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)

As abordagens através das quais a filosofia pode ser trabalhada na prática pedagógica assumem, neste artigo, um papel proeminente. Daí a ênfase na sala de aula, local das possíveis realizações, do confronto entre a antecipação e o acontecimento, do desafio maior da concretização de propostas educativas. Os modos de realização da aula, seus textos, problematizações e questionamentos deles decorrentes, enfim, a investigação filosófica coletiva propiciada pela aula constitui a temática principal deste artigo.

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 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)

BackgroundA child’s death is the most stressful event and the most complex grief that families face. The process of psychological adaptation to the illness and death of a child is difficult due to a variety of emotional reactions. Parental grief had received the attention of researchers only in recent years when it became clear that this reality differs substantially from the general grief process.ObjectiveThis work aims to highlight the needs of bereaved parents; increase the specificity and effectiveness of the therapeutic (...) approach to prevent complications in the process of loss-making; and find the recurrent thematic nuclei in the development of bereavement present in a therapeutic group of parents who have lost their child to an onco-hematological disease.MethodBetween 2011 and 2016, five therapeutic groups for the grief elaboration were made. The sample included a total of 50 parents of children who died from cancer between the ages of 0 and 21 years.Content analysis was carried out as a qualitative analysis method. The SAS® Text Miner software was used to read, interpret, classify and integrate the data from numerous sources.ResultsThe development and consecutive interpretation of the 5 clusters have been carried out to analyze the related topics using the node “Topic Analysis” and requesting the subdivision into five topics. Four topics have been well defined. Clear topics are reducible to categories of emotional relief, tools, legacy, and unfinished business. The topic analysis provides interesting indications about the different interpretive journeys of the bereavement situation and offers ideas regarding the different types of social responses.ConclusionsAfter reviewing the existing bibliography, we have confirmed the lack of specific literature on the problem of grief in parents whose children have died from cancer. Much research has shown that parents who lose a child to cancer want support, and there are still few studies on the most effective interventions for this group. (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.

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)

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.

This paper explores some of the assumptions orienting the debate about logical pluralism. I argue that these assumptions are grounded in the truth-conditional character of the semantic metavocabularies in which the debate is conducted. Then, I suggest an expressivist strategy to reinterpret the pluralist claim that there are different logics and I show how the expressive role of logical vocabularies can be equally well characterized by means of different expressive resources not involving the notion of truth.