Is rationality a cognitive faculty?

Standard Rationality versus Simon/Gigerenzer Rationality

Upon reading the title of this paper—namely, whether rationality is a cognitive faculty—it is probably clear to the reader what is “cognitive faculty.” However, it is probably less clear what is “rationality.” As the exposition of the Organismus economicus hypothesis below shows, this paper defines rationality à la standard economics. Specifically, rationality is about the coherence of preferences: the decision maker knows what bundles of goods they prefer over other bundles and, hence, is ready to select the best bundle allowed given the budget constraint, beliefs, and general circumstances (Gilboa, 2012; Khalil, 2025a). This paper focuses on this notion of rationality and asks whether such a standard notion is a cognitive faculty.

If some researchers deny the existence of this standard notion of rationality and proceed to offer non-standard definitions, this paper is not written to advance arguments to convince them otherwise. Specifically, this paper neither critiques Gigerenzer’s (2023) non-standard notion, which he calls “ecological rationality,” nor critiques Simon’s (1976) notion, which he calls “procedural rationality.” Simon and Gigerenzer basically argue, although in different ways, that the standard notion of rationality is fundamentally flawed. For them, decision makers cannot undertake decisions on the basis of optimization for a simple reason. The mechanism of optimization is based on beliefs about facts that also involve optimization, which leads to endless regression. That is, for Simon and Gigerenzer, the issue is not the fact that the cognitive processing of information is costly and hence rationality is bounded, what the neoclassical (standard) definition of rationality acknowledges.² Simon and Gigerenzer maintain that the entry point of standard economics is untenable even when cognitive costs are zero.

Instead, Simon and Gigerenzer propose a different entry point: “habits”, routines, or “intuitions” conceived as primordial, and hence, theorists need not explain them. Habits at the personal and collective levels are “norms” of behavior that explain behavior—which Kahneman and Miller (1986) also argue. The decision maker continues to use default habits, norms, or intuitions as long as they are useful in attaining some predetermined level of satisfaction—which Simon (1957) calls “satisficing”.

Other papers discuss the limitations of the Simon/Gigerenzer non-standard definition of rationality (Khalil, 2013a, b; Khalil, 2022). This paper does not discuss these limitations because the aim of this paper is not to advocate the importance of the standard definition of rationality. This paper poses a different question: given that research subscribes to the standard notion of rationality, is such a notion a cognitive faculty?

Why ignore dual process theory?

This paper also does not discuss dual process theory, but for a different reason. While Evans (1978) is usually credited with formally introducing dual process theory in the psychology literature, Stanovich (2010a) and Kahneman (2011) link dual process theory to the study of heuristics in relation to rationality. Dual process theory amounts to the proposition that thinking and deciding involves two systems. The first system, called “System 1”, amounts to deciding regarding a case according to ready-made beliefs, heuristics, and first impressions that are fast and spontaneous. The second system, called “System 2”, amounts to deciding by examining the case under focus with all its details. While System 1 is fast and spontaneous, System 2 is slow and deliberate.

As shown elsewhere (Khalil, 2025c; Khalil & Amin, 2023), dual process theory is fruitful not only in understanding heuristics and how decision makers suspend them but also in understanding routines, i.e., the physiological functions of organisms and their organs. However, this paper does not discuss dual process theory because it proposes that spontaneous System 1 is non-rational, whereas deliberative System 2 is rational. As argued elsewhere (Khalil, 2022, 2025c), System 1 and System 2 are rather organically linked: the logic of rational choice underpins the operation of both systems. We need a rational choice to explain why some actions become habitual and hence become part of spontaneous System 1. We also need a rational choice to explain why some habitual actions become suspended; hence, the decision is sent back to deliberative System 2.

Even if we salvage dual process theory from the connotation that spontaneous System 1 is non-rational, the question posed by this paper does not gain from refining thinking into two systems. Given that the two systems are organically linked, we can ask questions about the standard notion of rationality per se, namely, how it is related to cognitive faculty, without refining thinking and deciding into two systems. Indeed, the refinement of thinking and deciding amounts to a digression that takes us away from the question posed by this paper.

The need to avoid such unnecessary digression becomes even more poignant in light of the further refinement of System 2 undertaken by Stanovich (2010a). The impetus behind his refinement is to solve what he calls the “Great Rationality Debate”. The Great Rationality Debate is about a long-running question in the philosophical and psychological literature: how far human behavior is from the standard notion of rationality (the coherence of preferences and the efficiency of actions in light of probability theory and logical thinking). To answer this question, Stanovich argues that we should examine individual differences. This examination shows, to the surprise of the literature (but not to this paper), that people with high IQs need not make significantly more rational choices than people with normal IQs do.

While this paper welcomes Stanovich’s rationality/intelligence distinction (see also Stanovich, 2010b), he grounds the distinction on refining System 2 into two sub-processes: i) the reflective process that allows the decision maker to suspend the operation of spontaneous System 1 and ii) the algorithmic process that, once a task is decoupled from spontaneous System 1, undertakes the processing of information specific to the case under focus. For Stanovich, while the reflective process expresses rationality (which varies across individuals), the algorithmic process expresses intelligence.

While one may accept that the algorithmic process hinges on intelligence, Stanovich’s refinement implies that System 1 is non-rational, as he reserves rationality to the reflective process (part of deliberative System 2). As stated above, System 1 and System 2 are rather organically linked by the logic of rational choice. Given that the focus is on rational choice per se—namely, whether it is a cognitive faculty similar to memory or intelligence—it would be unnecessary to digress and refine the operation of rational choice.

The Organismus automaton hypothesis

The Organismus automaton hypothesis involves the treatment of rationality as a trait, specifically as a cognitive faculty. It is based on the fundamental thesis that the organism operates according to rules, where such rules are the products, ultimately, of natural selection. These rules are the operational functions of faculties, such as memory, intelligence, and supposed rationality. In this picture, the organism follows rules in the final analysis as an automaton.

This paper ignores sophisticated versions of the Organismus automaton hypothesis (e.g., Godfrey–Smith, 1996, 2009). This allows us to focus, as shown in Figure 1, on the basic minimal schemata of the optimization structure of the Organismus automaton:

Figure 1. Structure of the Organismus automaton.

where E = a set of fitness ends such as the flight speed of zebra (too much flight speed weakens other abilities and too little undermines the survival fitness of the organism); x_it_j = the particular trait (t) and the instinctual behavior requiring a certain set of goods (x) (different organisms are characterized by different combinations of t and x); TF_k = the transformational function of level or type k that transforms inputs into outputs; and OM = the optimization method that ensures that the optimum E (E_i^*) is selected or chosen.

It is crucial to distinguish among three entities in the above schemata: i) the trait-as-input, which is an element of the input set on the left-hand side; ii) the trait-as-technology, which acts as the binary operator of level k (TF_k) between the input set and the output set; and iii) the optimization method (OM), which acts as a binary relator.

To use a distinction borrowed from set theory, the OM is the “binary relator”, whereas TF_k is the “binary operator” (see Rai et al., 2012). The binary relator that acts as the OM performs two roles. The first role works within each set, as it ranks the different outputs in a consistent fashion; that is, it specifies which output is better than the other while abstracting from the constraints. For example, it can rank different flight speeds without considering constraints. The OM also ranks the different inputs correspondingly. However, the optimal solution cannot be determined without specifying the environmental constraints. This highlights the second role; once the constraints are specified, the OM relates the input with the output sets in a certain way that shows what is the appropriate input that produces the optimum output (E_i^*).

In contrast, the binary operator (TF_k) transforms inputs into outputs according to k-level trait-as-technology. As such, TF_k is neither the optimization method (OM) nor the trait-as-input (x_it_j) that makes up the left-hand input set. TF_k is merely the technical listing of outcomes that TF_k can produce from the given set of inputs.

The symmetry of the two hypotheses

The structure of the Organismus automaton hypothesis is almost identical to the structure of Organismus oeconomicus hypothesis. The input in the former is the population of individuals where each individual is characterized by an input set, whereas each gives rise to a different end, called a phenotype. The input in the latter is the bundle of goods, whereas each gives origin to a different end, called utility.

The Organismus oeconomicus hypothesis, based on standard rational choice, also consists of the binary relator assuring us the production of the optimum, i.e., the employment of OM, and the binary operator that expresses the transformational function, say, at k-level, i.e., the employment of TF _k. Again here, the binary relator (OM) has two roles. As for the first role, the theory of rationality assures us the ends, that is, the utility values, are consistent and, correspondingly, that the inputs are consistently ranked. Consistency depends on many axioms, the most important are two: transitivity and completeness (see Gilboa, 2012; Khalil, 2023). As for the second role, once constraints are determined, the binary relator identifies the optimum end, that is, the optimum utility, and its corresponding set of inputs.

As for the binary operator at k-level (TF _k), there is a set of technologies, institutions, and beliefs transforming each set of inputs into output. As in the case of the Organismus automaton hypothesis, the binary operator merely lists the technical aspect of what is the outcome of each set of inputs if the given TF _k is employed in their transformation. It neither assures any internal consistency nor determines the optimum outcome.

When the optimum is disturbed

Once an optimum is selected by nature or by choice, the optimum is stable as long as shocks disturb neither the set of inputs nor the set of environmental constraints. The stable decision equilibrium, not to be confused with market equilibrium, can be upset if at least one of the following two conditions changes: (i) a mutation of traits-as-inputs (t) or goods (x) takes place; or (ii) a change in the set of environmental constraints.

The set of environmental constraints is implicit in the above schemata. Specifically, the binary relator can select only the optimum end while considering such a set. Let us consider the consequences of the change in such a set of environmental constraints (C) from C_i to C_c. Nature should select or the decision maker should choose, as Figure 2 shows, a new set of inputs, x_ct_d^*, corresponding to the new optimum end, E^*_c:

Figure 2. The selection of the optimum end.

However, both nature and the decision maker may face hurdles, mainly arising from transitional costs (Marciano & Khalil, 2012; Khalil, 2013a), as they attempt to adjust. Hence, there can be an adjustment period or, worse, a lock-in arrangement where the status quo dominates. Natural selection or rational choice may opt for the status quo—i.e., the old end, E_i. In this case, natural selection or rational choice (OM) would still select the old inputs, x_it_j. If nothing happens, E_i will continue forever as the “second best” actual outcome, where the OM is denoted as second-best (OM^SB). In contrast, E^*_c continues to be the ideal or “first-best”, where the OM is denoted as first-best (OM^FB). However, what matters, the first-best (E^*_c) is suboptimal, whereas the second-best (E_i) is optimal—given the transitional cost that secures the lock-in arrangement.

This gap between E^*_c (first-best) and E_i (second-best) may shed light on the controversy between the “hard” and “soft” neo-Darwinian approaches. For the “hard” approach (for example, Dawkins, 1989; Dennett, 1984), the OM should surely generate the E^*_j. For the “soft” approach (for example, Gould & Lewontin, 1979), the binary relator is rather OM^SB, generating the seemingly suboptimal outcome E_i. However, as Marciano and Khalil (2012) explain, E_i is actually optimal if we (as we should) consider lock-in arrangements, such as the body plan of the organism or the technological/institutional/legal makeup of the community. E^*_c is optimal in the “ideal” sense, in a world that forcefully ignores transitional cost as if we live in an arrangement-free world.

In the given optimization problem above, the binary operator at the k-level (TF) cannot be the subject of the optimization method (OM). However, what guarantees that the binary operator is fit or efficient? In the above representation, there is no guarantee. It is taken as a given and, hence, cannot be assessed at this level of selection or choice. It can, however, be the subject of selection or choice when it is the object of rational choice or evolutionary selection. This could be the case, as Figure 3 demonstrates, if the binary operator is acting at a deeper level, such as at the k+1 level:

Figure 3. The Binary Operator at k+1 Level.

The binary operator, which consists of technology, rules/instructions, or body plans, involves a hierarchy. It can be at the k-level or deeper, such as the k+1 level. We do not find such a hierarchy with respect to the binary relator (OM) specifying the optimum.

While the elements of the input set and the corollary of the output set are different, the binary relator (OM) does not change, performing the same function irrespective of the level of hierarchy of the binary operator, i.e., whether it is TF_k or TF_k+1. In the above schemata, the OM selects or chooses x_iTF_k^* as the optimum input that corresponds to the optimum end, E^*_k. While the binary operator (TF_k) cannot play the role of natural selection (binary relator), it is the product of natural selection at a deeper level, i.e., at the k+1 level. However, when the binary relator functions, i.e., as the OM, it must take the binary operator, whether TF_k or TF_k+1, as given. Such a limited optimization function should not be taken, à la “soft” neo-Darwinians or à la the critics of standard economists (see Khalil, 2013a), as a shortcoming that undermines or repudiates the notion of optimization per se. To wit, the raison d’être of optimization is the existence of limits taken as given. Therefore, the term “limited optimization” is pleonasm.

There are other nuances, which this paper ignores, of the common structure that underpins the Organismus automaton and Organismus economicus hypothesis. Importantly, the structure of each hypothesis is the same and can handle different kinds of complications and qualifications at secondary and tertiary approximations. Most importantly, in this proposed structure, the trait-as-technology, i.e., the binary operator, functions as a transformation function that varies according to the level of the hierarchy. In contrast, the binary relator (OM) remains constant, i.e., irrespective of the level of hierarchy.

Are binary operators and binary relators opposite of each other?

While binary operators (cognitive capacity or technology) and binary relators (rational choice) are different, this does not mean that they are opposite of each other. While this paper argues that both binary linkages are analytically different, they are functionally linked. Indeed, it is impossible for the decision maker to make rational decisions—i.e., undertake binary relator actions—without relying on cognitive capacities, traits, physiological organs, or transformative technologies, i.e., binary operators.

For instance, Varian (1992) commences his influential graduate-level economics textbook with the binary operator. He dedicates Chapter 1 to discussing the capability of a firm—as expressed by the available technology, machines, buildings, space, and workers—to transform inputs into outputs. Varian then proceeds in Chapter 2 to discuss how the firm uses such capability, i.e., the binary operator, in different ways depending on the environment and other constraints. The firm’s objective is the maximization of profit, which prescribes a choice that amounts to a binary relator (rationality).

The fact that the binary relator (rational choice) relies on a binary operator (technology or capacity) should not lead us to conflate the two. Rationality cannot be both a binary relator and a binary operator. As a binary relator, rationality involves a binary operator. However, the opposite is not the case: Once a technology or a capacity (binary operator) is set up, its operation does not involve a binary relator (rationality).

The incoherence problem

The proposed distinction between the OM, which acts as a binary relator, and the transformational function (TF_k), which functions as a binary operator, entails the incoherence of what can be called “Rationality-qua-Trait Thesis”.

OM (the binary relator) can be either the standard rational choice or, equivalently, the neo-Darwinian natural selection. In contrast, TF_k (the binary operator) is the given technology or cognitive faculty, such as intelligence and memory. OM cannot be TF_k, as OM is not about transforming inputs to outputs in the technical sense.

More importantly, rational choice or OM cannot be trait-as-input, that is, an element of the left-hand input set. The OM (binary relator) cannot be a member of the set—when its function is about ensuring that the elements are consistently ranked. Treating the OM as a member of itself leads to self-contradiction, i.e., incoherence.

As shown above, TF_k—such as intelligence, memory, or other cognitive faculties—can be an element of the left-hand input set—but then the transformation takes place at a deeper level. There is a hierarchy of technology or body plans. The transformation function (TF) cannot apply to the OM, as the OM cannot become a member of the left-hand input set. There is no hierarchy of rationality, as in the case with TF. What applies to TF cannot apply to OM. If we conceive of the OM as a member of the input set, this leads to a self-reference paradox à la Russell Paradox.

The Russell Paradox

If we accept two theses, neo-Darwinian theory involves a serious self-reference paradox. The first thesis is that a standard sense of rationality exists. The second thesis is that such rationality is a trait. Therefore, standard rationality is a trait that changes and evolves depending on the optimization mechanism, i.e., the natural selection process. However, given the argument above, rationality is an optimization mechanism. Thus, it would be a contradiction, i.e., a self-reference paradox, to state that an optimization process selects the optimization process. If this conclusion is tenable, it is akin to the Russell Paradox (Russell, 1956).

To be clear, the Russell Paradox is not a proof of the argument of this paper. That is, the Russell Paradox does not substantiate this paper’s conclusion. Specifically, once we accept the two theses mentioned above, the neo-Darwinian approach invites the self-reference paradox. This paper employs only the Russell Paradox to illustrate the claimed self-reference paradox.

One helpful example of the Russell Paradox is the well-known Cretan liar paradox and, better, the Barber Paradox (Irvine & Deutsch, 2021). The only barber in a village has a sign posted in his shop that states, “I cut the hair of everyone in the village that does not cut his own hair.” However, who cuts the hair of the barber? If he cuts his own hair, then the barber cannot cut it. If he does not cut his own hair, then the barber cuts it. Such self-contradiction arises from treating the set, which is the barber’s statement, as a member of itself. Such treatment entails that the barber is an element of the set of people who do not cut their own hair, on the one hand, and the barber is the set itself as the one who cuts the hair of such people, on the other.

The Russell Paradox arises from what philosophers recognize as the problem of self-reference. In the case of the Rationality-qua-Trait Thesis, it treats rationality both as an OM and as an element of the set that is the subject of the OM. This self-reference is best illustrated by some of the drawings of M.C. Escher (see Hofstadter, 1980). The first role of the binary relator (OM) is to ensure that the output is consistently ranked and, corollary, that the corresponding inputs are also consistently ranked. Such an organization of inputs also cannot include OMs: how could the OM call for the substitution of one input in favor of another when the OM itself is one such input?