Gottfried Leibniz wrote, “the mathesis is the science of the things that are conceivable,” the mathesis representing that from which all mathematical disciplines evolved. Beginning with the relationship between ordinary objects, the philosopher and mathematician devised a philosophy of logic that laid the foundations of mathematics for centuries to follow, inspiring such advances as Turing machines and metamathematics.Classifying mathesis into several disciplines, arithmetic, theory of combinations, set theory, theory of manifolds, and mereology, each takes on the appearance of a distinct reality. Also drawing upon Bernard Bolzano's Contributions to a Better‐Grounded Presentation of Mathematics, the authors seek to mathematically structure his proposed truths into categories of "grounds" and "consequences" in the spirit of the Leibniz-Wolffian tradition as applies to the principle of sufficient reason. Tracing the history of mathematics and philosophy from Aristotle to advanced proof theory, Centrone, Negri, Sarikaya, and Schuster apply a modern perspective to Leibniz's and others' contributions, exploring reverse mathematics and intutionistic theory, constructed proofs, negated statements, and provability, computability and constructivity. Gathering leading experts in the fields of computer science, mathematics, logic and philosophy, Mathesis Universalis delves deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.weiterlesen