CONCEPT
Exchangeability
De Finetti's concept for the symmetry of belief that licenses learning from data—treating observations as interchangeable regardless of order—and whose violation is the precise mathematical name for what goes wrong when AI models fail to generalize.
Exchangeability is a property of belief, not of the world. A sequence of observations is exchangeable for a given reasoner if that reasoner assigns the same probability to any arrangement of the observations, caring only about how many of each outcome occurred rather than in what order they appeared. This is weaker, and more honest, than the frequentist's assumption of independent and identically distributed draws from a fixed true probability—it makes no claim about an objective frequency behind the data, only a statement about the symmetry of the reasoner's own uncertainty.
Bruno de Finetti's representation theorem is what makes this modest premise powerful: if an infinite sequence of binary observations is exchangeable in a reasoner's judgment, then those beliefs are mathematically identical to believing in an unknown objective probability being gradually learned. The subjective reasoner who assumes only symmetry is forced, by pure mathematics, to behave exactly as though learning a true distribution. Exchangeability is therefore the hidden premise beneath