The Concept of Probability

Abstract

This essay starts out from the assumption that none of the best known theories of probability provides a satisfactory and comprehensive analysis of the problems involved in this notion. They are implicitly criticised because quite often their scope is narrow and the concept of probability they presuppose, or explicitly construct, is not very useful to give an account of current scientific practice.

An alternative approach is explored which claims to be able to deal with the following problems: a) the diverse meanings of the term ‘probability’; b) the reference of probabilistic statements; c ) methods for the assignment of numerical probabilities, and d) procedures according to which rational individuals may arrive at decisions concerning bets, as in gambling games.

It is suggested that the theories under implicit criticism, namely, personalist theories, objective theories (range theory and frequency theory), propensity theories, performative theories and logical theory, normally focus on one of these problems (and quite often they have interesting things to say) , but they tend to leave the others out of account. The approach here put forward incorporates positive aspects of those theories, while it claims to set the basis for a more comprehensive and correct theory.

A distinction is made between two main notions of probability. ‘Probability1’ is drawn from the performative approach. It refers to a modal operator. It indicates the trust that a proposition is entitled to. Therefore it is here suggested that probability, is involved where there is no systematized theory which could be used to predict the occurrence of an event, but instead there is an effective procedure which, properly undertaken, would allow a definite decision as to the occurrence or non-occurrence of the event. An individual resorts to the modal use of probability in order to guard his assertions due to ignorance, either of the relevant theory —if it exists— or of the knowledge obtained through the proper execution of the decision procedure.

The concept of probability relevant for scientific purposes is referred to by the term ‘probability 2’. This notion presupposes that every event in the world is produced by a generative mechanism, and that every event can be seen as a relatively final state of a real system, Real systems, however, are known through theoretical models which represent them. ‘Probability2’ is analysed from an epistemological point of view as a resource human beings need in order to predict the occurrence of events when, for different reasons, they lack of the relevant knowledge of the real system which is responsible for the occurrence of the event under study.

The concept of probability relevant for scientific purposes is thus seen as a measure of the possibility of theoretical events, which can be analysed as states of the model representing the real system —that is, the event which actually occurs as a state of the real system must be seen as an instance of the possible theoretical states. The real event is produced according to the structure and history of the real system. In this sense it is a false problem to intend to assign a probability to the real event. Probabilities are assigned to theoretical representations of real events. Theoretical events are possible states of models partially representing real systems.

Probability is thus neither subjective in the sense of personalist theories, nor objective in the sense of being a property of events or of things in the physical world. Rather, probability must be seen as intersubjectively negotiated between social actors who continuously construct, discuss, accept or reject models of reality. Probability is a measure associated to rationally constructed models and the probability of a theoretical event depends on the specific model in which the event is embedded. The same type of event may have different probabilities, if it can be represented within different models. Thus progress in the knowledge of a real system may have the consequence of changing the probability associated to the occurrence of events seen within the models representing the real system.