As we have seen, any given situation (say, s*) may be associated with different orders of similarity depending on whether we look at its shortterm or long-term features. For example, s* could be similar to other short-term or long-term situations depending on which features we are considering. As the previous argument suggests, different patterns of similarity are normally associated with different orders of likelihood, too. This very possibility points to the need for appropriate 'balancing acts' in the assessment of uncertainty (see above). The open question here is how best to identify alternative sources of uncertainty so as to compare different orders of likelihood and to assess the possibility of crossover points among them. One may tentatively argue that 'hidden similarities' are the most critical ones, and that the recognition of those similarities is made possible by the availability of circumscriptions that are at the same time definite enough to allow effective distinctions among objects or situations and yet permeable enough to allow the discovery of associations among those objects or situations. Clearly, this condition presupposes a specific matching of the ontology and epistemic sets discussed in section 5.3. For structural change within the ontology set (fi) must be 'within reach' of the available categories included in the epistemic set (E ), while a shift to different categories within the epistemic set (E ) must be grounded in the existing set of objects and situations (fi) . The above condition may be difficult to achieve, however it is generally possible to identify objective conditions and reasoning criteria by which the intersection fi П E may be expanded. For example, structural change within the fi set may be identified in terms of change of certain compositional properties (such as hierarchy of constituent processes), which may not all be relevant within the same time horizon. Or, epistemic change within the E set may be identified in terms of a change of categories, which may or may not bring about radical innovation depending on the distance between old and new conceptual structures,21 while at the same time being grounded in the existing cognitive endowments of individuals and societies. For either structural change or epistemic change to be possible, reasoning must allow 'shifts' across different levels of ontology as well as across different levels of cognition. In a way, one must be prepared to drop the existing world of objects and situations so as to glimpse objects and situations that were previously inconceivable. But one must also be prepared to go back to previously conceived (and previously known) objects and situations so as to identify possible bridges between old and new ontologies, or sometimes bridges between old and new ways of looking at things. We may conjecture that this approach would enhance our understanding of the relationship between different orders of likelihood, and would thus allow better identification of critical situations at the juncture of different orders of likelihood, for example of crossover points where short-term and long-term likelihoods happen to coincide.
This framework may be useful in interpreting the distinction between risk and uncertainty. As Frank Knight pointed out in his classical contribution,
Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.
The term 'risk', as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, [...] are categorically different [...] The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character.
(Knight, 1940 , pp. 19-20)
We may conjecture that the situations to which the category 'risk' applies must belong to a particular intersection of the circumscription set and of the epistemic set. In other words, assessment of risk presupposes both a given ontology and a set of concepts adequate to its understanding. In addition to that, risk assessment presupposes that any given situation belongs to a single order of likelihood, and that such order of likelihood may be grounded in a single order of similarity. A necessary condition of risk measurement is that all relevant situations can be arranged in a single ordered series and that such ordered series be associated with a numerical representation of the additive type. In other words, 'arrangement by risk' presupposes a single order of similarity and derives a single order of likelihood from it. The former is provided by the numerical (cardinal) measurement of risk associated with any given situation; the latter is associated with the assumption that the only relevant order of likelihood is the one associated with the above measurement.22 Knightian uncertainty is related with the collection of all ontological and/or epistemic states for which a single order of similarity and likelihood must be excluded.23