According to frequentism, the probability of an event E happening is equal to the limit of NE(n)/n as n goes to infinity, where N(n) is the number of times that E-type outcome occurs in the first n independent trials. (If there are only finitely many trials in the history of the universe, we've got a serious problem, since then we get the conclusion—surely inconsistent with current physics—that all probabilities are rational numbers. I am guessing that in that case we need to make a counterfactual move—if we were to go to infinity, what limit would we get?)
But now here is a puzzle for the frequentist: Why is it that N(n)/n in fact has a limit at all? The non-frequentist has an answer—the Law of Large Numbers implies that, with probability one, N(n)/n converges to the probability of E, if E has a probability. But it would be circular for the frequentist to offer this explanation.