The title of this question is almost a retorical question. My point is that there is no way to define probability in a non circular manner.
Let's say the probality of getting a tail when tossing a coin is $\frac{1}{2}$, e.i the coin is fair. What does it mean? It means that the relative frequency of tails tends to $\frac{1}{2}$ as $N$ (the number of trials) tends to infinity. But what does the term "tends" means in this context? It means that the probability of getting any fixed relative frequency distinct from $\frac{1}{2}$ (say $\frac{1}{2}+0.0001$) tends to $0$ as $N$ tends to infinity. But we fall then in a circular definition!
Actually there is no way of knowing if the coin is fair, except by a physical exploration of the coin itself. (what, by quantum mechanics, won't really tell you with certainty if the coin is fair).
The only thing we can say, after tossing the coin a lot of times, is that the probability that the coin is fair enough is very high.
So my question is "What does it mean that the probablity of getting a tail is $\frac{1}{2}$?"