** The money analogy.**
Textbooks and Wikipedia say that money is
a *medium of exchange* and a *store of value* and a *unit of account*.
Generally we have no difficulty understanding that the same thing can have different uses.
But the usual treatment of
Interpretations of Probability
discusses
*Logical probability* and
* Subjective probability*
and * Frequency Interpretations*
and * Propensity Interpretations*
as if these were alternate theologies of which only one could be true.
But this is silly.
In discussing money, the issue isn't what money **is**, the issue is what money is **for**.
Analogously the issue is what probability is **for**, and having different
ways of thinking about what it is **for** is a good thing, not an obstacle.

**Earth, water, air, fire.** While other objects may be intuitively associated with one or more of these
classical elements,
few people nowadays believe this leads to a meaningful classification of objects in general.
Analogously, discussing
aleatoric and epistemic uncertainty
via iconic simple examples of each suggests that the writer believes it is practical
and useful to decompose a typical instance of uncertainty as some kind of mixture of these two concepts.
But I think this is simply not true for most instances of serious real-world uncertainty about the future,
as discussed here.

To me the fundamental question is

I don't claim to have a good answer, but will suggest ways of thinking about this question. One backgroundIn what real world contexts is it both practical and useful to attempt to estimate numerical probabilities?

A qualitative sense of likelihood, for instance a conscious recognition of some future events as likely and some as unlikely, is part of the common sense that the human species is endowed with.

- There is a NRS-11 pain scale with
ratings of
**pain**from 0 to 10. - Movie ratings are often given on a scale of 1 to 10, for instance on IMDb.
- Crime: one can use average length of prison sentences as indicators of seriousness of crimes.

- A pain rated 6 is twice as painful as a pain rated 3
- A movie rated 6 is twice as good as one rated 3
- A crime for which a conviction typically gets 6 years in prison is twice as serious as one getting 3 years.

Somewhat bizarrely, such ratings have even been used when asking for expert probability forecasts -- see this graphic from the 2016 Global Risks Landscape in which participants were asked to assess likelihood on a scale of 1 to 7. Doing so precludes the retrospective analysis of accuracy which can be done in proper prediction tournaments.

So all this is background for what I regard as the fundamental conceptual questionWhenever we think about probabilities, we are consciously recognizing unpredictability or uncertainty. But not conversely. There are many settings where we recognize unpredictability but do not naturally think in terms of chance. And there are many settings where we do think in terms of likely/unlikely but do not care to attempt a quantitative assessment of probability.

In what real world contexts is it both practical and useful to attempt to estimate numerical probabilities?