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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. Generalizing the algebra of physical quantities.Mark Sharlow - manuscript
    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. In Defence of Dimensions.Caspar Jacobs - forthcoming - British Journal for the Philosophy of Science.
    The distinction between dimensions and units in physics is commonplace. But are dimensions a feature of reality? The most widely-held view is that they are no more than a tool for keeping track of the values of quantities under a change of units. This anti-realist position is supported by an argument from underdetermination: one can assign dimensions to quantities in many different ways, all of which are empirically equivalent. In contrast, I defend a form of dimensional realism, on which some (...)
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  4. Comparativist Theories or Conspiracy Theories: the No Miracles Argument Against Comparativism.Caspar Jacobs - forthcoming - Journal of Philosophy.
    Although physical theories routinely posit absolute quantities, such as absolute position or intrinsic mass, it seems that only comparative quantities such as distance and mass ratio are observable. But even if there are in fact only distances and mass ratios, the success of absolutist theories means that the world looks just as if there are absolute positions and intrinsic masses. If comparativism is nevertheless true, there is a sense in which it is a cosmic conspiracy that the world looks just (...)
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  5. 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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  6. A Puzzle about Sums.Andrew Y. Lee - forthcoming - Oxford Studies in Metaphysics.
    A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard (...)
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  7. Ethics without numbers.Jacob M. Nebel - 2024 - Philosophy and Phenomenological Research 108 (2):289-319.
    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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  8. On Mereology and Metricality.Zee R. Perry - 2024 - Philosophers' Imprint 23.
    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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  9. Dimensional Analysis: Essays on the Metaphysics and Epistemology of Quantities.Mahmoud Jalloh - 2023 - Dissertation, University of Southern California
    This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of three related (...)
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  10. Degrees of Consciousness.Andrew Y. Lee - 2023 - Noûs 57 (3):553-575.
    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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  11. 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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  12. 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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  13. Heat in Renaissance Philosophy.Filip Buyse - 2020 - Encyclopedia of Renaissance Philosophy.
    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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  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. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. On the Question: How Fast Does Time Pass.Mahmoud Jalloh - 2017 - Aporia 17.
    In this paper, I take up the question of “how fast does time flow?” This question is usually asked as a rejoinder to the view that time is irreducibly tensed, which is motivated by the fact that we experience the passage of time. I consider what the meaning of this question could be and provide a defence of the view that the passage of time is meaningless (due to its rate of passage being dimensionless), undercutting the motivation for a tensed (...)
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  22. 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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  23. 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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  24. A Trope Nominalist Theory of Natural Kinds.Markku Keinänen - 2015 - In Ghislain Guigon & Gonzalo Rodríguez Pereyra (eds.), Nominalism About Properties: New Essays. New York, NY: 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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  25. Magnitudes: Metaphysics, Explanation, and Perception.Christopher Peacocke - 2015 - In Danièle Moyal-Sharrock, Volker Munz & Annalisa Coliva (eds.), Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium. Boston: 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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  26. Intrinsic Explanations and Numerical Representations.M. Eddon - 2014 - In Robert M. Francescotti (ed.), Companion to Intrinsic Properties. Boston: 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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  27. 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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  28. 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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  29. 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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  30. Quantity and number.James Franklin - 2013 - In Daniel Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. London: 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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  31. 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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  32. 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 (...)
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  33. Similarity and dimensional analysis (preprint - entry in handbook of philosophy of science, elsevier).S. G. Sterrett - 2009 - In Anthonie W. M. Meijers (ed.), Handbook of the Philosophy of Science.
    The topic of this Handbook entry is the relationship between similarity and dimensional analysis, and some of the philosophical issues involved in understanding and making use of that relationship. Discusses basics of the relationship between units, dimensions, and quantities. It explains the significance of dimensionless parameters, and explains that similarity of a physical systems is established by showing equality of a certain set of dimensionless parameters that characterizes the system behavior. Similarity is always relative -- to some system behavior. Other (...)
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  34. 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 (...)
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  35. Armstrong on Quantities and Resemblance.Maya 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.
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  36. 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 (...)
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  37. Sider on Determinism in Absolutist Theories of Quantity.David John Baker - manuscript
    Ted Sider has shown that my indeterminism argument for comparativist theories of quantity also applies to Mundy's absolutist theory. This is because Mundy's theory posits only "pure" relations, i.e. relations between values of the same quantity (between masses and other masses, or distances and other distances). It is straightforward to solve the problem by positing additional mixed relations.
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  38. Structural Mereology: A Formal Elucidation and Some Metaphysical Applications.Thomas Mormann - manuscript
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