Azar, probabilidad e incertidumbre. Una investigación filosófica sobre la tensión entre la matemática y su aplicación, apoyada en varios enfoques epistémicos

Resum

Almost all human life can be seen in the perspective of uncertainty. The human uncertainty leads, in one direction, to the discovery of chance and from it to a technical process to build controlled random processes. The paradigmatic object of these processes is the "dice". Trying to create a mathematical model of such processes the theory of probability is developed. Until the twentieth century, this theory fails to get rid of the dependency of controlled random processes. The theory is based on axioms and avoids, explicitly, any random heuristic connection, or any other interpretation. The aseptic mathematical theory (that here is associated with what is called probability of type P3.2) reversts, in a sharp ontological leap, to the realities beyond its world that it is trying to model. The leap into the world of objects built to handle the controlled random (such as "dice"; they are here associated to probability of type P3.1) is the easiest to take. The application to inference about a population from a sample (the paradigmatic example that is associated with the odds which are called P1 type, trying to avoid subjective - objective dichotomy that is not considered adequate) presents more problems. We consider that human uncertainty can be measured by what is called a probability of type P2. The core of this paper is to discuss in what fields, under what conditions and with what degree of usefulness and relevance, the mathematical theory of probability (which includes mathematical statistics, information theory, the theory of decision and risk theory) can contribute to understanding and modelling human uncertainty and life within this uncertainty. We study the factors considered most relevant to characterize human uncertainty: what is meant by certainty in both the mathematical and the anthropological worlds. What is meant by man, showing the difference between a "rational agent" and the "common man", the central object of study. The uncertainty arising mainly from cultural environment versus that which is more related to personal life. The human handling of the sample space, referring to mathematical entropy as model. In which way and with which means the individual estimates probabilities. Information as evidence (understood in its mathematical definition). The evolution of uncertainty over time. The ideas of utility and risk attitude. Different human strategies of action. We conclude that in the mathematics employed is important to use the numerical quantifications, whereas man's perceptions are qualitative and only in a second stage become (when they do) into numerical values. Both circumstances are the cause of most remarkable dissonance between model and reality. Consequently, the analysis allowed by the mathematical model cannot be extrapolated in a simplistic way to a reality where other factors have a decisive role. Particularly the numerical results may be rarely understood as a precise expression of reality, although often contribute to a qualitative understanding of this reality.