The World According to de Finetti: On de Finetti’s Theory of Probability and Its Application to Quantum Mechanics

Abstract

Abstract. Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finetti's interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finetti's verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bell's theorem.

Unscrambling Subjective and Epistemic Probabilities

“…For the purposes of the present paper, I need to make the case that purely subjective probabilities can be ontic, thus radical subjectivism about quantum probabilities (in a context in which quantum mechanics is taken to be irreducibly indeterministic) provides the ideal example, and in the following I shall rely heavily on my own previous discussion. (Alternatively, I could arguably have relied on Berkovitz (2012).) Note that what I need to convince you of is not that such a position is correct, but only that it is coherent, i. e. that there is an interesting sense in which one can combine the notion of purely subjective probabilities with that of ontic probabilities.…”

“…At that time, the Cambridge group was by far one of the largest research groups in philosophy of physics worldwide, and Wolfson had the largest share of the group. Among others, that included two further Israelis, my friends and fellow PhD-students Meir Hemmo, who is co-editing this volume, and Jossi Berkovitz, who had worked under Itamar's supervision on de Finetti's probabilistic subjectivism and its application to quantum mechanics (published in English as Berkovitz 2012). We were all lunch regulars at Wolfson, and discussions on the philosophy of physics, of probability, and of mathematics were thus not limited to the setting of the Friday seminars in the HPS department (or the immediately preceding lunches at the Eraina Taverna).…”

On Probabilities in Biology and Physics

“…3.5.4). But such a portrayal fails to distinguish between the ontological status of probability and the way it should be evaluated (Berkovitz 2012, Sect. 16.3.4, 2014.…”

“…For a critical discussion of this resolution, seeBub (1975) andBub and Pitowsky (1985).15 For examples of subjective interpretations of QM probabilities, seeCaves et al (2002aCaves et al ( , b, 2007,Pitowsky (2003) andBerkovitz (2012).…”

The Violation of Bell-CHSH Inequalities Leads to Different Conclusions Depending on the Description Used

“…Our starting point is the probability space, which is presented in detail in the next section. We adhere to the view that different probability spaces lead to different Bell’s inequalities [ 29 , 30 ]. While the inequalities look similar, they are not equivalent.…”