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Explore a mathematical framework for understanding intentional systems through this colloquium lecture that examines what it means for systems to possess beliefs, take actions, and pursue goals. Delve into philosophical and cognitive science perspectives including Dennett's intentional stance, the Bayesian brain hypothesis, and enactivism, discovering how mathematical formalization reveals unexpected compatibility between these seemingly disparate approaches. Learn about Dennett's core proposition that the crucial question isn't whether a system is an agent, but whether its behavior can be effectively described by treating it as one, involving the attribution of beliefs and goals to predict actions. Investigate a paradigm shift from asking what systems can solve specific problems to examining what problems given systems are capable of solving. Examine fundamental questions about the nature of beliefs, their temporal evolution in response to new information, scenarios where different belief attributions produce identical behaviors, and the critical issue of defining system boundaries when treating entities as agents. Engage with applications of categorical systems theory and category-theoretic probability throughout this mathematical exploration of intentional behavior and agency.
