The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working (...) in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)

The paper is devoted to an examination of the epistemic account of the notion of deductive inference recently provided by D. Prawitz, and based on the notion of ground. This is part of the general scenario constituted by the “Proof-theoretic semantics”, presented since the ’70s of the last century as an alternative to the standard model-theoretic explication of the notion of logical consequence.Our argument pivots on the so-called “Curry–Howard Correspondence”, which exploited the idea of considering proofs as proper mathematical objects (...) in a remarkable way. A sort of rational reconstruction of this idea is outlined, tracing it back to Hilbert and Husserl’s investigations. (shrink)

This paper is a study of the opening section of Gentzen’s first publication of 1932,Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen, a text which shows the relevance of Hertz’s work of the 1920’s for the young Gentzen. In fact, Gentzen borrowed from Hertz the analysis of the notion of consequence, which was given in terms of the rules of thinning (Verdünnung) and cut (Schnitt) on sequents (there called “sentences”(Sätze)). Moreover, following Hertz again, he also judged it necessary to justify (...) the forms of inference of the system by providing a semantics for them, so that it became possible to make precise the informal notion of consequence, and to show that the inference rules adopted are correct and sufficient. (shrink)

The theory that ``consistency implies existence'' was put forward by Hilbert on various occasions around the start of the last century, and it was strongly and explicitly emphasized in his correspondence with Frege. Since (Gödel's) completeness theorem, abstractly speaking, forms the basis of this theory, it has become common practice to assume that Hilbert took for granted the semantic completeness of second order logic. In this paper I maintain that this widely held view is untrue to the facts, and that (...) the clue to explain what Hilbert meant by linking together consistency and existence is to be found in the role played by the completeness axiom within both geometrical and arithmetical axiom systems. (shrink)

The aim of this paper is to reconsider several proposals that have been put forward in order to develop a Proof-Theoretical Semantics, from the by now classical neo-verificationist approach provided by D. Prawitz and M. Dummett in the Seventies, to an alternative, more recent approach mainly due to the work of P. Schroeder-Heister and L. Hallnäs, based on clausal definitions. Some other intermediate proposals are very briefly sketched. Particular attention will be given to the role played by the so-called Fundamental (...) Assumption. We claim that whereas, in the neo-verificationist proposal, the condition expressed by that Assumption is necessary to ensure the completeness of the justification procedure ( from the outside , so to speak), within the definitional framework it is a built-in feature of the proposal. The latter approach, therefore, appears as an alternative solution to the problem which prompted the neo-verificationists to introduce the Fundamental Assumption. (shrink)

The focus of this paper is on two attempts Sainati made to renew neo-idealistic themes by means of suggestions drawn from the famous Goedel’s Incompleteness Theorems of 1931. Sainati’s remarks on the relationship between «logo astratto » and «logo concreto» are here pursued by reference to some of Goedel’s unpublished texts.

This volume is a Festschrift in honour of Enrico Moriconi, to celebrate his 70th birthday and retirement. It consists of twelve original short essays by some of his friends, colleagues and former students, in the areas of general logic, proof theory, history of logic, philosophy of mathematics, epistemology and philosophy of language, mainly focused on some of his favourite research topics.

Our usual method" is an expression that Aristotle uses in a passage of the Politics (I.1, 1252a17-20) to describe the technique of subdividing a composite object of study into the elements that make it up, in order to study the possible combinations. What theory is the basis for this method? Is it really a usual method for Aristotle? Enrico Rini responds to these questions, starting with the analysis of some passages of the Aristotelian corpus that refer to concepts of (...) the part and the whole. From these passages, Rini attempts to extrapolate a theory that Aristotle states explicitly only on occasion. The mereology that emerges from this study is not a formal theory, unlike the logical mereology present today, and therefore takes into account different types of the whole and the part, with a scope that has applications for the field of biology. (shrink)

1. Epistemologia, logica e dialettica -- 2. Fisica, antropologia e metafisica -- 3. Filosofia pratica -- 4, pt. 1. L'influenza di Aristotele: antichità, Medioevo e Rinascimento -- v. 4, pt. 2. L'influenza di Aristotele: età moderna e contemporanea.

This is a book about food, philosophy, and intellectual property rights. Taken separately, these are three well-known subjects; but it is uncommon to consider them together. Delivering a rich field of disputes, the book is comprised of 50 case studies, organized around eight themes: images; genericity and descriptiveness; language traps; procedures; menus, recipes, and creativity; boundaries; biotech; and empowerment. The introductory chapter frames the selection of cases and encourages readers to look beyond them, envisaging new lenses to look at food (...) vis-à-vis intellectual property. The terrain encompassed is wide-ranging and reaches out to fine-grained aspects of food products, recipes, and cooking. Conceived for a wide scope of readers, the volume ultimately interrogates the links between food and cultural identity, bringing to the fore the ethical, political, aesthetic worth of culinary arts and gastronomic experiences. This accessible book will be of value to scholars, students, practitioners and others with interests in the areas of intellectual property, food law and food studies. (shrink)

Täglich verwenden wir Ausdrücke, mit denen wir etwas anderes meinen, als wir sagen. Wir ersetzen Unaussprechliches, wir bleiben höflich, und manche suchen unangenehme Wahrheiten oder ihre tatsächlichen Absichten zu verschleiern. Solche verhüllenden Ausdrücke wurden schon in der Antike als Euphemismen bezeichnet. Ihr Gegenteil, meist krasse Negativbezeichnungen, heißen Dysphemismen. Ob sie als Tabubruch, als Verstoß gegen Konventionen oder als unangemessenes Verhalten gelten, hängt von den Textsorten, den Situationen und Diskursen ab, in denen sie gebraucht werden. Oft geht es um Tod oder (...) Krankheiten, um den Mediendiskurs über Immigranten oder Minderheiten, aber auch um Arbeitszeugnisse oder die Werbung für Produkte und Dienstleistungen. Das alles sind Themen der Beiträge in diesem Buch. (shrink)

The stated aim of cryptocurrencies is to free the monetary system from the need to trust financial intermediaries, by relying on incentive design and technology. Many descriptive studies, however, have questioned cryptocurrencies’ delivery on the promise of trustlessness. This paper promotes a normative analysis of trust in cryptocurrencies by discussing (i) whether trust is in principle eliminable, and (ii) whether trustlessness is in itself a desirable goal. These issues are closely related, we argue, to the further issue of what kind (...) of institutions cryptocurrencies represent. We discuss the cognitive functions played by cryptocurrencies through the lens of the “extended mind” hypothesis in the philosophy of mind and hence conceive of cryptocurrencies as mind-extending institutions. As the models of institutional mind extension differ in the fiduciary bond they assume exists between individuals and institutional resources, we compare the reliance-based model of “scaffolding institutions” with the trust-based model of “cognitive institutions,” showing that the ineliminability and desirability of trust lead to seeing cryptocurrencies as instances of the latter. In the end, our discussion suggests that trust is a necessary component of cryptocurrencies’ cognitive functions and its promotion helps to perform such cognitive functions more effectively and sustainably. (shrink)

In this paper I argue that Rawlsians have largely misunderstood the idea of an overlapping consensus of reasonable comprehensive doctrines, thereby failing to delineate in an appropriate way the place of comprehensive doctrines in political liberalism. My argument rests on two core claims. The first claim is that (i) political liberalism is committed to three theses about the overlapping consensus. The first thesis concerns the subject of the overlapping consensus; the second thesis concerns the function of the overlapping consensus; the (...) third thesis explains how the overlapping consensus can serve its function in accordance with political liberalism’s commitment to epistemic neutrality. The second claim on which my argument relies is empirical: (ii) Rawlsians typically deny at least one of the three theses to which political liberalism is committed. Based on (i) and (ii), I conclude that Rawlsians have hitherto provided unconvincing accounts of the place of comprehensive doctrines in political liberalism. (shrink)

Enrico Müller legt hier die erste philosophische Gesamtdarstellung zur Bedeutung der Griechen für Nietzsches Denken vor. Er zeigt, wie sich in Auseinandersetzung mit dem Griechentum Nietzsches eigene Philosophie entwickelte, und problematisiert deren Abgrenzungen von der Logosphilosophie der griechischen Klassik. Müller kommt dabei zu dem Schluss, dass auch Nietzsches Philosophie letztlich auf die Vorgaben der sokratisch-platonischen Dialektik angewiesen bleibt.

Exploring the metaphysics of deep disagreements, Ranalli identifies several essential features shared by all such disputes. These very features constitute a set of adequacy conditions that any satisfactory theory of deep disagreements must meet. The paper explains how Coliva’s Wittgensteinian hinge theory can satisfy Ranalli’s persistence desideratum. According to this condition, any appropriate theory must explain why deep disagreements tend to be persistent and thus unresolved without presupposing that they are rationally irresolvable. First, the work critically discusses how Coliva utilizes (...) her proposed view to account for this desideratum. Second, the paper points out that Coliva’s response is partly problematic because of Ranalli’s definition of deep disagreements for Wittgensteinian hinge theories, which over-generates instances of genuine deep disagreements. Third, the work argues that Coliva’s theory can satisfy Ranalli’s persistence desideratum by resolving a deep disagreement between an anti-vaccination advocate and a proponent of vaccination using an expanded version of Pritchard’s side-on approach. Finally, the paper critically engages with Coliva on the solvability of deep disagreements. (shrink)