Last update:
06-Jun-2005

There are two main theories of probability. The first is based on the concept of statistical probability (as either the absolute value of the frequency or, more recently, the limit value of the relative frequency). The second is based on the concept of logical probability and, more recently, logical inductive probability. The real world, that in which we live and act, is uncertain and the only way to approach it systematically and scientifically is by measuring this uncertainty, using probability theory. The concept of probability is relative, partly to what we know and partly to what we do not know. Throwing a fair dice we know for sure, that of the six numbers one will result, but we do not know which. The ratio of the number that favors the appearance of an event to the total number of all possible cases is the measure of probability, on condition that all events have the same probability to occur (principle of indifference). In a more refined way, probability is the numerical value of the limit that the relative frequency tends to, in an infinite (theoretically) series of observations (outcomes). In the case of all mass, repeatable phenomena, as the number of observations increases, the relative frequencies become more and more stabilized and deviate less and less from a certain value, which can be taken as the probability of occurrence of this given event. The inductive logic on which physical sciences are based leads to probabilistic conclusions (for absolute certainty an infinite number of observations is needed). The concept of logical probability is similar to logical implication. When a numerical value is assigned to the logical probability, this is termed inductive logical probability, that is, an inductive system where, for any pair of logical propositions of which one verifies evidence E and the other states a hypothesis Y, it is possible to define a degree (numerical value) of certainty for the hypothesis Y, given the evidence E. The concept of inductive logical probability unifies the concepts of statistical (mathematical) probability and logical probability.

Key words: Classical probability theory, Inductive probability, Logical probability, Probability theory.