MATHEMATICAL AND PHILOSOPHICAL LECTURES
By
Nicolas Laos
For Nicolas Laos, thinking is not only an ontological characteristic of man and a practical necessity, but also a source of pleasure. Nicolas Laos is a mathematician and philosopher not only in the sense of formal, academic specialization and practical involvement in these fields, but also in the sense of an overall way of life. In other words, philosophy and mathematics constitute his primary and fundamental identity, and, in this sense, in the footsteps of Socrates, he identifies himself as a citizen of the world, specifically, the world of pure thought, of ideas.
Every civilized person must have some familiarity with structured, logical, and mathematical thinking, as well as with epistemology in general. This is necessary to develop reality awareness and efficient ways of action, which are necessary underpinnings of the dignity of humanity. The study of interdisciplinary mathematics and epistemology develops our capacity for logical and rational thinking, and it enables us to approach problems objectively, to thoroughly evaluate evidence, and to make rigorous judgments, fostering a methodical and creative approach to decision-making. This is a rigorous way of defending the dignity of humanity in the era of advanced modernity.
At the following link, you can download and read Nicolas Laos’s Lectures on Pure and Applied Mathematics and Epistemology (PDF). This series of Nicolas Laos’s Lectures covers the following topics: Mathematical Philosophy; Mathematical Logic; the Structure of Number Sets and the Theory of Real Numbers, Arithmetic and Axiomatic Number Theory, and Algebra (including the study of Sequences and Series); Matrices and Applications in Input-Output Analysis and Linear Programming; Probability and Statistics; Classical Euclidean Geometry, Analytic Geometry, and Trigonometry; Vectors, Vector Spaces, Normed Vector Spaces, and Metric Spaces; basic principles of non-Euclidean Geometries and Metric Geometry; Infinitesimal Calculus and basic Topology (Functions, Limits, Continuity, Topological Structures, Homeomorphisms, Differentiation, and Integration, including Multivariable Calculus and Vector Calculus); Complex Numbers and Complex Analysis; basic principles of Ordinary Differential Equations; as well as mathematical methods and mathematical modeling in the natural sciences (including physics, engineering, biology, and neuroscience) and in the social sciences (including economics, management, strategic studies, and warfare problems). In addition, within these Lectures, you will find a synopsis of Nicolas Laos’s philosophy, which he has called the “dialectic of rational dynamicity,” and it constitutes a creative synthesis of philosophical realism and philosophical idealism. Hence, according to Nicolas Laos, there is a dynamic continuity between the reality of the world and consciousness. Based on his studies and research in philosophy and mathematics, and utilizing his experience in mathematical modeling and policy analysis, Nicolas Laos maintains that strategic, conscious action in general and policy analysis in particular should be understood in terms of processes of organizing and managing information concerning the interplay between the reality of the world as a reservoir of opportunities and the reality of consciousness as a reservoir of intentions, in order to enable actors to act according to the dialectic of rational dynamicity.