  Below, some of the theoretical principles that philosophers have extracted from commonplace beliefs about chance will be outlined. (In so doing, we freely use probabilistic notation and concepts; see the  entry on interpretations of probability,  Hájek 2012:  §1,  for background probability theory required to understand these expressions.) Two such constraints have been widely accepted since the early days of the philosophy of probability. Firstly, it is required that the mathematics of chance should conform to some standard mathematical theory of probability such as Kolmogorov’s 1933 axiomatisation of the probability calculus (or some recognisable variant thereof, like Popper’s axiomatisation of conditional probability). Secondly, chance should be objective: mind-independent and not epistemic or evidential. But a number of other constraints have been articulated and defended in the literature. (Schaffer 2007: §4 contains a useful discussion of these and other constraints on the chance role.) While these principles have been termed ‘things we know about chance’, this shouldn’t be taken to preclude our discovering that there is no such thing as chance—rather, the philosophical consensus is that if there is any such thing as chance, it will (more or less) fit these constraints.