Carl Friedrich von Weizsäcker-Kolloquium

Mittwochs 17-18h

Im Carl Friedrich von Weizsäcker-Kolloquium werden wöchentlich Vorträge von Gästen und Mitarbeitern des CFvW-Zentrums angeboten, die sich im weiten Sinne mit Themen befassen, die am Zentrum diskutiert werden.

Das Kolloquium findet mittwochs von 17-18 Uhr statt, bis auf weiteres als Online-Veranstaltung über die Zoom-Plattform (und wird in der Regel aufgezeichnet).
Zur Teilnehme benutzen Sie bitte diesen Link.

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

Um die Ankündigungen zu den Kolloquiumsvorträgen zu erhalten, schicken Sie bitte eine e-mail an: Aleksandra Rötschke.

Die vergangenen Vorträge können auf dem YouTube Kanal des Zentrums gefunden werden. 

Aktueller Vortrag

Mittwoch 24.2.2021, 17 Uhr s.t.

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.

Vortragsliste

30.6.2021: Prof. Dr. Mathias Frisch (Hannover): TBA

21.4.2021: Dr. Christian Feldbacher-Escamilla (Düsseldorf): TBA

24.2.2021: 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.

 

17.2.2021: 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.

10.2.2021: 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'.

3.2.2021: 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).

27.1.2021: 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.

Lecture notes

20.1.2021: 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.

Lecture notes

13.1.2021: 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.

Lecture notes

16.12.2020: Prof. Dr. Klaus Mainzer (München & Tübingen): Verification and Standardization of Artificial Intelligence – Results of the German Steering Group (HLG) of AI Standardization Roadmap

9.12.2020: 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.

2.12.2020: 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

25.11.2020: 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).

18.11.2020: 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.

11.11.2020: 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.

4.11.2020: 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