MODULAR COURSE 2: INTRODUCTION TO MATERIALIST PHILOSOPHY OF MATHEMATICS: ONTO-EPISTEMOLOGICAL MODELS AND THEIR EFFECTS
Scope: Philosophy of mathematics demonstrates that mathematics is not only historically – in terms of its origins and traditions – but also in terms of questions it seeks to tackle enmeshed in philosophical quandaries. The question of certitude of knowledge, the presence of metaphysical quandaries and how they are tackled through mathematical method (but also the other way around), mathematical responses to the ideas of computability and its limits, humanity and its relation to technology (is the dream of “technological singularity” tenable), considerations of logic from the perspective of efficient calculability, considerations of rationality and Reason from the perspective of mathematics and, more narrowly, efficient calculus. All of this is will be approached in terms of philosophical discussion while doing justice to the presentation of the mathematical concepts in the context of their disciplinary possibilities and constrictions. Some of the topics we expect to be covered are: Topics: ontologies of mathematics, idealism versus materialism in mathematics, the epistemological and metaphysical dimensions of the themes of “effective calculability,” Gödel’s theorem of incompleteness, Hilbert’s Entscheidungsproblem, Greg Gregory Chaitin's constant; themes that are relevant for the individual research of both teachers.