 We may ask a number of questions about this formulation. When are events of the same kind? Intuitively, ‘heads’ and ‘tails’ are equally likely outcomes of tossing a fair coin; but if their kind is ‘ways the coin could land’, then ‘edge’ should presumably be counted alongside them. The “certain number of equally possible cases” and “that of all possible cases” are presumably finite numbers. What, then, of probabilities in infinite spaces? Apparently, irrational-valued probabilities such as \(1/\sqrt{2}\) are automatically eliminated, and thus theories such as quantum mechanics that posit them cannot be accommodated. (We will shortly see, however, that Laplace’s theory has been refined to handle infinite spaces.)