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Probabilities are not readily available in the world around us Expressing uncertainty probability represents precisely what is epistemically unavailable to us Also the concepts chaos and free choice indicate a lack of predictability of the world Probability is distinct from chaos and free will in that it presupposes some type of long run regularity In this section we shall deal with questions such as how probabilities can be assessed and evaluated and to what extent long run regularities are relevant to this issue Is every long run relative frequency a probability What is the probability of a single event There are several methods to assess a probability and they can be distinguished broadly in four different methods ie the frequency theory the propensity theory the logical theory and the personal theory Each of these methods has its own criteria of assessment and evaluation We shall advance an eclectic mixture of all four theories It seems to us that the wide semantic range of chance should be reflected in an equally rich interpretative approach to probability The quantum mechanical behavior of subatomic wave-particles is generally given a propensity interpretation whereas a die if not suspected of being biased exhibits probabilistically logical behavior The traffic in New York City has been modeled with a probabilistic frequentist model Decisions by drivers have been replaced by impersonal randomized events A doctor interprets the posterior probability of having breast-cancer given a positive test-result of the mammogram as the level of epistemic certainty she has on the basis of the test alone In the following sections we shall touch upon three separate issues of probability its interpretations methodologies and structure Besides an eclectic interpretation of probability it is our claim that any probability whatever interpretation suits best possesses a frequency structure ie it is always possible to express a probability in terms of a long-run relative frequencies One important methodological aspect of probability follows from our observations concerning coincidence Any
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