Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction

This book provides philosophers and logicians with a broad spectrum of views on contemporary research on the problem of deduction, its justification and explanation. The variety of distinct approaches exemplified by the single chapters allows for a dialogue between perspectives that, usually, barely communicate with each other.

The contributions concern (in a possibly intertwined way) three major perspectives in logic: philosophical, historical, formal. The philosophical perspective has to do with the relationship between deductive validity and truth, and questions the alleged conclusiveness of deduction and its epistemic contribution. It also discusses the role of linguistic acts in deductive practice, and provides a cognitive-didactic contribution on how we may learn through deduction. In the historical perspective, the contributions discuss the ideas of some major historical figures, such as Bolzano, Girard, Gödel, and Peano. Finally, in the formal perspective, the mathematics of deduction is dealt with mainly from an intuitionistic-constructivist or proof-theoretic point of view, with focus on ecumenic or internalistic approaches to logical validity, on the nature and identity of proofs, and on dialogical setups.

Chapter [14] is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Includes contributions by well-established researchers in the field of constructive logic, proof-theory, etc Discusses and analyses hotly debated issues relating to the concept of deduction Shows the reader a variety of positions and schools of thoughts and how they each interact

Autorentext

I obtained my Bachelor Degree in Philosophy at the "Federico II" University of Naples in 2009, and my Master Degree in Philosophy at the "La Sapienza" University of Rome in 2014. I achieved the Doctoral Degree in Philosophy in 2019, with a dissertation about Dag Prawitz's theory of grounds under the conjoint direction of prof. Gabriella Crocco (Aix-Marseille University) and prof. Cesare Cozzo ("La Sapienza" University of Rome). I am currently teaching History and Philosophy of Science, Logic and Philosophy of Logic, and Philosophy of Mathematics, at the Science and Philosophy Departments of the Aix-Marseille University.

Broadly, I deal with mathematical logic and philosophy of logic. More specifically, I am interested into constructive logics and proof-theoretic semantics (particularly Prawitz's semantics) stemming from the intuitionistic tradition. As a parallel project, I investigate whether Kreisel's informal rigour and Goedel's absolute provability can be read through the lens of contemporary constructivist approaches. A minor interest concerns a socio-epistemological study of scientific controversies.

Inhalt

1. Introduction: deduction at the crossroads (Antonio Piccolomini d'Aragona).- 2. The interdependence between the concepts of valid inference and proof revisited (Dag Prawitz).- 3. The completeness theorem? So what! (Goran Sundholm).- 4. Godel's absolute proofs and Girard's Ludics. Mutual insights (Gabriella Crocco and Myriam Quatrini).- 5. Dummett, analytic and synthetic deductions (Cesare Cozzo).- 6. From proof-objects to grounds (Enrico Moriconi).- 7. On an ecumenical natural deduction with stoup - Part I: the propositional case (Luiz Carlos Pereira and Elaine Pimentel).- 8. Martin-Lof on the validity of inference (Ansten Klev).- 9. Molecularity in the theory of meaning and the topic neutrality of logic (Nils Kurbis and Bernhard Weiss).- 10. Assertion, assumption and deduction (Peter Pagin).- 11. Deduction and ampliativity: a critical appraisal (Emiliano Ippoliti).- 12. A new conjecture about identity of proofs (Paolo Pistone).- 13. Godel's introduction to deduction (Milos Adzic).- 14. Karl Popper on deduction (Thomas Piecha).- 15. An epistemological view on the Peano School Axiomatics (Paola Cantu).- 16. Inferential quantification and the w-rule (Constantin Brincus).- 17. Chains of inferences in proof by induction: a cognitive analysis (Samuele Antonini and Bernardo Nannini).- 18. From strategies to derivations and back. An easy completeness proof for first-order intuitionistic dialogical logic (Davide Catta).- Index.