Lu Chen

2023 June, 1 - July, 31

Affiliation: Koç University/Turkey

Research for a study about:

Algebraicism and Dynamicism

(I) Univalent Foundations (UF) are the only logico-mathematical foundations where all isomorphic structures are identified and identity is rigorously defined. However, the philosophical implications of such a foundation have not been sufficiently explored. In this project, I will: (a) compare UF with other frameworks with similar ambitions, such as Dasgupta and Dewar's algebraicism, and highlight the unique benefits of UF; (b) elaborate on the significance of UF in relation to debates in the philosophy of physics, such as the hole argument and symmetries; and (c) identify and address potential conceptual problems with UF as a structuralist foundation, if any. The talk I plan to deliver will be a stand-alone sub-project, arguing that symmetries should be understood as isomorphisms (and thus fall within the purview of UF).

(II) Semi-realism offers a promising middle ground between complete realism and antirealism, aiming to avoid the pitfalls of both extremes. There have been some attempts to apply semi-realism to Quantum Field Theories (QFT), arguably the most empirically successful scientific theories available. However, it is not entirely clear which aspects of a QFT warrant a realist commitment. This ambiguity is partly due to the technical and conceptual challenges associated with renormalization, a central technique in QFT used to manage infinities. In this project, I will: (a) develop a clearer conceptual understanding of renormalization, and identify which parts of a QFT are variant or invariant under different renormalization schemes; and (b) scrutinize potential candidates for realist commitments, including physical/renormalized parameters, correlation functions, S-matrix, and scattering amplitudes.

Lecture

Symmetries are isomorphisms

This talk is going to be a in-person and hybrid event, at NIG (SR 2i) and can be followed via online Plattform.

Date: 2023 , June 22

Time: 3-4.30 pm CET

Online Plattform  access:

univienna.zoom.us/j/63035484129
Passcode: 226427 

No registered accounts are required, it's enough to click on the link and enter your name. Chrome or Firefox browsers work best.

Abstract:

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct. That is, two models related by symmetries are not necessarily isomorphic. I aim at offering a new and rigorous category-theoretical framework in which symmetries are reduced to isomorphisms between models, building on Wallace, Weatherall, Dewar, and others' work, as well as evaluating its philosophical significance. The models I will consider include traditional spacetime models (with electromagnetism as the primary example) as well as novel algebraic models that dispense with a spacetime manifold.

IVC Fellowship Progress Report

July 31, 2023
During the fellowship, I have been working on the following projects:

1. “Why Univalence matters” (draft completed with feedback solicited, under
revision)
Homotopy Type Theory (HoTT) with the univalence axiom, together known as ‘Univalent Foundations’ (UF), is a relatively new contender for the best logical foundations for philosophy and science. The exploration of its relevance to philosophy is currently limited to mathematical structuralism and its application to the hole argument. But it is particularly important to examine UF’s relationship with ontic structuralism, which holds that individuals do not have identities over and beyond the structure they occupy. This would help clarify what UF can uniquely contribute to many topics in philosophy of physics, including the hole argument and symmetries.
The challenges of this project include the technical obscurity (and exoticness) of UF (which is still under active development) and the conceptual obscurity of ontic structuralism. I have made good progress in arguing for UF’s distinctive advantages over other proposed logical frameworks for ontic structuralism, as well as its unique contribution to the hole argument. But there are still many remaining challenges, including better addressing Newman’s objection to structuralism (which is tricky since the objection itself is not framed clearly and tied to traditional logic/set theory), a clearer discussion of the potential problems of UF, including its lack of a distinction between mathematical structures and physical ones, as well as a more illuminating explanation of HoTT/UF to philosophers with background in (for example) standard set theory.

2. Symmetries are Isomorphisms (draft completed, awaiting feedback)
During the fellowship, I have given a talk on this project, which is related to the first one. To recall: I aim at offering a new and rigorous category-theoretical framework in which symmetries are reduced to isomorphisms between models, building on Wallace, Weatherall, Dewar, and others’ work, as well as evaluating its philosophical significance. (Consequently, univalence can apply to symmetries in general.) At the talk, I have got useful feedback for further revision and considerations, including (but not restricted to): 1. how the algorithm generalizes to the case of multiple fields or fields together with particles (I only focused on the simple models with one field); 2. how it generalized to unitary symmetry or more generally to symmetries outside of the context of classical gauge theories; 3. better motivate the project of reducing symmetries to isomorphisms (since it was not so clear why the isomorphism formulation is attractive). The preparation of the talk was also helpful for me to realize more intricacies of the relation between the projects and the prior work of Weatherall etc. These will help me revise the draft.

3. “How to be a Realist (and how to be an empiricist) about Quantum
Field Theories” (first draft completed)
Semirealism (also known as ‘selective realism’ or ‘restricted realism’) is a popular middle ground in the debate between scientific realism and antirealism (or ‘empiricism’). According to the view, we are justified to believe in the realistic interpretation of selective components of our best scientific theories that are responsible for their empirical success or otherwise epistemically special. However, if we apply this strategy to quantum field theories (QFTs), which are arguably the most empirically impressive theories of our time, it becomes incredibly murky as for what components of the theories should be taken realistically—and this is on top of all the controversies of semirealism in general. One primary source for this special difficulty is the essential role played by renormalization in QFTs, which is notoriously obscure both in its technical and conceptual respects. In this paper, I argue that correlation functions are the best bet for realistic commitment based on considerations that are relatively ignored in the literature. In addition, I argue if this fails and only observables can be taken seriously in QFTs, this still does not mean a definite triumph of antirealism over semirealism. To do this, I explain the sheer amount of ‘non-observables’ that go into the most standard observables of QFTs such as decay rates and cross sections, as well as more borderline cases, including scattering amplitudes and S-matrix. I have finished a first draft and will continue polishing it.