LECTURE
Formal Logic
Thematizing the Rational Foundations of Mathematics
by Ruel F. Pepa, PhD
Tuesday 26th May 2015, 19h
Aula Marqués de Lozoya
c/ Alburquerque nº 14, 28010 Madrid
From the lecturer's essay How Fundamental is Mathematics?:
"Four very important aspects of human experience that lead to knowledge are differentiation, classification, quantification and specification. In all these matters, mathematics plays an essentially crucial role. The most basic operationalization of mathematics is in being able to differentiate and classify in experience the data of perceptual knowledge. The process is so natural that on the one hand, a unit is spontaneously distinguished from another on the basis of certain obvious properties. Yet on the other hand and on the basis of the same properties, two or more similar units are deemed to be classified as belonging to the same genus or family or species technically called a “set” in the language of modern math’s set theory. In other events, one could rather find some differences in the properties of two units despite some aspects of significant similarities and thus define their intersection.
Then we closely focus our attention on a particular set of units and look at them individually. At this point, we begin to quantify and connect them. We determine the factors that make them related to each other and the conditions that make them affect each other as well. A further magnification of each of the unit with a more serious stress on its peculiarities brings us to the in-depth level of specification. We get to its detailed components and explore their systemic interconnectivity that effects functionality. Technically, we are into the epistemological realm of philosophical inquiry which fundamentally considers the importance of the basic instrumentality of mathematics. In other words, this is how we actually begin to comprehend empirical reality: through the mathematical path."
These are all grounded in Logic.
Professor Ruel F. Pepa is a former journalist and academic with more than 15 years of university stint as Associate Professor in: Philosophy and Logic, Social Sciences and Humanities. He has degrees in Philosophy and Theology. He is now based in Madrid and connected with some language academies teaching English in prestigious multinational companies like Grupo Cobra and Telefonica.
Plato (left) and Aristotle (right), a detail of "The School of Athens", a fresco by Raphael (source: wikipedia)