Conceptual and Mathematical Foundations of Science
November 3-4, 2023, 10 AM- 4:30 PM
Place: Social and Behavioral Sciences Gateway, Room 1321 (campus map)
Registration: forms.gle/9FQ2YytDRWfu7Pg87
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.
Friday, November 3, 2023
8:30-10 Breakfast/Informal Conversations
Morning Session Chair: Jingyi Wu (LSE)
10-10:45 Sam Fletcher (Minnesota): Spare the Rod: Relativity as Pure Chronometry
10:45-11:30 Neil Dewar (Cambridge): Oh God, Another Talk about the Hole Argument
11:30-11:45 Coffee Break
11:45-12:30 Jennifer Jhun (Duke): On Causation (and other things) in Industrial Organization
12:30-2:00 Lunch
Afternoon Session Chair: Helen Meskhidze (Harvard)
2:00-2:45 Sarita Rosenstock (Melbourne): Balancing Principles and Practice in Cluster Analysis
2:45-3:30 Chris Mitsch (Pittsburgh): Should Scientists be More Instrumentalist? Toward a Psychological Grounding of the Realism Debate
3:30-3:45 Coffee Break
3:45-4:30 Kevin Kadowaki (WUSTL): Value-laden Algorithms and the Gap Argument
4:30- 5:30 Special Session
7:00 Conference Dinner (by invitation)
Saturday, November 4, 2023
8:30-10 Breakfast/Informal Conversations
Morning Session Chair: Ellen Shi (UC Irvine)
10-10:45 Marian Gilton (Pittsburgh): Where counting counts: supporting a particle interpretation of particle physics.
10:45-11:30 Ben Feintzeig (Washington): The Continuity of Charge Structure from Classical to Quantum
11:30-11:45 Coffee Break
11:45-12:30 David Mwakima (UC Irvine): On the Quality of Perrin’s Evidence
12:30-2:00 Lunch
Afternoon Session Chair: Elliott Chen (Xavier)
2:00-2:45 Mike Schneider (Missouri): Finding Global Spacetime Structure in Quantum Gravity Research
2:45-3:30 Clara Bradley (UC Irvine): Conservation Laws in MOND and AQUAL
3:30-3:45 Coffee Break
3:45-4:30 Chris Smeenk (Western): Empirical Equivalence Revisited
This workshop is co-organized by James Owen Weatherall and Jingyi Wu. For inquiries, please write to [email protected] and [email protected].
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): Value-laden Algorithms and the Gap Argument
Abstract: Recently, a number of interesting positions have been staked out in the debate about the value-ladenness of science by drawing connections to machine learning, in some cases relying on formal theorems and interpretations thereof. In this talk, I address a particular argument by Dotan (2021), who argues that the No Free Lunch (NFL) theorems can be interpreted as a general argument for the value-ladenness of science generally. I claim that while this argument does not show what she purports, it nonetheless can be reframed to motivate an approach to the debate about the Value-Free Ideal; in particular, I argue that the NFL theorem should be understood as a reductio of a particular version of the Value-Free Ideal implicit in "gap" arguments for the value-ladenness of science.
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
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.
November 3-4, 2023, 10 AM- 4:30 PM
Place: Social and Behavioral Sciences Gateway, Room 1321 (campus map)
Registration: forms.gle/9FQ2YytDRWfu7Pg87
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.
Friday, November 3, 2023
8:30-10 Breakfast/Informal Conversations
Morning Session Chair: Jingyi Wu (LSE)
10-10:45 Sam Fletcher (Minnesota): Spare the Rod: Relativity as Pure Chronometry
10:45-11:30 Neil Dewar (Cambridge): Oh God, Another Talk about the Hole Argument
11:30-11:45 Coffee Break
11:45-12:30 Jennifer Jhun (Duke): On Causation (and other things) in Industrial Organization
12:30-2:00 Lunch
Afternoon Session Chair: Helen Meskhidze (Harvard)
2:00-2:45 Sarita Rosenstock (Melbourne): Balancing Principles and Practice in Cluster Analysis
2:45-3:30 Chris Mitsch (Pittsburgh): Should Scientists be More Instrumentalist? Toward a Psychological Grounding of the Realism Debate
3:30-3:45 Coffee Break
3:45-4:30 Kevin Kadowaki (WUSTL): Value-laden Algorithms and the Gap Argument
4:30- 5:30 Special Session
7:00 Conference Dinner (by invitation)
Saturday, November 4, 2023
8:30-10 Breakfast/Informal Conversations
Morning Session Chair: Ellen Shi (UC Irvine)
10-10:45 Marian Gilton (Pittsburgh): Where counting counts: supporting a particle interpretation of particle physics.
10:45-11:30 Ben Feintzeig (Washington): The Continuity of Charge Structure from Classical to Quantum
11:30-11:45 Coffee Break
11:45-12:30 David Mwakima (UC Irvine): On the Quality of Perrin’s Evidence
12:30-2:00 Lunch
Afternoon Session Chair: Elliott Chen (Xavier)
2:00-2:45 Mike Schneider (Missouri): Finding Global Spacetime Structure in Quantum Gravity Research
2:45-3:30 Clara Bradley (UC Irvine): Conservation Laws in MOND and AQUAL
3:30-3:45 Coffee Break
3:45-4:30 Chris Smeenk (Western): Empirical Equivalence Revisited
This workshop is co-organized by James Owen Weatherall and Jingyi Wu. For inquiries, please write to [email protected] and [email protected].
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): Value-laden Algorithms and the Gap Argument
Abstract: Recently, a number of interesting positions have been staked out in the debate about the value-ladenness of science by drawing connections to machine learning, in some cases relying on formal theorems and interpretations thereof. In this talk, I address a particular argument by Dotan (2021), who argues that the No Free Lunch (NFL) theorems can be interpreted as a general argument for the value-ladenness of science generally. I claim that while this argument does not show what she purports, it nonetheless can be reframed to motivate an approach to the debate about the Value-Free Ideal; in particular, I argue that the NFL theorem should be understood as a reductio of a particular version of the Value-Free Ideal implicit in "gap" arguments for the value-ladenness of science.
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
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.