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Polar and intermediate cases

Table 5.1 calls attention to the two-sided nature of uncertainty. In particular, the circumscription-similarity trade-off calls attention to the

Table 5.1 The circumscription-similarity trade-off and the nature of uncertainty

High similarity

Low similarity

High circumscription Low circumscription

Epistemic uncertainty

Ontological uncertainty

two following polar cases: (i) low circumscription and high similarity and (ii) high circumscription and low similarity. In the former case, uncertainty is generated by defective information and imperfect discriminating abilities (epistemic uncertainty). In the latter case, uncertainty is associated with inadequate similarities and clear distinctions between objects or situations. The two polar cases point to the existence of intermediate cases in which circumscription is sufficiently low to allow identification of partial similarity but similarity itself is not too high, so that occurrences beyond uniformities (that is, novelties) are possible. Uncertainty in the intermediate situations is inherently two-sided, as it is associated both with a circumscription gap and with a similarity gap. This means that intermediate cases are associated with variable combinations of epistemic uncertainty and ontological uncertainty. The circumscription-similarity trade-off suggests a relationship between the two types of uncertainty. Polar case (i) is such that, due to low circumscription of objects, uncertainty is primarily of the epistemic type: when uniformity is the rule uncertainty stems more from defective cognitive abilities than from the emergence of novelty. Polar case (ii) is such that, due to high circumscription of objects, uncertainty is primarily of the ontological type: when uniformity is virtually excluded, uncertainty stems more from emergence of novelties (new objects or situations) than from defective cognitive skills. We may conjecture that, as we move from polar case (i) to polar case (ii), there will be a decrease of epistemic uncertainty and an increase of ontological uncertainty. This is because, with higher circumscription, there is more scope for the emergence of novelty and less scope for the exploration of uniformities. Let w denote ontological uncertainty and e epistemic uncertainty. We assume w e [w max, wmin], and e e [e max, eminL where wmax is inversely related with e max , and w mjn is inversely related with e min . It is reasonable to conjecture that there will be a linear inverse relationship between maximum epistemic uncertainty and maximum ontological uncertainty (this follows from the inverse role of similarity in the two cases). Figure 5.1 shows the w - e uncertainty line (uncertainty trade off) for two different contexts.

Figure 5.1 deals with the case in which w e [0, wmax], and e e [0, emax] and represents the relation between the maximum values of epistemic uncertainty and ontological uncertainty.

The situation is different if we consider actual uncertainty as a combination of epistemic and ontological uncertainty. In this case, linearity can no longer be taken for granted and multiple cross-over points between uncertainty curves are possible (see Figure 5.2).

Monotonic linear relations between ontological uncertainty (ш) and epistemic uncertainty (г)

Figure 5.1 Monotonic linear relations between ontological uncertainty (ш) and epistemic uncertainty (г)

Non-linear uncertainty curves and multiple crossover points

Figure 5.2 Non-linear uncertainty curves and multiple crossover points

Figure 5.2 describes a possible configuration of uncertainty curves w and e as we move from 0 towards the corresponding upper bounds w max and e max. The important feature to notice is that the relationship between e and w is no longer of the linear type. This is because there is no reason to think that actual epistemic uncertainty and ontological uncertainty, even if constrained within their respective bounds and inversely related to one another, will vary by following a simple rule of proportional change. In most cases an increase of actual epistemic uncertainty will be associated with a more than proportional, or a less than proportional, decrease of actual ontological uncertainty (and vice versa). This entails the possibility of one or more cross-over points between uncertainty curves as one moves across the spectrum of similarity. This could happen for a variety of reasons. For example, a 'fine' description of the universe might give way to a more 'synthetic' description, such that specific events become associated with more comprehensive categories. In this case, the range of possible ontological uncertainty will most certainly shrink, as more synthetic descriptions may encompass a greater assortment of individual variations. However, this reduction of ontological uncertainty does not necessarily mean that there will also be a reduction of actual uncertainty. For more synthetic descriptions might be so imprecise that assignment of events to ontological categories might still be in doubt. A similar argument holds for cases in which a 'synthetic' description of the universe gives way to a 'fine' description of the same universe. Here the range of possible ontological uncertainty will most certainly expand, as more analytic descriptions may encompass a smaller assortment of individual variations. However, this increase of ontological uncertainty does not always mean that there will be an increase of actual uncertainty. The reason is that analytic descriptions may be so fine as to be impractical in a variety of situations. (For instance they may presuppose measurement instruments that are not always at hand.) If that is the case, actual uncertainty might not increase in spite of what we might expect as a result of the greater precision of individual descriptions. In short, variations in uncertainty ranges should not be confused with variations in actual uncertainty values as far as the human attitude to describing is concerned.

As we have seen, changes in the range of ontological uncertainty are associated with changes in the range of epistemic uncertainty. In particular, more synthetic descriptions allow for greater possible epistemic uncertainty even if actual uncertainty is not necessarily increased. This is because synthetic descriptions are often too imprecise to be of immediate relevance. (It may be difficult to assess information when categories are at the same time too general and too vague.) In this case, the nature of events may still be to a large extent uncertain, and epistemic considerations may play a relatively minor role in the organization of knowledge.

We are now in a position to discuss the relationship between the uncertainty curves of Figure 5.2. Any such curve describes realized combinations of epistemic uncertainty and ontological uncertainty, and both describe non-linear variations that are not necessarily of the monotonic type. When comparing different uncertainty curves (our a>- e curves), we compare different ways of combining epistemic uncertainty and ontological uncertainty under alternative scenarios. Both curves A and B call attention to the fact that the two types of uncertainty must each fall within a circumscribed range, and that the 'weight' of each component (epistemic and ontological) shows ups and downs as one moves along the two curves. In practice, each curve highlights a different trade-off between the weights of epistemic uncertainty and ontological uncertainty respectively. The specific character of each curve involves the possibility of one of more intersections at which the weighting criterion for the two types of uncertainty is the same. However, what follows from weighting changes along the two curves besides the intersection points is subject to great variety. This highlights the importance of context in the assessment of uncertainty. Indeed we may consider each context to be associated with a particular way of combining ontological uncertainty with epistemic uncertainty, and to vary their relative weights as one moves from one structure of similarity to another in the domain of events.

 
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