic; and iii) it is incompatible with a number of metaphysical theories that posit irreducibly non-categorical properties. I argue that, as a result of these problems, Lewis's account should (...) be rejected and replaced with an alternative account, which also analyses intrinsicality in terms of perfect naturalness, but which avoids these problems. (shrink)

I am going to argue for a robust realism about magnitudes, as irreducible elements in our ontology. This realistic attitude, I will argue, gives a better metaphysics than the alternatives. It suggests some new options in the philosophy of science. It also provides the materials for a better account of the mind’s relation to the world, in particular its perceptual relations.

Since the publication of David Lewis's ''New Work for a Theory of Universals,'' the distinction between properties that are fundamental – or perfectly natural – and those that are not has become a staple of mainstream metaphysics. Plausible candidates for perfect naturalness include the quantitative properties posited by fundamental physics. This paper argues for two claims: (1) the most satisfying account of quantitative properties employs higher-order relations, and (2) these relations must be perfectly natural, for otherwise the perfectly natural properties (...) cannot play the roles in metaphysical theorizing as envisaged by Lewis. (shrink)

In Science Without Numbers (1980), Hartry Field defends a theory of quantity that, he claims, is able to provide both i) an intrinsic explanation of the structure of space, spacetime, and other quantitative properties, and ii) an intrinsic explanation of why certain numerical representations of quantities (distances, lengths, mass, temperature, etc.) are appropriate or acceptable while others are not. But several philosophers have argued otherwise. In this paper I focus on arguments from Ellis and Milne to the effect that one (...) cannot provide an account of quantity in ''purely intrinsic'' terms. I show, first, that these arguments are confused. Second, I show that Field's treatment of quantity can provide an intrinsic explanation of the structure of quantitative properties; what it cannot do is provide an intrinsic explanation of why certain numerical representations are more appropriate than others. Third, I show that one could provide an intrinsic explanation of this sort if one modified Field's account in certain ways. (shrink)

In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Two grams mass, three coulombs charge, five inches long – these are examples of quantitative properties. Quantitative properties have certain structural features that other sorts of properties lack. What are the metaphysical underpinnings of quantitative structure? This paper considers several accounts of quantity and assesses the merits of each.

Lewis's notion of a "natural" property has proved divisive: some have taken to the notion with enthusiasm, while others have been sceptical. However, it is far from obvious what the enthusiasts and the sceptics are disagreeing about. This paper attempts to articulate what is at stake in this debate.

Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Aristotelians always prefer, an example that introduces the essential themes of the Aristotelian view of mathematics. A typical mathematical truth is (...) that there are six different pairs in four objects: Figure 1. There are 6 different pairs in 4 objects The objects may be of any kind, physical, mental or abstract. The mathematical statement does not refer to any properties of the objects, but only to patterning of the parts in the complex of the four objects. If that seems to us less a solid truth about the real world than the causation of flu by viruses, that may be simply due to our blindness about relations, or tendency to regard them as somehow less real than things and properties. But relations (for example, relations of equality between parts of a structure) are as real as colours or causes. (shrink)

Exotic ontologies are all the rage. Distant from common sense and often science as well, views like mereological essentialism, nihilism, and fourdimensionalism appeal to our desire to avoid arbitrariness, anthropocentrism, and metaphysical conundrums.1 Such views are defensible only if they are materially adequate, only if they can “reconstruct” the world of common sense and science. (No disrespect to the heroic metaphysicians of antiquity, but this world is not just an illusion.) In the world of common sense and science, bicycles survive (...) changes in their parts, billiard balls strike one another, and nothing travels faster than light. The mereological essentialist denies the rst, but offers this replacement: “there exist successions of numerically distinct, but appropriately related, bicycles with different parts” (Chisholm, , chapter ). The nihilist denies the second, but offers this replacement: “there exist X s and Y s such that the X s are arranged billiard-ball-wise, the Y s are also arranged billiard-ball-wise, and the X s strike the Y s”.2 The four-dimensionalist denies the third, but offers this replacement: “no sequences of matter-stages that are related by genidentity travel faster than light”.3 There is room for disagreement over what exactly “reconstruction” amounts to, but at a minimum: when a metaphysical theory reconstructs ordinary sentences φ1. . . as replacement sentences ψ1. . . , ordinary and scienti c evidence must not refute the view that, strictly speaking, it is ψ1. . . rather than φ1. . . that are true. The metaphysician needs reconstruction in order to face the tribunal of experience. An intriguing newcomer to the contemporary scene is the ancient doctrine of monism, the claim that “reality is one”.4 I will argue that, contrary to.. (shrink)

Natural properties are those that carve reality at the joints. The notion of carving reality at the joints, however, is somewhat obscure, and is often understood in terms of making for similarity, conferring causal powers, or figuring in the laws of nature. I develop and assess an account of the third sort according to which carving reality at the joints is understood as having the right level of determinacy relative to nomic roles. The account has the attraction of involving very (...) weak metaphysical presuppositions, but fails to capture several features that natural properties are presumed to have. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

This thesis is about making decisions when we are uncertain about what will happen, how valuable it will be, and even how to make decisions. Even the most sure-footed amongst us are sometimes uncertain about all three, but surprisingly little attention has been given to the latter two. The three essays that constitute my thesis hope to do a small part in rectifying this problem. The first essay is about the value of finding out how to make decisions. Society spends (...) considerable resources funding people (like me) to research decision-making, so it is natural to wonder whether society is getting a good deal. This question is so shockingly underresearched that bedrock facts are readily discoverable, such as when this kind of information is valuable. My second essay concerns whether we can compare value when we are uncertain about value. Many people are in fact uncertain about value, and how we deal with this uncertainty hinges on these comparisons. I argue that value comparisons are only sometimes possible; I call this weak comparability. This essay is largely a synthesis of the literature, but I also present an argument which begins with a peculiar view of the self: it is as if each of us is a crowd of different people separated by time (but connected by continuity of experience). I’m not the first to endorse this peculiar view of the self, but I am the first to show how it supports the benign view that value is sometimes comparable. We may be uncertain of any decision rules, even those that would tell us how to act when we face uncertainty in decision rules. We may be uncertain of how to decide how to decide how to... And so on. If so, we might have to accept infinitely many decision rules just to make any mundane decision, such as whether to pick up a five-cent piece from the gutter. My third essay addresses this problem of regress. I think all of our decisions are forced: we must decide now or continue to deliberate. Surprisingly, this allows us to avoid the original problem. I call this solution “when forced, do your best”. (shrink)

This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of three related (...) papers on: (1) the methodological and metaphysical foundations of dimensional analysis, (2) the use of dimensional analysis in determining physical symmetries, (3) the use of dimensional analysis in securing metrological extension. (shrink)

Physics presents us with a symphony of natural constants: G, h, c, etc. Up to this point, constants have received comparatively little philosophical attention. In this paper I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent inter-quantity structure in the form of relations between quantities with different dimensions. I use this account of G to settle a debate over whether mass scalings are symmetries of Newtonian Gravitation. I argue that they are not, (...) but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries. (shrink)

Axiomatic measurement theories are commonly interpreted as claiming that, in order to quantify an empirical domain, the qualitative structure of data about that domain must be mapped to a numerical structure. Such mapping is supposed to be established independently, i.e., without presupposing that the domain can be quantified. This interpretation is based on two myths: that it is possible to independently infer the qualitative structure of objects from empirical data, and that the adequacy of numerical representations can only be justified (...) by mapping such qualitative structures to numerical ones. I dispel the myths and show that axiomatic measurement theories provide an inadequate characterization of the kind of evidence required to detect quantities. (shrink)

Quantities like mass and temperature are properties that come in degrees. And those degrees (e.g. 5 kg) are properties that are called the magnitudes of the quantities. Some philosophers (e.g., Byrne 2003; Byrne & Hilbert 2003; Schroer 2010) talk about magnitudes of phenomenal qualities as if some of our phenomenal qualities are quantities. The goal of this essay is to explore the anti-physicalist implication of this apparently innocent way of conceptualizing phenomenal quantities. I will first argue for a metaphysical thesis (...) about the nature of magnitudes based on Yablo’s proportionality requirement of causation. Then, I will show that, if some phenomenal qualities are indeed quantities, there can be no demonstrative concepts about some of our phenomenal feelings. That presents a significant restriction on the way physicalists can account for the epistemic gap between the phenomenal and the physical. I’ll illustrate the restriction by showing how that rules out a popular physicalist response to the Knowledge Argument. (shrink)

This paper has two main aims. The first is to present a general approach for understanding “dispositional” and “categorical” properties; the second aim is to use this approach to criticize Russellian Monism. On the approach I suggest, what are usually thought of as “dispositional” and “categorical” properties are really just the extreme ends of a spectrum of options. The approach allows for a number of options between these extremes, and it is plausible, I suggest, that just about everything of scientific (...) interest falls in this middle ground. I argue that Russellian Monism depends for its plausibility on the unarticulated assumption that there are no properties in the middle ground. (shrink)

Let us agree that everything that there is exists, and that to be, to be real, and to exist are one and the same. Does everything that there is exist to the same degree? Or do some things exist more than others? Are there gradations of being? I argue that some entities exist more than others. Moreover, many of the notions in play in contemporary metaphysical discourse, such as fundamentality, perfect naturalness, and grounding ought to be cashed out in terms (...) of degree of existence. (shrink)

According to a standard picture, for any two comparable objects and a basis for comparison, either one is greater than the other or they are equal with respect to the basis. This picture has been called the Trichotomy Thesis, and although it is intuitive and plausible, it has been called into question by such philosophers as Derek Parfit, James Griffin, Joseph Raz, and Ruth Chang. Chang’s discussion is particularly rich, for she proposes and provides a detailed account of a possible (...) fourth relation that, she argues, provides a satisfying explanation of hard cases of comparison. In this paper, I will examine a version of the main argument against the Trichotomy Thesis and attempt to show that it is unsound. (shrink)

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

Relationist theories of space or space-time based on embedding of a physical relational system A into a corresponding geometrical system B raise problems associated with the degree of uniqueness of the embedding. Such uniqueness problems are familiar in the representational theory of measurement (RTM), and are dealt with by imposing a condition of uniqueness of embeddings up to composition with an "admissible transformation" of the space B. Friedman (1983) presents an alternative treatment of the uniqueness problem for embedding relationist theories, (...) developed independently of RTM. Friedman's approach differs from that of RTM in securing uniqueness by adding new primitives to the physical system A in contrast to the RTM approach which adds new axioms. Friedman's proposal has recently been developed and defended by Catton and Solomon (1988). This method of solving the uniqueness problem is here argued to be substantially inferior to the RTM method, both in practice and in principle. In practice we find that in none of the concrete examples offered to illustrate the method is the uniqueness problem actually solved in general. Moreover we find that in the most interesting case (addition to the system A of a finite number of relations of finite degree) the method is in principle incapable of success for mathematical reasons. In addition to these technical difficulties there are compelling methodological reasons for preferring the RTM method to the method of adding primitives. (shrink)

Hale proposes a neo-logicist definition of real numbers by abstraction as ratios defined on a complete ordered domain of quantities (magnitudes). I argue that Hale's definition faces insuperable epistemological and ontological difficulties. On the epistemological side, Hale is committed to an explanation of measurement applications of reals which conflicts with several theorems in measurement theory. On the ontological side, Hale commits himself to the necessary and a priori existence of at least one complete ordered domain of quantities, which is extremely (...) implausible because science treats the logical structure of quantities as subject to experimentally and theoretically motivated refinements and revisions. (shrink)

We propose a new theory based on the notions of marginal and large difference which has natural models in the context of nonstandard mathematics. We introduce the notion of finite marginality and show a representation result which ensures, for finitely marginal countable models, the existence of a homomorphism of the structure of marginal and large difference into a nonstandard model of the natural numbers, and show the extent to which any such homomorphism is unique. Finally, we show that our theory (...) constitutes part of the underlying abstract structure of three distinct philosophical theories of vagueness: Dean’s neofeasibilism, Itzhaki’s theory of nonstandard heuristics, and our own initial sketch of a nonstandard primitivism about vagueness. (shrink)

An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically (...) equivalent to the absolutist version of Newtonian gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism are highly questionable. (shrink)

An exploration of the details of counterpart theory, and some applications of the view. In Chapter 1, I set out the view and clarify the most important features: that the counterpart relation is a context dependent similarity relation, and that individuals are world-bound entities. I then set out what I take to be the most promising methods of filling in important details. Chapter 2 is a discussion of an alternative view, lump theory. I attempt to distinguish lump theory from counterpart (...) theory, and argue that several attempt to do so fail. Chapter 3 is an attempt to apply counterpart theory for individuals to properties. I attempt to stay as close to the standard view as possible, but find it necessary to modify the world-bound condition. I suggest a version of property counterpart theory that overcomes the obstacles I have identified. The final chapter is a discussion of a recent attempt to apply counterpart theory to the comparativist view of quantitative properties. I argue that an attempt to rely on counterpart theory to overcome an objection is unsuccessful. (shrink)

Tim Maudlin argues that we should take facts about distance to be analyzed in terms of facts about path lengths. His reason is that if we take distances to be fundamental, we must stipulate that constraints like the triangle inequality hold, but we get these constraints for free if we take path lengths to be prior. I argue that Maudlin is mistaken. Even if we take path lengths as primitive, the triangle inequality follows only if we stipulate that the fundamental (...) properties and relations obey constraints that are just as puzzling as the triangle inequality. (shrink)