There are 2 broad categories of probability interpretations, *[[#Physical]]* and *[[#Evidential]]*. # Physical These are related to how frequently something is likely to occur given a large number of trials. A deterministic trial will yield a 0 or 1 [[Probability]] while a random process may yield something in between. This is also called *Frequency Probability*. ## Frequency Frequentists include [[Venn]], [[Reichenbach]], and [[von Mises]]. It says that a probability of an event is how frequently it happens, *if it is measured an infinite number of times*. This has two flaws, first is that infinite measurement is impossible, so that different experimentalists may measure different values. Second, if this tries to be accounted for, you will need to rely on probabilistic error bounds, which circularly uses probability to measure probability. ## Propensity Put forth by [[Popper]], [[Miller]], [[Giere]] and [[Fetzer]]. Propensities, also known as chances, are not relative [frequencies](#Frequency), but are the purported causes of the observed stable relative frequencies. The main problem with this theory is that it is hard to say exactly what propensity means, which is hard to do adequately. Arguably, no one has ever done this. # Evidential This differs from frequency probability in that it deals with when a statement may be assigned a probability, even when no random process is involved, in order to assign the likelihood of a statement given available evidence. Probability in this sense is a sort of degree of belief a subject has. This is also called [[Bayesian Probability]]. ## Classical Championed by [[Pierre-Simon Laplace]]. This originated, apparently, when he formalized probabilities in games if chance. Basically, he said the likelihood of an event `A`, for instance is `P(A) = N_A/N`, where `N_A` is the number of occurrences that result in event `A`, and `N` is the number of total outcomes. The two limitations with this approach are that it doesn't account for infinite number of outcomes, and it has circular reasoning because it assumes all outcomes are equally probable, thereby using probability to define probability. ## Subjective This deals with the level of *credence* we give certain statements, and attempts to do so by formalizing the credence of statements based on the fence of others (called priors and evidences). One motivation for this is to justify beliefs in practical terms. For example, how likely it is that someone committed a crime, or whether an engineering project is likely to succeed? If two people agree on probabilities of priors and evidences, then it is possible for folks to agree on probabilities in this subjective sense. The problem arises when agreement can't be had, and so the theory is grounded solely on subjective judgment, as though probabilities we part of us, rather than as part of nature. ## Inductive Also known as epistemic probability, deals with questions of "what is the probability of hypothesis `H` given evidence `E`?" The inductivist believes that rational people may come to different conclusions on the likelihood of `H` while the [[#Logical]] belief says it should have a unique probability among interlocutors, at least in principle. ## Logical See [[#Inductive]] theory.