FOUNDATIONS OF MATHEMATICS: FROM LOGIC TO SET THEORY AND NUMBERS

by Alessandro Cordelli

Man observes the world, recognizes regularities, and build models. But Man is also able to analyze the process itself of building models, that is, logic. Reasoning, language, and science are deeply rooted in logic. This book is about how the thinking process is coded into the laws of logic, and how the very concept of number comes out from those laws. The subject is discussed into four sections. First, the fundamentals of logic, i.e. the law of non-contradiction and other basic principles, along with logical operators. The second section is devoted to sets, their relationship with propositional logic, and how the concept of number can be derived from them. In the third section, the process of proving is taken into account, and, in particular, the syllogism. Finally, mathematical induction is widely discussed with the aid of several examples. At the end of each section, there is a comprehension test and a number of problems, useful to deepen the understanding of the subject matter.
The author – Ph.D. in physics and in philosophy – is a scholar of philosophical aspects of science.

72 pages, Kindle Edition

First published March 6, 2015