Uploaded May 2021 | Updated September 2026, 3 hours ago
Recorded in the Carl Friedrich von Weizsäcker Colloquium on the 5th of May 2021.
Dr. Antonio Piccolomini d'Aragona (Aix-Marseille): Kreisel's Informal Rigour and Gödel's Absolute Provability. A tentative reading through and for Prawitz's semantics
In spite of their philosophical relevance, Kreisel’s theory of informal rigour and Gödel’s concept of absolute provability have proved elusive to rigorous mathematised treatments. In my talk, I will set out to connect Kreisel’s and Gödel’s ideas to Prawitz’s proof-based semantics. Prawitz’s semantics has been put forth and developed independently of Kreisel and Gödel, but some of its basic tenets may nonetheless match those of informal rigour and absolute provability. Both Kreisel and Gödel aim at bringing provability back into mathematical practice – against the post-Fregean and post-Hilbertian formalistic attitude – as well as at overstepping formal derivability – given Gödel’s and Turing’s limiting results. In order to do this, provability must become informal (i.e. independent of formal languages and systems) and absolute (i.e. formalism-free and/or universally applicable). This may be in line with the intuitionistic idea of giving provability a “semantic” role, an idea of which Prawitz’s semantics is a well-known instance. As a result, I argue that Prawitz’s semantics shares some issues with Kreisel’s informal rigour, while the link with Gödel’s absolute provability is more difficult to be established.
Recorded in the Carl Friedrich von Weizsäcker Colloquium on the 5th of May 2021.
Dr. Antonio Piccolomini d'Aragona (Aix-Marseille): Kreisel's Informal Rigour and Gödel's Absolute Provability. A tentative reading through and for Prawitz's semantics
In spite of their philosophical relevance, Kreisel’s theory of informal rigour and Gödel’s concept of absolute provability have proved elusive to rigorous mathematised treatments. In my talk, I will set out to connect Kreisel’s and Gödel’s ideas to Prawitz’s proof-based semantics. Prawitz’s semantics has been put forth and developed independently of Kreisel and Gödel, but some of its basic tenets may nonetheless match those of informal rigour and absolute provability. Both Kreisel and Gödel aim at bringing provability back into mathematical practice – against the post-Fregean and post-Hilbertian formalistic attitude – as well as at overstepping formal derivability – given Gödel’s and Turing’s limiting results. In order to do this, provability must become informal (i.e. independent of formal languages and systems) and absolute (i.e. formalism-free and/or universally applicable). This may be in line with the intuitionistic idea of giving provability a “semantic” role, an idea of which Prawitz’s semantics is a well-known instance. As a result, I argue that Prawitz’s semantics shares some issues with Kreisel’s informal rigour, while the link with Gödel’s absolute provability is more difficult to be established.
