The workshop takes place at Heinrich Heine University’s Haus der Universität on the 23rd and 24th May 2024. Attendance is free, but registration is mandatory.

Thursday (23/05/2024)

9:30-10:30

The Practice Turn in the Philosophy of Mathematics

The Practice Turn in the Philosophy of Mathematics

Dr. Silvia De Toffoli (School for Advanced Studies IUSS Pavia)
Invited Speaker

Twentieth-century mathematics gave rise to important debates on the foundations of mathematics, in which professional mathematicians became interested in core philosophical questions. In the first half of the century, philosophy and mathematics were closely connected. Nonetheless, in the second half, mathematicians and philosophers of mathematics often took different paths. Instead of finding inspiration from the new mathematics that was developing, philosophers of mathematics devoted themselves to more abstract questions that did not interest mathematicians. Only towards the end of the twentieth century did a new current in the philosophy of mathematics begin to emerge, the philosophy of mathematical practice. This label refers to a cluster of approaches to mathematics united by an interest in philosophical questions that derive directly from mathematical practice. Typically, approaches within the philosophy of mathematical practice reject a-historical conceptions of mathematics and are open to interdisciplinary research. In my talk, I will offer an overview of the philosophy of mathematical practice, focusing on epistemological issues. I will contend that it is only by conceiving the knowing subjects as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. Finally, I will illustrate some of the methodological guidelines of the philosophy of mathematical practice by discussing the role of diagrams in contemporary mathematics.
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10:30-10:45
10:45-11:30

Visual thinking and intuition in mathematics, as an argument against the radical opposition between mathematical models in mathematics and other sciences

Visual thinking and intuition in mathematics, as an argument against the radical opposition between mathematical models in mathematics and other sciences

Karolina Tytko (UPJPII)

The aim of this paper is to present two arguments for an approach that does not radically differentiate the methodology of mathematics from the methodology of other sciences (especially empirical ones), and that may be more effective or natural for mathematical practice.

A the beginning, the approach of Halina Mortimer [1], [2], one of the representatives of the Lviv-Warsaw School, who was concerned with the logic of induction, i.e. the methodology for developing the theory of empirical sciences, is presented,. Although Mortimer appreciated some of the solutions of Carnap and Hintikka in this area [3], [4], [5], she was of the opinion that they were too idealised. As an alternative, she proposed the solution of Henry Kyburg [6], who pointed out the connection between the system of inductive logic and a given empirical theory through mathematical probability. This proposal did not allow logic and mathematics to be treated as a priori theories explaining the reality described by the empirical sciences, but rather as tools for specifying and ordering these theories.

We will try to apply the above position to the analysis of two questions. First, we will comparatively analyse the methodology of Dedekind [7], [8], [9], [10], who constructed some mathematical models, and the methodology of Cantor [11], [12], [13], who used the genetic-deductive method. This may have been due to Cantor’s idealised Platonic assumptions about mathematics. This sometimes led to errors in his work, which were corrected by later communities of mathematicians. Dedekind, approached mathematics in a more empirical way. He also produced more effective solutions.

We also note the scientific environments that might have influenced the mathematicians. Dedekind’s early environment included mathematicians such as Gauss and Dirichlet, while Cantor’s included Weierstrass and Kronecker. Gauss was also known as an experimental physicist, while Weierstrass devoted himself exclusively to detailed work on mathematical problems [14].

Secondly, we will analyse for comparative purposes the mathematical model that Dedekind built in the Foundations of Mathematics (N) and the modern flow model for a social network [15], [16]. We will pay attention to common and different aspects that could (or might) accompany the creation or recreation of these models.

For this purpose, we will present a proposal for a general cognitive scheme for building a mathematical model in individual mathematical practice. Based on the definition of the model [17], we will use the proposal of Giaquinto [18], [19], who, following Kosslyn, shows how a structure can be “grasped” visually.

The conclusions of these considerations point to the need to pay more attention to the individual and social context of scientific discovery. This would allow us to show more generally that mathematical knowledge, as a product of individual and social practice, is not necessarily developed in a continuous way, where continuity is ensured by the use of the genetic-deductive method. New theoretical structures can also be constructed in relation to - broadly understood - experience, and not only in strict relation to current theory.

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11:30-12:15

What’s Up With Computer-Assisted Proofs?

What’s Up With Computer-Assisted Proofs?

Paul Hasselkuß (HHU Düsseldorf)

In the last decades, there has been a fiery debate about computer-assisted proofs (CAPs). Started by Appel & Haken’s (1977) proof of the four-color theorem and the mixed reception it received, the debate centers around two issues. Let t be a mathematical theorem such that there is a CAP for t, but no ordinary (i.e. non-computational) proof. Firstly, is t merely verified by the CAP or does the CAP amount to a full proof (Rota 1997)? Secondly, is t known a posteriori because there is no proof for t that could be surveyed (Tymozko 1979, Kitcher 1984, McEvoy 2007)?

In the talk, I’ll contribute to the debate in two ways. Firstly, I’ll report initial findings from an ongoing data-driven approach that aims to analyze articles published on the ArXiv to understand how, and to what extent, mathematicians rely on CAPs. Results may indicate whether the mathematical community takes CAPs to be on par with ordinary proofs or not.

Secondly, I’ll argue that the justification provided by a CAP is different in degree, but not in kind, from the justification provided by an ordinary proof. If the latter is taken to yield a priori justification, the former does provide a priori justification, too. The argument relies on the idea that a CAP can be translated into an ordinary proof. While the translated proof is notoriously complex and probably impossible to survey by a single human agent, these differences are insufficient to claim that the CAP provides merely an a posteriori justification.

References
  • Appel, Kenneth, and Wolfgang Haken. 1977. “Every Planar Map is Four Colorable. Part I: Discharging.” Illinois Journal of Mathematics 21 (3): 429–90.
  • Appel, Kenneth, Wolfgang Haken, and John Koch. 1977. “Every Planar Map is Four Colorable. Part II: Reducibility.” Illinois journal of Mathematics 21 (3): 491–567.
  • Kitcher, Philip. 1984. The Nature of Mathematical Knowledge. New York: Oxford University Press. https://doi.org/10.1093/0195035410.001.0001
  • McEvoy, Mark. 2007. “The Epistemological Status of Computer-Assisted Proofs.” Philosophia Mathematica 16 (3): 374–87. https://doi.org/10.1093/philmat/nkn014.
  • Rota, Gian-Carlo. 1997. “The Phenomenology of Mathematical Proof.” Synthese 111 (2): 183–96. https://doi.org/10.1023/A:1004974521326.
  • Tymoczko, Thomas. 1979. “The Four-Color Problem and Its Philosophical Significance.” The Journal of Philosophy 76 (2): 57–83. https://doi.org/10.2307/2025976.
Close
12:15-13:30
13:30-14:15

Scientific practices in universities – an underrepresented view?

Scientific practices in universities – an underrepresented view?

Sophia Bauer (University of Vienna)

In the Call for Abstracts (CfA) for the Workshop of the GDWP questions are raised concerning the notion of scientific practices as there is still no common definition. Mostly, the notion of scientific practices is still linked to laboratories, in which the works of Bruno Latour or Karin Knorr-Cetina took place and thrived in the 1970s and 1980s. (Concerning the special institutional frame of the works of Bruno Latour see, e.g., Lars GERTENBACH / Henning LAUX, Zur Aktualität von Bruno Latour. Einführung in sein Werk (Wiesbaden 2019), 87-88 and Matthias WIESER, Das Netzwerk von Bruno Latour. Die Akteur-Netzwerk-Theorie zwischen Science & Technology Studies und poststrukturalistischer Soziologie (Bielefeld 2012), 5. And concerning the notion of laboratories as primary places of early practice studies see for example WIESER, Das Netzwerk von Bruno Latour, 22 or 24.) But as such institutions are only one of many, where scientific practices emerge and are at work, it becomes evident that practices in other places are seldom acknowledged. One of them is universities – scientific institutions combined with an emphasis on higher education at the same time. If we think of universities as scientific institutions, what are scientific practices that we come across there? I would argue that teaching would be one answer, next to doing research, writing books and essays, etc., which already shows that scientific practices are different from those applied in laboratories.

However, it seems, that there is still no sufficient theoretical background for research on scientific practices in universities, such as, e.g., teaching, although this practice is often (but not always) shaped by the newest state of research and researchers themselves. At universities (ideally) knowledge is discussed and exchanged (mostly with a hierarchical stance between lecturer and students). So, if discussions on the newest research do take place in classes or lectures, science can be debated and enhanced in those very moments, which is, as I would argue, part of scientific practices as well.

Also, adding the historical perspective as another argumentative layer, in the case of, e.g., Austria it becomes even more evident that universities and most of all, university teaching, were both a big part of “science”. For example, especially since the Student Revolution of 1848/49, “science” was embedded in Austrian lecture halls and textbooks and embedded into universities. (See for example Thomas MAISEL, Lehr- und Lernfreiheit und die ersten Schritte zu einer Universitäts- und Studienreform im Revolutionsjahr 1848, in: Christof AICHNER, Brigitte MAZOHL (Hg.), Die Thun-Hohenstein’schen Universitätsreformen 1849-1860 (Wien / Köln / Weimar 2017), 99-117, 105-106.) Consequently, in terms of pre-20th-Century science, it becomes evident that the term “scientific practices” only linked to non-university institutions, such as laboratories, becomes narrow, and thus, scientific practices at universities (e.g., university teaching) and their specific mechanisms (1) should be included when we think of “scientific practices” and (2) should be investigated further in the context of the “practice turn”.

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14:15-15:00

Selecting for Science: A Pragmatist Account of Scientific Practice

Selecting for Science: A Pragmatist Account of Scientific Practice

Niall Roe (University of Cambridge)

When we talk about scientific practice do we describe behaviour, or do we prescribe what behaviour ought to be? Neither is sufficient. Scientific practice cannot be ideal behaviour, because then we have never encountered it. Nor can it be understood as a historical list of all scientific actions. It is something we will do tomorrow, too.

In this paper, I argue that when we talk about scientific practice we talk about:

  • actual systems of practices,
  • that have been retained because they have certain features,
  • which help us learn about the world.

I articulate this view and defend it against five related criticisms.

This a novel application of a selectionist teleological account (inspired by C.S. Peirce but developed over decades by T.L. Short). To give a sketch, scientific practices are actual, particular things with many features, but they have been retained because some of those features allow us to achieve a certain type of outcome. This type is the “final cause” of the practice.

Final causes are not strange efficient causes (e.g., backwards causation or the result of an omnipresent will). They are types of outcome that explain why certain actual traits were selected. “To tell time” answers the questions “why are these parts of a clock are assembled like this?” and “why did people build such things?”. Not every characteristic of scientific practice is explained by science’s aim, no more than every characteristic of a clock is explained by telling time.

Final causes do not require intentionality. No creature intentionally decided to retain retinal for the purpose of increasing visual acuity, yet that is why it was retained. A societal structure that provided free time enough for country priests to develop new experimental methods was not intended to develop such methods. Final causation explains why we have retained remnants of such methods, while new labs need not include parishes.

Rowbottom (2023) gives five arguments critical of this view, namely: Scientists (1) do not have a collective purpose; (2) are not directed by above to any end; (3) cannot be guided by an ideal (and are in fact often better off when acting non-ideally); (4) do not share any characteristic that could be called their aim; (5) and when practices are introduced for a purpose, they often do not serve that purpose, which is instead satisfied in multiple ways.

I address each with the pragmatist approach. As mentioned: intentionality (collective or otherwise) is not required, nor is a guiding will. A pluralism of practices is encouraged because increased variety provides more to select from.

The practice turn has provided much excellent work regarding how philosophers should understand practice. This paper aims to assist such work by providing a criterion for when such practices are scientific. But what is the aim of science? Answering this is also the task of science (including philosophy). Vaguely, it is to learn about the world. Philosophers provide more specific answers. Many have been and should be put forward. Only then can we learn about why some are retained.

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15:00-15:15
15:15-16:15

Epistemic communities and their situated practices

Epistemic communities and their situated practices

Prof. Dr. Michela Massimi (Edinburgh)
Invited Speaker

I present the rationale, motivation, and some of the highlights of my recent book Perspectival Realism (OUP, 2022) by looking at how the realist question in philosophy of science can be reconsidered once a plurality of scientific perspectives is taken on board. I focus on the importance of situated practices for knowledge of modally robust phenomena as a way of re-orienting the debate on realism and also as a way of discussing rights and obligations associated with scientific knowledge.
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16:15-17:00
17:00-17:45

Gaston Bachelard’s notion of scientific practice

Gaston Bachelard’s notion of scientific practice

Tryggvi Örn Úlfsson (Université Paris VIII Vincennes Saint-Denis)

I would like to present the work of French philosopher Gaston Bachelard as founded upon a notion of scientific practice. Bachelard’s conceives of science as essentially practical. A scientific theory cannot be understood without the experimental methods by which it is verified. For instance, the theory of relativity cannot be understood without understanding the limits of measurement of physical events. However, that is not to say that the theory is determined by the reality that it must register. Rather, Bachelard’s analyses stress the role of reflection in preparing the experiment. He famously claimed that an experimental apparatus is nothing but a ‘materialised theory’. A telescope allows a scientist to make observations and test his predictions about the movement of planets, but in order to construct the telescope he needs another theory that explains how the telescope functions, namely optics. Scientific practice therefore has an essentially historical aspect to it. A present moment of scientific activity cannot be understood without its past which conditions its practical possibilities. This historicity of scientific practice makes Bachelard’s account of science a satisfying alternative to the main alternatives in philosophy of science. Opposed to the Fregean tradition which strictly separates the justification of a theory from its historical context of discovery, Bachelard’s account can shed light on the fact that scientific theories must be elaborated within a given historical context. Opposed to Thomas Kuhn’s account of scientific revolutions, the understanding of science within Bachelard’s framework as essentially historical does not reduce any of its rationality, nor its claim to approximating some sort of objective truth. Bachelard’s concept of an epistemological profile enables us to conceive of scientific practice as oriented in history towards better and more truthful accounts of some already designated object. A theory is not only a synchronic unity of underlying assumptions and logical inferences. It is also a diachronic series of homonymic concepts that form an epistemological profile. The concept of mass does not only correspond to its current theoretical account but also to the history of its own historical elaboration. Only because of this reference to its own history can we understand the current theory as making a progress towards some objective limit that we can project onto reality as the real reference of the concept of mass. Only because we think of obsolete notions of mass while working to prepare experiments with a more elaborated notion can we think of our current measurements as a way to evolve our understanding of matter and make it more precise, more akin to what mass really is. I would thus like to present this theory as an interesting alternative in philosophy of science based on an account of science as practice. But I would also like to deal with the following problem inherent in Bachelard’s understanding of scientific practice: it is to me not clear to what extent scientific practice is determined by the thought process by which the experiment is prepared or the object that the experiment must receive. The question, in other words, is whether scientific practice should be understood as activity or as receptivity.
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17:45-18:30

The modal-explorative understanding of Newton’s experimental methodology

The modal-explorative understanding of Newton’s experimental methodology

Daian Bica (HHU Düsseldorf)

In this presentation I aim to show that Newton’s experimental philosophical methodology exhibits a salient modal-explorative nature (cf. Steinle 2006/2016, Gelfert 2016, Massimi 2019). First, I shall argue that Newton’s methodology of queries can be better qualified as being explorative in a modal sense (cf. Newton 1959-1977, 1713/1999, 1717/1952), i.e., Newton provides under the label of queries various scientific models with non-actual/fictional target-system (e.g., aether models with low resistance from his “Queries” to the Opticks). Queries have the methodological role of suggesting further experiments and advancing theoretical points for extending the boundaries of Newton’s existing knowledge. Via his aether models, Newton aims to find out plausible possible causal mechanisms for the production of gravitation.

Second, this modal-explorative methodology has immediate consequences over his metaphysics of laws of nature. Recent commentators (e.g., Biener & Schliesser 2017, Walsh 2017, Henry 2020, Hazelwood 2023) remarked that Newton’s definition of active principles as laws, causes, natures, or dispositions gives rise to various conceptual tensions. However, I aim to show that the tension inherent in his conception of laws is merely apparent since he is wrestling with multiple possibilities of making a theory of laws to work. According to the advanced modal-explorative reading, Newton attempts to find out a plausible contender for what laws of nature may be. Relative to the latter reading, his definition of active principles in terms of laws and dispositions should not be taken at face value, but seen as a “never-at-rest” explorative activity.

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19:00

Friday (24/05/2024)

9:30-10:30

Research and its presentations: different practices

Research and its presentations: different practices

Prof. Dr. Friedrich Steinle (TU Berlin)
Invited Speaker

It has often been observed by scientists and by those who reflect on science that there is a difference between what scientists actually do (or did) in their research and how they later talk (or talked) about their doing. In the ‘practice turn’ in history and sociology of science, high attention has been given to research practice, with remarkable results. That we cannot reliably understand how research goes (or went) on by only looking at published papers has become commonplace ever since, and this holds for experimental and field research as well as for theoretical and mathematical enterprises. In my talk, I shall focus on our ways to analyze both actual procedures and the ways in which they are transformed when it comes to presenting them for others. I shall illustrate my considerations with historical cases from the physical sciences.
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10:30-10:45
10:45-11:30

Scientific Explanations in the Wild: On Case Studies in the Philosophy of Science in Practice

Scientific Explanations in the Wild: On Case Studies in the Philosophy of Science in Practice

Julie Schweer (Heidelberg University)

In recent discussions, there is wide agreement that philosophy of science should be rooted in actual scientific practice. This trend is, perhaps, particularly evident in discussions around scientific explanations, where philosophers are moving away from idealized textbook examples to scrutinize real-world scientific explanations through an in-depth engagement with case studies from various fields. However, the use of case studies has elicited concerns regarding the risk of bias and overgeneralization. This paper addresses such concerns and underscores how case studies can play a role in philosophical examinations of science.

Building on a proposal by Hasok Chang, I suggest that rather than as starting points for inductive generalizations, one way in which case studies can figure in philosophical examinations is as resources for abstraction. Discussing a concrete example from molecular biology, I further spell out this idea and demonstrate how detailed analyses of patterns of scientific reasoning can offer nuanced insights into explanatory practices. I conclude by outlining how the suggested perspective on case studies also contributes to a more comprehensive understanding of normativity within the philosophy of science in practice.

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11:30-12:15

Individual Based Research – A new scientific practice?

Individual Based Research – A new scientific practice?

Marlene van den Bos (Universität Bielefeld)

In ecology, behavioral biology, and evolutionary biology a common scientific practice is to do research on a group-, a population-, and even on a species-level. This is done by collecting data of those groupings and calculating averages, standard deviations, growth rates, and other traits. However, a new trend seems to be taking root as scientists are becoming more and more interested in the individual differences and how these influence the groups, populations, and species (Bouchard and Huneman, 2013; Trappes, 2021, p. 5f; Uriarte and Menge, 2018). For example, if you want to know whether there are morphological size differences between two sexes of a population, you have to measure a number of individuals of both sexes and then group the results. By the end you have two groups of data based on individual measurements. You can now calculate the average sizes for both groups which may or may not reveal a significant size difference. With IBR, however, the information that can be gained, provides more insights into the individual and the intra-specific variation without losing any information about the group, population, or species.

Our research group is part of a larger collaborative research center (CRC) that includes biologists from ecology, behavioral, and evolutionary biology as well as two groups of philosophers of science. Within this CRC we have observed a shift from focusing on groups to focusing on individuals. To support our observations, we created a questionnaire, conducted interviews, and held a discussion round. Most of the participants claimed they were doing individual based research and described their methods and processes in detail. However, when asked to explain what IBR is, most answered with “doing research on individuals” in one variation or another. This explanation is rather unsatisfying as it would allow almost anything to pass as individual based research including the example given earlier. Also, this explanation clashes with the methods and processes the biologists described. We found that IBR has at least three main characteristics: identifiability, multiple measurements, and individual-based analysis. All individuals should be identifiable. This can be done by spatial separation (placing individual fruit flies into test boxes), phenotypic traits (individual markings of fire salamanders), tagging (ringing birds), or tracking (GPS trackers on sea lion, e.g.: Schwarz et al., n.d.). Multiple measurements means that there has to be more than one piece of information. This can be done with an ongoing test that takes place over a longer period of time, tests that are repeated in a certain interval, or measurements of multiple traits without repetition. Lastly,

the analysis of the data should be individual based. While the data can be grouped to calculate averages or variation within the groups, it is also analyzed in a way that allows a clear depiction of the individual. This makes the final results traceable and individually distinguishable.

This list of features is not exhaustive further analysis of IBR is taking place with the focus being on the epistemic consequences of conducting IBR.

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12:15-13:30
13:30-14:15

Transforming standards: Observation Contextualised

Transforming standards: Observation Contextualised

Sarwar Ahmed (University of Wuppertal)

Despite its central epistemic role, the nature of the standards by which an observational claim is accepted has received little philosophical and historical attention. Chalmers (1985, 2013) has noted the transition from an Aristotelian doctrine of observation based on perception to the acceptance of telescopic observations promoted by Galileo’s demonstrations. Franklin (2013) has discussed the rise of a discovery standard in particle physics based on statistical significance and its subsequent transitions. More recently, Dawid (2021) has noted the need to integrate meta-empirical assessments into the concept of empirical confirmation in the period of the acceptance of atomism that led to a justified observation of microphysical objects. However, these authors have focused on specific historical periods without intending to provide a broader understanding of the implications of these transformations. In this talk, I defend the claim that an atemporal set of standards that can be used as necessary and sufficient conditions for evaluating observational claims is alien to the nature of scientific practice.

The liberal attitude regarding the concept of observation in scientific practice is governed by the dynamical nature of standards of acceptability for observations. I argue that the historically influential empiricist view of observation, which sees perception as a static central standard for an observation, has overshadowed the long-standing dynamic nature of the concept of observation in scientific practice, which is governed by transformations in its standards.

Advances in science and technology have increasingly provided us with new observational methods and means to extend our senses and observe aspects of the world that are inaccessible to our optical instruments of observation. This has influenced our understanding of the concept of observation and allowed scientists to adopt a permissive attitude toward the concept. As a result, what qualifies as a standard for accepting a proper observational claim has become relative to the socio-historical context in which the observation is made. Thus, there do not seem to be universally fixed and static standards for evaluating scientific observations. Instead, the scientific community adheres to a specific set of standards in each context.

For the purposes of this talk, I will draw on the examples provided by the aforementioned authors to argue that, in general, at each stage, the community manages to accept an update to the standards by appealing to the common scientific and conceptual toolkit available in that context. The common toolkit may include, for example, background knowledge, basic shared assumptions, coincidence and robustness arguments, eliminative reasoning and technical skills. The introduction of new means of observation does not result in abrupt changes in standards. Instead, specific standards may persist or be layered through stages of theoretical and methodological changes. This suggests the need for a contextual understanding of observation. The above consideration further suggests that the community’s acceptance of the dynamic nature of observational standards in practice is not inconsistent with a rational understanding of scientific change.

References

  • Chalmers, Alan. “Galileo’s Telescopic Observations of Venus and Mars.” The British Journal for the Philosophy of Science 36, no. 2 (1985): 175–84.
  • Chalmers, Alan. What Is This Thing Called Science? The University of Queensland Press/The Humanities Press, 2013, 4th edition.
  • Dawid, R. “The role of meta-empirical theory assessment in the acceptance of atomism.” Stud Hist Philos Sci. 2021 Dec; 90:50-60.
  • Franklin, Allan. “Is Seeing Believing? Observation in Physics”. Phys. Perspect. 19 (2017): 321–423.
  • Franklin, Allan. Shifting Standards: Experiments in Particle Physics in the Twentieth Century. University of Pittsburgh Press, 2013.
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14:15-15:00

Understanding particle interactions – representation in Feynman diagrams in theory and practice

Understanding particle interactions – representation in Feynman diagrams in theory and practice

Karla Weingarten (MCMP, LMU Munich)

In particle physics practice, individual or subgroups of Feynman diagrams are often taken to be representative of particle interactions. In papers relating to the discovery of a Higgs candidate in 2012, the CMS Collaboration at the LHC used individual Feynman diagrams to illustrate different decay channels that produce a Higgs particle (see, e.g., The CMS Collaboration 2013). In quantum many-particle physics, so-called ladder diagrams appear, for example, in the Hartree-Fock method of approximating the energy of a quantum many-body system in its ground state. Only specific, ladder-looking types of Feynman diagrams are considered and summed over (see Broadhurst 1993, Ablinger et al. 2012).

It thus seems apparent that physicists use Feynman diagrams to visualize the content of the debate, illustrate their argumentations, and further the readers’ understanding of their paper – they use Feynman diagrams to represent the physical situation.

This conflicts with the general perception of Feynman diagrams in philosophy of science, where they are commonly considered mathematical artifacts of a perturbative approach to calculating cross sections. Only all infinite possibilities of some particles to interact, corresponding each to a Feynman diagram, are linked to one interaction. Therefore, it has been previously argued that, given the most common accounts of representation, individual diagrams do not represent (see Dorato and Rossanese 2018; Brown 2018).

In this talk, I present a revised account of representation suitable for areas where we have little knowledge of the target system. Returning to the most fundamental question of representation – in virtue of what does a model represent a target? – I develop an agent-centred account of representation in which Feynman diagrams, considered as a model of the corresponding particle interaction, represent the interaction in virtue of providing understanding of it. This aim is the justification for using the model to represent the target. It is thus a functionalist account of representation, aiming at understanding the target with the model, rather than at making causal inferences about the target system through model inferences. It allows the accommodation of models, in our case Feynman diagrams, to represent a target without having to make claims about the reality of the model ingredients, and without requiring isomorphic mapping or literal truthfulness. Hence, it is suitable for highly speculative areas of science, and reconciles scientific practice in particle physics with philosophy of science.

References

  • Ablinger, Jakob et al. (2012). ‘Massive 3-loop ladder diagrams for quarkonic local operator matrix elements’. In: Nuclear Physics B 864.1, pp. 52–84.
  • Broadhurst, D. J. (1993). ‘Summation of an infinite series of ladder diagrams’. In: Physics Letters B 307.1, pp. 132–139.
  • Brown, James Robert (2018). ‘How Do Feynman Diagrams Work?’ In: Perspectives on Science 26.4, pp. 423–442.
  • Dorato, Mauro and Emanuele Rossanese (2018). ‘The Nature of Representation in Feynman Diagrams’. In: Perspectives on Science 26.4, pp. 443–458.
  • The CMS Collaboration (2013). ‘Evidence for the 125 GeV Higgs boson decaying to a pair of leptons’. In: Journal of High Energy Physics 2014.5, pp. 587–609.
Close
15:00

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