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Meanings and understanding via proofs - Logical and epistemological approaches

Learn more about logical and epistemological approaches to meanings and understanding starting from the fundamental role that inferences and proofs play in the use of language in mathematics, philosophy, natural and social sciences, and many other areas

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CIVIS focus area
Society, culture, heritage
Open to
  • Bachelor's
  • Master's
  • Phd
Field of studies
  • Computer Science and IT
  • Natural Sciences and Mathematics
  • Social Science and humanities
  • Blended Intensive Programmes (BIP)
Course dates
5 June - 21 July 2023

This Blended Intensive Programme aims to provide the CIVIS students with the necessary thinking abilities for understanding and acting responsibly in a globalised knowledge society. One of the underlying ideas of the project is that meanings and understanding are by-products of the way in which epistemic agents use their language in the community they live in.

The inferentialist idea that meanings and understanding are better explained if we consider the use of words and sentences in inferences and proofs was advanced by the logicians, mathematicians, and philosophers G. Gentzen, R. Carnap, and L. Wittgenstein in the 1930s and then developed further by D. Prawitz, M. Dummett and R. Brandom, among others.

The inferentialist programme has been extended extensively in the meanwhile in logic (logical inferentialism), in philosophy (in philosophy of language and in philosophy of science), in mathematics and computer science (especially in the area of formalizing mathematics and within the proof mining programme), and in linguistics (the syntactical programmes).

This course will provide logical and epistemological approaches to meanings and understanding starting from the fundamental role that inferences and proofs play in the use of language in mathematics, philosophy, natural and social sciences, as well as in the teaching and learning of formal sciences, or in everyday argumentation and interactions.

This Blended Intensive Programme will provide courses on proof-theoretic semantics, logical inferentialism, propositional and quantificational reasoning, proof-theoretical aspects of meanings and understanding, epistemology of reasoning as well as on didactics of mathematics.

The objectives of the project are thus to:

  • Provide the necessary logical and epistemological instruments for assessing the use of language in theoretical contexts (as in inferences and proofs) and in practical contexts (as in communication, argumentation, and education).
  • Offer a clear-cut representation of the way in which the use of words and sentences in inferences and proofs determines meanings and understanding.
  • Explain the epistemological relevance of meanings and understanding for communication, argumentation, and practical activities.
  • Provide students with didactical tools for assessing the role of meanings of formal languages in the teaching and learning of proofs.

Main topics addressed

  • Inferentialism
  • Proof-theoretic semantics
  • Incompleteness phenomena
  • Propositional, quantificational, and modal reasoning
  • Proof-theoretical aspects of meanings and understanding
  • Epistemology of reasoning
  • Didactics of mathematics

Learning outcomes

Students will get acquainted with current logical and epistemological approaches to meanings and understanding via inferences and proofs, as well as on the logical, epistemological, and conceptual connections among these topics. This will allow them to adopt a strongly trans-disciplinary point of view on some of the most influential theories and research areas in philosophy, linguistics, logic, mathematics, and computer science. Moreover, students will also learn about the didactics of formal methods for conveying their knowledge. 

Dates: 5 June - 21 July 2023 Total workload: 75 hours
Format: Blended ECTS: 3*
Location: Bucharest, Romania Language: English (B2) 

*Recognition of ECTS depends on your home university.

Physical mobility

The physical part of the School will consist in five full days of courses (comprising lectures and seminars) that will take place at the University of Bucharest, Romania, in the period 17 to 21 July 2023. These courses will be taught by leading professors and scholars in logic, epistemology, philosophy of science, pedagogy of logic and mathematics (among others) from the partner universities of CIVIS.

Virtual part

The virtual component of this course will consist in online meetings that will take place from 5 June to 21 July, before the physical part of the course in Bucharest as well as in several online presentations that will be given by some invited speakers during the physical part of the School. In addition to this, the professors will also offer online supervision based on individual meetings with the students, when necessary.


This course is open to Bachelors', Masters' and PhD students at CIVIS member universities.

The students should be proficient in English and it is recommended that they have already taken an introductory course in epistemology, philosophy of language, philosophy of science or logic.

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.

Application process

Interested students should apply by filling in the online application form by 28 February 2022. 

Applications will be evaluated based on:

  • The adequacy of their application for the topics of the School
  • Their CV (courses, grades)
  • Their motivation letter relevance

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Oral evaluation based on a presentation given by each student (as a result from a team student work) at the end of the School. The students will also receive feedback from the professors after they present.

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.

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  • Annalisa Cusi, professor at the Mathematics Department of Sapienza Università di Roma. Her research interests are in tools and methods for teacher education; formative assessment in Math Education, design of digital tasks to support students’ learning and metacognitive processes; innovation in the teaching/learning of algebra and early algebra.
  • Mircea Dumitru, professor of logic and theoretical philosophy at the University of Bucharest. His research interests are in modal logic, philosophy of language, and analytical metaphysics of modality.
  • Valentin Goranko, professor of logic and theoretical philosophy at the Department of Philosophy, Stockholm University. His research interests are in logic: theory and applications to artificial intelligence, agency and multi-agent systems, computer science, and game theory.
  • Reinhard Kahle, Carl Friedrich von Weizsäcker Professor for history and theory of science at the University of Tübingen. His research interests are in mathematical and philosophical logic, philosophy of mathematics, philosophy of language, logic history, and social relevance of science.
  • Thomas Piecha, philosopher, physicist, and computer scientist. He has published on proof-theoretic and dialogical approaches in logic and currently works on proof-theoretic semantics.