The Epistemology and Ethics of Formal Methods in the sciences (with a focus on the life sciences and inner mathematical considerations)

1. Thorsten Altenkirch (University of Nottingham)

2. Ozan Altan Altinok (CELLS, Leibniz Universität Hannover)

3. Cornelius Borck (Universität zu Lübeck) 

4. Bernhard Fisseni (Universität Duisburg-Essen)

5. Christian Herzog (Universität zu Lübeck)

6. Deborah Kant (Universität Hamburg)

7. Benedikt Löwe (Universität Hamburg & Cambridge University) [Online]

8. José Antonio Perez-Escobar (UNED, Madrid) 

9. Deniz Sarikaya (Universität zu Lübeck & Vrije Universiteit Brussel)

10. Bernhard Schröder (Universität Duisburg-Essen) 

11. Cristina Villegas (Universidade de Lisboa)

12. Diedrich Wolter (Universität zu Lübeck)

Further participants (who wanted to be listed, in person and online)

Anusha Bhattacharya (Indian Institute of Science Education and Research, Mohali) 

Stefan Ciobaca (Alexandru Ioan Cuza University) 

Huimin Dong (TU Wien) 

Friedrich Wilhelm Grafe (independent philosophical research) 

Sarah Hiller (Free University Berlin)

Serkan Kılıç 

Luis Lopez (MCMP-LMU)

Mary Mirvis (University of California, San Francisco)

Christos Moyzes (University of Athens)

Rivas-Robledo Pablo (University of Amsterdam)

Luca Pezzini (Università di Torino) 

Vitaly Pronskikh (Oak Ridge National Laboratory)

Andrei Rodin (University of Lorraine) 

Nikolay Shilov (Innopolis University) 

Fatih Taş (Bartın University)

Luis Urtubey (Naional University of Cordoba (Argentina))

Frithjof Wegener (Northumbria University)

Daniela Zetti (Universität zu Lübeck) 

Day 1

10: 00 Opening and Greetings by Cornelius Borck (Universität zu Lübeck) 

10:15 - 11:15 Talk 1: Christian Herzog (Universität zu Lübeck)
11:15 - 12:15 Talk 2: Benedikt Löwe (Universität Hamburg & Cambridge University) [Online]

short break

12:25 - 13:25 Talk 3: Ozan Altan Altinok (CELLS, Leibniz Universität Hannover)

13:25 - 15:00 Lunch Break

15:00 - 16:00 Talk 4: Cristina Villegas (Universidade de Lisboa)
16:00 - 17:00 Talk 5: José Antonio Perez-Escobar (UNED, Madrid) 

short break

17:15 - 18:15 Talk 6: Deborah Kant (Universität Hamburg)

19:00 Conference Dinner: Restaurant Alte Mühle Lübeck

Day 2

09:00 - 10:00 Talk 7: Bernhard Schröder (Universität Duisburg-Essen)
10:00 - 11:00 Talk 8: Thorsten Altenkirch (University of Nottingham)

short break

11:15 - 12:15 Talk 9: Diedrich Wolter (Universität zu Lübeck)
12:15 - 13:15 Talk 10: Bernhard Fisseni (Universität Duisburg-Essen)
13:30 - 14:15 Talk 11: Deniz Sarikaya (Universität zu Lübeck & Virje Universiteit Brussels)

Joint Lunch (Optional)  - Lübecker Kartoffelkeller 

"From Greek to Code: Type Theory as a Bridge" by Thorsten Altenkirch (University of Nottingham)

Abstract: In mathematics, we often rely on Greek letters, while computer code is traditionally composed of ASCII characters. This illustrates a dichotomy between mathematical reasoning and programming languages. In my talk, I aim to show how Type Theory serves as a bridge across this divide.

I will demonstrate the use of the Agda system, an implementation of Type Theory, to represent mathematical constructs in a formalized, computable format. This includes an exploration of recent developments in Type Theory, specifically Homotopy Type Theory, and its practical application within cubical Agda. Through these examples, I’ll illustrate how Type Theory enables a seamless transition from abstract mathematical concepts to concrete implementations in code.

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"Diagrams as Performative Visual Representations of Life History in Imaginations and Research Programmes in Evolutionary Medicine" by Ozan Altan Altinok (CELLS, Leibniz Universität Hannover) 

Abstract. The epistemic goals of diagrams are seen pivotal in scientific representation, offering visual means to communicate complex ideas and data. I will argue that diagrams within evolutionary medicine are not only fulfilling a representational role that is typically seen as the main or even sole role of diagrams, but a performative role. I will argue that diagrams in evolutionary medicine are helpful in shaping research programmes and imaginations around research apart from truth apt representational content. This paper explores the epistemological implications in shaping research programmes and acting performatively through diagrams within evolutionary medicine.

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Frame the gap by Bernhard Fisseni (Universität Duisburg-Essen)  

Frames are a formalism from the area of knowledge representation. It has been applied to different areas, from linguistic knowledge (esp. verb valency) to the philosophical analysis of concepts. The talk will discuss applications of this concept to the language of mathematics. 

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"The Limits of Control — Between Reductionism and Synthesis" by Christian Herzog (Universität zu Lübeck)

Karl J. Åström, one of control theory’s greats, has once stated that “the goal of natural science is to understand. Its major tool is reductionism”, while “the goal of engineering science is to design. Its major tool is synthesis.” In control—a particularly strongly mathematized field—reductionist modeling from the natural sciences is explicitly used for synthesis, which, in control, refers to the automatic design of feedforward and feedback control laws through optimization. The principle of feedback control has rendered even highly reductionist mathematical representations “unreasonably effective” in guiding controller synthesis. However, seemingly justified by the very goal of control to maintain a state close to a modeled operating point, reductionist modeling was pushed to the brink of its effectiveness when optimality reigned supreme. Since then, adverse real-world effects of optimal control based on low-fidelity models have been the core motivations to advance concepts of robustness. Looking from the vantage point of control and mathematical modeling, we initiate a discussion on the limits of the concept of (feedback) control when applied to pressing societal or complex individual health issues, particularly involving modern approaches to data-driven and artificial intelligence-based algorithmic interventions.

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"The Philosophical Significance of Applying Set-Theoretic Methods in Other Mathematical Domains" by Deborah Kant (Universität Hamburg)

In mathematical practice, the application of one mathematical domain within another is widely understood as a form of "internal application." Just as mathematical applications outside mathematics, such as in the sciences, internal applications within mathematics itself are also philosophically significant. They prompt questions about the purity of methods and the nature of explanatory proofs. In this talk, I will explore some of the philosophical dimensions of internal applications within mathematics, focusing specifically on the use of set-theoretic methods in other mathematical domains. This approach reveals essential connections to foundational questions in the philosophy of mathematics.

A central philosophical question in set-theoretic foundations is whether we can justify new axioms to settle statements that are independent of the standard theory, such as the continuum hypothesis. Here, views diverge. Absolutist practitioners argue that it is possible, through the addition of extrinsically justified axioms like projective determinacy. Pluralist practitioners, on the other hand, argue that this is not possible, given the numerous alternative axioms, none of which can be deemed definitively preferable. Interestingly, both perspectives invoke set theory’s foundational role and its relevance to other mathematical domains. I will argue that resolving this philosophical tension hinges on the effectiveness of set-theoretic methods when applied in other mathematical domains.

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"'What makes stories similar?' Methodological lessons learned from an empirical formalisation project" by Benedikt Löwe (Universität Hamburg & Cambridge University) [Online]
 In this talk, I shall report on the project "What makes stories similar?", run at the Universität Hamburg and funded by the Templeton Foundation from 2011 to 2014. In the tradition of structuralist philology, the project started from the assumption that human readers of narratives are able to recognize whether two stories represent the same underlying narrative and that this underlying narrative can be captured in a formal system. This assumption forms the basis of the work in the field of 'Story Understanding' and closely relates to Gentner's Structure Mapping Theory.

I shall recount the story of our project in which our assumptions were repeatedly challenged by empirical results of our studies and draw conclusions for the methodology of formal work in the humanities and social sciences.

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"On the regulative properties of mathematics in biology" by José Antonio Pérez Escobar (UNED) 

Biological phenomena display variability and historicity and are inherently “messy”. To improve the reproducibility of experiments and develop a quantitative, rigorous biology biologists resort to numerous measurement strategies to control the messiness of biology. Measurement is key for quantification and involves a sort of order making. Although biology can be ordered in different ways that influence model building, the aim is to build models that represent real, empirical structures.

However, in their efforts to measure and mathematize messiness, scientists may also inadvertently use mathematical models in a way that culminates in epistemic circularity. Mathematical models can be used as rules on how to perform measurement instead of mere outputs of measurement and representing empirical structures. For example, they may be source of quantitative expectations on empirical phenomena, and a failure of the latter to adjust to the model may lead to questioning the measurement procedure. The same mathematical model can be used in a way or another depending on contextual nuances.

I present a case study on the brain’s “compass”, a brain system which encodes the facing direction of mammals. It is comprised of “head-direction” cells, each of which encodes a given angular direction in its electrophysiological activity. The early measuring of this cells is performed according to a compass analogy and yielded a mathematical model, inspired by the compass analogy too. However, subsequent measurement is influenced by the mathematical model itself, which places quantitative expectations on the cells’ activity. If the two do not match, the model can be revised, but also some cells may be excluded from analyses (“monster barring”) and others are measured in ways so that the model is fulfilled (mathematical model as rules of description instead of descriptions). I discuss what kind of contextual nuances in the scientific practice prompts each use of the mathematics.

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"Against a Global Conception of Mathematical Hinges: A Holistic Reading of Wittgenstein and Mathematics in Practice." by Deniz Sarikaya (Universität zu Lübeck & Vrije Universiteit Brussel)

Epistemologists have developed a diverse group of theories, known as hinge epistemology, about our epistemic practices that resort to and expand on Wittgenstein's concept of ‘hinges’ in On Certainty. Within hinge epistemology there is a debate over the epistemic status of hinges. Some hold that hinges are non-epistemic (neither known, justified, nor warranted), while others contend that they are epistemic. Philosophers on both sides of the debate have often connected this discussion to Wittgenstein's later views on mathematics. Others have directly questioned whether there are mathematical hinges, and if so, these would be axioms. Here, we give a hinge epistemology account for mathematical practices based on their contextual dynamics. We argue that 1) there are indeed mathematical hinges (and they are not axioms necessarily), and 2) a given mathematical entity can be used contextually as an epistemic hinge, a non-epistemic hinge, or a non-hinge. We sustain our arguments exegetically and empirically. 

We then elaborate some future direction this might offer for a joint project with Raphael. 

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Mind the gap - What proof-telling tells us about proof-thinking by Bernhard Schröder (Universität Duisburg-Essen) 

Mathematical proofs texts exhibit nearly all features of narratives in other domains. They usually have a temporal organisation, they combine entities to complexes, and show virtually all kinds of ambiguities, to mention only a few. But there are also some peculiaries which are uniques features of mathematical texts and texts in other mathematized areas, like their referential structure, the use of symbols, the explicit argumentative structure and the modularization. I will discuss in my talk what the linguistic simularities and differences could tell us about the cognitive organisation of proofs.

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Conceiving Evolutionary Possibilities: from Measurement to Computation by Cristina Villegas (Universidade de Lisboa)

Evolutionary developmental biology (commonly abbreviated as evo-devo) examines the evolution of developmental processes in multicellular organisms and their impact on phenotypic evolution. Although the field has deep historical and theoretical roots within the morphological and structural traditions of the natural sciences, its approach was largely overlooked in mainstream evolutionary theory, partly due to its lower level of formalization compared to population dynamics models. In recent decades, however, a surge in evo-devo models has highlighted the central role of development in theorizing and predicting potential evolutionary pathways. In this talk, I argue that this proliferation of modeling tools necessitates a rethinking of the concept of chance in evolution. First, I discuss the implications of evo-devo models for individualizing and measuring phenotypic traits. Next, I propose that certain computational models of development in evolution are best understood as propensity models, where dynamic properties account for probabilities. Finally, I advocate for a pluralistic understanding of chance in evolution, informed by the interdisciplinary work embodied in evo-devo models.

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Reasoning for Unravelling Meaning in Natural Language by Diedrich Wolter (Universität zu Lübeck)

Logics have a long tradition as means for specifying meaning in science. In the area of Natural Language Understanding, logics have been developed to capture the meaning of words, phrases, or sentences. But there may be more to determining the meaning of a given sentence than mapping natural language to logic formulae. In this talk I will argue for the utility of considering models of logic formulae that aim to capture semantics. The idea has been used successfully in a study for interpreting spatial language, in particular natural language descriptions of place. I discuss first ideas on generalizing this approach to a broader class of natural language.

Die Akademie der Wissenschaften in Hamburg, Ethical Innovation Hub of the Universität zu Lübeck, and Institut für Medizingeschichte und Wissenschaftsforschung der Universität zu Lübeck. The Event is also endorsed by the CIPSH Chair: Diversity of Mathematical Research Cultures and Practices.