Knowledge and Games
I would like to share some personal experiences of contributing to well-established research areas outside pure Math.
The first story concerns Epistemology, or more precisely, the characterization of Knowledge. Since Plato, Justification, along with other features, has been considered a principal element of Knowledge. However, the mathematical theory of Knowledge used the existing machinery of modal logic, which lacked the very notion of Justification and hence had certain notorious defects. I undertook some foundational mathematical studies which extended the format of the logic of knowledge and ultimately led to a coherent model of Justification in general.
The second story’s subject is Game Theory, a flourishing field with applications in Economics, Politics, the Social Sciences, etc. At the center of Game Theory lies a doctrine of probabilistic rational decision making under uncertainty, developed by von Neumann & Morgenstern in the 1940s. However, some important classes of games (e.g., so-called games of perfect information) do not rely on probabilistic assumptions. There was no corresponding theory and only a very few extreme, special cases were studied. I noticed that a complete theory of rational non-probabilistic decision making, which far exceeds what had been commonly perceived, can be derived from standard game theoretical postulates.
I will conclude with some reflections about imagination, vision, and discovery.
Click here to download (pdf format) the slides from the presentation.
