Events are more fundamental than random variables

One should stress events rather than random variables in the foundations of probability. This is because, most of the time, events are less controversial than random variables. For example, the data are usually uncontroversial from the philosophical point of view. If the blood pressure of a patient was measured to be 110, then this is accepted as a fact and does not lead to philosophical disputes. But the philosophical status of unknown quantities (unknown constants or random variables) can be controversial. Consider the following probabilistic claim about the speed of light L which may arise from an experiment.

(*) P(x < L < y) = 0.99.

In classical statistics, L is an unknown constant and the endpoints x and y of the "confidence interval" (*) are random variables (functions of data). In Bayesian statistics, L is a random variable and x and y are known constants. In this case, (*) is called a "credible interval." Hence, there is no agreement on the philosophical status of the numbers L, x and y.

At some point in the future, using a better technology than that currently available, we may be able to improve the accuracy of measurement of L many times, say 1000 times, and then we will effectively know whether it is true that x < L < y or not. There will be little controversy about the philosophical meaning of the statement that "x < L < y". In other words, the event that {x < L < y} invites much less philosophical controversy than numbers (unknown constants or random variables) L, x and y.

In real life, it may be hard to determine whether an event actually occurred - a typical example is provided by criminal trials. But all practical difficulties encountered while trying to determine whether an event happened apply equally to determining the value of a random variable.