The distinction between rules and similarity is central to our understanding of much of cognitive psychology. Two aspects of existing research have motivated the present work. First, in different cognitive psychology areas we typically see different conceptions of rules and similarity; for example, rules in language appear to be of a different kind compared to rules in categorization. Second, rules processes are typically modeled as separate from similarity ones; for example, in a learning experiment, rules and similarity influences would be described on the basis of separate models. In the present article, I assume that the rules versus similarity distinction can be understood in the same way in learning, reasoning, categorization, and language, and that a unified model for rules and similarity is appropriate. A rules process is considered to be a similarity one where only a single or a small subset of an object's properties are involved. Hence, rules and overall similarity operations are extremes in a single continuum of similarity operations. It is argued that this viewpoint allows adequate coverage of theory and empirical findings in learning, reasoning, categorization, and language, and also a reassessment of the objectives in research on rules versus similarity.

Normative accounts in terms of similarity can be deployed in order to provide semantics for systems of context-free default rules and other sophisticated conditionals. In contrast, procedural accounts of decision in terms of similarity (Rubinstein 1997) are hard to reconcile with the normative rules of rationality used in decision-making, even when suitably weakened.

The target article postulates that rule-based and similarity-based categorization are best described by a unitary process. A number of recent empirical dissociations between rule-based and similarity-based categorization severely challenge this view. Collectively, these new results provide strong evidence that these two types of category learning are mediated by separate systems.

Rules and similarity refer to qualitatively different processes. The classification of a stimulus by rules involves abstract and usually domain-specific knowledge operating primarily on the target representation. In contrast, similarity is a relation between the target representation and another representation of the same type. It is also useful to distinguish associationist processes as a third type of cognitive process.

We agree that treating rules and similarity as dichotomous opposites is unproductive. However, describing all categorization operations as a continuum of varied similarity process obscures a multidimensional contrast. We describe two processes, instantiated rules and abstract analogy, both of which have aspects of rules and similarity, and question whether they can be compared informatively as points on a continuum.

Pothos's revision of rules and similarity in the area of language illustrates the impression that the classicist/connectionist debate is in a blind alley. Under his continuum proposal, both hypotheses fall neatly within the information-processing paradigm. In my view, the paradigm shift that dynamic systems theory represents (Spencer & Thelen 2003) should be submitted to critical scrutiny. Specific formalizations of the Rules versus Similarity distinction may not lead to a form of unification under Generalized Context Models or connectionist networks.

Pothos's analysis is difficult to relate to real human mental processes. He tackles four quite different areas of psychology and adduces evidence from a large number of paradigms. Yet despite this very large scope, he employs a single, simplistic descriptive framework. An epistemological analysis, supported by illustrations from real world decision-making, shows that this steers us away from, rather than towards, an understanding of real human cognitive processes.

In general, we agree with Pothos's claim that similarity and rule knowledge are best viewed as situated on the extreme points of a single representational continuum. However, we contend that a distinction can be made between “rule-like” and “rule-based” knowledge: Rule-based, symbolic knowledge is necessarily conscious when it is applied. Awareness thus provides a useful criterion for distinguishing between sensitivity to functional similarity and knowledge of symbolic rules.

Evidence from aphasia is considered that leads to a distinction between abstract and concrete thought processes and hence for a distinction between rules and similarity. It is argued that perceptual classification is inherently a rule-following procedure and these rules are unable to be followed when a patient has difficulty with name comprehension and retrieval.

A qualitative difference between Rules and Similarity in categorization can be described in terms of “commitment”: Rules entail it, Similarity does not. Commitment derives from people's knowledge of a domain, and it is what justifies people's inferences, selective attention, and dismissal of irrelevant information. Studies show that when children have knowledge, they manifest these aspects of commitment, thus overcoming Similarity.

In arguing for a rules-similarity continuum, Pothos should demonstrate that a single process or mechanism (a neural network model, for example) can handle the entire continuum. Pothos deliberately avoids this exercise as beyond the scope of the current research. In this context, I will present simulation, neuropsychological, neurophysiological, and experimental psychological results, arguing against the continuity hypothesis.

Rules and similarity are two sides of the same phenomenon, but the number of features has nothing to do with transition from similarity to rules; threshold logic helps to understand why.

Difficulty of distinguishing rules and similarity in categorization comes from reliance on relatively simple manipulation-response designs and a style of modeling with abstract parameters, rather than assessment of intervening and controlling mental states. This commentary proposes a strategy in which rules and similarity would be distinguished by their different roles in a theory interrelating reportable conscious contents in deliberative categorization.

The key weakness of the proposed distinction between rules and similarity is that it effectively converts what was previously seen as a consequence of rule or similarity-based processing, into a definition of rule and similarity themselves – evidence is elevated into a conceptual distinction. This conflicts with fundamental intuitions about processes and erodes the relevance of the debate across cognitive science.

Unless restricted to explicitly held, sharable beliefs that control and justify a person's behavior, the notion of a rule has little value as an explanatory concept. Similarity-based processing is a general characteristic of the mind-world interface where internal processes (including explicitly represented rules) act on the external world. The distinction between rules and similarity is therefore misconceived.

The proposal regarding rules and similarity is considered in terms of ability to provide insights regarding previous work on reasoning and categorization. For reasoning, the issue is the relation between this proposal and one-process as well as two-process accounts of deduction and induction. For categorization, the issue is how the proposal would simultaneously explain both similarity-to-rule and rule-to-similarity shifts.

We argue that the Rules-Similarity continuum is only a useful formalism for particular, isolated tasks and must rest on the assumption that representations formed during a particular task are independent of other tasks. We show this to be an unrealistic conjecture. We additionally point out that describing categorization as selective weighing and abstracting of features misses the important step of discovering what the possible features are.

Criteria that aim to dichotomize cognition into rules and similarity are destined to fail because rules and similarity are not in genuine conflict. It is possible for a given cognitive domain to exploit rules without similarity, similarity without rules, or both (rules and similarity) at the same time.

Pothos suggests dispensing with the distinction between rules and similarity, without defining what is meant by either term. We agree that there are problems with the distinction between rules and similarity, but believe these will be solved only by exploring the representations and processes underlying cases purported to involve rules and similarity.

Contrary to Pothos, rule- and similarity-based processes cannot be distinguished by dimensionality. Rather, one must consider the goal of the processing: what the system will do with the resulting representations. Research on speech perception demonstrates that the degree to which speech categories are gradient (or similarity-based) is a function of the utility of within-category variation for further processing.