Patterns of similarity
Ontological criteria and epistemic criteria
The above argument suggests that similarity is central to the discussion of uncertainty, and that it is grounded in the interplay of structural and epistemic conditions. Any given context, say CT, may be defined, for the purpose of the present analysis, as a coupling (O, E), such that O is the set of events that can be identified under any given rule of circumscription (or circumscription set) and E is the set of the ampliative states that are feasible under any given rule of inference (or epistemic set). In general, similarity is specific to any given pair (O, E). This means that similarity patterns identified in context CT = (O, E) would normally be different from similarity patterns in contexts (O', E), (O, E' ), and (O', E' ). In other words, similarity would normally reflect both a rule of circumscription and a rule of ampliative inference, and its character would change depending on which combination of rules we are considering. A particular way of circumscribing events (that is, a particular ontology) cannot generate a deliberate pattern of similarity unless it is associated with a particular way of bringing together events (that is, a particular set of epistemic criteria).10 As we have seen, moving from higher to lower circumscription involves the introduction of synthetic descriptions and the possibility of identifying features of similarity that would not otherwise be detected. In short, moving from a world of singletons to a world of categories is a necessary condition for similarity patterns to be identified. However, not all similarity patterns compatible with a given circumscription are in fact 'active' under that circumscription. Actual similarity between objects or situations presupposes epistemic states capable of turning a potential category into an active principle of apprehension. This epistemic criterion allows the very first step of induction, that is, the step by which a collection of attributes are brought together under a common description. However, this latter stage presupposes a definite circumscription of events. In general, it would be hopeless to strive for identification of similarities when events themselves are so described as to make similarities impossible to detect. There is thus a kind of mutual negative implication at work here: circumscription is unproductive if we lack adequate categories, but categorization is infeasible in the absence of adequate circumscription.
Different (Ц, E) pairs are generally associated with different patterns of similarity (see above). An insight into those principles is provided by consideration of which similarity patterns are relevant under given circumscription and epistemic sets. The previous discussion suggests that high circumscription is associated with weak similarities: the more precise and focused our view of the world is, the less likely we are to detect similarities across a wide range of events. Indeed, those similarities that may be detected may be arbitrary as they rely upon relatively 'minor' features quite distant from the central distinctive attributes that are being compared for different objects. For example, medieval and early modern scientists used to assign principal identity to singletons (such as particular species or even individuals within any given species), so that identification of similarities would often derive from secondary features (such as colour, preferred habitat, or even most frequent conceptual associations in creative writings). The situation is different if we consider the case of low circumscription. Here, strong similarities are more likely: a view of the world less centred upon the individual features of objects may allow for identification of similarities closer to the 'internal structure' of a whole collection of objects, quite independently of what distinguishes one object from another within any given collection. For example, modern biology is more interested in the determination of identical structures across different individuals or species than in the description of what makes any given individual different from all others. In short, patterns of similarity may be strikingly different depending upon which circumscription we choose to follow. There may, however, be a tension between the similarity patterns allowed under a given circumscription of objects and the similarity patterns allowed by existing epistemic conditions. A circumscription compatible
Figure 5.3 Circumscription, epistemic states and similarity
with the 'structural decomposition' of objects and their rearrangement into abstract categories may in fact not be feasible because of epistemic states in which those abstract categories are not allowed.
Figure 5.3 describes the relationship between circumscribed states and epistemic states, and its relevance to the identification of similarity.
Figure 5.3 shows the relationship between the ontology of objects (as shown by the П set, which contains all objects conceivable under a given rule of circumscription) and the set of feasible epistemic states, as shown by the E set. Any given П set contains all objects conceivable under a given circumscription; any given E set contains all categories available under a given epistemic rule. The intersection S includes the objects (events) for which a similarity relation can be introduced and which are compatible with existing circumscription and epistemic rules.