This discussion will present proper definitions for uncertainty and risk. Such definitions are required since the current definitions in common use are rather erroneous and generate conceptual problems.
Uncertainty
The new definitions are - see also Figure 40:
(1) First there is the distinction between certainty and uncertainty.
[(2) Uncertainty forks into known categories and unknown categories. ]
(3) Known categories forks into known and unknown probabilities.
(4) Unknown probabilities forks into assuming a uniform distribution (Laplace) or use non-probabilistic techniques like minimax or neglect.
Note that these definitions only use certainty, knowledge and the distinction about categories (category-uncertainty), and that they do not use the term ‘risk’. Thus an independent definition of ‘risk’ is possible.
A.S. Hornby (1985) “Oxford Advanced Learner’s Dictionary of Current English” defines ‘uncertain’ as: “1 changeable; not reliable: ~ weather; a man with an ~ temper. 2 not certainly knowing or known: be/feel ~ (about) what to do next; a woman of ~ age, one whose age cannot be guessed”. The above fits this.