Naslov
What is probability and why does it matter

Autori
Šikić, Zvonimir

Izvornik
European journal of analytic philosophy (1845-8475) 10 (2014), 1; 21-43

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
probability; bayesianism; frequentism; Cox theorem

Sažetak
The idea that probability is a degree of rational belief seemed too vague for a foundation of a mathematical theory. It was certainly not obvious that degrees of rational belief had to be governed by the probability axioms as used by Laplace and other prestatistical probabilityst. The axioms seemed arbitrary in their interpretation. To eliminate the arbitrariness, the statisticians of the early 20th century drastically restricted the possible applications of the probability theory, by insisting that probabilities had to be interpreted as relative frequencies, which obviously satisfied the probability axioms, and so the arbitrariness was removed. But the frequentist approach turned more subjective then the prestatistical approach, because the identifications of outcome spaces, the choices of test statistics, the declarations of what rejection regions are, the choices of null- hypothesis among alternatives, the contradictory choices between sizes and powers etc., depend on thoughts or even whims of the experimenter. Frequentists thus failed to solve the problems that motivated their approach, they even exacerbated them. The subjective bayesianism of Ramsey and de Finetti did not solve the problems either. Finally Cox provided the missing foundation for probability as a degree of rational belief, which makes the bayesian probability theory (which is based on this foundation) the best theory of probable inference we have. Hence, it is quite unbelievable that it is not even mentioned in recent philosophy textbooks devoted to the probable inference. The reason could be that it requires fairly sophisticated mathematics. But even not to mention it? We explain this hole history and prove the Cox theorem in a novel way.

Izvorni jezik
Engleski

Znanstvena područja
Filozofija

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