# Is defining the concept of Probability still an open problem in the Philosophy of Science?

There exist several interpretations of the concept of Probability:

https://en.wikipedia.org/wiki/Probability_interpretations

Being the assumption of Repeatability an important difference between them.

I was wondering if the interpretation of the concept of probability is still an open problem (or a problem of interest) in Philosophy of Science, and if there are any new/more recent definitions beyond the Frequentist and Bayesian definitions?

• You can see SEP’s entry dedicated to the Interpretation of Probability for overview and references to current literature Sep 9 '20 at 9:53
• @MauroALLEGRANZA Thanks! That's an interesting reference! Sep 9 '20 at 10:36
• It is not that defining probability is a problem. There are plenty of definitions, too many, and no consensus as to which one is "right" or "most fundamental". Or even if there is a "right" one at all rather than different ones for different purposes. That is something of a perennial problem. In addition to frequentism and Bayesianism (itself split into subjective and objective with shades in between) there are also evidentialism, propensities and best-systems, to name the main ones. Sep 10 '20 at 5:04
• One approach is to give an operational definition to 'probability' and say that any quantity can be considered a probability iff it obeys the probability calculus. Frequencies do; credences do, at least to a good approximation; many other quantities do as well. Probability then needs to be interpreted as a specific quantity in order to make use of it, but any interpretation is satisfactory provided it obeys the calculus. Oct 9 '20 at 20:00
• "Is defining the concept of Probability still an open problem in the Philosophy of Science?" Probably. Oct 11 '20 at 2:08

Besides questions along the lines of Frequentism vs. Subjectivism (as addressed in the Stanford Encyclopedia on Philosophy entry on interpretations of probability, mentioned in the comments above), there are also still problems where what is actually the "right" probability is still in dispute, such as the Sleeping Beauty problem.

Yes, it absolutely is an open question, as can be seen in applications in quantum mechanics.

Like Unitarity, and challenges to it - though I am inclined to think they are definitional (along Cartwright's 'How The Laws Of Physics Lie' lines) rather than epistemic.

And the expanded probability ensemble, as briefly discussed in a question here with links, though sadly not answered yet https://physics.stackexchange.com/questions/11049/does-the-extended-probability-ensemble-interpretation-of-quantum-mechanics-make

Electron orbitals seem to have negative probabilities. This is a bit deceptive, because they only do so relationally, when a paired electron is there with opposite spin, yet somehow preserving in the total state that one electron is less likely to be where it's orbital partner is than located at the nucleus (because this wave-like behaviour is captured in the imaginary part, lost in observations).

Like entropy, we feel with probabilities we grasp an absolute, an intrinsic quality of a system, but find in practice it is often, usually, relative, about a change between ststems rather than absolute terms from first principles - reality, and useful conceptualisation/abstraction, is often too complex for that, and toy systems lead us to over-optimism.

Investigating the deep meaning of probabilities is key to future physics. The transition between fermions and bosons responsible for superconductiin & superfluidity for instance. Blackholes are now thought to be a (bosonic) superfluid that has an absolute maximum of entropy for a given volume. Penrose's Conformal Cyclic Cosmology seems to equate a pure photon soup to the opposite, a white hole. Somehow the transition between these (ie, a timeline including both the big bang, a white hole, and evaporating blackholes) has to either preserve entropy increase, and conservation of information, or show how these can be violated. These heuristics are the deepest principles of our understanding of the world, and we know there is an inconsistency. A better understanding the true implications of probability is clearly key to resolving this.

• Why do you think that black holes are a bosonic superfluid? What particles are the bosons and how do they form a superfluid? Do you mean the entangled photins in Haking radiation? These do not cinstitute the hole. Though other photons inside the hole (created from fermions and quarks fallen in the hole) might. The outward going Hawing radiation is only entangled with the inward going Hawking radiation. Not with the particles already present in the hole. The inside particles already present are destroyed by the ingoing Hawking radiation. There is no causal cinnection between the HR and particle Jul 8 '21 at 8:16
• @DescheleSchilder: As I understand it, based off the fluid-gravity correspondence (eg ias.edu/idea-tags/fluid-gravity-correspondence). See newscientist.com/article/… Exploring Hawking radiation sciencedaily.com/releases/2017/03/170321110344.htm and extremetech.com/extreme/… and to explore blackhole surface dynamics newscientist.com/article/… Jul 8 '21 at 10:59