Is it true? Let’s prove it! Educational, epistemological and logical approaches to critical thinking

This BIP continues the “Proofs, arguments and dialogues: history, epistemology and logic of justification practices” (Aix-Marseille and Tübingen, 2022), “Meanings and Understanding via Proofs. Logical and Epistemological Approaches” (Bucharest, 2023), and “Let’s prove it! Logical, epistemological, educational and juridical aspects of critical thinking” (Athens, 2025) programmes. 

It explores the concepts of argumentation and proof as they are defined and used in different fields of knowledge and cultural contexts, and examines their role in the development of critical thinking. Arguments, proofs and other forms of justification are central to the production and validation of knowledge, but their characteristics vary across disciplines and epistemologies of inquiry. 

In mathematics, logic and computer science, proofs generally refer to abstract concepts and structures and are expected to be conclusive. Other disciplines and everyday contexts rely on different combinations of deductive reasoning, empirical evidence and argumentative practices. The programme therefore brings together perspectives from logic, philosophy, mathematics, computer science, linguistics, pedagogy and mathematics education. 

Through online activities and a five-day physical mobility at Sapienza University of Rome, students will investigate how language, reasoning, argumentation and proof contribute to the acquisition of knowledge and to responsible participation in a globalised knowledge society. Particular attention will also be devoted to educational approaches to argumentation and proof and to the ways in which artificial intelligence tools can support, challenge or transform human reasoning.

Participation in both the virtual and physical components is compulsory.

The programme addresses the following topics:

• Inferences, arguments and proofs in theoretical and practical contexts
• Logic as the science of valid reasoning and proof
• Logical and epistemological approaches to argumentation and proof
• The role of language in reasoning and justification
• Proofs in mathematics and computer science
• Argumentation and justification across different disciplines and cultures
• Teaching and learning argumentation and proof
• Educational approaches to the development of critical thinking
• Artificial intelligence tools and human reasoning
• The use of digital and collaborative environments to support argumentation and discussion

By the end of the programme, students will:

• understand key logical and epistemological approaches to arguments, inferences and proofs;
• analyse how arguments and proofs are constructed and communicated through language;
• recognise the epistemological role of argumentation and proof in justifying beliefs and producing knowledge;
• compare justification practices across different disciplines and cultural contexts;
• critically assess arguments and proofs used in theoretical, educational and other practical settings;
• understand educational approaches that foster the development of argumentation, proof and critical-thinking competences;
• collaborate effectively in interdisciplinary and intercultural groups;
• communicate and discuss complex ideas through oral presentations and collaborative activities;
• reflect critically on the potential and limitations of artificial intelligence tools in relation to human reasoning. 

The physical component will take place from 5 to 9 July 2027 at the Department of Mathematics of Sapienza University of Rome.

It will consist of five days of academic and collaborative activities, including lectures, seminars, workshops, round-table discussions and student presentations. The activities will be led and supervised by scholars in logic, epistemology, philosophy, mathematics, computer science, linguistics, pedagogy and mathematics education, together with invited external stakeholders.

The physical component will consolidate and extend the knowledge developed during the virtual phase. Lectures will introduce key concepts and current debates, while workshops and round tables will provide opportunities for active participation and interdisciplinary exchange. Students will refine the collaborative work begun online and connect theoretical perspectives with concrete examples and educational practices.

The provisional schedule is:

• 5–7 July: lectures, seminars, workshops and round-table discussions, from 09:00 to 13:00 and from 15:00 to 19:00;
• 8 July: half-day excursion and individual or group work in preparation for the final presentations;
• 9 July: final student presentations and closing session.

The programme includes 32 contact hours. The activities conducted on 8 July will also support intercultural exchange, community building and preparation of the students’ final work.

Assessment will be formative and continuous throughout both the virtual and physical components. It will focus on students’ participation in collaborative activities, engagement with the assigned readings, ability to analyse and discuss arguments and proofs, and development of interdisciplinary understanding.

Students will prepare and deliver group presentations during both phases of the programme. These presentations, together with participation in paper discussions, workshops and round tables, will make their reasoning, communication and collaboration skills visible.

Learning objectives and assessment criteria will be clarified at the beginning of the programme. Students will receive continuous and dialogic feedback from lecturers and peers during online discussions, collaborative work, workshops and presentations. They will also be encouraged to evaluate one another’s contributions and reflect on their own learning.

Successful completion will require active participation in the virtual and physical activities, completion of the assigned individual and group work, and delivery of the virtual and final presentations.

Motivation Letter

CV

Other

Applications will be evaluated on the basis of:

• the applicant’s motivation to participate in the programme;
• the relevance of their academic background, interests or experience to the themes of reasoning, argumentation, proof, epistemology or education;
• their willingness to engage in interdisciplinary and intercultural collaboration;
• their ability to work and communicate effectively in English;
• the overall disciplinary, institutional and geographical balance of the selected group.

Priority may be given to applicants whose profile contributes to the interdisciplinary character of the programme and who clearly explain how participation in the BIP relates to their studies, research interests or future professional activities.

• Constantin Brîncuș is Assistant Professor in the Department of Theoretical Philosophy at the University of Bucharest. His teaching and research concern logic, epistemology, metaphysics and related philosophical topics.
• Paola Cantù is a CNRS Research Director at the Centre Gilles-Gaston-Granger and the Department of Philosophy of Aix-Marseille Université. Her research interests include the philosophy and history of logic and mathematics, epistemology, and the relationships between mathematical practices, reasoning and argumentation.
• Annalisa Cusi is Professor of Mathematics Education at the Department of Mathematics of Sapienza University of Rome. Her research focuses on the teaching and learning of algebra, classroom mathematical discussions, formative assessment, teacher education, and the design and use of digital resources and artificial intelligence tools in mathematics education. She is the academic coordinator of the programme.
• Vladimiros Katranidis is a PhD candidate in the Department of History and Philosophy of Science at the National and Kapodistrian University of Athens. His research interests concern logic, philosophy of science, epistemology and the history of reasoning practices.
• 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 is a researcher in the Department of Computer Science at the University of Tübingen. His work focuses on logic, proof theory, dialogical approaches to reasoning and the logical foundations of computer science.

Additional lecturers, researchers and external stakeholders from the partner institutions will contribute to the online talks, seminars, workshops and round-table discussions. The complete list of lecturers will be published with the detailed programme.

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.

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