# Probability and Decision Theory

Anna Longo

Modern probability theory, in particular Bayesian methods, cannot be separated from decision theory. This is evident in the work of the mathematicians that elaborated the paradigm of Bayesian inductive reasoning in the first half of the 20th Century: Frank Ramsey, Bruno de Finetti and Leonard Savage. In particular, Savage established the model of the rational agent that grounds Friedman’s economic theory. It is this same model that informs contemporary AI. To clarify the relation between rational decision theory and the learning paradigm that allows contemporary AI to develop predictive theories almost autonomously, I will introduce the first attempt to automatize inductive reasoning by referring to the Bayesian Ray Solomonoff’s theory of algorithmic probability. This will help me to deal with Ray Kurzweil’s theory of technological singularity and to explain why he claims that AI’s learning process leads to increasing order and complexity while being an unpredictable process the results and the effects of which cannot be anticipated.

Anna Longo is a philosopher; she got her PhD at the University Panthéon Sorbonne. She is currently directing the program “Technologies of Time” at Collège international de philosophie (CIPh, Paris). Her last book, Le jeu de l’induction: automatisation de la connaissance et refléxion philosophique, reconstructs the transformations of inductive reasoning that lead to the automatization of knowledge production thanks to probability theory.