Philosophers commonly say that beliefs come in degrees. Drawing from the literature, I make precise three arguments for this claim: an argument from degrees of confidence, an argument from degrees of firmness, and an argument from natural language. I show that they all fail. I also advance three arguments that beliefs do not come in degrees: an argument from natural language, an argument from intuition, and an argument from the metaphysics of degrees. On the basis of these arguments, I conclude (...) that beliefs do not come in degrees. (shrink)

In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...) Finally, (3) I consider in what sense relations have order, and whether to make sense of this we are required to conceive of relations as having direction or argument positions. (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)

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.

Many are reluctant to accept primitive modality into their fundamental picture of the world. The worry often traces to this thought: we shouldn't adopt any more primitive - that is, unexplained - notions than we need in order to explain all the features of the world, and primitive modal notions are not needed. I examine one prominent rival to modal primitivism, combinatorialism, and show that in order to account for all the modal features of the world the combinatorialist must adopt (...) two additional primitive notions. My own modal primitivist view takes as primitive the notion of incompatibility between properties or relations. I show how the non-modal notions that the combinatorialist must adopt as primitive may be analyzed using my notion. The upshot is that with respect to the number of primitive notions, my modal primitivist theory comes out ahead. (shrink)

This paper defends the view that Newtonian forces are real, symmetrical and non-causal relations. First, I argue that Newtonian forces are real; second, that they are relations; third, that they are symmetrical relations; fourth, that they are not species of causation. The overall picture is anti-Humean to the extent that it defends the existence of forces as external relations irreducible to spatio-temporal ones, but is still compatible with Humean approaches to causation (and others) since it denies that forces are a (...) species of causation. (shrink)

In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a degreed property to count as degrees of consciousness, (...) and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

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.

2020 update of the entry "Properties".

Revelation, or the view that the essence of phenomenal properties is presented to us, is as intuitively attractive as it is controversial. It is notably at the core of defences of anti-physicalism. I propose in this paper a new argument against Revelation. It is usually accepted that low-level sensory phenomenal properties, like phenomenal red, loudness or brightness, stand in relation of similarity and quantity. Furthermore, these similarity and quantitative relations are taken to be internal, that is, to be fixed by (...) what their relata are. I argue that, under some plausible additional premises, no account of what grounds these relations in the essence of their relata is consistent with Revelation, at least if we take common phenomenological descriptions for granted. As a result, the plausibility of Revelation is undermined. One might however resist this conclusion by weakening the epistemic relation postulated between subjects and their phenomenal properties. (shrink)

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 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)

Degree‐sentences, i.e. sentences that seem to refer to things that allow of degrees, are widely used both inside and outside of philosophy, even though the metaphysics of degrees is much of an untrodden field. This paper aims to fill this lacuna by addressing the following four questions: [A] Is there some one thing, such that it is degree sensitive? [B] Are there things x, y, and z that stand in a certain relation to each other, viz. the relation that x (...) has more y than z? [C] In those cases in which degree sentences do not refer to phenomena that are degree sensitive, what is responsible for their prima facie seeming to do so? [D] If there are degree sensitive things, to which ontological categories do they belong? We answer each of these questions by arguing that there are, metaphysically speaking, different phenomena that degree sentences refer to: some refer to determinates that emanate from a certain determinable, others to tokens that are instantiations of a certain type, and yet others to what we call ‘complex, resultant properties that are constituted by stereotypical properties’. Finally, we show the relevance of our answers by applying them to the notions of freedom and belief. (shrink)

Quantities are properties and relations which exhibit "quantitative structure". For physical quantities, this structure can impact the non-quantitative world in different ways. In this paper I introduce and motivate a novel distinction between quantities based on the way their quantitative structure constrains the possible mereological structure of their instances. Specifically, I identify a category of “properly extensive” quantities, which are a proper sub-class of the additive or extensive quantities. I present and motivate this distinction using two case studies of successful (...) physical measurements.. I argue that the best explanation for the success of the length measurement requires us to adopt a notion of proper extensiveness, which is distinct from mere additivity, which is exhibited by inertial mass. I further discuss the consequences of this distinction, sketching an application of proper extensiveness for the project of producing a non-mathematical and non-metrical reductive metaphysics of quantity. (shrink)

The topic of my dissertation is the hedonic calculus. The hedonic calculus presupposes that pleasure and pain come in amounts amenable to addition, subtraction, and aggregation operations. These operations are ones that utilitarianism and related normative ethical theories treat as central to moral phenomena. The first chapter is an introduction to the problem--in it, I explain what the hedonic calculus is, why it is important, and why it has recently come under disfavor. The second chapter explores the nature of hedonic (...) phenomena, arguing that pleasure and pain are propositional attitudes; they are not feelings or feeling-tones, nor are they fundamentally a matter of desire or motivation. The third and fourth chapters concern the nature of quantitative phenomena. I argue that quantities are determinate properties whose determinables enter into greater-than, less-than, or equal-to relationships that are homomorphic with the structure of the real number line. These structures include the presence of a unique order; the possibility of equal intervals; and a natural, non-arbitrary zero point. The fifth chapter is a defense of the thesis that there are exactly three relations of quantitative comparison from a recent attack. I argue that apparent instances of being on a par are in fact instances of vagueness or complexity and do not threaten the truth of the trichotomy thesis. The sixth chapter addresses arguments that pleasure and pain fail to meet these formal conditions. One argument stems from the observation that pleasures and pains are essentially transient and ephemeral. Another argument proceeds from the observation that interpersonal comparisons of pleasure and pain appear to be impossible. A third, closely related to the first two, argues that pleasure and pain are too heterogeneous to be quantitative. A final argument holds that, for a variety of reasons, the various mathematical operations constitutive of quantitativeness are not applicable to pleasure or pain. I argue that each argument suffers from at least one fatal flaw. Some arguments crucially involve a failure to distinguish between the existence of a quantity and our ability to perform reliable measurements of it. Others involve false analogies between hedonic and other sorts of phenomena. The seventh chapter addresses arguments in favor of the legitimacy of the calculus. Many philosophers, such as Bentham, Mill, Ross, and Plato, seem to assume, without any serious argument, that pleasure and pain are quantitative. Others attempt to argue that, for example, two people enjoying something must involve more pleasure than if just one person were enjoying it. A third type of argument rests on the claim that it is sometimes rational to be indifferent between a longer lasting, less intense episode of pleasure and a more intense but shorter episode. This suggests that since duration is clearly quantitative, intensity must be, too, because if it were not, there could be no equivalence between the brief but intense and the lengthy but mellow episodes. Several of these arguments are unsound or question-begging. Finally, I present an argument in favor of the hedonic calculus that I endorse, along with possible objections and my replies. I begin by acknowledging the central point of the "hedonic trade-offs" argument, and then proceed, via reductio, by pointing out the various absurd or unpalatable consequences of the denial of the thesis that pleasure and pain are quantitative. (shrink)

Comparativism maintains that physical quantities are ultimately relational in character. For example, an object’s having 1 kg rest mass depends on the relations it stands in to other objects in the universe. Comparativism, its advocates allege, reveals that quantities are not metaphysically mysterious: Quantities are reducible to familiar relations holding among physical objects. Modal accounts of intrinsicality—such as Lewis’s duplication account or Langton and Lewis’s combinatorial account—are popular accounts preserving many of our core intuitions regarding which properties are intrinsic. I (...) argue that to endorse both comparativism and a modal account of intrinsicality, we must reject the plausible thesis that determinable properties are instantiated solely in virtue of their determinates. I call this ‘the determinacy tension’ and I suggest approaches for dissolving it. (shrink)

Dispositional Essentialism and Ontic Structural Realism aim to account for modality. Dispositional Essentialism takes properties to account for laws. In particular, it takes determinate properties to account for laws of nature, which are determinable. Ontic Structural Realism does the reverse. According to Steven French, Ontic Structural Realism takes laws and symmetries to be part of the fundamental structure of the world. Determinate properties are “dependent” on laws. The core difference between Dispositional Essentialism and Ontic Structural Realism’s accounts of modality is (...) the direction of the dependence between properties and laws. As a result, French describes Ontic Structural Realism as a reverse-engineering of Dispositional Essentialism, and Chakravartty differentiates them by saying that Dispositional Essentialism gives a bottom-up account of modality whereas Ontic Structural Realism’s is top-down. Both views face significant problems. The main problems these views face stem from relational individuation. Properties are individuated by their relations to further properties. As such, it is hard to see how they can be metaphysically prior to those relations as per Dispositional Essentialism. Equally, laws are relations between properties. As such, it is hard to see how they could be metaphysically prior to the properties they relate as per Ontic Structural Realism. Both properties and laws seem dependent on each other. By requiring one to come first and explain the other, dispositional essentialists and ontic structural realists end up in a chicken-egg scenario. I propose a hybrid between Dispositional Essentialism and Ontic Structural Realism. My hybrid view does away with the dogma of ontological priority between properties and laws. Instead, properties and laws symmetrically depend. I argue that my hybrid view is the way out of the chicken-egg-property-law conundrum. It paves a new way for making sense of modality from a structuralist perspective. (shrink)

To state an important fact about the photon, physicists use such expressions as (1) “the photon has zero (null, vanishing) mass” and (2) “the photon is (a) massless (particle)” interchangeably. Both (1) and (2) express the fact that the photon has no non-zero mass. However, statements (1) and (2) disagree about a further fact: (1) attributes to the photon the property of zero-masshood whereas (2) denies that the photon has any mass at all. But is there really a difference between (...) saying that something has zero mass (charge, spin, etc.) and saying that it has no mass (charge, spin, etc.)? Does the distinction cut any physical or philosophical ice? I argue that the answer to these questions is yes. Put briefly, the claim of this paper is that some zero-value physical quantities are not mere “privations”, “absences” or “holes in being”. They are respectable properties in the same sense in which their non-zero partners are. This, I will show, has implications for the debate between two rival views of the nature of property, dispositionalism and categoricalism. (shrink)

This paper concerns the ways in which one can/cannot combine extensive quantities. Given a particular theory of extensive measurement, there can be no alternative ways of combining extensive quantities, where 'alternative' means that one combining operation can be used instead of another causing only a change in the number assigned to the quantity. As a consequence, rectangular concatenation cannot be an alternative combining operation for length as was suggested by Ellis and agreed by Krantz, Luce, Suppes, and Tversky. I argue (...) as well that a theory which imposes such restrictions on the combining operation is more desirable than less stringent rival theories. (shrink)

Degree-sentences, i.e. sentences that seem to refer to things that allow of degrees, are widely used both inside and outside of philosophy, even though the metaphysics of degrees is much of an untrodden field. This paper aims to fill this lacuna by addressing the following four questions: [A] Is there some one thing, such that it is degree sensitive? [B] Are there things x, y, and z that stand in a certain relation to each other, viz. the relation that x (...) has more y than z? [C] In those cases in which degree sentences do not refer to phenomena that are degree sensitive, what is responsible for their prima facie seeming to do so? [D] If there are degree sensitive things, to which ontological categories do they belong? We answer each of these questions by arguing that there are, metaphysically speaking, different phenomena that degree sentences refer to: some refer to determinates that emanate from a certain determinable, others to tokens that are instantiations of a certain type, and yet others to what we call ‘complex, resultant properties that are constituted by stereotypical properties’. Finally, we show the relevance of our answers by applying them to the notions of freedom and belief. (shrink)

I argue that there can be value relations without individual values to support them. The fact that an item is better than another item does not have to be explained by reference to the values of the individual items. Instead, value relations can be grounded directly and exhaustively in descriptive facts about their relata. I show that my suggestion fits well with plausible perspectives on the nature of values and reasons, respectively. One of them is the fitting‐attitudes view, according to (...) which facts about value and value relations are facts about reasons for attitudes. The other is the descriptive view, according to which facts about reasons for attitudes can be grounded directly and exhaustively in descriptive considerations. (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.

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)

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)

La théorie russellienne des relations est ordinairement conçue comme le résultat d'une réflexion logique et ontologique sur l'ordre et l'asymétrie. Le présent article vise à présenter une autre généalogie, centrée sur les concepts de grandeur et de vecteur. Nous montrons en premier lieu que la thèse de l'irréductibilité des relations est avancée pour la première fois en 1897, à l'occasion d'une reformulation de la dialectique hégélienne de la quantité. Nous soulignons, en second lieu, que la notion de grandeur fait, autour (...) des années 1898-1899, l'objet d'une formalisation mathématique, complètement indépendante de la théorie des relations et fondée exclusivement sur les algèbres vectorielles. Nous montrons enfin que Russell, en possession de sa nouvelle doctrine logique, développe dès 1901 une théorie relationnelle des grandeurs vectorielles. Tout se passe donc comme si un des intérêts de la nouvelle théorie était, pour le philosophe, de permettre la substitution des relations aux grandeurs. (shrink)