In a vigorously argued passage of the oration Pro L. Flacco, Cicero defends his client L. Valerius Flaccus against the charge that he had acted improperly during his governorship of Asia three years previously in claiming as heres legitimus the estate of one Valeria, wife of Sextilius Andro, who had died intestate in the province. This section of the speech involves Cicero in a brief display of his knowledge of the civil law concerning tutela, the forms of acquiring manus (...) in marriage by usus and coemptio and inheritance ah intestate, and it is described by the scholiast as ‘negotialis quaestiuncula’. The passage is regularly cited in the handbooks to illustrate those features of the civil law which Cicero treats, but the Valeria in question is otherwise wholly obscure. (shrink)
Achille Varzi è uno dei maggiori metafisici viventi. Nel corso degli anni ha scritto testi fondamentali di logica, metafisica, mereologia, filosofia del linguaggio. Ha sconfinato nella topologia, nella geografia, nella matematica, ha ragionato di mostri e confini, percezione e buchi, viaggi nel tempo, nicchie, eventi e ciambelle; e non ha disdegnato di dialogare con gli abitanti di Flatlandia, con Neo e con Terminator. Tra le sue opere principali: Holes and Other Superficialities e Parts and Places. The Structures of Spatial Representation, (...) entrambi scritti insieme a R. Casati per MIT Press; Il mondo messo a fuoco, Laterza; e il suo libro più recente: Le tribolazioni del filosofare, con C. Calosi, per Laterza. -/- Da una giornata all’Università di Urbino nasce questa conversazione a molte voci sulla e con la filosofia di Achille C. Varzi. In un dialogo critico al quale l’Autore si presta con generosità e onestà intellettuale, Andrea Borghini, Francesco Calemi, Claudio Calosi, Elena Casetta, Valeria Giardino, Pierluigi Graziani, Patrizia Pedrini, Daniele Santoro e Giuliano Torrengo lo interrogano e mettono alla prova sui temi affrontati, nel corso degli anni, in campi diversi. Il risultato è un percorso che si snoda attraverso molti mondi, dalla logica alla metafisica, dalla filosofia del linguaggio alla filosofia della matematica, dalla mereologia alla filosofia del tempo, spingendosi in qualche caso oltre i confini del saggio filosofico. (shrink)
In Aristotle and Menander on the Ethics of Understanding , Valeria Cinaglia offers a parallel study of Menander’s New Comedy and Aristotle’s philosophy and she explores the depth and implications of their analogies in subjects ranging from epistemology and psychology to ethics.
This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...) of the properties of usage associated with signs. In Section 2 we illustrate these ideas with a case study of diagrammatic representation: the evolution from Euler diagrams to Venn diagrams. Section 3 is correspondingly devoted to pictorial representation, illustrated by the comparison between parallel and linear perspective drawing. We conclude with open questions, and then briefly summarize the articles to follow.Types of IconicityAs early as 1868, Charles S. Peirce distingu .. (shrink)
The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced.
The aim of this article is to investigate speciﬁc aspects connected with visualization in the practice of a mathematical subﬁeld: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justiﬁcations can be based on sequences of pictures. Three theses will be defended. First, the representations used (...) in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect diﬀerent pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a speciﬁc practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology. (shrink)
The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...) develop a specific form of enhanced manipulative imagination, in order to draw inferences from knot diagrams by performing epistemic actions. Moreover, it will be argued that knot diagrams not only can promote discovery, but also provide evidence. This case study is an experimentation ground to evaluate the role of space and action in making inferences by reasoning diagrammatically. (shrink)
The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp deﬁnition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the speciﬁc forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identiﬁed above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the deﬁnition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)
Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that (...) sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems. (shrink)
There have been recurrent reports of fragilities in the Brazilian health system, especially in public institutions. In this commentary, I argue that moral distress in nursing in Brazil can still be considered an innovative and important subject of study. I also highlight the relevance of engaging educational institutions in the development of policies about environmental sustainability. It is relevant to continue studying moral distress in nursing and in health care generally in order to contribute to the transformation of reality by (...) confronting the multiple common situations in the work environment that are recognized by many as morally problematic because they infringe upon the rights of people, patients, and health care professionals and are an affront to environmental health. (shrink)
Las tesis de Lévinas sobre la violencia han sido frecuentemente vinculadas con su noción de totalidad. Postulamos que si bien la violencia está en relación con la crítica a la filosofía de la totalización, no puede reducirse a ella. Mientras el concepto de totalidad refiere al ejercicio del poder y la dominación, la cuestión de la violencia remite a una situación extrema, que Lévinas vincula con el asesinato en cuanto solución final. Esto supone sostener la impotencia de la totalización frente (...) a la absoluta alteridad del otro hombre, lo que permite pensar la relación mismo-otro bajo una nueva y paradójica lógica jurídica. Ella tiene como principio el mandato “no matarás”, y demuestra que la violencia es el verdadero problema de la ética. Sin embargo, la de Lévinas no es una ética ingenua que postularía una pura no-violencia en el origen. Siguiendo a J. Derrida y respondiendo a sus demandas, mostraremos como la ética de Lévinas puede entenderse como una violencia crítica de la violencia del asesinato. (shrink)
Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional inference (...) rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of constructive hybrid logics. This shows that constructive hybrid logics are a viable enterprise and opens up the way for future applications. (shrink)
Equal respect for persons is often appealed to as the grounding principle of democratic rule. I argue here that if it needs to account for the specific content of democratic political rights, it must be understood as respect for people as competent political decision-makers. However, the claim that respect is due to people as a response to their actual equal competence leads to a conflation of democratic legitimacy and substantive justice, resting on implausible factual assumptions and making it impossible to (...) advocate the effective equalization of political capabilities. Therefore, I suggest that the principle of equal respect should be decoupled from such a claim and be rephrased as simply prescribing that people be treated or publicly recognized as equally competent. I defend this interpretation against the publicity objection, according to which this take on the principle implies insincerity and therefore cannot serve as a public justification for democratic authority. (shrink)