Much has been said and written about probability. Therefore,
instead of presenting the different views, or accounting for
its historical developments, I go straight
to an example, which I like to present
as an experiment, as indeed it is: the boxes and the
balls are real and they represent the `Physical World'
about which we `do Science,' that is 1) we try,
somehow, to gain
our knowledge about it by making observations; 2) we try, somehow,
to anticipate the results of future observations.
`Somehow' because we usually start
and often remain in conditions of uncertainty.
So, instead of starting by saying
“probability is defined as such and such”,
I introduce the toy experiment, explain the rules of the `game,'
clarifying what can be directly observed and what can only be guessed,
and then let the discussion go, guiding it with proper questions
and helping it by evaluating interactively numbers of interest (some lines of
R code are reported in the paper for the benefit of the reader).
Later, I make the `players' aware of the implications of their answers
and choices.
And even
though initially some of the numbers do not come out right
- the example is simple enough that
rational people will finally agree on the numbers
of interest - the main concepts do:
subjective probability as degree of belief;
physical `probability' as propensity of systems to behave in a given way;
the fact that we can be uncertain about the values of propensity,
and then assign them probabilities; and even that degrees of beliefs
can themselves be
uncertain and often expressed in fuzzy terms like `low', 'high',
`very high' and so on - when this is the case they
need to be defuzzified before they can
be properly used within probability theory, without the need to invent
something fancy in order to handle them.
Other points touched in the paper are the myth that
propensities are only related to long-term relative frequencies
and the question of verifiability of events
subject to probabilistic assessments.
