Ruhr University Bochum

(in English)

Abstract. In Knowledge and Social Imagery, the sociologist David Bloor posed the question of whether there could be an alternative mathematics, an idea controversial enough at the time to be called a “monstrous absurdity’’. Yet there are many apparent candidates for alternativeness: historical revolutions; non-standard mathematics; mathematics based on non-classical logics; and more. Some of the questions we will tackle in this course, through discussion of various examples from the literature, are: What does it mean for a logic or mathematics to be “alternative’’? What does the existence of alternative mathematics entail for the philosophy of mathematics? Can any alternative mathematics resist exclusion or assimilation under the mainstream paradigm? Should an alternative mathematics be adopted? What is the relationship between alternatives and revolutions in mathematics?

Abstract. We will study a number of papers on the history of connexive logic, including a survey paper by Richard Sylvan, and articles by Everett Nelson, Christopher Martin, and some papers by 20th century British philosophers. The prerequisites for this seminar are (i) some knowledge of classical logic and non-classical logic, (ii) an interest in the history of logic and the concepts of negation and implication, and (iii) the readiness to present a paper. (Lessons based on M. Nasti de Vincentis, Logiche della connessività. Fra logica moderna e storia della logica antica. Bern: Haupt, 2002)

Summer Schools