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Dans cet article, je présente et discute la possibilité d’élaborer une classification diagrammatique. Cette classification se révèle utile lorsqu’il s’agit d’explorer dans le détail le domaine du raisonnement par diagrammes. Les diagrammes seront classés par rapport à leur utilisation qui peut être statique ou dynamique, ainsi que par rapport à la correspondance entre la structure de leur espace et la structure de l’espace des données qu’ils représentent. La base de cette recherche n’est pas guidée par l’opposition visuel/non-visuel, mais par la considération de l’interaction continue entre diagrammes et langage. Le raisonnement par diagrammes est caractérisé par une dualité, parce qu’il réfère à un objet, le diagramme, qui a ses propres caractéristiques, et à un sujet, l’utilisateur, qui interprète le diagramme. Une place particulière au sein de la classification sera conférée aux diagrammes constructifs, qui fournissent à l’utilisateur les instructions relatives à la manière dont certaines procédures peuvent être appliquées.

IntroductionONCO-TreC platform consists of a mobile application delivered to patients as electronic diary and a web-based dashboard managed by healthcare professionals. We aim to compare the effectiveness of ONCO-TreC electronic diary with a standard paper diary, in improving adherence to oral cancer therapy in patients with solid and haematological tumours.Methods and analysisThis is an open label, superiority, randomised controlled trial conducted in two Italian oncology units. Patients will be randomised with a 1:1 ratio to electronic or paper diary. For both groups a counsellor will be responsible for drug and diary delivery. The evaluation period will end after six cycles of therapy. The primary aim is to compare the proportion of non-adherent patients in the two arms. Adherence will be measured through pill count; anyone who takes less than 90% of the total prescribed drug dose will be considered non-adherent. Assuming a percentage of non-adherent patients to oral therapy of 40% in arm B, and a 60% reduction in this percentage in arm A, a sample of 124 patients will provide 80% power to identify an absolute difference greater than 24 percentage points using a bilateral Fisher’s exact test with a significance level of 0.05. Considering a dropout rate of 10%, approximately 136 patients will have to be enrolled. The primary analysis will be performed on the intention-to-treat population. Secondary aims are to describe the reasons for non-adherence, the level of satisfaction of patients and healthcare professionals with the paper and electronic diary, and the impact of non-adherence in terms of healthcare costs.Ethics and disseminationEthical approval was obtained from Romagna Ethics Committee (CEROM), study ID 2108, prot. n. IRST 100.28 of 10/04/2020. Informed consent will be obtained from all study participants. Findings will be disseminated through peer-reviewed journals, conferences and event presentations.Protocol versionVersion 2, 6 April 2021.Trial registration numberNCT04826458.

BACKGROUND The use of oral treatments is constantly growing in the area of onco-hematology, raising adherence and safety issues. There is an increasing body of literature highlighting the importance of patient empowerment in the self-management of cancer therapies. Within this scenario, the ONCO-TreC platform was customized and fine-tuned through a prospective multicenter training-validation study in cancer patients treated with oral anticancer drugs. OBJECTIVE This prospective randomized trial was designed to compare the effectiveness of two different strategies, ie, an electronic diary (ONCO-TreC) and a paper diary, for the management of oral cancer treatments in patients with solid and hematological tumors. METHODS Ad hoc strategies are planned to measure and monitor adherence to treatment and to assess usability and acceptability of the electronic diary. Informed consent will be obtained from all study participants. RESULTS This innovative eHealth system is expected to contribute to increasing the adherence to and safety of cancer care, promoting patient empowerment and improving patient-doctor communication. Ethical approval was obtained from the Independent Ethics Committees of the participating institutions (CEIIAV protocol no. 2982/2020; reference no. 2108). CONCLUSIONS Findings will be disseminated through peer-reviewed journals, conferences and event presentations. CLINICALTRIAL ClinicalTrials.gov NCT04826458; Institutional ID no. IRST100.28

International audience; 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.

International audience; In a recent paper, De Toffoli and Giardino analyzed the practice of knot theory, by focusing in particular on the use of diagrams to represent and study knots [1]. To this aim, they distinguished between illustrations and diagrams. An illustration is static; by contrast, a diagram is dynamic, that is, it is closely related to some specific inferential procedures. In the case of knot diagrams, a diagram is also a well-defined mathematical object in itself, which can be used to classify knots. The objective of the present paper is to reply to the following questions: Can the classificatory function characterizing knot diagrams be generalized to other fields of mathematics? Our hypothesis is that dynamic diagrams that are mathematical objects in themselves are used to solve classification problems. To argue in favor of our hypothesis, we will present and compare two examples of classifications involving them: (i) the classification of compact connected surfaces (orientable or not, with or without boundary) in combinatorial topology; (ii) the classification of complex semisimple Lie algebras.

In a recent paper, De Toffoli and Giardino analyzed the practice of knot theory, by focusing in particular on the use of diagrams to represent and study knots [1]. To this aim, they distinguished between illustrations and diagrams. An illustration is static; by contrast, a diagram is dynamic, that is, it is closely related to some specific inferential procedures. In the case of knot diagrams, a diagram is also a well-defined mathematical object in itself, which can be used to classify knots. The objective of the present paper is to reply to the following questions: Can the classificatory function characterizing knot diagrams be generalized to other fields of mathematics? Our hypothesis is that dynamic diagrams that are mathematical objects in themselves are used to solve classification problems. To argue in favor of our hypothesis, we will present and compare two examples of classifications involving them: (i) the classification of compact connected surfaces (orientable or not, with or without boundary) in combinatorial topology; (ii) the classification of complex semisimple Lie algebras.

International audience; 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.

It is possible to argue that the only ‘genuine’ experiments in mathematics are in fact thought experiments. Nevertheless, one preliminary question is to ask what genuine mathematica experiments are, and whether the activity of experimentation is a proper mathematical activity. In this article, I will consider which kind of conception of mathematics allows for the existence of experiments in mathematics and I will present the constraints these experiments are subject to. Then, I will discuss three examples to arrive at a general conclusion: experimentation is indeed a genuine mathematical activity, but its mechanisms are particular with respect to experimentation in the natural sciences.

The objective of the present chapter will be to review the most recent studies about diagrammatic reasoning in mathematics. Section 22.3 will focus on the very much discussed topic of the role and of the features of diagrams and diagrammatic reasoning in Euclidean geometry. Section 22.4 will be devoted to the proposal of considering diagrams as representations that are introduced in support of other symbolic practices and whose power resides in their ambiguity. In Sect. 22.5, the attention will turn toward studies discussing diagrammatic reasoning in contemporary mathematics. In Sect. 22.6 , computational perspectives on how to implement diagrammatic reasoning in computer programs will be introduced, both for Euclidean geometry and theory of numbers. In Sect. 22.7, it will be discussed how the study of diagrammatic reasoning can shed light onto the nature of mathematical thinking in general. Finally, in Sect. 22.8, some brief conclusions about diagrammatic reasoning in mathematics will be drawn. The choice of reviewing the research about diagrammatic reasoning along these lines is of course at least in part arbitrary. The aim of such a regrouping is to provide the reader with a map that can be helpful for exploring the various and already copious literature that has been recently produced on the subject. The ambition is that such a map will be as extensive as possible.

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 target 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 cognitive capacities demanded 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 light 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 various notations, and the constant and fruitful feedback from one representation to another. Finally, some suggestions for further research are given in the conclusion.

1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic ...

International audience; 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.

International audience; 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.

In recent years, many articles and books have been concerned with the subject of the use of visualization and visual thinking in the process of reasoning, and most of all in the process of valid reasoning, that is in scientific argumentation. I say ’many’ in relationship to the neglect this topic has suffered in the past century, when a kind of topic has suffered in the past century, when a kind of ‘‘logocentric’’ approach not only to reasoning, but to science in general—mathematics and logic in particular—has had a strong influence on the philosophical debate. It is true that since its beginnings, philosophy has been devoted to the investigation of the different forms of knowledge that are available to the human mind, and therefore to some extent it is not correct to claim that this interest in the visual forms of knowledge is totally new. Nevertheless, it is only thanks to the reconsideration of the twentieth century linguistic paradigm that an entire domain of research has reappeared in all its complexity.

International audience; In this article, I propose an operational framework for diagrams. According to this framework, diagrams do not work like sentences, because we do not apply a set of explicit and linguistic rules in order to use them. Rather, we become able to manipulate diagrams in meaningful ways once we are familiar with some specific practice, and therefore we engage ourselves in a form of reasoning that is stable because it is shared. This reasoning constitutes at the same time discovery and justification for this discovery. I will make three claims, based on the consideration of diagrams in the practice of logic and mathematics. First, I will claim that diagrams are tools, following some of Peirce’s suggestions. Secondly, I will give reasons to drop a sharp distinction between vision and language and consider by contrast how the two are integrated in a specific manipulation practice, by means of a kind of manipulative imagination. Thirdly, I will defend the idea that an inherent feature of diagrams, given by their nature as images, is their ambiguity: when diagrams are ‘tamed’ by the reference to some system of explicit rules that fix their meaning and make their message univocal, they end up in being less powerful.

In his work, Floridi introduces several notions to describe our relationship with information and technology. According to him, in recent times humanity has experienced a fourth revolution – the Information revolution – starting from the work of Alan Turing. This revolution has deeply affected our understanding of ourselves as agents. Our generation is still a generation of “e-migrants”, but our children will be born in the infosphere and will recognize themselves from their birth as inforgs. In my article I will focus on the notions of infosphere and inforgs, and more generally on the notion of information Floridi makes use of. According to Floridi, in re-ontologizing ourselves as inforgs, we recognize how significantly but not dramatically different we are from smart, engineered artifacts, since we have, as they do, an informational nature. Nevertheless, if one focuses on semantic information, which requires meaning and understanding, then there is still a dramatic difference between ourselves and our artifacts: we are the only agents who spontaneously reason semantically. Finally, I will argue how crucial for philosophy today is to understand how our semantic powers will be affected by us becoming inforgs living in the infosphere.

National audience; Nous sommes actuellement submergés par les «?révolutions?» technologiques, plus particulièrement par l'intelligence artificielle et la robotique, notions larges et souvent floues pour le grand public. Entre réussites et fantasmes, promesses et inquiétudes, ces technologies semblent destinées à bouleverser nos quotidiens, du travail jusqu’à l’intime. Cet ouvrage prend le temps de croiser des regards, parfois critiques, sur ces avancées et leurs perceptions par le public.

International audience

International audience