Abstract: As Hilbert and Ackerman wrote in the early 1930s, “The first clear idea of a mathematical logic was formulated by Leibniz. The first results were obtained by A. Morgan and G. Boole”. These “first results” in the first half of the nineteenth century were followed by the invention of the quantifier notation in the late nineteenth century, then the invention of higher-order logic and modern set theory, and then the literally epoch making discovery of modern computer science, beginning with the definition of a computable function by Gödel and Herbrand, and the “translation” of that definition into computer language by Alan Turing. These developments were also simultaneous with the proof of his famous Incompleteness Theorems by Kurt Gödel, the introduction of the semantic conception of truth by Alfred Tarski, and the formalization of metamathematics...and the list could go on and on. In this lecture, I offer a non-technical account of two of the unifying ideas or themes of this remarkably rapid development and some reflections on those themes: the themes being the formalization of not one but two informal notions: the notions of deduction and the (more often talked about) notion of computability. I close by discussing the contributions of this modern logic to philosophy, and the danger of overestimating the utility of the new tools it provides.