Prologue. The philosophy of mathematics and logic has been an object of my reeections ever since I rst undertook serious study of these subjects. Over many years I have slowly developed a global way of thinking about the foundations, not only of mathematics, but of abstract concepts in general (see 7], 8], 9] and the introduction of 12]). Recently, the fertility of such a global approach, at wh...

In contrast to other constructivist schools, for Brouwer, the notion of “constructive object” is not restricted to be presented as ‘words’ in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer’s constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputati...

My eld is mathematical logic, with a special interest in constructivism, and I would not dare to call myself a computer scientist. But some computer scientists regard my work as a contribution to their eld; and in this text I shall try to explain how this is possible, by taking a look at the history of ideas. I want to describe how two interrelated ideas, connected with the con-structivistic tr...

This paper attempts to provide a critical approach to the issue of regional integration, one of the most important subjects over the last two decades and currently one of the leading debates that are taking place in the South. Although the importance of regional integration –given its correlation to the process of pacific change in international relations–, it seems that there is no satisfactor...

The gods have certainty, whereas to us as men conjecture [only is possible] – Alcmaeon 1 PRELIMINARY REMARKS Within the limits of one chapter, an unconventional way of thinking can certainly not be thoroughly justified, but it can, perhaps, be presented in its most characteristic features anchored here and there in single points. There is, of course, the danger of being misunderstood. In the ca...

Teachers’ epistemological and pedagogical beliefs and their attitude about ICT are identified as the second-order barrier for the integration of ICT into classrooms. In this paper, we report the findings obtained from our recent survey and conducted among Singaporean and Taiwanese pre-service teachers (N=108). The results indicate that the teachers’ epistemological beliefs were generally relati...

As mentioned in French secondary school official texts, teaching science implies teaching scientific process. This poses the problem of how to teach epistemology, as traditional science teaching is mostly dogmatic and based on contents. Previous studies show that pupils, science students and teachers mostly own positivist and realist spontaneous conceptions of science and scientific discovery. ...

This study aims to understand teachers’ perspectives on their roles in higher education, their views about the adoption of a social-constructivist approach to teaching and learning and the integration of online collaborative learning in blended learning environments in higher education from a cross cultural perspective. We interviewed 60 Chinese teachers from Beijing Normal University and Capit...

This paper examines the evolution of pedagogy in an online graduate program developed from a social constructivist perspective. One professor’s first year of teaching was explored through an end-of-year interview, as well as an analysis of newsgroup threads from fall and spring courses. The analyses suggest that this professor gave over more control of course discussions and activities to the s...