Introduction

This paper develops a new interpretation of probability, which sidesteps the usual difficulties intrinsic to the various standard interpretations and, on the other hand, in some sense incorporates much of the intuition behind them. I call it Physicalist Interpretation. The term ``physicalist'' is borrowed from the philosophy of mind. According to the physicalist account of mind, the mental is completely describable in physical terms. In other words, the mental supervenes<sup>2</sup> on the physical. Similarly, the main idea of the physicalist interpretation of probability is that there is no such property of an event as its ``probability.'' Rather, I argue that probability is a reducible concept, supervening on physical quantities characterizing the state of affairs corresponding to the event in question. More radically, I claim that probability is a concept which can be completely eliminated from the scientific discourse. The term ``probability'' can be used only collectively: it means different dimensionless $\left[0,1\right]$-valued physical quantities, more precisely, different dimensionless normalized measures composed by different physical quantities in the different particular situations.

According to this approach, the physical quantity identified with ``probability'' is not the limiting value of relative frequency, and not even necessarily related to the notion of frequency. Although, in some cases, the conditions of the sequential repetitions of a particular situation are such, that the ``probability'' (the corresponding physical quantity) is approximately equal to the relative frequency of the event in question. Neither is ``probability'' a new objective property of a system, expressing its propensity to behave in a certain way, although, the physical quantities characterizing the system are definitely capable to describe such a propensity. In this approach, ``probability'' is not the measure of the degree of belief of an agent in one proposition or another. However, according to the physicalist account of mind, one can imagine a collection of physical quantities characterizing the agent's brain, which compose a dimensionless measure playing the same role in a typical betting scenario as the ``subjective probability.''