Edited by Zee R. Perry (Rutgers University - New Brunswick)
About this topic
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.
Related categories

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  1. Classical Physical Abstraction.Ernest W. Adams - 1993 - Erkenntnis 38 (2):145 - 167.
    An informal theory is set forth of relations between abstract entities, includingcolors, physical quantities, times, andplaces in space, and the concrete things thathave them, or areat orin them, based on the assumption that there are close analogies between these relations and relations between abstractsets and the concrete things that aremembers of them. It is suggested that even standard scientific usage of these abstractions presupposes principles that are analogous to postulates of abstraction, identity, and other fundamental principles of set theory. Also (...)
  2. Are Quantities Relations? A Reply to Bigelow and Pargetter.D. M. Armstrong - 1988 - Philosophical Studies 54 (3):305 - 316.
  3. Some Consequences of Physics for the Comparative Metaphysics of Quantity.David John Baker - unknown
    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 (...)
  4. Symmetry and the Metaphysics of Physics.David John Baker - 2010 - Philosophy Compass 5 (12):1157-1166.
    The widely held picture of dynamical symmetry as surplus structure in a physical theory has many metaphysical applications. Here, I focus on its relevance to the question of which quantities in a theory represent fundamental natural properties.
  5. Zero-Value Physical Quantities.Yuri Balashov - 1999 - Synthese 119 (3):253-286.
    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 (...)
  6. An Argument for the Extrinsic Grounding of Mass.William A. Bauer - 2011 - Erkenntnis 74 (1):81-99.
    Several philosophers of science and metaphysicians claim that the dispositional properties of fundamental particles, such as the mass, charge, and spin of electrons, are ungrounded in any further properties. It is assumed by those making this argument that such properties are intrinsic, and thus if they are grounded at all they must be grounded intrinsically. However, this paper advances an argument, with one empirical premise and one metaphysical premise, for the claim that mass is extrinsically grounded and is thus an (...)
  7. Science and Necessity.John Bigelow & Robert Pargetter - 1990 - Cambridge University Press.
    This book espouses an innovative theory of scientific realism in which due weight is given to mathematics and logic. The authors argue that mathematics can be understood realistically if it is seen to be the study of universals, of properties and relations, of patterns and structures, the kinds of things which can be in several places at once. Taking this kind of scientific platonism as their point of departure, they show how the theory of universals can account for probability, laws (...)
  8. Quantities.John Bigelow, Robert Pargetter & D. M. Armstrong - 1988 - Philosophical Studies 54 (3):287 - 304.
  9. Quantifizierung — Metrisierung.Gernot Böhme - 1976 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 7 (2):209-222.
    Summary This paper attempts to distinguish the methods of the constitution of a realm of scientific objects from the methods of their mathematical representation. In its investigations into the procedures for forming quantitative concepts analytical philosophy of science has thematized the numerical representation of empirical relational systems (metricizing). It is the task of an historical epistemology to identify the methods and historical processes through which relams of phenomena have been made representable in such a way (quantification). In preparing such investigations (...)
  10. Alternative Combining Operations in Extensive Measurement.Dragana Bozin - 1998 - Philosophy of Science 65 (1):136-150.
    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 (...)
  11. 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 (...)
  12. The Fabric of Space: Intrinsic Vs. Extrinsic Distance Relations.Phillip Bricker - 1993 - Midwest Studies in Philosophy 18 (1):271-294.
  13. Quantitative Relations Between Infinite Sets.Robert Bunn - 1977 - Annals of Science 34 (2):177-191.
    Given the old conception of the relation greater than, the proposition that the whole is greater than the part is an immediate consequence. But being greater in this sense is not incompatible with being equal in the sense of one-one correspondence. Some who failed to recognize this formulated invalid arguments against the possibility of infinite quantities. Others who did realize that the relations of equal and greater when so defined are compatible, concluded that such relations are not appropriately taken as (...)
  14. Humean Supervenience, Vectorial Fields, and the Spinning Sphere.Ralf Busse - 2009 - Dialectica 63 (4):449-489.
  15. Fundamentale Größen in Einer Lewis'schen Eigenschaftstheorie.Ralf Busse - 2007 - Philosophia Naturalis 44 (2):183-218.
    According to D. Lewis, fundamental physical quantities such as mass are families of perfectly natural properties. The best theory of naturalness, however, is nominalistic. But the nominalistic Lewisian has to account for the unity of the particular masses in terms of fundamental ordering and congruence relations among individuals. Such a first-order relational theory can do without perfectly natural mass qualities, without making the having of a particular mass extrinsic. This strictly relational account can be applied to fundamental vectorial quantities such (...)
  16. 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, (...)
  17. Galileo and Spinoza.F. Buyse (ed.) - 2013 - Routledge.
  18. 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 (...)
  19. Spinoza and Galileo Galilei: Adequate Ideas and Intrinsic Qualities of Bodies.Filip A. A. Buyse - 2008 - Historia Philosophica 6:117-127.
  20. Realist Foundations of Measurement.Henry C. Byerly & Vincent A. Lazara - 1973 - Philosophy of Science 40 (1):10-28.
    This paper defends a realist interpretation of theories and a modest realism concerning the existence of quantities as providing the best account both of the logic of quantity concepts and of scientific measurement practices. Various operationist analyses of measurement are shown to be inadequate accounts of measurement practices used by scientists. We argue, furthermore, that appeals to implicit definitions to provide meaning for theoretical terms over and above operational definitions fail because implicit definitions cannot generate the requisite descriptive content. The (...)
  21. Distance.William Charlton - 1983 - Analysis 43 (1):19 - 23.
  22. 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. (...)
  23. Mathematical Explanation and Indispensability Arguments.Chris Daly & Simon Langford - 2009 - Philosophical Quarterly 59 (237):641-658.
    We defend Joseph Melia's thesis that the role of mathematics in scientific theory is to 'index' quantities, and that even if mathematics is indispensable to scientific explanations of concrete phenomena, it does not explain any of those phenomena. This thesis is defended against objections by Mark Colyvan and Alan Baker.
  24. Absolutism Vs Comparativism About Quantity.Shamik Dasgupta - 2013 - Oxford Studies in Metaphysics 8:105-150.
  25. 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 (...)
  26. Species of Measurement Structures.Zoltan Domotor - 1972 - Theoria 38 (1-2):64-81.
  27. The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective.Zoltan Domotor & Vadim Batitsky - 2008 - Measurement Science Review 8 (6):129-146.
    In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources of mathematical analysis) are used as a unified mathematical framework for modeling (a) the time-dependent behavior of natural systems, (b) interactions between natural systems and measuring instruments, (c) error and uncertainty in measurement, and (d) the formal propositional language for describing and reasoning about measurement results. We also discuss how a celebrated theorem in analysis, known as Gelfand (...)
  28. Is Time a Continuum of Instants.Michael Dummett - 2000 - Philosophy 75 (4):497-515.
    Our model of time is the classical continuum of real numbers, and our model of other measurable quantities that change over time is that of functions defined on real numbers with real numbers as values. This model is not derived from reality or from our experience of it, but imposed on reality; and the fit is very imperfect. In classical mathematics, the value of a function for any real number as argument is independent of its value for any other argument: (...)
  29. The Mathematical Form of Measurement and the Argument for Proposition I in Newton's Principia.Katherine Dunlop - 2012 - Synthese 186 (1):191-229.
  30. Intrinsic Explanations and Numerical Representations.M. Eddon - 2014 - In 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 (...)
  31. 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.
  32. 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 (...)
  33. Quantity and Quality: Naturalness in Metaphysics.M. Eddon - 2009 - Dissertation, Rutgers University
    Ever since David Lewis argued for the indispensibility of natural properties, they have become a staple of mainstream metaphysics. This dissertation is a critical examination of natural properties. What roles can natural properties play in metaphysics, and what structure do natural properties have? In the first half of the dissertation, I argue that natural properties cannot do all the work they are advertised to do. In the second half of the dissertation, I look at questions relating to the structure of (...)
  34. Armstrong on Quantities and Resemblance.M. Eddon - 2007 - Philosophical Studies 136 (3):385-404.
    Resemblances obtain not only between objects but between properties. Resemblances of the latter sort - in particular resemblances between quantitative properties - prove to be the downfall of a well-known theory of universals, namely the one presented by David Armstrong. This paper examines Armstrong's efforts to account for such resemblances within the framework of his theory and also explores several extensions of that theory. All of them fail.
  35. Negative, Infinite, and Hotter Than Infinite Temperatures.Philip Ehrlich - 1982 - Synthese 50 (2):233 - 277.
    We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...)
  36. Incommensurability and Measurement.Brigitte Falkenburg - 1997 - Theoria 12 (3):467-491.
    Does incommensurability threaten the realist’s claim that physical magnitudes express properties of natural kinds? Some clarification comes from measurement theory and scientific practice. The standard (empiricist) theory of measurement is metaphysically neutral. But its representational operational and axiomatic aspects give rise to several kinds of a one-sided metaphysics. In scientific practice. the scales of physical quantities (e.g. the mass or length scale) are indeed constructed from measuring methods which have incompatible axiomatic foundations. They cover concepts which belong to incomensurable theories. (...)
  37. Can We Dispense with Space-Time?Hartry Field - 1984 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:33-90.
    This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.
  38. Quantities in Quantum Mechanics.John Forge - 2000 - International Studies in the Philosophy of Science 14 (1):43 – 56.
    The problem of the failure of value definiteness (VD) for the idea of quantity in quantum mechanics is stated, and what VD is and how it fails is explained. An account of quantity, called BP, is outlined and used as a basis for discussing the problem. Several proposals are canvassed in view of, respectively, Forrest's indeterminate particle speculation, the "standard" interpretation of quantum mechanics and Bub's modal interpretation.
  39. Laws of Nature as Relations Between Quantities?John Forge - 1999 - In Howard Sankey (ed.), Causation and Laws of Nature. Kluwer Academic Publishers. pp. 111--124.
  40. Bigelow and Pargetter on Quantities.John Forge - 1995 - Australasian Journal of Philosophy 73 (4):594 – 605.
  41. Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
    Once the reality of properties is admitted, there are two fundamentally different realist theories of properties. Platonist or transcendent realism holds that properties are abstract objects in the classical sense, of being nonmental, nonspatial, and causally inefficacious. By contrast, Aristotelian or moderate realism takes properties to be literally instantiated in things. An apple’s color and shape are as real and physical as the apple itself. The most direct reason for taking an Aristotelian realist view of properties is that we perceive (...)
  42. Aristotelian Realist Philosophy of Mathematics.James Franklin - 2014 - 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 (...)
  43. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...)
  44. 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 (...)
  45. Quantity and Quantity Value.Alessandro Giordani & Luca Mari - 2011 - Proc. TC1-TC7-TC13 14th IMEKO Joint Symposium.
    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 relations. This paper proposes a duality between quantities and quantity values, a proposal that simplifies their characterization and makes it consistent.
  46. Towards a Concept of Property Evaluation Type.Alessandro Giordani & Luca Mari - 2010 - Journal of Physics CS 238 (1):1-6.
    An appropriate characterization of property types is an important topic for measurement science. This paper proposes to derive them from evaluation types, and analyzes the consequences of this position for the VIM3.
  47. Meinong on Magnitudes and Measurement.Ghislain Guigon - 2005 - Meinong Studies 1:255-296.
    This paper introduces the reader to Meinong's work on the metaphysics of magnitudes and measurement in his Über die Bedeutung des Weber'schen Gesetzes. According to Russell himself, who wrote a review of Meinong's work on Weber's law for Mind, Meinong's theory of magnitudes deeply influenced Russell's theory of quantities in the Principles of Mathematics. The first and longest part of the paper discusses Meinong's analysis of magnitudes. According to Meinong, we must distinguish between divisible and indivisible magnitudes. He argues that (...)
  48. Real Numbers, Quantities, and Measurement.Bob Hale - 2002 - Philosophia Mathematica 10 (3):304-323.
    Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. (...)
  49. Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
    On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...)
  50. On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics.Hans Halvorson - 2000 - Journal of Philosophical Logic 30 (1):27-50.
    Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than in classical (...)
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