Let's prove it! Reasoning in different contexts

CIVIS focus area: Society, culture, heritage
Open to: Bachelor's

Master's

Phd

PhD candidates/students
Field of studies: Computer Science and IT

Law

Natural Sciences and Mathematics

Social Science and humanities
Type: Blended Intensive Programmes (BIP)
Course dates: 6 March 2025 - 11 July 2025

The course is meant to be the continuation of the CIVIS programme: “Proofs, arguments and dialogues: history, epistemology and logic of justification practices” (held in 2022 in Aix-Marseille and Tübingen) and the CIVIS programme “Meanings and Understanding via Proofs. Logical and Epistemological Approaches” (held in Bucharest 2023).

The BIP is concerned with the significance of the concept of proof as it is defined and used in different fields of knowledge (e.g., logic, computer science, mathematics, physics, social sciences, linguistics, and law) and with its role in the development of critical thinking abilities. The concept of proof has been central to theoretical thinking since its beginning in Ancient Greece, and proofs are the most rigorous and solid way to establish truth and acquire knowledge.

There is a variety of proofs depending on their applications in different areas of inquiry. For example, typically, a mathematical proof, as used in logic and computer science, will have to refer to abstract concepts or structures and be conclusive, whereas a proof in physics, while still being required to be conclusive, will involve some form of empirical or experimental elements. Likewise, proofs are used in law, social sciences, and everyday argumentation practices in a more liberalized form. For instance, empirical evidence and deductive arguments are important proofs in courts of law, political and economical debates, statistical inquiries, historical research, philosophy of science, and education (pedagogy).

The course aims at providing CIVIS students with the necessary thinking abilities for understanding and acting responsibly in a globalized knowledge society. One of the underlying ideas of the School is that acquisition of truth and knowledge is a by-product of the way in which epistemic agents use their language for arguing and proving their ideas in the community they live in.

Main topics addressed

The program provides to the students knowledge related to the following fields:

Introduction to inferences and proofs and their use in theoretical contexts (as in science and philosophy) and in practical contexts (as in communication, argumentation and education)

Logic as the science of proofs
The emergence of logic from argumentative practices in ancient Greece
The epistemological relevance of inferences and proofs
Proofs in mathematics
Proofs and arguments in law
Teaching and learning proofs: their use in education

Learning outcomes

Students will get acquainted with current logical and epistemological approaches to inferences and proofs, as well as to the logical, epistemological and conceptual connections between those topics. This will allow them to adopt a strongly transdisciplinary point of view on some of the most important theories that are discussed or used in philosophy, linguistics, logic, mathematics, and computer science.
Students will also learn about teaching approaches fostering the development of competences in argumentation and proof and about how these competences can be applied in juridical and other practices. Participation in the programme will provide students with 5 ECTS credits.
Roughly 3 ECTS correspond to the virtual component (attending the online talks, tutorials,and reading groups, making virtual presentations, and doing individual work).
Roughly 2 ECTS correspond to the physical part (attending the lectures, doing some individual or team work, and making physical presentations).

Dates: 6 March - 11 July 2025	Total workload: 125 hours
Format: Blended	ECTS: 5*
Location: Athens, Greece	Language: English (B2)
Contact: letsproveit2025@outlook.com

*Recognition of ECTS depends on your home university.

Physical mobility

The physical mobility part will be running from 7 to 11 July 2025. The physical part will be held in Athens, Greece.

Moreover, the schedule of the physical part is set out as follows:

Monday, 7 July 2025, 9:00-13:00 CET and 17:00-21:00 CET, teaching of courses.
Tuesday, 8 July 2025, 9:00-13:00 CET and 17:00-21:00 CET, teaching of courses.
Wednesday, 9 July 2025, 9:00-13:00 CET and 17:00-21:00 CET, teaching of courses.
Thursday, 10 July 2025, half-day excursion, as well as time for students to prepare their physical presentations.
Friday, 11 July 2025, 9:00-13:00 CET and 17:00-21:00 CET, students' physical presentations.

Virtual part

The virtual part will be running from 6 March to 27 June 2025.

Moreover, the schedule of the virtual part is set out as follows:

6 March 2025: Introductory meeting.
13 March 2025: Online talk 1: Propositional logic.
20 March 2025: Online talk 2: First-order logic.
26 March 2025: Meeting 1 for students to form groups, choose topics, etc.
28 March 2025: Meeting 2 for students to form groups, choose topics, etc.
10 April 2025: Online talk 3.
30 April 2025: Online talk 4.
5 May 2025: (Student-) group I: discussion of papers
6 May 2025: Group II: discussion of papers.
7 May 2025: Group III: discussion of papers.
8 May 2025: Group IV: discussion of papers.
9 May 2025: Group V: discussion of papers.
29 May 2025: Online talk 5.
23 June 2025: Group I: virtual presentations.
24 June 2025: Group II: virtual presentations.
25 June 2025: Group III: virtual presentations.
26 June 2025: Group IV: virtual presentations.
27 June 2025: Group V: virtual presentations.

Requirements

This course is open to Bachelor's, Master's and PhD students at CIVIS member universities with a backround in the scientific fields of Logic, Philosophy, Linguistics, Mathematics, Computer Science, Law and Educational Sciences.

Needed skills: Critical thinking, rigorous reasoning, appreciation of the importance of proofs in theoretical and practical contexts. It is also recommended that students have already taken an introductory course in Epistemology, Philosophy of language, Philosophy of Science, Logic, Law, or Mathematical Education.

Applicants should also submit a transcript of records for undergraduate courses (if they are undergraduate students) or a transcript of records of graduate courses (if they are MA/MSc students).

NB: Visiting Students - Erasmus Funding Eligibility

To be eligible for your selected CIVIS programme, you must be a fully enrolled student at your CIVIS home university at the time you will be undertaking the programme. Click here to learn more about the eligibility criteria.

This course is also open to students with the same academic profile, who are enrolled at a CIVIS strategic partner university in Africa. Please check here, if you can apply and this particular course is open to applications from your university. Successful applicants will receive an Erasmus+ grant covering travel and subsistence costs during their stay. Applicants should be willing to extend their stay at the host university for 1-3 weeks for additional research and/or training purposes.

Application process

Send your application by filling in the online application form by 31 October 2024, including:

CV
Motivation letter
Level of english (According to CEFR)
Transcript of records

Apply now

Assessment

After its completion the BIP will be evaluated by the students and discussed by the professors with a view to possibly improving the programme.

More details about the programme are available on the dedicated webpage.

Blended Intensive Programme

This CIVIS course is a Blended Intensive Programme (BIP): a new format of Erasmus+ mobility which combines online teaching with a short trip to another campus to learn alongside students and professors across Europe. Click here to learn more about CIVIS BIPs.

GDPR Consent

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Constantin C. Brîncuș, Researcher in the Department of Logic and Metaphysics of the Institute of Philosophy and Psychology (Romanian Academy). He teaches courses on various logical and philosophical topics in different faculties of the University of Bucharest.
Annalisa Cusi is an Associate Professor in Mathematics Education at the Department of Mathematics at Sapienza Università di Roma. Her main research interests are: (1) early-algebra and the teaching of algebra as a thinking tool, (2) analysis of teaching/learning processes, with a focus on the role played by the teacher during classroom discussions, (3) methodologies for pre- and in-service teacher education, (4) analysis of the dynamics that characterize teachers and researchers’ interactions within communities of inquiry, (5) formative assessment practices in Mathematics within technology-enhanced classrooms, (6) design and use of digital tools and resources at University level.
Antonio Piccolomini d’Aragona is a DFG-researcher at the University of Tübingen, with an individual project on the applicability of Kuhn’s and Lakatos’ theories to the History of Logic, in particular to the opposition between realism and constructivism in Logic and the Foundations of Mathematics. He also teaches Philosophy of Logic at the University of Siena. His main areas of interest are Proof-Theory and Proof-Theoretic Semantics, and the relation between the latter and (the philosophical aspects of) Intuitionistic Type Theory.
Thomas Piecha is a philosopher, physicist, and computer scientist. He regularly lectures on logic and theoretical computer science at the University of Tübingen, where this year he received the teaching award of the board of studies at the Department of Computer Science. He has made contributions to proof-theoretical and dialogical approaches in logic as well as to the logical writings of Karl Popper and is interested in the logical and physical foundations of computer science.
Yannis Stephanou is an Associate Professor of philosophy at the National and Kapodistrian University of Athens. His research focuses on philosophical logic, but extends to philosophy of language, metaphysics and ancient philosophy. He has taught various branches of philosophy.