I am in broad agreement with the general position defended in Barbey & Sloman's (B&S's) excellent article. In particular, it is plausible that the data on tasks involving base-rate information are best explained on the following general assumptions:

• Dual-process Thesis: Many kinds of reasoning, including those involving base-rate information, depend on the existence and interaction of two (sorts of) cognitive systems: call them System 1 and System 2.

• Nested Set Thesis: Set inclusion operations play a central role in base-rate facilitation.

But although B&S painstakingly distinguish various frequentist hypotheses, they opt rapidly for one specific construal of the above pair of commitments. Specifically, they adopt a rule-utilization hypothesis in which base-rate facilitation depends on the use by System 2 of set theoretic rules. In what follows, I first highlight that there are many alternative ways of combining the dual-process and nested set theses. I then suggest that there is currently little reason to favor the rule-utilization hypothesis over some of the alternatives.

Varieties of nested set and dual process hypotheses. We can distinguish different versions of the nested set and dual-process theses in terms of how they address the following issues:

• Issue A: What kinds of cognitive structure are specialized for the execution of set theoretic operations?'

• Issue B: What specific role(s) does System 2 play in base-rate facilitation?

Regarding Issue A: In a manner that mirrors B&S's own discussion of frequentist hypotheses, we can distinguish (at least) three variants of the nested set thesis:

1. 1a. Set Inclusion Mechanism: Base-rate facilitation depends in part on the activity of a specialized mechanism or “module” for elementary set theoretic operations.

2. 2a. Set Inclusion Algorithm: Base-rate facilitation depends in part on the activity of an algorithm for elementary set theoretic operations.

3. 3a. Set Inclusion Rules: Base-rate facilitation depends in part on the deployment of rules for elementary set theoretic operations.

These options are not exhaustive; and nor are they mutually exclusive. But B&S appear to endorse only 3a.

Regarding Issue B: Dual-process theories are ubiquitous in cognitive science, and at least the following functions have been assigned to mechanisms responsible for the sorts of controlled, effortful, and relatively slow processing associated with System 2:

1. 1b. Censorship: System 2 censors the outputs from System 1 processes thereby preventing them from becoming overt responses.

2. 2b. Selection: System 2 selects between the outputs of different System 1 processes.

3. 3b. Inhibition: System 2 inhibits the activity of System 1 processes.

4. 4b. Allocation: System 2 allocates cognitive resources, such as attention and information to System 1 processes.

5. 5b. Rule utilization: System 2 computes solutions to judgmental problems by executing rules of inference.

Notice that of these options only the last requires that System 2 compute solutions to judgmental tasks. In contrast, the other four are broadly executive functions, in the sense that they involve the regulation of cognitive resources, information flow and the flow of control. Again, these options are neither jointly exhaustive nor mutually exclusive. But while B&S endorse 5b – viewing System 2 as a consumer of set theoretic rules – they remain largely neutral on which, if any, of the other functions System 2 might perform.

Is there any reason to endorse the rule-utilization hypothesis? So, there are different versions of both the nested set and dual-process theses; and they can be combined in different ways to produce distinct but related hypotheses about the cognitive systems underlying base-rate facilitation. Perhaps all B&S really want to claim is that some such account is plausibly true. This would already be a substantial and contentious hypothesis. But, as already indicated, another more specific proposal is suggested by much of what they say: a rule-utilization hypothesis that combines claims 3a and 5b. If this is the hypothesis B&S seek to defend, however, then it's far from clear that it is preferable to other ways of combining the dual-process and nested set theses.

First, the data cited in the target article do not settle the matter. To explain these data within a dual-process framework requires that: (1) Set theoretic operations are performed in cases of base-rate facilitation. (This explains the pattern of facilitation.) (2) System 2 is involved when facilitation occurs. (This explains, for example, the effects of incentives, and correlation between intelligence and performance.) But it does not follow that System 2 must itself perform these set theoretic operations. For all the data show, it may instead be that System 2 only plays an executive role while some System 1 mechanism is responsible for performing set theoretic operations.

Suppose, for illustrative purposes, that there exists a mechanism dedicated to set theoretic operations – a “set theory module,” if you like (option 1a). Moreover, assume that System 2 performs one or more executive function, such as allocating resources to the set theory mechanism or inhibiting the operation of other mechanisms (options 1b–4b). Such a proposal could accept B&S's contentions that: (1) an associative System 1 process is responsible for base-rate errors, (2) facilitation involves System 2, and (3) it occurs when inputs make set theoretic relations transparent. Thus, System 2 activity could still be invoked to explain the influence of incentives and intelligence; and facilitation could still be explained by reference to the performance of set theoretic operations. But in contrast to the rule-utilization hypothesis, System 2 would play some kind of executive function as opposed to actually computing solutions to judgmental tasks. An account along these lines might offer a possible explanation of the data, while making claims that differ in important respects from those enshrined in the rule-utilization hypothesis.

But perhaps the rule-utilization hypothesis should be preferred on general theoretical grounds? In particular, one might think that the alternatives are in tension with general assumptions of dual-process theory. Most obviously, one might think the following:

• Dual-process theories posit only two reasoning systems. In which case, since System 1 is responsible for errors, System 2 is presumably responsible for successful responses.

• System 1 processes are associative, whereas System 2 processes are rule-based. In which case, set-theoretic operations cannot be subserved by System 1 since they are not associative. Therefore, System 2 must be responsible for the execution of set-theoretic operations.

But it would be a mistake to adopt the rule-utilization hypothesis on such grounds. Though some versions of the dual-process theory incorporate these assumptions, they are at best highly contentious and indeed have been the subject of much recent debate. First, there is considerable debate among dual-process theorists over whether “System 1” and “System 2” label individual systems or kinds of systems. Indeed, there is a growing consensus amongst researchers that there are many System 1 mechanisms (Evans, forthcoming; Stanovich Reference Stanovich2004). In which case, a mechanism for set-theoretic operations is wholly consistent with the claims dual-process theorists make about the plurality of reasoning systems.

Similarly, there is no reason to assume at this time that all System 1 processes must be associative and System 2 rule-based. Admittedly, many dual-process theorists, B&S included, appear to make this assumption. (At any rate, B&S adopt the convention of labeling them as such “in an effort to use more expressive labels”; sect. 1.2. 5, para 1.) But once more, these assumptions are highly contentious; and many prominent dual-process theorists are happy to categorize non-associate mechanisms – including a hypothetical frequentist module – as components of System 1 (Evans, forthcoming; Stanovich Reference Stanovich2004). At this time, the issue of whether System 1 processes are exclusively associative should, it seems to me, be treated as an open empirical matter.

Of course, it may just be that B&S find the rule-utilization hypothesis more attractive on grounds of parsimony since it avoids any commitment to specialized mechanisms for set-theoretic inference. If so, I sympathize. But, given the current widespread popularity of modularity hypotheses, such considerations are unlikely to bear much weight. Even if B&S are right to advocate the nested set and dual-process theses, much more work is required to adjudicate between the various versions of this general proposal.