To Teach Modal Logic: An Opinionated Survey

I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy, which do not stem mainly from mathematical issues, but which is motivated by central problems of philosophy and language. I will point out some themes to start elaborating a guide for a more comprehensive approach to teach modal logic, and consider the contributions of dual-process theories in cognitive science, in order to explore a pedagogical framework for the proposed point of view.Comment: Proceedings of the Fourth International Conference on Tools for Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M. Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat, Fran\c{c}ois Schwarzentrube

Gentzen-Prawitz Natural Deduction as a Teaching Tool

We report a four-years experiment in teaching reasoning to undergraduate students, ranging from weak to gifted, using Gentzen-Prawitz's style natural deduction. We argue that this pedagogical approach is a good alternative to the use of Boolean algebra for teaching reasoning, especially for computer scientists and formal methods practionners

Categories without structures

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.Comment: 28 page

Synchronous Online Philosophy Courses: An Experiment in Progress

There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class

Poly-infix operators and operator families

Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an ordered sequence of entities with the same connecting primitive.Comment: 8 page

Group deliberation and the transformation ofjudgments: an impossibility result

While a large social-choice-theoretic literature discusses the aggregation ofindividual judgments into collective ones, there is relatively little formalwork on the transformation of individual judgments in group deliberation. Idevelop a model of judgment transformation and prove a baselineimpossibility result: Any judgment transformation function satisfying someinitially plausible condition is the identity function, under which no opinionchange occurs. I identify escape routes from this impossibility result andargue that successful group deliberation must be 'holistic': individualscannot generally revise their judgments on a proposition based on judgmentson that proposition alone but must take other propositions into account too. Idiscuss the significance of these findings for democratic theory.group deliberation, judgment aggregation, judgmenttransformation, belief revision

Carnap: an Open Framework for Formal Reasoning in the Browser

This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications

Responsible research and innovation in science education: insights from evaluating the impact of using digital media and arts-based methods on RRI values

The European Commission policy approach of Responsible Research and Innovation (RRI) is gaining momentum in European research planning and development as a strategy to align scientific and technological progress with socially desirable and acceptable ends. One of the RRI agendas is science education, aiming to foster future generations' acquisition of skills and values needed to engage in society responsibly. To this end, it is argued that RRI-based science education can benefit from more interdisciplinary methods such as those based on arts and digital technologies. However, the evidence existing on the impact of science education activities using digital media and arts-based methods on RRI values remains underexplored. This article comparatively reviews previous evidence on the evaluation of these activities, from primary to higher education, to examine whether and how RRI-related learning outcomes are evaluated and how these activities impact on students' learning. Forty academic publications were selected and its content analysed according to five RRI values: creative and critical thinking, engagement, inclusiveness, gender equality and integration of ethical issues. When evaluating the impact of digital and arts-based methods in science education activities, creative and critical thinking, engagement and partly inclusiveness are the RRI values mainly addressed. In contrast, gender equality and ethics integration are neglected. Digital-based methods seem to be more focused on students' questioning and inquiry skills, whereas those using arts often examine imagination, curiosity and autonomy. Differences in the evaluation focus between studies on digital media and those on arts partly explain differences in their impact on RRI values, but also result in non-documented outcomes and undermine their potential. Further developments in interdisciplinary approaches to science education following the RRI policy agenda should reinforce the design of the activities as well as procedural aspects of the evaluation research