Non-exclusion, uncertainty, and similarity thresholds: concluding remarks
The previous argument calls attention to the ontological and epistemic roots of uncertainty, and emphasizes the plurality of grounds that could make evidence uncertain and induction tentative. In particular, we have seen that the sources of uncertainty are manifold because of the interplay of circumscription difficulty and epistemic complexity. However, it is precisely this lack of determinacy that allows the handling of uncertainty by means of a principle of non-exclusion. This is because the domain of similarity relations coincides with the partial overlap of the ontological and epistemic sets (see above). As a result, we may derive the similarity domain by allowing that ontology separates grounded from ungrounded categories, and that the epistemic endowment separates knowable from unknowable objects and situations. Ontology allows us (at least in principle) to distinguish, within the E set, the categories circumscribing real objects and situations from the categories unfit to that purpose. Similarly, the epistemic endowment allows us (at least in principle) to distinguish, within the Q set, the objects and situations that may be known from those that lie outside the reach of existing categories. Figure 5.3 suggests a distinction between different types of uncertainty: (i) what belongs to the Q set but is excluded from its intersection with the E set is clearly unknown and cannot be known in terms of existing categories; (ii) what belongs to the E set but is excluded from its intersection with the Q set is ungrounded and cannot be grounded in terms of the existing ontology; (iii) what belongs to the intersection of the Q and E sets may be both known and grounded, and allows the introduction of similarity relationships among objects or situations.24 Of course, degrees of similarity may be different, and the same is true for degrees of likelihood. Indeed, as we have seen, it is generally possible to identify a variety of similarity orders and of likelihood orders. In short, 'pure' ontological uncertainty cannot be handled by means of existing categories, and does not allow the introduction of similarity relationships across objects or situations. On the other hand, 'pure' epistemic uncertainty cannot be associated with existing ontology, and is also incompatible with identifiable similarity relationships. Such relationships are impossible if objects or situations cannot be categorized; they are also impossible if categories do not have a clear association with existing objects and situations. This leaves us with a collection of intermediate states of the world in which objects (and situations) are matched with categories, but multiple orders of similarity are possible (see above). The relationship between similarity and likelihood implies that multiple orders of likelihood are also possible: any given situation may be less or more likely depending on which particular order we are considering. In short, the domain of knowable uncertainty is constrained both on the ontological side and on the epistemic side. Within that domain, uncertainty allows similarity relationships and permits the assessment of likelihood. Multiple orders of likelihood may be associated with different degrees of rational belief as they are not all founded on an equally solid knowledge basis. However, as we have seen, multiple overlaps of likelihood orders may be possible. It is reasonable to conjecture that confidence in the likelihood assessment for any given situation would increase if a variety of different orders of likelihood were to assign the same assessment for that particular situation. For example, situations associated with different orders of likelihood for the short term and the long term may in fact be associated with strongest likelihood confidence in the case of crossover points A and B, because at those points both short-term and long-run considerations are associated with the same assessment of likelihood (see Figure 5.5). In short, uncertainty at its most fundamental level is associated with coexistence of different orders of similarity and likelihood. This coexistence makes it very difficult to assess particular situations, as they might look likely or unlikely depending on which features are considered. Clearly this difficulty may arise from the way in which any given situation is circumscribed or from the categories available to make sense of existing circumscriptions. However, different likelihood orders may sometimes intersect one another (see above). This means that the very plurality of uncertainty dimensions that makes it difficult in general to assess any given situation may turn out to be an advantage when facing the special circumstances in which the same assessment of the situation in view is grounded in a plurality of different orders of likelihood.