Probability in Quantum Mechanics

The research question aims to understand what a metaphysical analysis of uncertainty in quantum mechanics might suggest about the ultimate nature of reality and our role in it. The thesis is structured into four chapters. In the first chapter, a "toolbox" is introduced for handling interpretations of probability. A classification system based on two orthogonal matrices is proposed: ontic/epistemic and objective/subjective. This framework allows for distinguishing four categories of probability interpretation (epistemic-objective, epistemic-subjective, ontic-objective, ontic-subjective), each represented by an exemplary interpretation. The metaphysical analysis focuses on probabilities, not on entities, as giving entities metaphysical status might detract from the metaphysical status of probabilities. For example, deterministic theories, such as hidden variables, reduce probabilities to mere approximations. The second chapter introduces quantum mechanics and its paradoxes, analyzing the Copenhagen School's interpretation, which is both innovative and ambiguous. It cannot be classified according to the proposed matrix, leaving room for further interpretations. The interpretation of probability by the Copenhagen School, distinct from classical probability, is examined, with reference to von Neumann's formulation and concepts like quantum logic. The chapter also delves into the "measurement problem," which introduces two seemingly contradictory innovations: the intrinsic indeterminacy of reality and the exceptional nature of the subject (the observer). Dissatisfaction is expressed with the common distinction between classical (deterministic) and quantum (indeterministic) mechanics, suggesting that the metaphysical nature of uncertainty is fundamentally a philosophical question. In the third chapter, it is noted that most interpretations of probability in quantum theories are objective, overlooking the centrality of the subject. The contemporary debate on uncertainty in quantum mechanics is explored, with a focus on two key figures of the 20th century: Popper, who contributed to collapse theories, and Bohm, who supported hidden variable theories. It is emphasized that the distinction between ontic/epistemic is independent of the distinction between objective/subjective. The fourth chapter focuses on a minority subjective interpretation of probability, represented by Quantum Bayesianism (QBism). This interpretation preserves the innovative spirit of the Copenhagen School but overcomes its ambiguities. QBism offers a subjective interpretation of probability that, unlike classical Bayesianism, can be accompanied by an ontic attitude. This suggests that reality in itself has no intrinsic meaning but gains meaning only when we attribute it. In conclusion, the thesis argues that a subjective-ontic interpretation of probability, such as that of QBism, provides a fertile theoretical framework not only for quantum mechanics but also for philosophy, proposing that reality takes shape only through interaction with the subject.