Harvey M. Friedman
Distinguished University Professor
Department of Mathematics
The origins of Logic, as the science of reasoning, are grounded in the work of Aristotle (384-322 BC). The subject remained largely dormant until the explosive developments by the philosopher Gottlob Frege (1848-1925), through his Begriffsschrift or Concept Script (1879), Foundations of Arithmetic (1884), and Basic Laws of Arithmetic (1893, 1903). Frege’s work was followed by the pioneering work of Bertrand Russell (1902, 1908), David Hilbert (1902), Ernst Zermelo (1908), and Abraham Fraenkel (1922). Their work culminated with our present foundations of mathematics through the formalism known as ZFC (Zermelo Fraenkel set theory with the axiom of choice).
This early work firmly established the position of Logic in Philosophy and laid the groundwork for the spectacular advances of Kurt Gödel (completeness and incompleteness, 1928-1940) and Alfred Tarski (real closed fields and elementary geometry 1951, 1959), firmly establishing the position of Logic in Mathematics.
The pioneering insights of Alan Turing (models of computation, 1936), developed in the context of the Gödel era, have led to the position of Logic in Theoretical Computer Science. In Applied Computer Science, Logic is a driving force behind developments in hardware and software verification, programming language design, and software engineering—active areas in the Department of Computer Science and Engineering at The Ohio State University.
Practical uses of Logic in computer-assisted education starting with Patrick Suppes (1968-1980, currently EPGY), and continuing through the Syrus Project at Ohio State, promise to establish the position of Logic in Education.
We will discuss these interdisciplinary adventures in mathematics, philosophy, computer science, and education.