#### Conceptual and Mathematical Foundations of Science

**Event Registration:** forms.gle/9FQ2YytDRWfu7Pg87

**Event Schedule:** https://www.jingyiwu.org/cmfs.html

**Confirmed speakers and discussants:**

Sam Fletcher, Ben Feintzeig, Sarita Rosenstock, Marian Gilton, Chris Mitsch, Elliott
Chen, Mike Schneider, Neil Dewar, Jenn Jhun, Kevin Kadowaki, Helen Meskhidze, Jingyi
Wu, Chris Smeenk, David Mwakima, Clara Bradley, Ellen Shi, and James Owen Weatherall.

**Abstracts:**

**Sam Fletcher (Minnesota): Spare the Rod: Relativity as Pure Chronometry**

At the dawn of general relativity’s golden age in the 1950s, Irish mathematician and
physicist John Synge proposed to reduce spatial concepts to temporal concepts. Synge
argued that the structure of the spacetime metric allows one to define length in terms
of time, a reduction of chronogeometry to what he calls pure chronometry. Synge’s
arresting proposal nevertheless has two problems. First, he retains an inadequate
operationalist definition of durations in terms of “standard clocks.” Second, his
technical argument only defines infinitesimal length in terms of infinitesimal durations.
In light of these criticisms, I defend a more moderate version of Synge’s thesis and
sketch a mathematical argument to establish it.

**Neil Dewar (Cambridge): Oh God, Another Talk about the Hole Argument**

In 2018, Weatherall published a paper about the Hole Argument whose central thesis
was that the debate over it (at that stage just beginning to settle down) had in fact
been unnecessary in the first place. Both ironically and predictably, this led to
a new outbreak of debate about the Hole Argument—or rather, of debate about the debate,
since this new debate was less about how to resolve the problems of the Hole Argument,
and instead about what kind of problems (if any) the Hole Argument concerned. This
talk ratchets up the navel-gazing yet another notch, by offering some philosophical
reflections on what this new debate tells us about different communities’ commitments
within contemporary philosophy of physics.

**Jennifer Jhun (Duke): On Causation (and other things) in Industrial Organization**

Miller et al (2022), in a paper authored by no fewer than twenty-six economists, argue
that there is no causal relationship to be found between the Herfindal-Hirschman index
(HHI) of a market and the price of the good in that market. Therefore, using regressions
of price on HHI at most reveal a correlational relationship, and we should not infer
that HHI has a causal effect on price. That is, such a regression is not informative
about whether or not a merger will have adverse competitive effects. In this paper,
we examine in detail some of the claims of Miller et al concerning the inapplicability
of regression techniques to certain problems in industrial organization, in the specific
context of antitrust analysis.

**Sarita Rosenstock (Melbourne): Balancing Principles and Practice in Cluster Analysis**

There is a growing literature in theoretical computer science dedicated to building
and promoting axiomatic approaches to data analysis. These authors purport to offer
objective, principled methods to rehabilitate what is often seen as a problematic
culture of subjective and ad-hoc data analytic practice, exacerbated by the incursion
of increasingly opaque ML models. In contrast, many practitioners are happy to sacrifice
methodological clarity in exchange for the obvious promise of the modern data analytic
methods that appear to allude axiomatization. Using cluster analysis as a central
example, I explain why axiomatic approaches largely fail to capture crucial features
of data analytic practice, and suggest a path towards a more nuanced framework.

**Chris Mitsch (Pittsburgh): Should Scientists be More Instrumentalist? Toward a Psychological
Grounding of the Realism Debate**

The scientific realism debate is (for the most part) not currently grounded in concepts
that allow one to draw inferences about how scientists should behave or how practices
like funding review should proceed. I propose a re-conceptualization of the debate
so that it can support such inferences. In particular, I suggest that the debate be
reformed using psychological research on concept formation, and I will show how this
avoids the inapplicability problem plaguing the usual debate. If time allows, I will
contrast my suggestion with recent realist positions (e.g., Sandra Mitchell) that
rely on J.J. Gibson's notion of affordance.

**Kevin Kadowaki (WUSTL)**

Abstract TBD

**Marian Gilton (Pittsburgh): Where counting counts: supporting a particle interpretation
of particle physics.**

There is a general consensus that QFT does not admit of a particle interpretation,
and that therefore the actual phenomena in the world studied by particle physics does
not in fact include any particles--at least, not `fundamentally.' This seems to put
QFT in tension with both experimental and theoretical particle physics, as these latter
two make frequent appeals to the notion that particles exist and are the basic objects
of study. Subsequent philosophical research has sought to address this tension by
developing accounts of emergent particles (Wallace 2001), or by recovering particles
in the classical limit (Feintzeig et al 2021), or by otherwise explaining how our
talk of particles is a useful fiction (Halvorson and Clifton 2002). In this talk,
I will turn to reassessing the implications of the original results showing that QFT
does not admit of a particle interpretation. I will focus on the issue of counting
distinct particle states in interacting QFT. I will argue that there is actually very
little tension between what interacting QFT on the one hand, and theoretical and experimental
particle physics on the other, have to say regarding the conditions under which we
can count distinct particle states.

**Ben Feintzeig (Washington): The Continuity of Charge Structure from Classical to Quantum
(joint work with Jer Steeger)**

We consider a structure-preserving correspondence between classical and quantum mechanics
given by a pair of functors. The relevant morphisms are charge representation preserving
maps, which provide a means of inducing representations of an observable algebra,
where each representation contains states with a fixed total charge. We consider
a "quantization" functor defined by Landsman, which preserves the structure of classical
charge representations, and a "classical limit" functor we define, which preserves
quantum charge representations. We conjecture these functors provide a categorical
equivalence and discuss the significance of categorical methods for philosophical
questions surrounding structural continuity between successive theories.

**David Mwakima (UC Irvine): On the Quality of Perrin’s Evidence**

An important question in contemporary cosmology has to do with evaluating the evidence
we have for “unobservable” components/parameters (such as dark energy and dark matter)
of some of our best models. This is not the first time in the history of physics that
we have been in this epistemic situation. By focusing on the confirmation of the atomic
hypothesis in the early twentieth century, I argue, using Bayes Factors, that the
quality of Perrin's evidence was good because it was highly specific and discriminating.
Perhaps there are some lessons from this episode that could guide our evaluation of
the pieces of evidence we have for our cosmological models.

**Mike Schneider (Missouri): Finding Global Spacetime Structure in Quantum Gravity Research**

Abstract TBD

**Clara Bradley (UC Irvine): Conservation Laws in MOND and AQUAL**

The prevailing theory to account for discrepancies between observations of cosmological
phenomena and the predictions based on our best theories of gravity is the theory
of dark matter. However, an alternative theory adopted by a smaller community of scientists
proposes that it is the theories of gravity that are in fact wrong at certain acceleration
scales. The non-relativistic version of such a theory is called Modified Newtonian
Dynamics (MOND). There are several issues facing MOND that have prevented its wider
acceptance. One problem is that it fails to satisfy the usual conservation laws, such
as conservation of momentum and conservation of energy. However, Bekenstein & Milgrom
(1984) argue that one can make MOND compatible with these conservation laws by reformulating
the theory as a Lagrangian theory called AQUAL. In this talk, I consider two arguments
given by Bekenstein & Milgrom for this claim. I argue that both are fallacious, and
I pinpoint the crucial difference between Newtonian Gravity and AQUAL that means the
former satisfies the conservation laws but not the latter.

**Chris Smeenk (Western): Empirical Equivalence Revisited**

Jim has proposed that two theories are equivalent if they are empirically equivalent,
they have equivalent mathematical structures, and these two equivalences are compatible
(in a precise sense). While much recent discussion has focused on the second and third
aspects of this proposal, here I will focus on the first -- and propose an account
of empirical content characterized in terms of measurement. Physical theories provide
us with an account of what systems can be used to reliably measure some fundamental
quantity introduced by the theory, and over what domains they can be successfully
applied. Schematically, a ``measuring device'' M is a physical system whose ``meter
reading'' is correlated with a property of a target system P within a specified domain
of applicability. The correlations between M and P, and the situations under which
M can serve as a useful measuring device for P's properties, follow from the description
of the two systems and their interaction within a given theory. Taking the empirical
content of a theory to consist of a set of possible measurements in this sense is
substantially richer than, e.g., requiring merely isomorphism between a model of the
theory and a data model. Assessing the reliability of measurements requires claims
that extend beyond a single model, since these implicitly consider a range of counterfactual
circumstances. This proposal leads to a refinement of the claim (e.g., Norton 2008)
that empirically equivalent theories must share common structure. Here I will sketch
the proposal and consider some objections to it.

*This workshop is co-organized by James Owen Weatherall and Jingyi Wu. For inquiries, please write
to weatherj@uci.edu and Jingyi.Wu@lse.ac.uk*

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