## Carl Friedrich von Weizsäcker-Colloquium

### Wednesday 17-18h

The Carl Friedrich von Weizsäcker-Colloquium hosts weekly talks from guests and members of the CFvW-Center. In the broadest sense the topics resemble the issues that are discussed in the center.

The Colloquium takes place on *Wednesdays between 5pm and 6pm*, until further notice via the Zoom-Platform. (usually we record them for our YouTube Channel)

To take part please follow this link.

Prof. Dr. Reinhard Kahle und Dr. Thomas Piecha.

To get the announcements for the colloquium-lectures please send an email to: Aleksandra Rötschke.

# Upcoming Talk

**Wednesday **23 June 2021**, 17**pm** s.t.**

**Wednesday**

**, 17**pm

**s.t.**

## Dr. Daniel Kostić (Radboud University):

## Perspectivism and Vertical-Horizontal Explanatory Modes in Ecological Networks

We show how the perspectival criteria help to determine the explanatory relevance in ecological network models. We provide counterfactual analysis of explanatory power of a marine network model, which includes the perspectival criteria for using a horizontal mode (when the counterfactual relata are at the same level) and a vertical mode (when the counterfactual relata are at different levels). Distinguishing vertical and horizontal counterfactual modes is important for understanding how are different organizational levels of a system functionally related as well as how do exogeneous changes affect each of the levels. We show that perspectival criteria play a more important epistemic role than merely informing the modeling decisions. If such criteria were not available, it wouldn’t have been intelligible how the relevant counterfactual figures in an explanation. They determine explanatory relevance conditions for a counterfactual. Based on this theoretical framework, we further point out how our analysis can be used in designing more sustainable spatial management policies for aquatic resources.

## List of Lectures

## 28 July 2021: Prof. Dr. Maximilian Schich (The University of Texas at Dallas): TBA

## 21 July 2021: Christoph Peylo (Bosch Center for Artificial Intelligence): TBA

## 14 July 2021: Prof. Dr. Federico Pailos (Buenos Aires): TBA

## 7 July 2021: reserved

## 30 June 2021: Prof. Dr. Mathias Frisch (Hannover): TBA

## 23 June 2021: Dr. Daniel Kostić (Radboud University): Perspectivism and Vertical-Horizontal Explanatory Modes in Ecological Networks

We show how the perspectival criteria help to determine the explanatory relevance in ecological network models. We provide counterfactual analysis of explanatory power of a marine network model, which includes the perspectival criteria for using a horizontal mode (when the counterfactual relata are at the same level) and a vertical mode (when the counterfactual relata are at different levels). Distinguishing vertical and horizontal counterfactual modes is important for understanding how are different organizational levels of a system functionally related as well as how do exogeneous changes affect each of the levels. We show that perspectival criteria play a more important epistemic role than merely informing the modeling decisions. If such criteria were not available, it wouldn’t have been intelligible how the relevant counterfactual figures in an explanation. They determine explanatory relevance conditions for a counterfactual. Based on this theoretical framework, we further point out how our analysis can be used in designing more sustainable spatial management policies for aquatic resources.

## 9 June 2021: Dr. Silvia De Toffoli (Princeton University): What Are Mathematical Diagrams?

Although traditionally neglected, mathematical diagrams have recently attracted much attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and proof. Certain preliminary questions have, however, been bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations (or both). I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing a precise definition, I explain (away) certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading.

## 2 June 2021 (15-18h): Prof. Dr. Aaron Sloman (University of Birmingham): Unsolved problems linking physics, biology, consciousness, philosophy of mathematics, and chemical information processing.

There are types of spatial intelligence, detecting and employing varieties of spatial possibility, necessity,and impossibility, that cannot be explained by currently known mechanisms. Evidence from newly hatched animals suggests that mechanisms using still unknown chemistry-based forms of computation can provide information that goes beyond regularity detection, concerned with possibility spaces and their restrictions. Ancient human spatial intelligence may be based on multi-generational discovery of what is possible, necessarily the case, or impossible, in complex and changing environments, using related mechanisms of spatial cognition, centuries before Euclid, that enabled discoveries regarding possibility, impossibility and necessity in spatial structures and processes, long before modern mathematical, symbolic, logic-based, or algebraic formalisms were available.

Immanuel Kant characterised such mathematical cognition in terms of three distinctions largely ignored in contemporary psychology, neuroscience, and AI research: non-empirical/empirical, analytic/synthetic, and necessary/contingent. He argued that ancient geometric cognition was not based simply on empirical generalization, nor on logical deduction from arbitrary definitions. The truths discovered were non-empirical, synthetic, and non-contingent.

Neither formal logic-based characterizations of mathematics (used in automated theorem provers), nor postulated neural networks collecting statistical evidence to derive probabilities can model or explain such mathematical discoveries. E.g. necessity and impossibility are not extremes on a probability scale.

Unexplained facts about spatial competences of newly hatched animals, before neural networks can be trained in the environment, may be related to mechanisms underlying ancient spatial intelligence in humans and other animals.

Chemical mechanisms inside eggs, available before hatching, somehow co-existing with the developing embryo, apparently suffice. Such mechanisms may be partly analogous to types of "virtual machinery" only recently developed in sophisticated forms that provide services across the internet (like zoom meetings) that "float persistently" above the constantly changing, particular physical mechanisms at work, without occupying additional space.

While chemical mechanisms in early stages of reproduction are well-studied, little is known about enormously complex types of machinery required for later stages, e.g., of chick production, including creation of control mechanisms required for actions soon after hatching. I suggest that development of the foetus uses many stages of control by increasingly sophisticated *virtual *machines controlling and coordinating chemical mechanisms as they create new chemical mechanisms *and* new layers of virtual achinery.

Different sub-types must have evolved at different times, and the later, more complex virtual machines may have to be assembled by earlier virtual machines, during foetus development, whereas earliest stages of reproduction simply use molecular mechanisms controlling formation and release of chemical bonds linking relatively simple chemical structures.

I suspect Alan Turing's work on chemistry-based morphogenesis (published 1952) was a side effect of deeper, more general, thinking about uses of chemistry-based spatial reasoning in intelligent organisms. But he died without publishing anything to support that suspicion, though he did assert in 1936 that machines can use mathematical ingenuity, but not mathematical intuition, without explaining the difference (on which Kant might have agreed). We may never know how far his thinking had progressed by the time he died.

Extended version:

https://www.cs.bham.ac.uk/research/projects/cogaff/misc/unsolved.html

## 19 May 2021: Dr. Vincenzo Politi (University of Oslo): Anticipative reflection in an interdisciplinary research team: a case study

Responsible Research and Innovation (RRI) and similar science policy frameworks aim at reinforcing the social responsibility of science and technology by promoting a reflective and anticipatory attitude among researchers. Such an attitude requires the ability to imagine future scenarios in order to predict and assess the potential societal implications of innovative research. Responsible research, therefore, requires a future-oriented attitude. ‘Future’, however, may mean different things. In this talk, I discuss the results of a qualitative study conducted with an interdisciplinary research team working on innovative personalised targeted cancer therapies. The study reveals that, within the research team, different individuals think about different kinds of future. Depending on which kind of future they think about, researchers anticipate different kinds of impact of their work, which I define ‘internal’ and ‘external impact’. In the conclusions, I will investigate which kind of knowledge and expertise researchers should be equipped with in order to develop the ability to think about the future implications of their work.

## 12 May 2021 (18-19h!): Sandro Radovanović (University of Belgrade): Effects of Affirmative actions in algorithmic decision-making

In today’s business, decision-making is heavily dependent on algorithms.

Algorithms may originate from operational research, machine learning, or

decision theory. Regardless of their origin, the decision-maker may create

unwanted disparities regarding race, gender, or religion. More specifically,

automation of the decision-making process can lead to unethical acts with

legal consequences. To mitigate unwanted consequences of algorithmic decision-

making one must adjust either input data, algorithms, or decisions. In this

talk, an overview of fairness in algorithmic decision-making from a machine

learning point of view is going to be presented, as well as developed

approaches in the literature. This talk aims at presenting a way to ensure

fairness in algorithmic decision-making that ensures a lack of disparate

impact as well as ensuring equal odds. After presenting the methodology, we

discuss what is flawed with approaches that the machine learning community

adopted while “fighting unfairness”, and as a result what are the properties

of true affirmative actions in algorithmic decision-making and how they can be

achieved.

## 5 May 2021: Dr. Antonio Piccolomini d'Aragona (Aix-Marseille): Kreisel's informal rigour and Gödel's absolute provability. A tentative reading through and for Prawitz's semantics

In spite of their philosophical relevance, Kreisel’s theory of informal rigour and Gödel’s concept of absolute provability have proved elusive to rigorous mathematised treatments. In my talk, I will set out to connect Kreisel’s and Gödel’s ideas to Prawitz’s proof-based semantics. Prawitz’s semantics has been put forth and developed independently of Kreisel and Gödel, but some of its basic tenets may nonetheless match those of informal rigour and absolute provability. Both Kreisel and Gödel aim at bringing provability back into mathematical practice – against the post-Fregean and post-Hilbertian formalistic attitude – as well as at overstepping formal derivability – given Gödel’s and Turing’s limiting results. In order to do this, provability must become informal (i.e. independent of formal languages and systems) and absolute (i.e. formalism-free and/or universally applicable). This may be in line with the intuitionistic idea of giving provability a “semantic” role, an idea of which Prawitz’s semantics is a well-known instance. As a result, I argue that Prawitz’s semantics shares some issues with Kreisel’s informal rigour, while the link with Gödel’s absolute provability is more difficult to be established.

## 21 April 2021: Dr. Christian Feldbacher-Escamilla (Düsseldorf): AI for a Social World – A Social World for AI

AI is not only supposed to help to tackle social problems but it is also frequently used to in fact solve such problems. AI-assisted systems play an increasingly important role in the legal domain, the health sector, environmental research, public policy-making and the like. Research in this field is numerous and diverse. In this talk, we want to argue, however, that it is also interesting to have a look at the opposite direction: How can our knowledge of the social world and its structural features help us to approach problems of AI? In particular, we will investigate how a social perspective on problems of justification helps us to address epistemic problems of machine learning theory.

## 6 April 2021: Prof. Dr. Helen Longino (Stanford University): Critical Contextual Empiricism, Diversity and Inclusiveness

Watch the recording on Facebook.

Humanity looks to the scientific community, now more than ever, in order to provide solutions to today's challenges. Decisions made by scientists thus directly and deeply influence human lives. The Carl Friedrich von Weizsäcker Center is interested in the foundations of responsible science. For example, how can we identify and avoid scientific misconduct, e.g. plagiarism and fraud, or the abuse of science for commercial purposes? How do we navigate issues of morally questionable research, research funding, and global inequalities? How can scientists ensure optimal knowledge production in the face of the replication crisis, cognitive biases in science, and the politics of peer review? Further, how can we protect scientists from becoming commodities when their products are so ardently sought by politicians and society?

## 6 April 2021: Prof. Dr. Nancy Cartwright (Durham University): Responsible Science - Responsible Use

Watch the Recording on Facebook.

Humanity looks to the scientific community, now more than ever, in order to provide solutions to today's challenges. Decisions made by scientists thus directly and deeply influence human lives. The Carl Friedrich von Weizsäcker Center is interested in the foundations of responsible science. For example, how can we identify and avoid scientific misconduct, e.g. plagiarism and fraud, or the abuse of science for commercial purposes? How do we navigate issues of morally questionable research, research funding, and global inequalities? How can scientists ensure optimal knowledge production in the face of the replication crisis, cognitive biases in science, and the politics of peer review? Further, how can we protect scientists from becoming commodities when their products are so ardently sought by politicians and society?

## 24 February 2021: Prof. Dr. Marco Panza (Paris 1) & Prof. Dr. Daniele Struppa (Chapman University): Agnostic Science and Mathematics

We'll firstly illustrate the notion of agnostic science (science without understanding), and reflect, then, on the effect that the practicer of agnostic science has on the use of maths in science, and for the development of maths itself.

## 17 February 2021: Dr. Benedikt Ahrens (Birmingham): The Univalence Principle

Michael Makkai's "Principle of Isomorphism" stipulates that mathematical reasoning is invariant under equivalence of mathematical structures. Inspired by Makkai, Vladimir Voevodsky conceived the Univalent Foundations (UF) of Mathematics as a foundation of mathematics in which only equivalence-invariant properties and constructions can be formulated. Coquand and Danielsson proved that UF indeed provides an isomorphism-invariant language for *set-level* structures, such as groups and rings, that form a 1-category. Ahrens, Kapulkin, and Shulman proved an extension for 1-categories: any property and construction that can be expressed in UF transfers along equivalence of categories—as long as “categories” are correctly defined to satisfy a local “univalence” condition. In the semantics of UF in simplicial sets, this univalence condition corresponds to Charles Rezk’s completeness condition for (truncated) Segal spaces.

In this talk, based on joint work with Paige Randall North, Michael Shulman, and Dimitris Tsementzis, I will show how to generalize this result to other higher-categorical structures. We devise a notion of signature and theory that specifies the data and properties of a mathematical structure. Our main technical achievement lies in the definition of isomorphism between two elements of a structure, which generalizes the notion of isomorphism between two objects in a category. Such isomorphisms yield the companion notion of univalence of a structure. Our main result says that for univalent structures M, N of a signature, the identity type M = N coincides with the type of equivalences M ≃ N. This entails that any property and construction on a univalent structure transfers along a suitable notion of equivalence of structures. Our signatures encompass the aforementioned set-level structures but also topological spaces, (multi-)categories, presheaves, fibrations, bicategories, and many other (higher-)categorical structures.

## 10 February 2021: Marcel Ertel (Tübingen): Independence and truth-value determinacy in set theory

We discuss the philosophical significance of classical and more recent results in the metamathematics of set theory: the Gödel-Cohen independence theorem of the Continuum Hypothesis (CH) from first-order set theory; Zermelo's quasi-categoricity result characterizing models of second-order set theory and Lavine's improvement thereof in an extended first-order framework (using Feferman's idea of a "full schema" allowing substitution of formulas from arbitrary language-expansions); and Väänänen's internal categoricity results.

In light of these technical results, we assess the ongoing debate between proponents of a set-theoretic multiverse (likening the CH to Euclid's parallel postulate in geometry) and defenders of the determinacy of the truth-value of the CH. We present two arguments against the multiverse view, and end with a discussion of the philosophical difficulties in explaining what it means 'to be a solution of the continuum problem'.

## 3 February 2021: Paulo Guilherme Santos (Tübingen): k-provability in PA

We study the decidability of k-provability in PA – the decidability of the relation 'being provable in PA with at most k steps' – and the decidability of the proof-skeleton problem – the problem of deciding if a given formula has a proof that has a given skeleton (the list of axioms and rules that were used). The decidability of k-provability for the usual Hilbert-style formalisation of PA is still an open problem, but it is known that the proof-skeleton problem is undecidable for that theory. Using new methods, we present a characterisation of some numbers k for which k-provability is decidable, and we present a characterisation of some proof-skeleton for which one can decide whether a formula has a proof whose skeleton is the considered one (these characterisations are natural and parameterised by unification algorithms).

## 27 January 2021: Dr. Roberta Bonacina (Tübingen): Introduction to Homotopy Type Theory III

Homotopy type theory is a vibrant research field in contemporary Mathematics. It aims at providing a foundation of Mathematics extending Martin-Löf type theory with the central notion of univalence, which induces a connection between types and homotopy spaces.

We will begin the short course defining the simple theory of types, and showing how it can be extended to Martin-Löf type theory and then to Homotopy type theory. We will stress the propositions-as-types interpretation between the type theories and intuitionistic logic, and study in detail the notion of equality. Then we will show how classical logic can be done in this intuitionistic setting, allowing to introduce the law of excluded middle and the axiom of choice as axioms. Finally, we will analyse the different definitions of equivalence, which are fundamental to introduce univalence.

## 20 January 2021: Dr. Roberta Bonacina (Tübingen): Introduction to Homotopy Type Theory II

Homotopy type theory is a vibrant research field in contemporary Mathematics. It aims at providing a foundation of Mathematics extending Martin-Löf type theory with the central notion of univalence, which induces a connection between types and homotopy spaces.

We will begin the short course defining the simple theory of types, and showing how it can be extended to Martin-Löf type theory and then to Homotopy type theory. We will stress the propositions-as-types interpretation between the type theories and intuitionistic logic, and study in detail the notion of equality. Then we will show how classical logic can be done in this intuitionistic setting, allowing to introduce the law of excluded middle and the axiom of choice as axioms. Finally, we will analyse the different definitions of equivalence, which are fundamental to introduce univalence.

## 13 January 2021: Dr. Roberta Bonacina (Tübingen): Introduction to Homotopy Type Theory I

Homotopy type theory is a vibrant research field in contemporary Mathematics. It aims at providing a foundation of Mathematics extending Martin-Löf type theory with the central notion of univalence, which induces a connection between types and homotopy spaces.

We will begin the short course defining the simple theory of types, and showing how it can be extended to Martin-Löf type theory and then to Homotopy type theory. We will stress the propositions-as-types interpretation between the type theories and intuitionistic logic, and study in detail the notion of equality. Then we will show how classical logic can be done in this intuitionistic setting, allowing to introduce the law of excluded middle and the axiom of choice as axioms. Finally, we will analyse the different definitions of equivalence, which are fundamental to introduce univalence.

## 16 December 2020: Prof. Dr. Klaus Mainzer (München & Tübingen): Verification and Standardization of Artificial Intelligence – Results of the German Steering Group (HLG) of AI Standardization Roadmap

## 9 December 2020: Prof. Dr. Eberhard Knobloch (TU Berlin): Leibnizens Konzept einer ars characteristica oder ars combinatoria. Beispiele aus der Mathematik

Leibnizens Konzept einer ars characteristica oder ars combinatoria verdeutlicht den engen Zusammenhang zwischen seinem philosophischen und seinem mathematischen Denken. Der theoretische erste Teil des Vortrags stellt dieses Konzept mit seinen vier Vorteilen vor. Symbolische Algebra diente Leibniz als Modell für dieses Konzept. Daher wird der zweite Teil des Vortrags das Konzept an algebraischen Beispielen, insbesondere am Beispiel der symmetrischen Funktionen exemplifizieren. Diese waren sein zentrales Hilfsmittel bei der Suche nach der algorithmischen Auflösung einer algebraischen Gleichung beliebigen Grades.

## 2 December 2020: Dr. Richard Lawrence (Tübingen): Hankel's formalism, Frege's logicism, and the analytic-synthetic distinction

I will discuss some research on Hermann Hankel, an early proponent of a formalist viewpoint in the foundations of mathematics, and the relation of his view to Gottlob Frege's logicism. I will argue that Hankel had an important influence on Frege. In particular, Hankel's understanding of the analytic-synthetic distinction, and his argument against Kant's view of arithmetic, play an important role in Frege's understanding of his logicism in the *Foundations of Arithmetic*. Frege thinks of the distinction the same way Hankel does, and shares Hankel's basic strategy for arguing that arithmetic is analytic, rather than synthetic. Given these similarities, an important question arises about how Frege's view differs from Hankel's; I will close with some comments about the differences.

Also, here is a link to the paper, in case anyone is interested in reading it: https://philpapers.org/rec/LAWFHA

## 25 November 2020: Dr. Michael T. Stuart (Tübingen): Guilty Artificial Minds: An Experimental Study of Blame Attributions for Artificially Intelligent Agents

The concepts of blameworthiness and wrongness are of fundamental importance in human moral life. But to what extent are humans disposed to blame artificially intelligent agents, and to what extent will they judge their actions to be morally wrong? To make progress on these questions, we adopted two novel strategies. First, we break down attributions of blame and wrongness into more basic judgments about the epistemic and conative state of the agent, and the consequences of the agent’s actions. In this way, we are able to examine any differences between the way participants treat artificial agents in terms of differences in these more basic judgments about, e.g., whether the artificial agent “knows” what it is doing, and how bad the consequences of its actions are. Our second strategy is to compare attributions of blame and wrongness across human, artificial, and group agents (corporations). Others have compared attributions of blame and wrongness between human and artificial agents, but the addition of group agents is significant because these agents seem to provide a clear middle-ground between human agents (for whom the notions of blame and wrongness were created) and artificial agents (for whom the question is open).

## 18 November 2020: Natalie Clarius, B.A. (Tübingen): Automated Model Generation, Model Checking and Theorem Proving for Linguistic Applications

We present a model generator, model checker and theorem prover we developed for applications in linguistics. Alongside a live demonstration of the system, we will discuss a selection of phenomena with respect to their formal and computational tractability, as well as the theoretical foundations and limitations of such automated reasoning systems.

## 11 November 2020: Dr. Maël Pégny (Tübingen): Machine Learning and Privacy: What's Really New?

In this presentation, I will try to capture the new challenges for the respect of privacy raised by machine learning. I will use both a (very) long term perspective inspired by anthropological work on the effects of cognitive techniques and the origins of writing, and a short-term perspective based on comparisons with other types of algorithms and data treatment. I will try to show that machine learning has very specific and fundamental effects, which include challenging some of the basic categories on which our legal data protection regimen was built.

## 4 November 2020: Prof. Dr. Klaus Mainzer (München & Tübingen): Künstliche Intelligenz im globalen Wettstreit der Wertsysteme

Das „Atomzeitalter“, von dem Carl Friedrich von Weizsäcker in den 1950er und 1960er Jahren ausging, war gestern. Heute und morgen geht es um Digitalisierung und Künstliche Intelligenz (KI) – ein globales Zukunftsthema, das unsere Lebens- und Arbeitswelt dramatisch verändert. In Corona-Zeiten erhält diese Entwicklung eine zusätzliche Beschleunigung. Diese technischen Möglichkeiten treffen auf unterschiedliche weltanschauliche Resonanzböden, auf denen wie in USA oder China Big Business, Technokratien und Staatsmonopolismus gedeihen können. Wie kann ein europäisches Wertesystem dazu beitragen, dass KI zur nachhaltigen Innovation wird?

Literaturhinweise:

K. Mainzer, Künstliche Intelligenz. Wann übernehmen die Maschinen? Springer 2. Aufl. 2019 (engl. Übers. Springer 2019);

ders., Leben als Maschine: Wie entschlüsseln wir den Corona-Kode? Von der Systembiologie und Bioinformatik zu Robotik und Künstlichen Intelligenz, Brill Mentis 2020

Video des Vortrags: https://www.youtube.com/watch?v=Tf4ccAetTSM