# July Quantities Workshop

### (July 9-11th 2024)

### Scientific Quantitativeness, Reduced and Explained

## Workshop Schedule

All events are in the ERI (European Research Institute) Building on the Edgbaston campus. (Located at G3 Pritchatts Rd, Birmingham B15 2SB aka here: https://maps.app.goo.gl/

### July 9th (in ERI Room 149)

- 4:15pm to 5:15pm -
**Zee Perry**- Workshop introduction and some general stage-setting. - 5:30- 6:30pm -
**Isaac Wilhelm**(remote) - Typicality-Based Chance. [Abstract][Handout] - 7:30
**Workshop Dinner**(A pub in Harborne or Moseley TBD)

### July 10th (in ERI Room 144)

- 10:00am-10:45am -
**Caspar Jacobs**(remote) - On the Objectivity of Dimensions [Abstract] - 11:00am-12:10pm -
**Alastair Wilson**- Open Systems as Metaphysically Fundamental: Some Questions [Abstract] **Lunch**12:15 to 2:30pm- 2:30pm-3:40pm -
**Claudio Calosi**- Extension and Simplicity [Abstract] - 3:50pm-4:50pm -
**Oliver Marshall**(remote) - Topic: Peacocke's Realism about Magnitudes and Response to Lee - 5:00pm-6:00pm -
**Zee Perry**- There's no Speed of Light, So What the heck did Michelson Measure? [Abstract] - 7:15pm
**Workshop Dinner**(Probably) at the Blue Piano in Edgbaston

### July 11th (in ERI Room 224)

- 10:00-11:00 -
**Robert Michels**- Gradable Qualities [Abstract] - 11:10-12:10 -
**M. Townsen Hicks**(remote) - (How) do Symmetries Explain Conserved Quantities? [Abstract]

##### Remote Participation

This is a hybrid in-person and remote workshop. Registration is required for all remote participants. The Zoom information is as follows:

**Topic:**SQuaRed-Ex - July Quantities Workshop (9-11 July 2024)**Meeting ID:**824 6785 9313**Join Link:**https://bham-ac-uk.zoom.us/j/82467859313

##### Register here:

## 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 Cha

#### 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, α, 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.

### Scientific Quantitativeness, Reduced and Explained

- This research is supported by UKRI grant number EP/X022625/1, Project “SQuaRed-EX” (University of Birmingham).
- “SQuaRed-EX” HORIZON-MSCA-2021 Project No. 101067459