Barbey & Sloman (B&S) observe that nested set operations (NS) do not eliminate error, and point to the potential facilitating effect of, for example, question form. Still, greater caution is in order: The commonest mistake in the medical probability case – answering with the “hit rate” – can utilize NS (have disease/have disease and test positive/take test); it simply does not recognize which nesting is critical (positive and have disease/test positive, including false positives). So, what predictions concerning accuracy follow simply from people's use of NS?

Looking at the bright side, this situation underlines the generality of NS, in that they can support not only good reasoning, but also the bad and the ugly. Moreover, NS need not be restricted to rule-based reasoning: they can support either complex rule-following processes (as with more difficult syllogisms), or associative processes (e.g., making category connections merely by keeping track of similarity-based groupings). Further, NS can support reasoning at different levels of determinateness: that of simple subset relations, where these, in turn, represent elementary quantitative relations of greater, less, and equal; that of finer, but still coarse, comparisons of size, as with Euler circles drawn more-or-less “to scale”; that of determinate set size, with cardinality represented by numerals, grids, and so on. The medical probability calculation requires the third level; others need only the first or second. In sum, within any domain to which they may apply, NS constitute a highly versatile instrument of thought. In the remaining space I indicate some significant domains in which the role of NS has (apparently) been under-explored.

Deductive reasoning. NS are central to many elementary syllogistic inferences, and this area has been intensively studied (Evans et al. Reference Evans, Newstead and Byrne1993). But at least one psychologically and logically important item has not been sufficiently examined. Traditional categorical syllogistic can be modified to produce a system just as powerful as first-order logic (Sommers Reference Sommers1982). Among other things, one may add the Leibnizean principle, “If all As are Bs, then everything that is related in manner R to an A is related in manner R to a B.” This allows one to formulate many simple relational inferences not expressible in older syllogistic. For example, “Since all natural disasters are acts of god, all cases of damage caused by natural disasters are cases of damage caused by acts of god.” (“The Leibniz Clause”; check your insurance policy.) Combined with the provision that no damage caused by god is insured, the company infers that your earthquake damage is not covered. The gist of this powerful principle is simple and intuitive; it directly exploits elementary NS, and suggests a new angle for psychological exploration of everyday relational inference.

Modal deductive reasoning. Aristotle invented modal syllogistic in part to represent possible forms of human thought; yet it is still largely terra incognita for the psychology of reasoning. In this approach, people think in terms of (modally) different ways in which predicates relate to subjects: All As are B; all As are necessarily B; all As are possibly/possibly not Bs. Inferences consist of any mix of modal and non-modal premises and conclusions. One difficult issue would be how people represent the difference between modalities de dicto (a statement [dictum] is necessarily true, e.g., a law of nature, or a “definitional” truth such as, “All bachelors are unmarried”), versus de re (a predicate is necessarily true of some thing [res], as in, “Everything in the barnyard is necessarily a chicken”). NS can handle the latter by distinguishing the set of things possessing some property from the subset of things necessarily possessing that property (and from the coordinate subset of things contingently possessing that property). An empirical point of entry would be the question of whether people judge correctly the validity of these two modal syllogisms (the notorious “Two Barbaras”; Patterson Reference Patterson1985):

One predictable source of error is confusion between de dicto and de re understandings of the modal propositions. On the former, both Barbaras are invalid; on the latter, only the second is valid. There are literally thousands of modal and mixed modal/non-modal syllogisms awaiting investigation, and the most fundamental of these will be crucial to reasoning involving the modally distinct ways in which sets may be nested.

Causal reasoning. If one thinks of the “causal scenario” of an event E as representing E and its causal effects (a set of events branching into the future, say), NS can naturally capture causal chains: If event A causes B, B causes C, and so forth, the causal scenario of C is nested within that of B, and B's within A's; therefore C's scenario is nested within A's, and causality is transitive. If prevents is understood as causes the non-occurrence of, prevention simply becomes another link in a causal chain/nesting. NS can also support thought involving “enablers,” where these are construed as background or normal conditions in the presence of which something causes an event, by nesting the set of situations in which the causal sort of event occurs within the set of enabling-condition situations. (This is admittedly a hotly contested issue.) Even causal thought via simulation of concrete events will implicitly involve NS – provided, as is often the case, the simulation is construed as representing types of causal events (e.g., physical or psychological forces acting in some manner to produce a given sort of effect).

NS are also involved in simple deontic reasoning, classificatory schemata and inferences of all sorts, essentialist (e.g., biological) schemata in particular, and much more. B&S admirably marshal evidence for the important role of NS in probabilistic reasoning, and their claim of generality for NS is highly suggestive with regard to avenues of future research.