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Bibliography: Quantities in Metaphysics
  1. Jennifer McRobert, Kant on Negative Quantities, Real Opposition and Inertia.score: 24.0
    Kant's obscure essay entitled An Attempt to Introduce the Concept of Negative Quantities into Philosophy has received virtually no attention in the Kant literature. The essay has been in English translation for over twenty years, though not widely available. In his original 1983 translation, Gordon Treash argues that the Negative Quantities essay should be understood as part of an ongoing response to the philosophy of Christian Wolff. Like Hoffmann and Crusius before him, the Kant of 1763 is at (...)
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  2. Angelo Gilio & Giuseppe Sanfilippo (2013). Conditional Random Quantities and Compounds of Conditionals. Studia Logica:1-21.score: 24.0
    In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as ${XH + \mathbb{P}(X|H)H^c}$ ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give (...)
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  3. Patrick Suppes (1951). A Set of Independent Axioms for Extensive Quantities. Portugaliae Mathematica 10 (4):163-172.score: 21.0
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  4. Paola Cantù (2010). Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities. Synthese 174 (2):225 - 235.score: 20.0
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...)
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  5. Daniel Nolan (2008). Finite Quantities. Proceedings of the Aristotelian Society 108 (1part1):23-42.score: 18.0
    Quantum Mechanics, and apparently its successors, claim that there are minimum quantities by which objects can differ, at least in some situations: electrons can have various “energy levels” in an atom, but to move from one to another they must jump rather than move via continuous variation: and an electron in a hydrogen atom going from -13.6 eV of energy to -3.4 eV does not pass through states of -10eV or -5.1eV, let along -11.1111115637 eV or -4.89712384 eV.
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  6. Jeremy Butterfield, On Symmetry and Conserved Quantities in Classical Mechanics.score: 18.0
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic (...)
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  7. Mark Sharlow, Generalizing the Algebra of Physical Quantities.score: 18.0
    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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  8. I. Pitowsky, On Symmetry and Conserved Quantities in Classical Mechanics.score: 18.0
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether’s “first theorem”, in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics’ grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem’s main “ingredient”, apart from cyclic (...)
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  9. Hans Halvorson (2001). On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics. Journal of Philosophical Logic 30 (1):27-50.score: 18.0
    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 (...)
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  10. Bob Hale (2002). Real Numbers, Quantities, and Measurement. Philosophia Mathematica 10 (3):304-323.score: 18.0
    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, (...)
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  11. Henry E. Kyburg Jr (1997). Quantities, Magnitudes, and Numbers. Philosophy of Science 64 (3):377-410.score: 18.0
    Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the (...)
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  12. Kathleen C. Cook (1975). On the Usefulness of Quantities. Synthese 31 (3-4):443 - 457.score: 18.0
    I have argued that there is a philosophical problem posed by a need to determine the reference of expressions which seem to refer to kinds of stuff or matter and to make identity claims about it (e.g., ‘the gold’, ‘the same clay’). Ordinary sortal expressions such as ‘lump’, and ‘piece’ have been shown to be inadequate to the task of providing reference for the expressions in question. What is necessary is an expression which does not have an ordinary sortal use (...)
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  13. Yuri Balashov (1999). Zero-Value Physical Quantities. Synthese 119 (3):253-286.score: 18.0
    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 (...)
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  14. Tomislav Ivezić (2006). Four-Dimensional Geometric Quantities Versus the Usual Three-Dimensional Quantities: The Resolution of Jackson's Paradox. [REVIEW] Foundations of Physics 36 (10):1511-1534.score: 18.0
    In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors Ns, Nt and Ms, Mt, respectively, are given. The torques Ns, Nt (the angular momentums Ms, Mt), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\varvec{E,\,B,\,F,\,L,\,N}$ etc. and their transformations are objected from the viewpoint of (...)
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  15. Fred Ablondi (2012). On the Ghosts of Departed Quantities. Metascience 21 (3):681-683.score: 18.0
    On the ghosts of departed quantities Content Type Journal Article Category Book Review Pages 1-3 DOI 10.1007/s11016-011-9606-5 Authors Fred Ablondi, Department of Philosophy, Hendrix College, Conway, AR, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  16. Antonina Kowalska (2008). Quantities Enduring in Time. Dialogue and Universalism 18 (9-10):27-38.score: 18.0
    Despite changeability of the world, the human mind also ponders on those quantities that remain constant over time. This was the case in ancient times, in the middle ages, and the same applies in modern physics. This paper discusses i.a. Zenon paradoxes, the principle of inertia, and the Emma Noether theorem, ending with the modern, so-called Zeno’s quantum effect. The foot-notes concern the ancient “Achilles” paradox, spot speed, as well as some of the facts taken out of the life-history (...)
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  17. Julian Reiss (2001). Natural Economic Quantities and Their Measurement. Journal of Economic Methodology 8 (2):287-311.score: 18.0
    This paper discusses and develops an important distinction drawn by Jevons, viz . that between natural and fictitious quantities. This distinction provides a basis for a theory of economic concept formation that aims at picking out families of models that are phenomenally adequate, explanatory and exact simultaneously. Essentially, the theory demands of an economic quantity to be natural that (1) it is explained by a causal model, (2) it is measurable and (3) the measurement procedure is justified. The proposed (...)
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  18. Roi Cohen Kadosh Korbinian Moeller, Elise Klein, Hans-Christoph Nuerk (2012). A Unitary or Multiple Representations of Numerical Magnitude? – the Case of Structure in Symbolic and Non-Symbolic Quantities. Frontiers in Psychology 3.score: 18.0
    Currently, there is a controversial debate on whether there is an abstract representation of number magnitude, multiple different ones or multiple different ones that project onto a unitary representation. The current study aimed at evaluating this issue by means of a magnitude comparison task involving Arabic numbers and structured as well as unstructured non-symbolic patterns of squares. In particular, we were interested whether a specific numerical effect, the unit-decade compatibility effect reflecting decomposed processing of tens and units complying with the (...)
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  19. J. A. McGrane (2009). Are Psychological Quantities and Measurement Relevant in the 21st Century? Frontiers in Psychology 1:22-22.score: 18.0
    Are Psychological Quantities and Measurement Relevant in the 21st Century?
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  20. K. C. Burns Nicola Armstrong, Alexis Garland (2012). Memory for Multiple Cache Locations and Prey Quantities in a Food-Hoarding Songbird. Frontiers in Psychology 3.score: 18.0
    Most animals can discriminate between pairs of numbers that are each less than four without training. However, North Island robins (Petroica longipes), a food hoarding songbird endemic to New Zealand, can discriminate between quantities of items as high as eight without training. Here we investigate whether robins are capable of other complex quantity discrimination tasks. We test whether their ability to discriminate between small quantities declines with 1. the number of cache sites containing prey rewards and 2. the (...)
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  21. Orly Rubinsten Avishai Henik, Tali Leibovich, Sharon Naparstek, Liana Diesendruck (2011). Quantities, Amounts, and the Numerical Core System. Frontiers in Human Neuroscience 5.score: 18.0
    Quantities, Amounts, and the Numerical Core System.
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  22. Phil Dowe (1995). Causality and Conserved Quantities: A Reply to Salmon. Philosophy of Science 62 (2):321-333.score: 16.0
    In a recent paper (1994) Wesley Salmon has replied to criticisms (e.g., Dowe 1992c, Kitcher 1989) of his (1984) theory of causality, and has offered a revised theory which, he argues, is not open to those criticisms. The key change concerns the characterization of causal processes, where Salmon has traded "the capacity for mark transmission" for "the transmission of an invariant quantity." Salmon argues against the view presented in Dowe (1992c), namely that the concept of "possession of a conserved quantity" (...)
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  23. John Forge (2000). Quantities in Quantum Mechanics. International Studies in the Philosophy of Science 14 (1):43 – 56.score: 16.0
    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.
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  24. Sébastien Gandon (2008). Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics. History and Philosophy of Logic 29 (1):1-30.score: 16.0
    This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible 'by logical principles from logical principles' does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV-V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's logicism (...)
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  25. Gianni Cassinelli & Pekka J. Lahti (1989). The Measurement Statistics Interpretation of Quantum Mechanics: Possible Values and Possible Measurement Results of Physical Quantities. [REVIEW] Foundations of Physics 19 (7):873-890.score: 16.0
    Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.
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  26. Janneke Jehee Dana H. Ballard (2012). Dynamic Coding of Signed Quantities in Cortical Feedback Circuits. Frontiers in Psychology 3.score: 16.0
    In the early sensory and motor areas of the cortex, individual neurons transmit information about specific sensory features via a peaked response. This concept has been crystallized as `labeled lines,' to denote that axons communicate the specific properties of their sensory or motor parent cell. Such cells also can be characterized as being polarized, that is, as representing a signed quantity that is either positive or negative. We show in a model simulation that there are two important consequences when learning (...)
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  27. Dana H. Ballard & Janneke Jehee (2012). Dynamic Coding of Signed Quantities in Cortical Feedback Circuits. Frontiers in Psychology 3.score: 16.0
    In the early sensory and motor areas of the cortex, individual neurons transmit information about specific sensory features via a peaked response. This concept has been crystallized as `labeled lines,' to denote that axons communicate the specific properties of their sensory or motor parent cell. Such cells also can be characterized as being polarized, that is, as representing a signed quantity that is either positive or negative. We show in a model simulation that there are two important consequences when learning (...)
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  28. Helen Morris Cartwright (1970). Quantities. Philosophical Review 79 (1):25-42.score: 15.0
  29. M. Eddon (2007). Armstrong on Quantities and Resemblance. Philosophical Studies 136 (3):385 - 404.score: 15.0
    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.
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  30. John Bigelow, Robert Pargetter & D. M. Armstrong (1988). Quantities. Philosophical Studies 54 (3):287 - 304.score: 15.0
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  31. Noam Agmon (1977). Relativistic Transformations of Thermodynamic Quantities. Foundations of Physics 7 (5-6):331-339.score: 15.0
    A unique solution is proposed to the problem of how thermodynamic processes between thermodynamic systems at relative rest “appear” to a moving observer. Assuming only transformations for entropy, pressure, and volume and the invariance of the “fundamental thermodynamic equation,” one can derive transformations for (thermodynamic) energy and temperature. The invariance of the first and second laws entails transformations for work and heat. All thermodynamic relations become Lorentz-invariant. The transformations thus derived are in principle equivalent to those of Einstein and Planck, (...)
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  32. John Forge (1999). Laws of Nature as Relations Between Quantities? In Howard Sankey (ed.), Causation and Laws of Nature. Kluwer. 111--124.score: 15.0
  33. Jonathan Riley (1993). On Quantities and Qualities of Pleasure. Utilitas 5 (02):291-.score: 15.0
  34. John Forge (1995). Bigelow and Pargetter on Quantities. Australasian Journal of Philosophy 73 (4):594 – 605.score: 15.0
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  35. J. Gibson Winans (1977). Quaternion Physical Quantities. Foundations of Physics 7 (5-6):341-349.score: 15.0
    Quaternions consist of a scalar plus a vector and result from multiplication or division of vectors by vectors. Division of vectors is equivalent to multiplication divided by a scalar. Quaternions as used here consist of the scalar product with positive sign plus the vector product with sign determined by the right-hand rule. Units are specified by the multiplication process. Trigonometric functions are quaternions with units that can satisfy Hamilton's requirements. The square of a trigonometric quaternion is a real number provided (...)
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  36. D. M. Armstrong (1988). Are Quantities Relations? A Reply to Bigelow and Pargetter. Philosophical Studies 54 (3):305 - 316.score: 15.0
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  37. Paul Teller (1979). Quantum Mechanics and the Nature of Continuous Physical Quantities. Journal of Philosophy 76 (7):345-361.score: 15.0
  38. Amanda Brandone, Andrei Cimpian, Sarah-Jane Leslie & Susan Gelman (2012). Do Lions Have Manes? For Children, Generics Are About Kinds, Not Quantities. Child Development 83:423-433.score: 15.0
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  39. David Sherry (1991). The Logic of Impossible Quantities. Studies in History and Philosophy of Science Part A 22 (1):37-62.score: 15.0
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  40. Linda M. Moxey & Anthony J. Sanford (1993). Communicating Quantities: A Psychological Perspective (Essays in Cognitive Psychology). Psychology Press.score: 15.0
  41. Nigel Holmes (2007). False Quantities in Vegetius and Others. Classical Quarterly 57 (02).score: 15.0
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  42. Michael S. C. Thomas & Anthony P. Atkinson (1999). Quantities of Qualia. Behavioral and Brain Sciences 22 (1):169-170.score: 15.0
    We address two points in this commentary. First, we question the extent to which O'Brien & Opie have established that the classical approach is unable to support a viable vehicle theory of consciousness. Second, assuming that connectionism does have the resources to support a vehicle theory, we explore how the activity of the units of a PDP network might sum together to form phenomenal experience (PE).
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  43. Pavel Gregoric (2006). Quantities and Contraries: Aristotle's "Categories" 6, 5b11-6a18. Apeiron 39 (4):341 - 358.score: 15.0
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  44. A. Sloman (1912). Hidden Quantities. The Classical Review 26 (07):220-221.score: 15.0
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  45. Hartmut Traunmüller (1998). Measuring Time and Other Spatio-Temporal Quantities. Apeiron 5 (3-4):213.score: 15.0
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  46. Carl D. Buck (1913). Hidden Quantities Again. The Classical Review 27 (04):122-126.score: 15.0
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  47. B. Guerts (1997). Book Review. Communicating Quantities. Linda M Moxey and Anthony J Sanford. [REVIEW] Journal of Semantics 14 (1):87-94.score: 15.0
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  48. W. D. Hart (1993). Mathematics as a Science of Quantities. Ancient Philosophy 13 (2):440-440.score: 15.0
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  49. Aaron M. Scherer, Paul D. Windschitl, Jillian O'Rourke & Andrew R. Smith (2012). Hoping for More: The Influence of Outcome Desirability on Information Seeking and Predictions About Relative Quantities. Cognition 125 (1):113-117.score: 15.0
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