Tools for Thought: The Case of Mathematics

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

Vision to reason : using diagrams to think

The aim of this project is to provide a theory that deals with the heterogeneity of reasoning and the way we were able to increase the powers of our limited mind relying on external cognitive tools

Manipulative imagination: how to move things around in mathematics

In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from pre-existing cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “make-believe” is discussed to give an account of cognitive tools in mathematics as props; to better specify the claim, the notion of “affordance” is explored in its possible extension from concrete objects to representations

Manipulative imagination: how to move things around in mathematics

In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from pre-existing cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “make-believe” is discussed to give an account of cognitive tools in mathematics as props; to better specify the claim, the notion of “affordance” is explored in its possible extension from concrete objects to representations

The Practical Turn in Philosophy of Mathematics: A Portrait of a Young Discipline

In the present article, the current situation of the so-called philosophy of mathematical practice is discussed. First, its emergence is evaluated in relation to the “practical” turn in philosophy of science and in philosophy of mathematics. Second, the variety of approaches concerned with the practice of mathematics and the new topics being now object of research are introduced. Third, the possible replies to the question about what counts as mathematical practice are taken into account. Finally, some of the problems that are still open in the philosophy of mathematical practice are presented and some possible new directions of research considered

Mettere a fuoco il mondo. Conversazioni sulla filosofia di Achille Varzi

International audienc

Forms and Roles of Diagrams in Knot Theory

International audienceThe 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

Introduction: From Practice to Results in Mathematics and Logic

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 ..

Urea-induced ROS generation causes insulin resistance in mice with chronic renal failure.

Although supraphysiological concentrations of urea are known to increase oxidative stress in cultured cells, it is generally thought that the elevated levels of urea in chronic renal failure patients have negligible toxicity. We previously demonstrated that ROS increase intracellular protein modification by O-linked β-N-acetylglucosamine (O-GlcNAc), and others showed that increased modification of insulin signaling molecules by O-GlcNAc reduces insulin signal transduction. Because both oxidative stress and insulin resistance have been observed in patients with end-stage renal disease, we sought to determine the role of urea in these phenotypes. Treatment of 3T3-L1 adipocytes with urea at disease-relevant concentrations induced ROS production, caused insulin resistance, increased expression of adipokines retinol binding protein 4 (RBP4) and resistin, and increased O-GlcNAc–modified insulin signaling molecules. Investigation of a mouse model of surgically induced renal failure (uremic mice) revealed increased ROS production, modification of insulin signaling molecules by O-GlcNAc, and increased expression of RBP4 and resistin in visceral adipose tissue. Uremic mice also displayed insulin resistance and glucose intolerance, and treatment with an antioxidant SOD/catalase mimetic normalized these defects. The SOD/catalase mimetic treatment also prevented the development of insulin resistance in normal mice after urea infusion. These data suggest that therapeutic targeting of urea-induced ROS may help reduce the high morbidity and mortality caused by end-stage renal disease

Use of the ONCO-TreC electronic diary compared with a standard paper diary to improve adherence to oral cancer therapy in patients with solid and haematological tumours: protocol for a randomised controlled trial

Introduction ONCO-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 analysis This 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 dissemination Ethical 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