About

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.