This page is dedicated to my DFG Research Project Revolutions and paradigms in logic. The case of proof-theoretic semantics. The project (started October 1st 2024) is part of the activities of the Carl Friedrich von Weizsäcker Center of the University of Tübingen.
Kuhn’s theories on scientific revolutions and paradigms, and Lakatos’ theories on scientific research programmes constitute two major contributions to the philosophical reconstruction of the historical-conceptual development of science. Both these approaches have been fruitfully applied to empirical sciences such as physics and chemistry; it is on the contrary much debated whether they can be employed also for the assessment of formal sciences. While the applicability of Kuhn’s and Lakatos’ theories to mathematics is somewhat debated, the issue is instead mostly unexplored when referred to the more specific field of (formal) logic.
In my project, I aim at addressing the topic of a potential Kuhnian and Lakatosian rendering of post-Fregean and post-Hilbertian logic. Although this general question is of course expected to be dealt with as a starting point of my investigation, I shall otherwise endorse a sort of case-wise strategy, trying to draw broad conclusions from smaller but significant samples. In particular, I shall focus on the crucial case-study of the logical opposition between realism and (anti-realist) constructivism. My pivotal claim is the following: logic is currently dominated by a realist Kuhnian paradigm, constituted by the combination of model theory and set theory. Against this, one can detect a (currently) minor but well-established constructivist Lakatosian research programme, which I shall mainly understand as given by the combination of Prawitz’s semantics and Martin-Löf’s intuitionistic type theory. The realist paradigm arose in response to a critical moment in the history of logic, i.e. the discovery of semantic and set-theoretic paradoxes and the proof of limiting results such as Gödel’s incompleteness theorems. This determined the abandonment of previous foundational attitudes, and the adoption of new core-concepts for the analysis of validity and the foundations of mathematics. However, some ingredients from the previous frameworks survived, and merged into a sequence of theories which led to today’s wide field of proof-theoretic semantics.
The proposed approach is expected to have a number of advantages. First, it permits to ground in a philosophical-historical perspective one of the classical themes of philosophy, otherwise addressed in usually metaphysical terms, i.e. the fight between realists and anti-realists. Second, via Kuhn’s influence, the perspective may be also sociological; more specifically, one may understand the competition between theories also as a fight between different “geo-theoretical” traditions, each with its places and “champions”. Third (but the list may not be exhaustive), the research may constitute the first step towards a more ambitious project, i.e. a history of general proof-theory from Gentzen to the present time, a crucial, but so far missing piece in the otherwise variegated tradition of proof-theoretic studies.
2025
Some results in non-monotonic proof-theoretic semantics, in Studia Logica, https://doi.org/10.1007/s11225-025-10195-9 [article in journal]
Intensionality of consequence and identity of proofs in Prawitz's Theory of Grounds, in Logica Universalis, https://doi.org/10.1007/s11787-025-00370-w [article in journal]
A note on a Kuhnian-Lakatosian reading of the debate between realism and constructivism in logic, in Isonomia [article in journal]
with D. Catta, Informal and absolute provability: from Kreisel and Gödel to Prawitz and Girard, in Philosophical Inquiries [article in journal]
* = invited
July 2025 LATD 2025 at the University of Siena. "Uniform validity of atomic Kreisel-Putnam rule in monotonic proof-theoretic semantics"
May 2025* Mathematical Logic Seminar at the University of Lisbona. "Uniform validity of atomic Kreisel-Putnam rule in monotonic proof-theoretic semantics"
May 2025* PhilMatMed 2025 at the Aix-Marseille University. "Normalisation et sémantique des preuves. Vers une interpretation Hilbertienne de la proof-theoretic semantics"
April 2025* Logica Universalis Webinar. "Intensionality of consequence and identity of proofs in Prawitz's Theory of grounds"
April 2025* Seminar of the Department of Mathematics "Renato Caccioppoli" of the "Federico II" University of Naples. "Proof-theoretic semantics: approcci, completezza e problemi aperti"
February 2025* 5th Symposium on Proof-Theoretic Semantics at the Institute of Philosophy of the University of London. "From normalisation to proof-theoretic semantics: the semantic role of harmony, atomic bases and reductions".
January 2025* Logic in Bochum Colloquia at the Ruhr University of Bochum. "From normalisation to proof-theoretic semantics: the semantic role of harmony, atomic bases and reductions".
January 2025 Carl Friedrich von Weizsäcker Colloquium at the University of Tübingen. "Some ideas for a Kuhnian-Lakatosian reading of the opposition between realism and constructivism in logic and the foundations of mathematics".
November 2024* Naples Seminar Series in the History of Logic at the "Federico II" University of Naples. "Atavismo logico".