This talk was first given as a keynote in the 2024 SIAM Conference on Mathematics of Data Science
Imagine a machine that can read a story and generate a meaningful continuation, that is, one that complies with the narrative demands of the story and makes sense to a meaningful fraction of the readers. Because what is true in the world of the story needs not be true in our world, this machine cannot be expected to say the truth. It only knows narrative necessity. This machine is of course an idealized model of modern AI systems, from language models and chatbots to movie generation. It is also an opportunity to formulate important questions and sometimes catch a glimpse of their answers. How can we define such a machine more rigorously? What can it compute? How does it compare to logic and mathematical reasoning? Can it be used to make inferences about our world even though its output is not constrained by what is true in our world? Such questions are not only relevant to artificial intelligence, but also useful to understand certain aspects of human intelligence and society.