SQuaRed-EX: Scientific Quantitativeness Reduced and Explained
Lead Research Organisation:
University of Birmingham
Department Name: School of Philosophy Theology & Religion
Abstract
Physical quantities - things like length, mass, charge, and volume-are commonly represented in science and everyday practice with mathematical entities, like numbers and vectors. We explain why I cannot reach the iced coffee 105cm away from me on the table by citing the fact that my arm is 72cm long and 72 < 105. However, we don't think that the arithmetical '<' relation between the numbers 72 and 105 is directly explaining anything about my arm or the coffee. Rather, these mathematical terms explain indirectly by representing some directly explanatory physical feature of the system itself. A complete account of the physical world should give us an understanding of the underlying "quantitative structure" in virtue of which these mathematical representations are successful. This is the Problem of Quantity. Although researchers in the metaphysics of science and philosophy of physics recognize that the quantitative structure of the world cries out for explanation, attempts to resolve the problem have hitherto relied on taking some quantitative structure to be fundamental, "unexplained primitives" (using these primitives to explain the rest of that quantity's structure). I reject this approach, which I call "quantitative primitivism", and propose a groundbreaking and ambitious approach that allows me to give fully reductive and complete explanations a quantity's structure. The project, "Scientific Quantities: Reductively Explained" or "SQuaRed- EX" aims to 1) develop complete reductive accounts of quantitative structure that use fundamental physical quantities' role in the physical world to explain why they can be so well represented by mathematics, 2) develop extensions of the reductive-explanatory approach to quantities outside of fundamental physics, including quantities in thermodynamics and chemistry, and 3) disseminate these results and the reductive-explanatory approach used to produce them, guiding future research in the field in a more fruitful direction.
Organisations
Publications
Perry Z
(2024)
On Mereology and Metricality
in Philosophers' Imprint
Perry Z
(2023)
Against Quantitative Primitivism
in Philosophy of Science
Perry Z.R.
(2023)
EXPLANATORY PROBLEMS FOR MASS ADDITIVITY AND DYNAMICS
in Critica-Revista Hispanoamericana de Filosofia
Perry, Z
(2024)
Routledge Companion for the Philosophy of Time
| Description | The problem of quantity is the problem of identifying what about the physical world explains why it can be so well represented with mathematical entities. The SQuaRed-EX project has: - argued that a reductive account of quantitativeness can provide a full solution to the problem of quantity. - developed a reductive account of the structure of certain physical quantities in terms of their mereology: 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. - argued that the resulting account is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they're called upon to describe and explain. - offered a novel dissolution of the long-standing absolutist-comparativist debate based on the new reductive account. - identified unique metaphysical consequences of reductive accounts of quantity. - presented a new argument against the view that the additivity of mass (i.e., the property according to which a composite object's mass is the "sum" of its parts') is metaphysically independent of dynamical laws governing massive bodies. - developed new and powerful objection to certain influential theories about the fundamental structure of physical quantities -most notably the magnitude realism of Christopher Peacocke and the second-order absolutist accounts defended by Brent Mundy and Maya Eddon. - resolved a long-standing puzzle over the speed of light (c) in special relativity: the value of c, 299,792 km/s, merely describes something about our choices of spatial and temporal units. - explained why our choices of spatial and temporal units give rise to an a posteriori discoverable fact (c) in special relativity: the theory makes an independent unit of spatial distance redundant. - explained why c is so readily represented as a speed, and how Michelson's measurement could track such a relationship. |
| Exploitation Route | The improved reductive accounts of scientific quantitativeness developed in SQuaRed-EX are likely to be widely explored and applied within the metaphysics of science, with further uptake across metaphysics and philosophy of science more broadly. Although important progress has been made concerning the prospects for reductively explaining the quantitative structure of some physical properties in terms of qualitative structure (specifically parthood), challenges remain for specific families of quantities playing important roles in physics, such as vector and tensor quantities. All future work on the philosophy of quantities will need to take the results of SQuaRed-EX into account, since it pushes the reductive project further than it has previously been taken. |
| Sectors | Digital/Communication/Information Technologies (including Software) Education Other |
| Description | Aug 2023 "Against Quantitative Primitivism" Society for the Metaphysics of Science, 8th Annual Meeting, Dalhousie University, Halifax NS |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "Against Quantitative Primitivism" presented to experts at Society for the Metaphysics of Science, 8th Annual Meeting, Dalhousie University, Halifax NS |
| Year(s) Of Engagement Activity | 2023 |
| Description | December 2022 "In Special Relativity, there's no speed of light, so what the heck did Michelson measure?! Or, why getting ontology from our models is a mistake" FraMEPhys Models and Modals in Physics Workshop. University of Birmingham. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "In Special Relativity, there's no speed of light, so what the heck did Michelson measure?! Or, why getting ontology from our models is a mistake" presented to experts at FraMEPhys Models and Modals in Physics Workshop. University of Birmingham. |
| Year(s) Of Engagement Activity | 2022 |
| Description | June 2023 "Can Dynamics Explain the Quantitative? Prospects for a Nomological Theory of Quantity" Syracuse Philosophy Annual Workshop and Network (SPAWN), Laws of Nature workshop, Syracuse NY (I) |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "Can Dynamics Explain the Quantitative? Prospects for a Nomological Theory of Quantity" presented to experts at Syracuse Philosophy Annual Workshop and Network (SPAWN), Laws of Nature workshop, Syracuse NY (I) |
| Year(s) Of Engagement Activity | 2023 |
| Description | March 2023 "Against Quantitative Primitivism" SQuaRed-Ex Quantities, Metaphysics and Reduction Workshop, University of Birmingham. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "Against Quantitative Primitivism" presented to experts at SQuaRed-Ex Quantities, Metaphysics and Reduction Workshop, University of Birmingham. |
| Year(s) Of Engagement Activity | 2023 |
| Description | March 2023 - SQuaRed-Ex Quantities, Metaphysics and Reduction Workshop |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | March 2023 - SQuaRed-Ex Quantities, Metaphysics and Reduction Workshop organized and hosted online over Zoom with a panel of expert presentations. |
| Year(s) Of Engagement Activity | 2023 |
| Description | May 2023 "Can Dynamics Explain the Quantitative? Prospects for a Nomological Theory of Quantity" FraMEPhys Metaphysical Explanation in Physics Conference, University of Birmingham. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "Can Dynamics Explain the Quantitative? Prospects for a Nomological Theory of Quantity" presented to experts at FraMEPhys Metaphysical Explanation in Physics Conference, University of Birmingham. |
| Year(s) Of Engagement Activity | 2023 |
| Description | November 2022 "Against Quantitative Primitivism" Philosophy of Science Association Annual Meeting, Pittsburgh |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | "Against Quantitative Primitivism" presented to experts at Philosophy of Science Association Annual Meeting, Pittsburgh |
| Year(s) Of Engagement Activity | 2022 |
| Description | Workshop on Quantities, July 2024 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | SQuaRed-Ex - July Quantities Workshop (9-11 July 2024) This was a hybrid in-person and remote workshop at the University of Birmingham, involving several talks from an international lineup of speakers addressed at the metaphysics of quantities. 15 academics and postgraduate researchers attended in person or online. Talk abstracts: Isaac Wilhelm - "Typicality-Based Chance" Abstract: I use typicality to formulate and defend a functional characterization of chance. According to this characterization, called `Typicality-Based Chance', to be a chance is to be typically approximated by possible frequencies, where the details of the approximation are expressed by the law of large numbers. Among its many other benefits, Typicality-Based Chance offers a replacement for a more popular functional characterization of chance which invokes the Principal Principle: whereas the latter characterizes chances in terms of their relationship to credences, the former characterizes chances in terms of their relationship to frequencies. In addition, I answer a persistent question in the literature---often raised by those who are suspicious of typicality---about what empirical quantities justify the typicality measures which accounts like Typicality-Based Chance invoke. Roughly put, the answer merely invokes empirical observations of frequencies, along with the standard scientific assumption that the results of experiments are not quasi-miraculous, atypical flukes. Alastair Wilson - "Open Systems as Metaphysically Fundamental: Some Questions" (with Jørn Kløvfjell Mjelva and Joshua Quirke) Abstract: If open systems are metaphysically fundamental, as Cuffaro and Hartmann have recently proposed, then what is the fate of the system that corresponds to the entire physical universe? One option is that the universe exists but is non-fundamental. This amounts to priority pluralism, the converse of Schaffer's priority monism (2009). Monism itself has often been defended by appeal to quantum physics; arguments from entanglement to monism/holism can be traced back at least to Teller (1986). We first ask how Cuffaro and Hartmann's proposal manages to avoid the argument from quantum physics to priority monism, and raise some worries about their strategy. Even granting their response, however, a real but derivative universe remains puzzling. We suggest an alternative metaphysics for the open systems view which lacks a complete cosmos altogether. Metaphysical realists about the content of physical theories typically assume that there is such a thing as the totality of physical reality: a well-defined physical entity on which the fundamental laws of nature operate holistically. We explore some potential consequences for the metaphysics of physics of dropping this assumption and embracing a picture of physical reality as indefinitely extensible. Claudio Calosi - "Extension and Simplicity" Abstract: The paper discusses different notions of extension in the light of several requirements, in particular: (i) it should allow for extended simple regions, (ii) should be able to provide a "quantitative measure" of extension, and (iii) should yield a definition of comparative notions such as "x is less extended than y" Zee Perry - "There's no Speed of Light, So What did Michelson Measure?" Abstract: Here are two claims, both of which (I maintain) are very plausibly true: (1) In the late 1870s, A. A. Michelson measured the speed of light to within 99% accuracy; and, (2) Strictly speaking, in special relativity, there is no such thing as the speed of light. The purpose of this talk is to resolve the tension between (1) and (2). I first defend the truth of both claims. The former is an uncontroversial historical fact, but the second claim is remarkably controversial even among working physicists and philosophers of science. I argue that this controversy is due to a confusion about the role of co-ordinate representations in characterizing different theories of space-time. Once this confusion is resolved, it becomes clear that the claim that light has a speed at all is nothing more than an artifact of our representational scheme, and not an accurate reflection of the space-time structure of relativity. This has interesting consequences to the way philosophers of physics reason about symmetries, models, and co-ordinate systems. I close by resolving the tension and explaining what it is that Michelson, in fact, measured. Robert Michels and Claudio Calosi - "Gradable Qualities" Abstract: The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, another based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multi-dimensional properties. Our second aim is to demonstrate that the choice between these account can make a substantial metaphysical difference. To make this point, we rely on a case study in which we apply the accounts in order to model an apparent cases of metaphysical gradedness. M. Townsen Hicks - "(How) do Symmetries Explain Conserved Quantities?" Abstract: The tight connection between symmetry principles and conservation laws, with Noether's First Theorem showing that for every variational symmetry of a Lagrangian there is an associated conserved quantity. But is this connection explanatory? One obvious reason against the idea that symmetries explain conservation laws is that there is also a converse Noether's theorem, showing that for every conserved quantity there is an associated symmetry of the Lagrangian. In this talk, I'll argue that the symmetrical relationship between conserved quantities and symmetry principles is no reason to doubt that the symmetry principles explain the conservation laws, but that to break the symmetry we need more than the dynamics: we need to understand what the symmetry principles represent. I'll then look at two ways in which symmetry principles can explain conservation laws: first, they can constrain the dynamics to necessitate the conservation laws, and second, the symmetry principle can ground the fact that the quantity is conserved. Caspar Jacobs - "On the Objectivity of Dimensions" Abstract: It is often said that dimensionless quantities are more fundamental than dimensioned ones. There is a prima facie plausible reason to consider dimensionless quantities to be more objective: they have the same value in any system of units. For example, the mass of an electron-a dimensioned quantity-has a different numerical value depending on whether it is measured in grams or in ounces; but the ratio of the electron mass to the proton mass is the same no matter what system of units is used. This objectivity claim is most often made about fundamental constants, where it entails that dimensionless numbers such as the fine structure constant, a, are more fundamental than the constant speed of light, c, or Planck's constant, h. This view was first espoused by Dirac (1937) and is still found in much of the contemporary literature (Baez 2011; Rich 2013, Duff 2014). The idea of a 'dimensionless physics' has re-occurred numerous times over the past few decades (Whyte 1954, Volovik 2021). But there is something puzzling about this position. Dimensionless quantities are pure numbers, and as such they are not a measure of any amount of physical 'stuff': mass, distance, time, and so on. Given that the world does contain physical quantities, then, how could it fundamentally consist of dimensionless numbers? In order to solve this puzzle it is necessary to critically examine the supposed objectivity of dimensionless quantities. There are two ways in which I will question this objectivity. The first is to consider examples of quantities that are dimensionless yet not unit-invariant. For example, consider a ratio of temperatures, R=T1/T2. Since T1 and T2 both have dimensions of temperature, their ratio is dimensionless. Nevertheless, the value of R is not the same in all systems of units. Suppose that T1 = 100 °C and T2 = 50 °C, then R = 2 in Celsius. In Fahrenheit, however, R ~ 74. The reason is that temperature is not defined on a ratio scale, but on an interval scale. There are more examples of non-ratio quantities, such as sound pressure or relativistic velocity. These quantities put pressure on the claim that dimensionless quantities are objective. The second challenge to the objectivity of dimensionless quantities concerns alternative measurement scales for quantities that are defined on a ratio scale. Consider the case of length. Different systems of units for length-the metre, the inch, the AU-are all related to each other by a constant scale factor. But Ellis (1966) has pointed out that there are alternative, non-linear length scales. He defines a 'dinches' scale which is such that an object of n inches is n2 in dinches. Although this scale seems unusual, it turns out that it is isomorphic to the inches scale (Eddon 2014). However, a dimensionless ratio of lengths is not invariant under a transformation from inches to dinches: a/b is not equal to a2/b2. The existence of such alternative scales puts further pressure on the objectivity claim. |
| Year(s) Of Engagement Activity | 2024 |
| URL | http://zrperry.com/july-quantities-2024/ |