Dag Prawitz’s theory of grounds proposes a fresh approach to valid inferences. Its main aim is to clarify nature and reasons of their epistemic power. The notion of ground is taken to denote what one is in possession of when in a state of evidence, and valid inferences are described in terms of operations that make us pass from grounds we already have to new grounds. Thanks to a rigorously developed proof-as-chains conception, the ground-theoretic framework permits Prawitz to overcome some (...) conceptual difficulties of his earlier proof-theoretic explanation. Though from different points of view, anyway, the two accounts share an issue of recognizability of relevant operational properties. (shrink)

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.

One of Etchemendy's arguments against the Tarskian and model‐theoretic notion of logical truth is based on a reduction principle according to which a universally quantified sentence is true if, and only if, all of its instances are logically true. The reduction of logical truth to mere truth reveals that the concept of validity at play in Tarski and in model‐theory relies upon extra‐logical assumptions. A similar reduction had already been put forward by Prawitz, although not with focus on extra‐logical assumptions. (...) Prawitz's reduction concerns rather the possibility of understanding the Tarskian and model‐theoretic approach as implying any epistemic modality. We take into account a possible strategy that an advocate of Tarski and model‐theory may use against Etchemendy's objection, and argue that this strategy fails with respect to Prawitz's criticism. This permits us to shed light upon a difference between Prawitz's and Etchemendy's standpoints: while Etchemendy's reduction shows that the Tarskian and model‐theoretic notion of logical truth cannot be understood as an adequate formal counterpart of truth‐preservation solely by virtue of logical form, Prawitz's reduction insists on the fact that truth‐preservation solely by virtue of logical form is insufficient for epistemic modality to obtain. (shrink)

This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes (...) an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved. (shrink)

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. (shrink)

1. Esistenza e libertà -- 2. Interiorità e persona -- 3. Verità e linguaggio -- 4. Storia e politica.

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.

This paper examines the view held by Francesco Piccolomini (1523-1607) on the relation between prime matter and extension. In his discussion of prime matter in the Libri ad scientiam de natura attinentes Piccolomini develops a theory of prime matter that incorporates crucial elements of the viewpoint adhered to by the Neoplatonist Simplicius. The originality of Piccolomini’s undertaking is highlighted by contrasting it with the ideas found in Jacopo Zabarella’s De rebus naturalibus . The case of Piccolomini (...) shows that, in order to classify early modern metaphysical theories of prime matter, the category ‘prime matter as sheer dimensionality’ is indispensable. (shrink)

Francesco Piccolomini (1523–1607) interprets Aristotle’s theory of friendship from a Christian-Neoplatonic perspective. This paper focuses on the various (ancient, medieval, and Renaissance) sources of Piccolomini’s interpretation and shows that he succeeds in expounding a coherent doctrine in which the Aristotelian ideal of civic friendship is integrated into a theocentric ethics of spiritual love.

Francesco Piccolomini interprets Aristotle’s theory of friendship from a Christian-Neoplatonic perspective. This paper focuses on the various sources of Piccolomini’s interpretation and shows that he succeeds in expounding a coherent doctrine in which the Aristotelian ideal of civic friendship is integrated into a theocentric ethics of spiritual love.

‘Honor’ is one of the key notions in Renaissance ethics. The present paper analyzes the honor code which Francesco Piccolomini articulates in his Vniuersa Philosophia de Moribus. Drawing not only on Aristotle, Plato, and ancient Stoicism, but also on medieval and early-modern Christian authorities, he argues that ‘proper honor’ is situated in the inner of a virtuous person because “everybody is the artificer of their own merits of honor.” Despite the aristocratic and patriarchal aspects of his ethics, he propounds (...) an interiorizing and non-militarist interpretation of honor, which runs parallel with Montaigne’s concept of vray honneur and even anticipates to some extent Kant’s Ehrliebe. (shrink)

This paper offers a reconstruction of Alessandro Piccolomini's philosophy of mathematics, and reconstructs the role of Themistius and Averroes in the Renaissance debate on Aristotle's theory of proof. It also describes the interpretative context within which Piccolomini was working in order to show that he was not an isolated figure, but rather that he was fully involved in the debate on mathematics and physics of Italian Aristotelians of his time. The ideas of Lodovico Boccadiferro and Sperone Speroni will (...) be analysed. This paper demonstrates that Piccolomini's attack on the certitude of mathematics was a product of discussions between Aristotelians. (shrink)

El Papa y humanista Eneas Silvio Piccolomini (Pío II) es aquel autor medieval que más explícita e insistentemente se ha ocupado del problema de Europa, no sólo como entidad geográfica sino también política, religiosa y cultural. El artículo analiza los rasgos fundamentales de su concepción de Europa, en el horizonte de los grandes problemas de su tiempo. Por una parte la amenaza turca sobre Europa y por otra las transformaciones internas de Europa, tanto políticas como religiosas.

The landscape descriptions in the ‘Commentarii’ of Pius II represent a characteristic element of this autobiographical text. One might ask whether his depictions of nature stem from own experience and encounters, or whether the landscapes depict a fictitious and literary world and are thus a construct of a humanist whose text abounds with classical citations. The following article addresses this topic from two directions. On the one hand the Pope’s physical presence in the open landscape is verified through reference to (...) other sources; on the other hand his specific way of perceiving and describing nature is investigated. The letters of his entourage and the dispatches of diplomats do show that excursions took place as described by Pius, and that the journeys of this gout-ridden pope even into impassable areas convinced them of his love for nature. Pius’ companions affirm, often with a certain critical distance, his intimate bond with the landscape; they speak of picnics on the banks of a brook rather than in the neighbouring villa, of work-sessions in the forest instead of the palace, and of spectacular views from arduous mounted heights. All of this implied a logistical organization on the part of the courtiers, to which they were not accustomed. Pius’ description of views both near and far, and his desire to be in the midst of nature attest directly to a certain feeling characteristic of the early Italian Renaissance feeling, an epoch whose art too perceives landscape in a new form. (shrink)

What did it mean to “vulgarize” in Renaissance Italy? Was it simply a matter of translating into the vernacular, or did it mean making a text more accessible to the people – to in some sense popularize it? The answer is far from simple and certainly never one-sided; therefore, each individual case needs to be independently assessed on its own merits. This article seeks to shed some light at least on the major treatments of the theory of vulgarization by the (...) likes of Ludovico Castelvetro, Faustus Longianus, Francesco Robortello, Alessandro Piccolomini, Orazio Toscanella and Girolamo Catena, which were central to the debate from the 1540s onwards. (shrink)

La letteratura veneziana degli anni Trenta del Cinquecento è caratterizzata da una volontà di reazione nei confronti della tradizione letteraria precedente. Gli effetti delle guerre d’Italia e la conseguente discesa di Carlo V comportò profondi cambiamenti politici e culturali e una decadenza del sistema delle corti. Autori come Aretino, Speroni e Piccolomini furono tra i primi a cogliere questi mutamenti, scrivendo opere che polemizzano nei confronti di testi ambientati a corte come gli Asolani di Bembo e il Cortegiano di (...) Castiglione. Un aspetto che accomuna questa produzione letteraria è rappresentato dal ruolo preminente che viene affidato ai personaggi femminili. Nei Ragionamenti di Aretino, nella Raffaella di Piccolomini e nel Dialogo d’amore di Speroni, le donne diventano lo strumento principale per esprimere opinioni nuove e polemiche nei confronti delle ipocrisie e delle idealizzazioni del mondo della corte. Nel presente articolo, si evidenzieranno gli aspetti più importanti di queste opere, mostrando come la scelta di personaggi femminili non risponda ad una semplice moda letteraria ma derivi piuttosto da ragioni ideologiche. (shrink)

The traditional ascription of the Neoplatonic commentary on the De Anima to Sim­plicius has prominently been disputed by Carlos Steel and Fernand Bossier, along with J.O. Urmson and Francesco Piccolomini, among others. Citing problems with terminology, diction, cross-references, doctrine, and other features, these authors have argued that the commentary cannot have been composed by Simplicius and that Priscian of Lydia is a favored alternative. In this paper, I present some new arguments for why the traditional attribution to Simplicius is, (...) in fact, the correct one. In particular, while addressing some of the terminological facts that have also been discussed by Christina Luna, Peter Lautner, Patricia Huby, and Philippe Vallat,1 among others, I offer a more secure basis for identifying the author of the De Anima commentary with Simplicius than has so far been proposed. In place of the disputes regarding terminology, which the debate has largely centered upon, I argue that certain unique and characteristic interpretive procedures, which one only finds in the undisputed Simplician works, allow us to identify the authorship of the De Anima commentary with Simplicius securely. Further, comparison of these methodological features with the extant works of Priscian rules out the possibility of his authorship of the commentary. I also provide some suggestions for resolving a few remaining issues of cross-reference between the De Anima commentary and the rest of Simplicius’s work. Finally, I conclude with some words on how that particular form of harmonization pursued by Simplicius’s contemporaries differs from both that of the De Anima commentary as well as his other works. (shrink)