### Looking for references: phenomenology of probability

A number of lines of inquiry have all been pointing in the same direction for me. I now have a question and I’m on the lookout for scholarly references on it. I haven’t been able to find anything useful through my ordinary means.

I’m looking for a phenomenology of probability.

Hopefully the following paragraphs will make it clearer what I mean.

By phenomenology, I mean a systematic account (-ology) of lived experience (phenomen-). I’m looking for references especially in the “cone” of influences on Merleau-Ponty, and the “cone” of those influenced by Merleau-Ponty.

By probability, I mean the whole gestalt of uncertainty, expectation, and realization that is normally covered by the mathematical subject. The simplest example is the experience of tossing a coin. But there are countless others; this is a ubiquitous mode of phenomenon.

There is at least some indication that this phenomenon is difficult to provide a systematic account for. Probabilistic reasoning is not a very common skill. Perhaps the best account of this that I can think of is in Philip Tetlock’s Superforecasting, in which he reports that a large proportion of people are able to intuit only two kinds of uncertainty (“probably will happen” or “probably won’t happen”), another portion can reason in three (“probably will”, “probably won’t”, and “I don’t know”). For some people, asking for graded expectations (“I think there’s a 30% chance it will happen”) is more or less meaningless.

Nevertheless, all the major quantitative institutions–finance, telecom, digital services, insurance, the hard sciences, etc.–thrive on probabilistic calculations. Perhaps there’s a concentration here.

The other consideration leading towards the question of phenomenology of probability is the question of the interpretation of mathematical probability theory. As is well known, the same mathematics can be interpreted in multiple ways. There is an ‘objective’, frequentist interpretation, according to which probability is the frequency of events in the world. But with the rise of machine learning ‘subjectivist’ or Bayesian interpretations became much more popular. Bayesian probability is a calculus of rational subjective expectations, and transformation of those expectations, according to new evidence.

So far in my studies and research, I’ve never encountered a synthesis of Merleau-Pontean phenomenology with the subjectivist intepretation of probability. This is somewhat troubling.

Is there a treatment of this anywhere?