Prawitz has recently developed a theory of epistemic grounding that differs in many respects from his earlier semantics of arguments and proofs. An innovative approach to inferences yields a new conception of the intertwinement of the notions of valid inference and proof. We aim at singling out three reasons that may have led Prawitz to the ground-theoretic turn, i.e.: a better order in the explanation of the relation between valid inferences and proofs; a notion of valid inference based on which (...) valid inferences and proofs are recognisable as such; a reconstruction of the deductive activity that makes inferences capable of yielding justification per se. These topics are discussed by Prawitz with reference to a very general and ancient question: why and how correct deduction has the epistemic power to compel us to accept its conclusions, provided its premises are justified? We conclude by remarking that, in spite of some improvements, the ground-theoretic approach shares with the previous one a problem of vacuous validity which, as Prawitz himself points out, blocks in both cases a satisfactory explanation of epistemic compulsion. (shrink)

We define a class of formal systems inspired by Prawitz’s theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to epistemically compel to accept the conclusion. Validity is defined in terms of typed objects, called grounds, that reify evidence for given judgments. An inference is valid when a function exists from grounds for the premises to grounds for the conclusion. Grounds are described (...) by formal terms, either directly when the terms are in canonical form, or indirectly when they are in non-canonical form. Non-canonical terms must reduce to canonical form, and two terms may be said to be equal when they converge towards equivalent grounds. In our systems these properties can be proved through rules distinguished according to whether they concern types or logic. Type rules involve type introduction and elimination, equality for application of operational symbols, and re-writing equations for non-canonical terms. The logic amounts to a sort of intuitionistic system in a Gentzen format. To conclude, we show that each system of our class enjoys a normalization property. (shrink)

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

In Prawitz’s semantics, the validity of an argument may be defined, either relatively to an atomic base which determines the meaning of the non-logical terminology, or relatively to the whole class of atomic bases, namely as logical validity. In the first case, which may be qualified as local, one has to choose whether validity of arguments is or not monotonic over expansions of bases, while in the second case, which may be qualified as global, one has to choose whether the (...) reduction functions which justify non-primitive inferences are or not base-depending. I claim that these oppositions enjoy some conceptual symmetries, and that these symmetries may be understood as putting restrictions on one’s choice both at the local and at the global level. This produces two different proof-theoretic semantics in line with Prawitz’s tenets. However, I also argue that the symmetries stem from a deeper interaction within Prawitz’s semantics, i.e. non-logical meanings vs interpretation of rules. This interaction is in turn based on some primitive ingredients which, when suitably combined, produce other two Prawitz-compatible readings. The four readings form a diagram where some order relations hold. I finally claim that this diagram is complete, namely that, if we combine the ingredients in ways other than those giving rise to the four readings above, we obtain nothing new, or nothing compatible with general semantic requirements. Thus, symmetries between the local and the global level, and interaction between non-logical meaning and interpretation of rules, produce a complete classification of potential Prawitzian semantics. (shrink)

This broad and insightful book presents current scholarship in important subfields of philosophy of science and addresses an interdisciplinary and multidisciplinary readership. It groups carefully selected contributions into the four fields of I) philosophy of physics, II) philosophy of life sciences, III) philosophy of social sciences and values in science, and IV) philosophy of mathematics and formal modeling. Readers will discover research papers by Paul Hoyningen-Huene, Keizo Matsubara, Kian Salimkhani, Andrea Reichenberger, Anne Sophie Meincke, Javier Suárez, Roger Deulofeu, Ludger Jansen, (...) Peter Hucklenbroich, Martin Carrier, Elizaveta Kostrova, Lara Huber, Jens Harbecke, Antonio Piccolomini d'Aragona and Axel Gelfert. This collection fosters dialogue between philosophers of science working in different subfields, and brings readers the finest and latest work across the breadth of the field,illustrating that contemporary philosophy of science has successfully broadened its scope of reflection. It will interest and inspire a wide audience of philosophers as well as scholars of the natural sciences, social sciences and the humanities. The volume shares selected contributions from the prestigious second triennial conference of the German Society for Philosophy of Science/ Gesellschaft für Wissenschaftsphilosophie (GWP.2016, March 8, 2016 - March 11, 2016). (shrink)

I provide a general introduction to the notion at issue in this volume, i.e. deduction, and to some akin notions like inference and reasoning. I also argue that logic is, or should be concerned with three attitudes: an archaeological attitude, a nomological attitude, and an aetiological attitude. Then, I sum up the content of the contributions in this volume.