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Structural Realism as a Philosophy of Nature

English title Structural Realism as a Philosophy of Nature
Applicant Esfeld Michael
Number 140201
Funding scheme Project funding (Div. I-III)
Research institution Section de Philosophie Faculté des Lettres Université de Lausanne
Institution of higher education University of Lausanne - LA
Main discipline Philosophy
Start/End 01.05.2012 - 30.09.2013
Approved amount 80'894.00
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Keywords (7)

quantum mechanics; general relativity; mathematical structuralism; applicability of mathematics; structural realism; metaphysics of science; causation

Lay Summary (English)

Lead
Lay summary

Structuralism is a philosophical position that emphasizes the importance of the relations that objects stand in as opposed to what the objects are in themselves. Structuralism has risen to importance both in philosophy of mathematics and philosophy of science. On the mathematical side, mathematical structuralism favors a characterization of the subject matter of mathematics in terms of, say, the structure of natural numbers, not in terms of natural numbers themselves. On the scientific side, structural realists claim that the subject matter of theories in physics such as quantum mechanics and relativity theory is best understood in terms of relations, or even that relations are all there is according to these theories. What has been neglected, however, is the question of how mathematical and physical structures are related, and what the use of mathematics in the application to the physical world is. The goal of this project is to take some steps in the analysis and solution of these questions. In broad terms, we want to contribute to a better philosophical understanding of the prominent role that mathematics plays in empirical science.

We start with the mathematical side of the story by critically analyzing a recent proposal of how to conceive of mathematical structures. Then we focus on how mathematical and physical structure, and mathematics and the empirical domain in general are related. Here we will first have to make some conceptual distinctions between different ways in which mathematics and the world can be said to be related. We will for example explore the idea that the main difference between mathematical and physical structure is causality, i.e. the fact that mathematical structures such as the natural numbers do not cause anything, whereas physical structures are thought to stand in causal relations. We will also scrutinize the plausible idea that the primary function of mathematical structure is to represent, i.e. stand for physical structure in scientific theories. We hope to highlight strengths and weaknesses of this idea. To give an example, it could be that if mathematics is only there to stand for something else, it cannot help in giving explanations, which is not plausible.

As the subject matter of our philosophical investigations is science, we will work with several scientific case studies which will guide us and also help us check whether philosophical reasoning has lead us astray. We will use several smaller case studies, but also big cases, one from the early history of general relativity and one from quantum mechanics.

Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
A dilemma for the emergence of spacetime in canonical quantum gravity
Lam Vincent, Esfeld Michael (2013), A dilemma for the emergence of spacetime in canonical quantum gravity, in Studies in History and Philosophy of Modern Physics , 44, 286-293.
Modeling causal structures. Volterra’s struggle and Darwin’s success
Scholl Raphael, Räz Tim (2013), Modeling causal structures. Volterra’s struggle and Darwin’s success, in European Journal for Philosophy of Science, 3, 115-132.
On the Application of the Honeycomb Conjecture to the Bee's Honeycomb
Räz Tim (2013), On the Application of the Honeycomb Conjecture to the Bee's Honeycomb, in Philosophia Mathematica, 21, 351-360.
Ontic structural realism and the interpretation of quantum mechanics
Esfeld Michael (2013), Ontic structural realism and the interpretation of quantum mechanics, in European Journal for Philosophy of Science , 3, 19-32.
The structural metaphysics of quantum theory and general relativity
Lam Vincent, Esfeld Michael (2012), The structural metaphysics of quantum theory and general relativity, in Journal for General Philosophy of Science , 43, 243-258.

Collaboration

Group / person Country
Types of collaboration
Tilman Sauer United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
Mauro Dorato Italy (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Vincent Lam Australia (Oceania)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events



Self-organised

Title Date Place
Metaphysics of science: Objects, relations and structures 12.10.2012 Lausanne, Switzerland

Associated projects

Number Title Start Funding scheme
124462 Structural Realism as a Philosophy of Nature 01.05.2009 Project funding (Div. I-III)

Abstract

This project is situated in the context of structural realism in philosophy of science. In the debates surrounding ontic structural realism (OSR), it has become increasingly clear that there is a need to clarify the distinction between mathematical and physical structures. Our main goal is to take some steps in the analysis and solution of this problem. We will divide the problem into the following parts. First, we will discuss how we should conceive of mathematical structures. Second, we will scrutinize the idea that the distinction between mathematical and physical structures can be spelled out in causal terms, that is, we characterize physical structures.It has proven useful to broaden the context in which we tackle these questions. For the question of how mathematical structures are best characterized, we critically discuss a solution from philosophy of mathematics, namely mathematical structuralism, using case studies from graph theory and complex number. Then, the recent debate on the applicability of mathematics by authors such as Mark Steiner, Mark Colyvan and Christopher Pincock is a fruitful setting for the general question of how mathematical and physical domain are related. The most important philosophical lessons from this debate are the following points: a) Several senses in which mathematics can be said to be related to the world should be carefully distinguished. Especially the distinction between the metaphysical relation between acausal-mathematical and causal-physical structures on the one hand and the descriptive adequacy of mathematics in application, e.g. in explanations, can help to disentangle the purported `mystery' of how mathematics is helpful in application; b) it has sometimes been claimed that the role of mathematics is a merely representational one, that is, the relation between mathematics and the world is like the relation between a map and the city it depicts. We are sceptical that this is universally true, and advocate a more pluralistic picture of the role of mathematics, e.g. as explanatory.We will confront our philosophical findings with scientific practice in several case studies. First, we will use `toy examples' from the debate on the applicability of mathematics such as the `Königsberg bridges' case and from the debate on the indispensability of mathematics, e.g. periodic cicadas. Second, we will present two `real life' case studies from fundamental physics, one from the early history of general relativity, one from quantum mechanics. These case studies will connect our results to discussions in philosophy of physics.Our research will result in the PhD thesis of Tim Räz, in publications by Michael Esfeld and Tim Räz including a joint publication.
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