The target article's title suggests two messages to take home. Current theories of ecological rationality rest on weak grounds (we generally agree), and data patterns of base-rate neglect provide empirical support for dual-process theory (we generally disagree). Barbey & Sloman's (B&S's) analysis is mistaken on two grounds.

First, they commit the fallacy of false alternatives: Demonstrating that 4 out of 5 theoretical accounts are false does not necessarily imply the truth of the remaining one unless the list of hypotheses is exhaustive, which it is not (we label the 5 accounts considered by B&S as T1–T5). T1–T5 do not instantiate an exclusive set of (plausible) theoretical possibilities. This becomes evident when analyzing T5 into its conjunctive parts: (1) the hypothesis that explicating nested set relations facilitates Bayesian reasoning (T-NESTED), and (2) the hypothesis that the mind has a dual-process architecture with associative processing occurring in parallel with rule-based processing (T-DUAL). Clearly, T-NESTED and T-DUAL are two distinct and separable theoretical claims (hence we already have T1–T6 different accounts, with T6 being equal to T-NESTED without T-DUAL). There is no reason we can see – nor do the authors provide one – for the nested set hypothesis to be married specifically to a dual-process architecture of mind. It seems as plausible (a priori at least) that a single-, or multi-process architecture can implement the benefits from nested set representations.

This leads directly to B&S's second fallacy: Even if the non-rejected account (nested sets) has some merits, in no way does it imply or support a dual process (two-systems) perspective. It is well known that representation and computation can trade spaces, in the sense that computation can be facilitated, or otherwise affected, by changing between (logically equivalent) representational formats (Clark & Thornton Reference Clark and Thornton1997; Marr Reference Marr1982). This general cognitive principle has been demonstrated in areas as diverse as problem solving, memory retrieval, and visual imagery. Also, the cognitive facilitation afforded by Venn diagrams, and diagrams in general (Larkin & Simon Reference Larkin and Simon1987), is well known (yet, unrelated to dual process theories). Framing effects in decision making also illustrate how changes in representational format affect cognitive judgments. The nested sets facilitation hypothesis, reported by B&S, seems to be yet another (potential) example.Footnote ¹ As such, the hypothesis, though viable, is neither novel nor surprising. Because of its generalized flavor it seems particularly ill-suited as a basis for conjecturing a particular architecture of mind: almost any architecture of mind (whether single-, dual- or multi-process; whether associative, rule-based, both or neither) could accommodate the effect.

Apparently, B&S do consider evidence in favor of the nested set hypothesis as also constituting support for the idea that human minds have a dual-process architecture. Arguing for such a general theoretical position, based on the available performance data alone, is simply trying to do the impossible. This is also illustrated by the target article's Table 2. Close inspection of the table shows that the available data cannot decide between theories that assume modular or non-modular architectures (predictions for T1 and T2 are identical), and cannot decide between theories postulating evolutionary or non-evolutionary adaptations (predictions for T3 and T4 are identical). In the same vein, the available data cannot decide between theories that postulate dual- or single-process architectures. Table 2 may seem to suggest otherwise because the predictions of T5 appear to be unique. However, it should be noted that the table is missing a column and thus is incomplete. The authors should have included a sixth column listing predictions for T6 identical to the predictions for T5 (granting that T5 is really making the listed predictions – which seems questionable to begin with, yet is insubstantial for our claim that the reviewed findings cannot discriminate between T5 and T6). Including such a sixth column may have highlighted that the dual process assumption is superfluous in the authors' explanation of base-rate neglect.

Here B&S are confronted with the fact that theoretical frameworks in science generally cannot be justified on the basis of a small set of empirical phenomena (Lakatos Reference Lakatos1977).Footnote ² Rather, theoretical frameworks derive their explanatory power from making insightful a large corpus of seemingly unrelated findings that would otherwise be puzzling or anomalous. B&S make no attempt to argue for the explanatory superiority of dual-process architectures (compared to other architectures of mind); and as we have argued, effects of representational format (e.g. nested set relations) on cognitive processing are not puzzling in any event.

In short, B&S do not provide any argument for why support for the nested-set hypothesis constitutes evidence for dual-process (two-systems) theories. The presumed superiority of dual-process architectures is presumably established by citing other authors who advocate a two-systems theory (e.g., Evans & Over Reference Evans and Over1996; Kahneman & Fredrick Reference Kahneman, Frederick, Gilovich, Griffin and Kahneman2002; Sloman Reference Sloman1996a; Stanovich & West Reference Stanovich2000). Indeed, there has recently been an upsurge in theoretical frameworks alluding to the existence of two different processing systems that supposedly operate according to different rules. Recently, we (Keren & Schul, under review) have pointed to the lack of robust and reliable evidence that would support the two-systems architecture of the mind. The target article seems to offer arguments that question the viability of the natural frequencies approach, and more generally the ecological rationality framework. Yet, it does not add any forceful evidence in support of the alternative favored by the authors, namely the dual-process approach. The possibility that both theoretical frameworks (i.e., ecological rationality and dual processes) are undefendable, cannot be ruled out.