# Quantities

Edited by Zee R. Perry (New York University, Shanghai)
 Summary Two characteristics distinguish quantities from non-quantitative properties and relations. First, every quantity is associated with a class of determinate “magnitudes” or “values” of that quantity, each member of which is a property or relation itself. So when a particle possesses mass or charge, it always instantiates one particular magnitude of mass or charge -- like 2.5 kilograms or 7 Coulombs. Second, the magnitudes of a given quantity (alternatively, the particulars which instantiate those magnitudes) exhibit “quantitative structure”, which comprises things like: ordering structure, summation/concatenation structure, ratio structure, directional structure, etc. We often represent quantities using similarly-structured mathematical entities, like numbers, vectors, etc. Classic debates about quantities concern attempts to give a metaphysical account of quantitative structure without appealing to mathematical entities/structures. Other questions include: How do quantities play the roles they do in measurement, the laws of nature, etc? Are a quantity's magnitudes fundamentally absolute (like 2.5 kilograms) or comparative (like twice-as-massive-as)?
 Key works Mundy 1987 is a seminal paper in this area. Field 1980 and Field 1984 are not directly concerned with the metaphysics of quantity proper, but represent an early and very influential attempt to account for quantitative structure without relying on mathematics. The exchange between Bigelow et al 1988 and Armstrong 1988 is an influential treatment of the absolute/comparative debate in the metaphysics of quantity.
 Introductions Eddon 2013 provides a very useful opinionated introduction.
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1. Nominalism and Immutability.Daniel Berntson - manuscript
Can we do science without numbers? How much contingency is there? These seemingly unrelated questions--one in the philosophy of math and science and the other in metaphysics--share an unexpectedly close connection. For as it turns out, a radical answer to the second leads to a breakthrough on the first. The radical answer is new view about modality called compossible immutabilism. The breakthrough is a new strategy for doing science without numbers. One of the chief benefits of the new strategy is (...)

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2. In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.

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3. The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism.Mahmoud Jalloh - forthcoming - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford: Oxford University Press.
In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and (...)

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4. Degrees of Consciousness.Andrew Y. Lee - forthcoming - Noûs.
Is a human more conscious than an octopus? 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 (...)

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5. Ethics Without Numbers.Jacob M. Nebel - forthcoming - Philosophy and Phenomenological Research.
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 (...)

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6. On Mereology and Metricality.Zee Perry - forthcoming - Philosophers' Imprint.
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.

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7. Riemann’s Scale: A Puzzle About Infinity.Øystein Linnebo - 2023 - Erkenntnis 88 (1):189-191.
Ordinarily, the order in which some objects are attached to a scale does not affect the total weight measured by the scale. This principle is shown to fail in certain cases involving infinitely many objects. In these cases, we can produce any desired reading of the scale merely by changing the order in which a fixed collection of objects are attached to the scale. This puzzling phenomenon brings out the metaphysical significance of a theorem about infinite series that is well (...)

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8. Aggregation Without Interpersonal Comparisons of Well‐Being.Jacob M. Nebel - 2022 - Philosophy and Phenomenological Research 105 (1):18-41.
This paper is about the role of interpersonal comparisons in Harsanyi's aggregation theorem. Harsanyi interpreted his theorem to show that a broadly utilitarian theory of distribution must be true even if there are no interpersonal comparisons of well-being. How is this possible? The orthodox view is that it is not. Some argue that the interpersonal comparability of well-being is hidden in Harsanyi's premises. Others argue that it is a surprising conclusion of Harsanyi's theorem, which is not presupposed by any one (...)

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9. Intrinsicality and determinacy.Erica Shumener - 2022 - Philosophical Studies 179 (11):3349-3364.
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 (...)

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10. Some Consequences of Physics for the Comparative Metaphysics of Quantity.David John Baker - 2020 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume 12. Oxford University Press. pp. 75-112.
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 (...)

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11. A puzzle about rates of change.David Builes & Trevor Teitel - 2020 - Philosophical Studies 177 (10):3155-3169.
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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12. Heat in Renaissance Philosophy.Filip Buyse - 2020 - In Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Berlin: Springer.
The term ‘heat’ originates from the Old English word hǣtu, a word of Germanic origin; related to the Dutch ‘hitte’ and German ‘Hitze’. Today, we distinguish three different meanings of the word ‘heat’. First, ‘heat’ is understood in colloquial English as ‘hotness’. There are, in addition, two scientific meanings of ‘heat’. ‘Heat’ can have the meaning of the portion of energy that changes with a change of temperature. And finally, ‘heat’ can have the meaning of the transfer of thermal energy (...)

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13. Measures of Similarity.Karin Enflo - 2020 - Theoria 86 (1):73-99.
This article analyses the relationship between the concept of single aspect similarity and proposed measures of similarity. More precisely, it compares eleven measures of similarity in terms of how well they satisfy a list of desiderata, chosen to capture common intuitions concerning the properties of similarity and the relations between similarity and dissimilarity. Three types of measures are discussed: similarity as commonality, similarity as a function of dissimilarity, and similarity as a joint function of commonality and difference. Relative to the (...)

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14. Newton on active and passive quantities of matter.Adwait A. Parker - 2020 - Studies in History and Philosophy of Science Part A 84:1-11.
Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call ‘additivity’ the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze and assess manuscript versions of (...)

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15. Boyle, Spinoza and Glauber: on the philosophical redintegration of saltpeter—a reply to Antonio Clericuzio.Filip A. A. Buyse - 2019 - Foundations of Chemistry 22 (1):59-76.
The so-called ‘redintegration experiment’ is traditionally at the center of the comments on the supposed Boyle/Spinoza controversy. A. Clericuzio influentially argued in his publications that, in De nitro, Boyle accounted for the ‘redintegration’ of saltpeter on the grounds of the chemical properties of corpuscles and “did not make any attempt to deduce them from mechanical principles”. By way of contrast, this paper argues that with his De nitro Boyle wanted to illustrate and promote his new corpuscular or mechanical philosophy, and (...)

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16. Dispositional and categorical properties, and Russellian Monism.Eric Hiddleston - 2019 - Philosophical Studies 176 (1):65-92.
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 (...)

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17. Quantity Tropes and Internal Relations.Markku Keinänen, Antti Keskinen & Jani Hakkarainen - 2019 - Erkenntnis 84 (3):519-534.
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 (...)

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18. The Problem of Fregean Equivalents.Joongol Kim - 2019 - Dialectica 73 (3):367-394.
It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...)

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19. A Trope Theoretical Analysis of Relational Inherence.Markku Keinänen - 2018 - In Jaakko Kuorikoski & Teemu Toppinen (eds.), Action, Value and Metaphysics - Proceedings of the Philosophical Society of Finland Colloquium 2018, Acta Philosophica Fennica 94. Helsinki: Societas Philosophica Fennica. pp. 161-189.
The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...)

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20. Trooppiteoriat ja relaatiossa olemisen analyysi.Markku Keinänen - 2018 - Ajatus 75 (1):121-150.
Trope theories aim to eschew the primitive dichotomy between characterising (properties, relations) and characterized entities (objects). This article (in Finnish) presents a new trope theoretical analysis of relational inherence as the best way out of the impasse created by the alleged necessity to choose between an eliminativist and a primitivist ("relata-specific") view about relations in trope theory.

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21. Kinds of Tropes without Kinds.Markku Keinänen, Jani Hakkarainen & Antti Keskinen - 2018 - Dialectica 72 (4):571-596.
In this article, we propose a new trope nominalist conception of determinate and determinable kinds of quantitative tropes. The conception is developed as follows. First, we formulate a new account of tropes falling under the same determinates and determinables in terms of internal relations of proportion and order. Our account is a considerable improvement on the current standard account (Campbell 1990; Maurin 2002; Simons 2003) because it does not rely on primitive internal relations of exact similarity or quantitative distance. The (...)

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22. Metaphysics of Quantity and the Limit of Phenomenal Concepts.Derek Lam - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy (3):1-20.
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 (...)

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23. Is There a Humean Account of Quantities?Phillip Bricker - 2017 - Philosophical Issues 27 (1):26-51.
Humeans have a problem with quantities. A core principle of any Humean account of modality is that fundamental entities can freely recombine. But determinate quantities, if fundamental, seem to violate this core principle: determinate quantities belonging to the same determinable necessarily exclude one another. Call this the problem of exclusion. Prominent Humeans have responded in various ways. Wittgenstein, when he resurfaced to philosophy, gave the problem of exclusion as a reason to abandon the logical atomism of the Tractatus with its (...)

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24. Macroscopic Metaphysics: Middle-Sized Objects and Longish Processes.Paul Needham - 2017 - Cham: Springer.
This book is about matter. It involves our ordinary concept of matter in so far as this deals with enduring continuants that stand in contrast to the occurrents or processes in which they are involved, and concerns the macroscopic realm of middle-sized objects of the kind familiar to us on the surface of the earth and their participation in medium term processes. The emphasis will be on what science rather than philosophical intuition tells us about the world, and on chemistry (...)

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25. The Metaphysics of Quantities and Their Dimensions.Bradford Skow - 2017 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics: Volume 10. Oxford University Press. pp. 171-198.
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26. Quantity of Matter or Intrinsic Property: Why Mass Cannot Be Both.Mario Hubert - 2016 - In Laura Felline, Antonio Ledda, F. Paoli & Emanuele Rossanese (eds.), New Developments in Logic and Philosophy of Science. London: College Publications. pp. 267–77.
I analyze the meaning of mass in Newtonian mechanics. First, I explain the notion of primitive ontology, which was originally introduced in the philosophy of quantum mechanics. Then I examine the two common interpretations of mass: mass as a measure of the quantity of matter and mass as a dynamical property. I claim that the former is ill-defined, and the latter is only plausible with respect to a metaphysical interpretation of laws of nature. I explore the following options for the (...)

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27. What Are Quantities?Joongol Kim - 2016 - Australasian Journal of Philosophy 94 (4):792-807.
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 (...)

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28. The Distinction between Primary Properties and Secondary Qualities in Galileo's Natural Philosophy.F. Buyse - 2015 - Cahiers du Séminaire Québécois En Philosophie Moderne / Working Papers of the Quebec Seminar in Early Modern Philosophy 1:20-45.
In Il Saggiatore (1623), Galileo makes a strict distinction between primary and secondary qualities. Although this distinction continues to be debated in philosophical literature up to this very day, Galileo's views on the matter, as well as their impact on his contemporaries and other philosophers, have yet to be sufficiently documented. The present paper helps to clear up Galileo's ideas on the subject by avoiding some of the misunderstandings that have arisen due to faulty translations of his work. In particular, (...)

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29. Maudlin on the Triangle Inequality.Marco Dees - 2015 - Thought: A Journal of Philosophy 4 (2):124-130.
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 (...)

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30. Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
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 (...)

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31. A Trope Nominalist Theory of Natural Kinds.Markku Keinänen - 2015 - In Ghislain Guigon & Gonzalo Rodriguez-Pereyra (eds.), Nominalism about Properties. Routledge. pp. 156-174.
In this chapter, I present the first systematic trope nominalist approach to natural kinds of objects. It does not identify natural kinds with the structures of mind-independent entities (objects, universals or tropes). Rather, natural kinds are abstractions from natural kind terms and objects belong to a natural kind if they satisfy their mind-independent application conditions. By relying on the trope theory SNT (Keinänen 2011), I show that the trope parts of a simple object determine the kind to which it belongs. (...)

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32. Heavy Duty Platonism.Robert Knowles - 2015 - Erkenntnis 80 (6):1255-1270.
Heavy duty platonism is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that they (...)

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33. Magnitudes: Metaphysics, Explanation, and Perception.Christopher Peacocke - 2015 - In Annalisa Coliva, Volker Munz & Danièle Moyal-Sharrock (eds.), Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium. De Gruyter. pp. 357-388.
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.

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34. Properly Extensive Quantities.Zee R. Perry - 2015 - Philosophy of Science 82 (5):833-844.
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 (...)

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35. Anaxagorae Homoeomeria.David Torrijos-Castrillejo - 2015 - Elenchos 36 (1):141-148.
Aristotle introduced in the history of the reception of Anaxagoras the term “homoiomerous”. This word refers to substances whose parts are similar to each other and to the whole. Although Aristotle’s explanations can be puzzling, the term “homoiomerous” may explain an authentic aspect of Anaxagoras’ doctrine reflected in the fragments of his work. Perhaps one should find a specific meaning for the term “homoiomerous” in Anaxagoras, somewhat different from the one present in Aristotle. This requires a review of the sense (...)

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36. Intrinsic Explanations and Numerical Representations.M. Eddon - 2014 - In Robert M. Francescotti (ed.), Companion to Intrinsic Properties. De Gruyter. pp. 271-290.
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 (...)

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37. Quantity and number.James Franklin - 2014 - In Daniel D. Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. New York, USA: Routledge. pp. 221-244.
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.

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38. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
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 (...)

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39. Galileo and Spinoza.F. Buyse (ed.) - 2013 - Routledge.

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40. Absolutism vs Comparativism About Quantity.Shamik Dasgupta - 2013 - Oxford Studies in Metaphysics 8:105-150.

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41. Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.
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.

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42. Fundamental Properties of Fundamental Properties.M. Eddon - 2013 - In Karen Bennett Dean Zimmerman (ed.), Oxford Studies in Metaphysics, Volume 8. pp. 78-104.
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 (...)

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43. Multi‐track dispositions.Barbara Vetter - 2013 - Philosophical Quarterly 63 (251):330-352.
It is a familiar point that many ordinary dispositions are multi-track, that is, not fully and adequately characterisable by a single conditional. In this paper, I argue that both the extent and the implications of this point have been severely underestimated. First, I provide new arguments to show that every disposition whose stimulus condition is a determinable quantity must be infinitely multi-track. Secondly, I argue that this result should incline us to move away from the standard assumption that dispositions are (...)

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44. The ontological distinction between units and entities.Gordon Cooper & Stephen M. Humphry - 2012 - Synthese 187 (2):393-401.
The base units of the SI include six units of continuous quantities and the mole, which is defined as proportional to the number of specified elementary entities in a sample. The existence of the mole as a unit has prompted comment in Metrologia that units of all enumerable entities should be defined though not listed as base units. In a similar vein, the BIPM defines numbers of entities as quantities of dimension one, although without admitting these entities as base units. (...)

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45. The mathematical form of measurement and the argument for Proposition I in Newton’s Principia.Katherine Dunlop - 2012 - Synthese 186 (1):191-229.
Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...)

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46. Property evaluation types.Alessandro Giordani & Luca Mari - 2012 - Measurement 45 (3):437-452.
An appropriate characterization of property types is an important topic for measurement science. On the basis of a set-theoretic model of evaluation and measurement processes, the paper introduces the operative concept of property evaluation type, and discusses how property types are related to, and in fact can be derived from, property evaluation types, by finally analyzing the consequences of these distinctions for the concepts of ‘property’ used in the International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (...)

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47. Quantity and Quantity Value.Luca Mari & Alessandro Giordani - 2012 - Metrologia 49 (6):756-764.
The concept system around 'quantity' and 'quantity value' is fundamental for measurement science, but some very basic issues are still open on such concepts and their relation. This paper argues that quantity values are in fact individual quantities, and that a complementarity exists between measurands and quantity values. This proposal is grounded on the analysis of three basic 'equality' relations: (i) between quantities, (ii) between quantity values and (iii) between quantities and quantity values. A consistent characterization of such concepts is (...)
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48. From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction.Brian Skyrms - 2012 - Oxford, England: Oxford University Press.
Pt. I. Zeno and the metaphysics of quantity. Zeno's paradox of measure -- Tractarian nominalism -- Logical atoms and combinatorial possibility -- Strict coherence, sigma coherence, and the metaphysics of quantity -- pt. II. Coherent degrees of belief. Higher-order degrees of belief -- A mistake in dynamic coherence arguments? -- Dynamic coherence and probability kinematics -- Updating, supposing, and MAXENT -- The structure of radical probabilism -- Diachronic coherence and radical probabilism -- pt. III. Induction. Carnapian inductive logic for Markov (...)

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49. Nomological Resemblance.Robin Stenwall - 2012 - Metaphysica 14 (1):31-46.
Laws of nature concern the natural properties of things. Newton’s law of gravity states that the gravitational force between objects is proportional to the product of their masses and inversely proportional to the square of their distance; Coulomb’s law states a similar functional dependency between charged particles. Each of these properties confers a power to act as specified by the function of the laws. Consequently, properties of the same quantity confer resembling powers. Any theory that takes powers seriously must account (...)