Wim De Neys
email: wim.de-neys@parisdescartes.fr

On Dual and Single Process Models Of Thinking

Popular dual process models of thinking have long conceived intuition and deliberation as two qualitatively different processes. Single process model proponents claim that the difference is a matter of degree and not of kind. Psychologists have been debating the dual vs single process question for at least 30 years. In the present paper I argue that it is time to leave the debate behind us. I present a critical evaluation of the key arguments and critiques and show that-pace both dual and single model proponents-there is currently no good evidence that allows us to decide the debate. Moreover, I clarify that even if the debate were to be solved, it would be irrelevant for psychologists because it does not advance our understanding of the processing mechanisms underlying human thinking.

Introduction

One of the clearest characteristics of our mental life is that some thought processes are easy for us and others are hard. If you are asked "What is your name?" or "How much is 2 + 2?", the answer pops up in a split second without any effort. However, if you are asked "What is the name of the American president who succeeded Dwight Eisenhower" or "How much is 231 x 22?", arriving at a decision will take more time and effort. This distinction between an effortless and effortful or "intuitive" and "deliberate" mode of cognitive processing lies at the heart of the influential dual process models that have been prominent in psychological research on human thinking since the 1960s (e.g., [START_REF] Evans | Dual-processing accounts of reasoning, judgment, and social cognition[END_REF][START_REF] Evans | Reasoning, biases and dual processes: The lasting impact of Wason (1960)[END_REF][START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF][START_REF] Sloman | The empirical case for two systems of reasoning[END_REF][START_REF] Smith | Dual-process models in social and cognitive psychology: Conceptual integration and links to underlying memory systems[END_REF] .

It is presumably hard to overestimate the popularity of dual process models. They have been applied in a very wide range of fields, including research on logical reasoning [START_REF] Evans | Logic and human reasoning: An assessment of the deduction paradigm[END_REF][START_REF] Wason | Dual processes in reasoning?[END_REF], social cognition (Chaiken & Trope, 1999;[START_REF] Gawronski | Two of what? A conceptual analysis of dual-process theories[END_REF], morality [START_REF] Greene | The rise of moral cognition[END_REF], economic decision-making [START_REF] Rand | Spontaneous Giving and Calculated[END_REF], time perception [START_REF] Hoerl | Thinking in and about time: A dual systems perspective on temporal cognition[END_REF], management science [START_REF] Achtziger | Fast or rational? A response-times study of Bayesian updating[END_REF], medical diagnosis [START_REF] Djulbegovic | Dual processing model of medical decision-making[END_REF], religiosity [START_REF] Gervais | Analytic thinking promotes religious disbelief[END_REF][START_REF] Tremlin | Divergent religion: a dual-process model of religious thought, behavior, and morphology. Mind and religion: psychological and cognitive foundations of religiosity[END_REF], health behavior [START_REF] Hofmann | Impulsive versus reflective influences on health behavior: A theoretical framework and empirical review[END_REF], theory of mind [START_REF] Wiesmann | Two systems for thinking about others' thoughts in the developing brain[END_REF], intelligence [START_REF] Kaufman | Intelligence and the cognitive unconscious[END_REF], creativity [START_REF] Barr | Reasoned connections: A dual-process perspective on creative thought[END_REF][START_REF] Cassotti | Inhibitory control as a core process of creative problem solving and idea generation from childhood to adulthood[END_REF], and fake news [START_REF] Bago | Fake news, fast and slow: Deliberation reduces belief in false (but not true) news headlines[END_REF]. They have been featured in best-selling books [START_REF] Kahneman | Thinking, Fast and Slow[END_REF], popular media (e.g., [START_REF] Atlas | The amygdala made me do it[END_REF], and even inspired policy recommendations by the World Bank (e.g., World Bank Group, 2015).

However, despite the extreme popularity of dual process models, they have also been criticized. A key concern has been put forward by proponents of single (or "uni") process models (e.g., [START_REF] Arkes | A levels of processing interpretation of dual-system theories of judgment and decision making[END_REF][START_REF] Hammond | Human judgment and social policy[END_REF][START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF][START_REF] Kruglanski | Only one? The default interventionist perspective as a unimodel-Commentary on Evans & Stanovich[END_REF][START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF][START_REF] Melnikoff | The mythical number two[END_REF][START_REF] Osman | An evaluation of dual-process theories of reasoning[END_REF]. The foundational dual process assumption is that intuition and deliberation are two qualitatively different processes. Intuition and deliberation are assumed to be characterized by fundamentally different operation characteristics, principles, and functions. According to the single process model view there is no such qualitative difference. The single model view does not deny that we can distinguish a more intuitive and more deliberate type of thinking and that these can be subjectively experienced as being quite different. But according to the single model view, this difference is a matter of degree and not kind. The difference between intuition and deliberation is assumed to be merely quantitative in nature. Put differently, intuition and deliberation are conceived to lie on opposite ends of one and the same scale rather than on two completely different scales.

The dual vs single process model debate has been around for a long time and continues to fill the pages of prominent journals (e.g., [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] De Houwer | Moving Beyond System 1 and System 2[END_REF][START_REF] Keren | A tale of two systems: A scientific advance or a theoretical stone soup? Commentary on Evans & Stanovich[END_REF][START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF][START_REF] Melnikoff | The mythical number two[END_REF][START_REF] Osman | Persistent Maladies: The Case of Two-Mind Syndrome[END_REF][START_REF] Pennycook | The mythical dualprocess typology[END_REF]Stephens, Dunn, & Hayes, 2018). My goal in the present paper is to convince the community that it is time to move on and leave the debate behind us. The paper is organized around two main sections. In the first section I review and evaluate key arguments and critiques that have been put forward by single and dual process proponents. Based on this evaluation I argue that here is currently no empirical data or theoretical principle that allows us to decide the debate. In the second section, I clarify that it can be questioned whether the debate can ever be solved and that even if it could, it would be irrelevant for our understanding of the psychological processing mechanisms underlying human thinking. This leads me to conclude that it is pointless for empirical scientists to continue the debate any further.

Before moving on to the main sections I briefly clarify some points with respect to the nomenclature I will be using and the scope of the paper.

Nomenclature and Scope

Single, dual, and multiple processes

Dual process models are a special case of multiple process models. Dual process models assume that we need to posit two qualitatively different processes to characterize human thinking. However, one can make further subdivision and argue for three, four, or more qualitatively different types of processes (e.g., [START_REF] Evans | Reflections on reflection: the nature and function of Type 2 processes in dual-process theories of reasoning[END_REF][START_REF] Houdé | 3-system Theory of the Cognitive Brain: A Post-Piagetian Approach to Cognitive Development[END_REF][START_REF] Samuels | The magical number two, plus or minus: Dual-process theory as a theory of cognitive kinds[END_REF][START_REF] Sherman | On building a better process model: It's not only how many, but which ones and by which means?[END_REF]. All these multiple process models can be opposed to single process models that argue against any qualitative difference [START_REF] Gilbert | What the mind's not[END_REF]. I use the popular dual process label here as an umbrella term for all multiple process models. All the arguments I make with respect to dual process models apply to multiple process models. Put bluntly, if we cannot decide between two qualitatively different processes, a fortiori, we cannot decide between multiple qualitatively different processes.

Dual process and dual systems

Dual process models are also being referred to as dual system models. These labels are often used interchangeably but sometimes they are used to refer to a specific subclass of models. For example, some dual process models are more specific in their scope, others more general [START_REF] Gawronski | Dual-process theories[END_REF]. The more specific models are developed to account for specific phenomena or tasks, the more general ones are intended to be more integrative and apply to various phenomena. Some authors use the system label to specifically refer to the latter, more general models. However, the dual system label can also be used to refer to a further subdivision within the subclass of general models. As I will clarify, dual process theorists have often pointed to various opposing features of intuitive (e.g., fast, effortless) and deliberate thinking (e.g., slow, effortful). Dual systems models can then also refer to those models that assume that there is a perfect alignment between these features. To avoid confusion, I will explicitly refer to this specific view as the perfect alignment dual process view. In all other instances, the labels process and system can be used interchangeably and all arguments apply to the more specific and general instantiations of dual process models.

Dual process model, theory, framework, or view

I will also use the labels model, theory, framework, or view interchangeably. In theory, these labels may carry implications about how advanced, developed and/or specific the predictions of the "theory" are conceived to be. I take a neutral stance in this debate. My use of these labels has no further implications with respect to the specificity or generality of the claims.

Received dual process view

Given the popularity of dual process models it will be no surprise that there are many different types of models. These often share some minimal superordinate family resemblance (e.g., the postulation of two qualitatively different thought processes) but the specifics can vary widely. One could indeed claim that there are as many dual process theories as dual process theorists. Friends and enemies of the framework often call upon the generic or "received" superordinate version in their discussions [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]. This can be problematic because any specific dual process theorist can be criticized for claims they never explicitly made themselves [START_REF] Evans | Dual Process Theories: Perspectives and problems[END_REF]. In the present paper my generic use of the label dual process model simply refers to any model that postulates that there is a qualitative difference between intuitive and deliberate thinking. Whenever making more specific claims the authors in question will be directly cited.

Single and dual process models of thinking

As I noted, dual process models have been applied in a wide range of fields and domains. The main scope of the present paper is the field of thinking (e.g., reasoning and decision-making). It most directly implies the seminal work of authors such as, for example, [START_REF] Kahneman | Thinking, Fast and Slow[END_REF], [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF], [START_REF] Epstein | Integration of the cognitive and the psychodynamic unconscious[END_REF], [START_REF] Sloman | The empirical case for two systems of reasoning[END_REF], or [START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF]. Although I believe the arguments are relevant for dual process models in other fields too (e.g., memory, learning) they will not be directly considered. Hence, as the title suggests, the scope of this paper concerns the discussion between single and dual process models of thinking.

Dual vs Single Model Arguments

In this section I review key arguments around which the dual vs single process debate has centered: feature alignment, defining features, Criterion S, parsimony, and the misinformation issue. I present an illustrative overview and clarify misconceptions that have plagued either side of the debate.

Feature alignment

An introduction to dual process theory typically comes with a table such as Table 1 in which various alleged opposing features of intuitive and deliberate processing are listed. Intuitive thinking is characterized as, for example, fast, effortless, independent of cognitive capacity, etc. whereas deliberation is characterized as being slow, effortful, dependent on cognitive capacity, etc. Why have dual process theorists ever referred to these "listof-features" tables? One reason is that many features often seem to go hand in hand. If I ask you to tell me your name, you can answer in a split second, it does not take you any noticeable effort, and you don't need an Einstein level IQ to answer correctly. In this sense, the list of features simply conveys the quite uncontroversial information or observation that many of these features can be correlated. However, one can also develop a more extreme position and argue that the features do not simply cooccur to some extent but that they necessarily have to do so. Under this extreme view, the features are perfectly aligned along the various dimensions that are listed in the table. A process is always fast and effortless (and so on) or slow and effortful (and so on). You can't have one without the other. If one feature is present all the others in the column are too, and all the opposing features in the other column are not. Under this view, the alignment is posited as a mandatory rule of nature. Such a perfect, natural alignment can then be used to argue for the existence of qualitative differences. The fact that intuition and deliberation are so perfectly contrasted on so many dimensions, might give the impression that they must be two fundamentally different mental "species".

The perfect alignment dual process view is highly problematic in many respects. First, in essence, the "alignment = qualitative difference" argument is not sound. The fact that different features might go hand in hand, does not necessarily inform us about the nature of these differences. Even if all the features in Table 1 were indeed perfectly aligned and always co-occurred, this does not imply that the difference between intuition and deliberation therefore becomes qualitative rather than quantitative. Although it might be persuasive to argue for qualitative differences on the basis of a perfect alignment, there is no logical necessity here. In theory, perfect alignment does not preclude a mere quantitative difference per se. Likewise, at the other end of the spectrum, non-alignment does not argue against the dual process position. The core dual process claim is that there is a qualitative difference between intuitive and deliberate processing. Hence, as long as there exists a qualitative difference along one single dimension (e.g., speed), there is no need for such a difference along multiple features. In sum, the alignment question is orthogonal to the dual vs single process discussion. The extent to which the different features are aligned does not allow us to decide in favor or against a single or dual process model.

A second fundamental problem for the perfect alignment dual process view is that there is a wealth of empirical evidence against it. All one needs is a single example of a case of non-alignment (e.g., a process is slow and effortless). Such cases are not hard to find. One long-known example is the incubation phenomenon [START_REF] Wallas | The Art of Thought[END_REF] whereby setting a problem aside (i.e., not explicitly thinking about it) for some time facilitates solutions. The classic example is a case where after a good night sleep we see the light and realize how to solve a problem we had been struggling with the evening before (for a review of recent empirical work, see [START_REF] Gilhooly | Incubation and intuition in creative problem solving[END_REF]. Incubation is effortless but also slow. One needs to quite literally "sleep on it" or set a problem aside for minutes or even hours. In this sense it is nothing like the snap-second solving of "2 + 2 = 4". Hence, although effortless processes can be fast (as in the "2 + 2 = 4" case), they can be (very) slow too.

The incubation example illustrates that effort and speed do not necessarily align. Effortless processes can be fast but sometimes they will also require extensive "cooking in the back". Obviously, cases of non-alignment are not restricted to the speed and effort features. A good example concerns the alleged alignment between reasoning accuracy and deliberation. Intuitive reasoning processes are often characterize as cueing incorrect ("biased") solutions to logical reasoning problems whereas deliberative processes are assumed to lead to correct solutions. However, a clear counter-example against such alignment can be found in the "rationalization" phenomenon [START_REF] Evans | Rationalization in a reasoning task[END_REF]. Reasoners will often spend quite some time and effort to come up with justifications for incorrect responses. Bluntly put, they engage in deliberation to "make up excuses" and find explicit reasons to support an intuitively cued answer. After such rationalization people will often be more convinced that their erroneous answer was in fact correct [START_REF] Koehler | Explanation, imagination, and confidence in judgment[END_REF][START_REF] Shynkaruk | Confidence and accuracy in deductive reasoning[END_REF]. Hence, this is clear example of a case where deliberation leads to more "bias".

Over the years, critics of the perfect alignment dual process view have systematically identified cases of non-alignment (for reviews see, e.g., [START_REF] Bargh | The four horsemen of automaticity: Awareness, intention, efficiency, and control in social cognition[END_REF][START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF][START_REF] Melnikoff | The mythical number two[END_REF]; see also [START_REF] Hassin | Yes it can: On the functional abilities of the human unconscious[END_REF][START_REF] Moors | Examining the mapping problem in dual process models[END_REF]Moors & De Houwer, 2006a[START_REF] Moors | Problems with dividing the realm of processes[END_REF]. As in the above illustrative classic examples, this makes it crystal clear that the perfect alignment view can be readily rejected. However, from here, the dual vs single process model debate has become muddled. Critics of the dual process view have tended to equate the dual process view and the extreme, perfect alignment view. The evidence against a perfect feature alignment has then been used to argue against the dual process view per se [START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF][START_REF] Melnikoff | The mythical number two[END_REF][START_REF] Osman | An evaluation of dual-process theories of reasoning[END_REF][START_REF] Osman | Persistent Maladies: The Case of Two-Mind Syndrome[END_REF]. Arguably, this confusion results at least partially from the fact that the early dual process theorists have not always been explicit at how strict or perfect the alignment was hypothesized to be [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]. Nevertheless, the feature alignment question is orthogonal to the question as to whether or not intuition and deliberation are qualitatively different. The case for non-alignment does not imply that the difference is quantitative in nature. As long as there exists a qualitative difference along one single dimension, there is no need for such a difference along multiple features [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Pennycook | The mythical dualprocess typology[END_REF]. Consequently, the empirical observation of (non-) alignment does not allow us to decide the debate.

Defining features

In recent years, dual process theorists have explicitly denounced the perfect alignment view [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Stanovich | Defining features versus incidental correlates of Type 1 and Type 2 processing[END_REF]. They have stressed that the dual process view only requires that there is one single feature along which a qualitative difference arises. Such a critical feature is referred to as a defining feature. Its presence or absence allows us to decide whether we are dealing with an intuitive or deliberate process. All other features in the list are merely correlated features. Under specific conditions, they might co-occur with the defining feature but their presence or absence is neither necessary, nor sufficient for intuition or deliberation.

So a first question is: what are the defining features? In theory, a qualitative difference might arise along any of the listed features. Various dual process theorists can have different opinions about which specific feature or features they conceive as defining. Nevertheless, the discussion has typically centered around three specific features: working memory involvement, cognitive decoupling-mental simulation, and autonomy. Some authors posit but a single defining feature [START_REF] Thompson | Why it matters: The implications of autonomous processes for dual process theories-Commentary on Evans & Stanovich[END_REF][START_REF] Pennycook | A perspective on the theoretical foundation of dual-process models[END_REF], others multiple (e.g., [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]. But in general, dual process proponents have argued that there is clear evidence for qualitative processing differences along at least one or some of these three specific features [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Thompson | Why it matters: The implications of autonomous processes for dual process theories-Commentary on Evans & Stanovich[END_REF][START_REF] Pennycook | A perspective on the theoretical foundation of dual-process models[END_REF]. Single process proponents have questioned this claim [START_REF] Keren | A tale of two systems: A scientific advance or a theoretical stone soup? Commentary on Evans & Stanovich[END_REF][START_REF] Kruglanski | Only one? The default interventionist perspective as a unimodel-Commentary on Evans & Stanovich[END_REF][START_REF] Osman | A case study: Dual-process theories of higher cognition-Commentary on Evans & Stanovich[END_REF].

A central issue in the debate-next to the question as to what the defining features are-is that the various defining features are not dichotomous but continuous in nature. A dichotomous feature can only take two values, it is either present or absent (e.g., dead-alive, solid-liquid, male-female1 ). If a feature is dichotomous, we can measure whether it is present or absent and consequently decide whether we are dealing with an intuitive or deliberate thought process. A continuous feature lies on a continuum and can take an infinite number of values. Consequently, in order to establish whether we are looking at an intuitive or deliberate process, we need to determine a cut-off point or threshold. As long as we have X amount of feature A, processing is intuitive in nature, once we're above threshold X, processing will be deliberate in nature. The general problem is that determining this threshold is far from straightforward (e.g., [START_REF] Moors | Examining the mapping problem in dual process models[END_REF][START_REF] Moors | Problems with dividing the realm of processes[END_REF].

I will illustrate the problem with the speed feature. There is little discussion that speed is continuous in nature. No matter how fast intuitive processing is assumed to be, given that it is instantiated in a physical substrate (the brain), it will always take some time. Hence, to determine whether we are dealing with an intuitive or deliberate process we cannot simply check whether the feature is present (the process takes time) or absent (the process takes no time). This implies that we'll need to define and (empirically) determine a threshold at which the qualitatively different type of processing arises. In the case of speed this implies that a process that takes less than X time will be intuitive and a process that takes a nanosecond more will have a completely different quality and become deliberative. Although it might not be easy to imagine how such a difference would arise, in theory, one cannot exclude that processes below and above the threshold will indeed be qualitatively different. In practice, the problem is that we have no principled way of determining and testing where the threshold lies. How would we know whether processes that take less and longer than X time have different qualities? At this point the alignment issue rears its head again. Presumably, we will need to look at correlated features. For example, we might establish that processes above and below the speed threshold are experienced as effortless and effortful. Or we might find that they load differently on working memory, etc. Clearly, this cuts the ground under the defining feature argument: We assume that speed is the defining feature but to test this empirically, we measure effort (or another correlated feature). Hence, speed itself is not the defining feature, effort is.

To be clear, I used speed as an illustrative example. To my knowledge, no dual process theorist has claimed that speed should be considered a defining feature. However, as I will readily demonstrate, the exact same problems plague each of the three features that have been explicitly put forward as defining features. Moreover, the postulated defining features face an additional problem: Whereas we know what speed is and how to measure it (see again footnote 1), the alleged defining features are conceptually vague and less well-defined. I will clarify how this complicates the threshold issue further.

Working memory

In their seminal 2013 paper, Evans and Stanovich posited that a first defining feature of deliberate processing is that it loads on working memory whereas intuitive processing does not. They characterized working memory as the limited capacity, controlled or executive attention system such as it has been put forward in the influential work of [START_REF] Baddeley | Working Memory, Thought, and Action[END_REF] or Engle [START_REF] Barrett | Individual differences in working memory capacity and dualprocess theories of the mind[END_REF][START_REF] Engle | Working memory and executive attention: A revisit[END_REF]. At a very general level of description it is clear what Evans and Stanovich have in mind. Few scholars would contest that attentional resources play a critical role for many higher order functions, including reasoning (e.g., [START_REF] Vandierendonck | Working memory benchmarks-A missed opportunity: Comment on Oberauer et al[END_REF]. However, if we want to use working memory engagement as a defining feature to argue for qualitative differences in a two process model, we need a more fine-grained definition and operationalization. The problem is that there are quite different views and theories on the nature and characteristics of working memory (see for an excellent overview [START_REF] Oberauer | Benchmarks for models of short-term and working memory[END_REF]. This theoretical vagueness complicates drawing a clear, sharp distinction between a process that burdens working memory and one that does not. Put bluntly, if it is not clear how the defining feature needs to be defined, it is hard to know whether or not it has been engaged and whether the postulated qualitatively different type of processing should be observed or not.

In this light it is also illustrative to take recent evolutions in the working memory-or more specifically controlled attention (i.e., one of the processes assumed to underlie working memory, [START_REF] Barrett | Individual differences in working memory capacity and dualprocess theories of the mind[END_REF][START_REF] Engle | Working memory and executive attention: A revisit[END_REF]-literature into account. It has been shown that various processes that had long been considered the hallmark of controlled attention, can also operate unconsciously (e.g., [START_REF] Desender | Comparing Conscious and Unconscious Conflict Adaptation[END_REF][START_REF] Jiang | EEG neural oscillatory dynamics reveal semantic and response conflict at difference levels of conflict awareness[END_REF][START_REF] Jiang | The relationship between conflict awareness and behavioral and oscillatory signatures of immediate and delayed cognitive control[END_REF][START_REF] Linzarini | Cognitive control outside of conscious awareness[END_REF]. For example, traditionally, controlled attention was believed to be critical to override or inhibit interfering stimuli. A classic illustration can be found in the Stroop task in which participants have to name the color of the ink in which a word is written. People are slower to do this and make more errors when the ink color conflicts with the written word (e.g., the word "WHITE" written in black ink) then when the ink color and word are congruent (e.g., the word "BLACK" written in black ink). The standard rationale is that because reading is so automated for educated adults, it is hard to refrain from doing it. Therefore, not giving in to the tendency to read the color word is assumed to require effortful controlled processing.

A classic finding in the Stroop literature is that people will perform better on an incongruent trial when it is preceded by a previous incongruent (vs congruent) trial. The fact that one will already recruit cognitive control when trying to solve the first incongruent trial will facilitate the solving of the subsequent incongruent problem [START_REF] Braem | Getting a grip on cognitive flexibility[END_REF]. However, in recent years it has become clear that this "adaptation" effect is also observed when the first trial is presented subliminally, outside of conscious awareness [START_REF] Desender | Comparing Conscious and Unconscious Conflict Adaptation[END_REF]Jiang et al., 2015a;[START_REF] Jiang | The relationship between conflict awareness and behavioral and oscillatory signatures of immediate and delayed cognitive control[END_REF][START_REF] Linzarini | Cognitive control outside of conscious awareness[END_REF]. Hence, even when you cannot consciously perceive the first trial, you will show facilitation on the subsequent, consciously presented trial. This suggests that control was unconsciously exerted on the subliminal trial without any intent of the participant. These and related findings have resulted in broader theoretical advances that indicate how attentional control mechanisms can simply result from low-level associative mechanisms [START_REF] Abrahamse | Grounding cognitive control in associative learning[END_REF][START_REF] Algom | Reclaiming the Stroop Effect Back From Control to Input-Driven Attention and Perception[END_REF][START_REF] Braem | Getting a grip on cognitive flexibility[END_REF].

Against this backdrop, it becomes clear that working memory and more broadly attentional control engagement needs to be conceived on a continuum. Obviously, there might be differences in complexity. Deliberate thinking can still be characterized as requiring more extensive attentional control than intuitive thinking. However, the problem then becomes to determine the precise splitting point. Exactly what level of attentional control defines deliberate thinking? How do we test whether people's thinking above the threshold is really qualitatively different? These are the exact same problems I highlighted with the speed example above.

Note that dual process proponents may be tempted to reply to this critique by pointing to findings with experimental cognitive constraints paradigms [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]; see [START_REF] Osman | A case study: Dual-process theories of higher cognition-Commentary on Evans & Stanovich[END_REF]. For example, during a reasoning task participants may be given a secondary task (e.g., memorizing a complex visual pattern, e.g., De Neys, 2006) that requires controlled attention resources. Because the secondary task will take up some attentional control resources, fewer of these resources can be allocated to the reasoning task. If reasoning accuracy decreases under the secondary task load, we can therefore conclude that the reasoning process requires attentional control resources. This allows us to operationally classify the reasoning process as a deliberate one. However, dual process theorists are mistaken when arguing that this shows that the process is qualitatively different from intuitive processing. Obviously, even if one assumes that there is a mere quantitative difference between intuition and deliberation, one can still posit that a deliberate process will need more attentional control (i.e., working memory) resources than an intuitive one. If the required amount of resources for proper deliberation is not available, the process cannot be completed successfully. Consequently, the qualitative and quantitative view can make the exact same prediction with respect to the impact of cognitive constraints (e.g., [START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF]. In sum, the cognitive constraints paradigm is a great tool to help us decide whether a process is more intuitive or deliberate in nature, but it does not allow us to conclude anything with respect to the qualitative vs quantitative nature of the two processes.

Cognitive decoupling and mental simulation

According to [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF], a second defining feature of deliberate thinking is that it involves cognitive decoupling and mental simulation. Mental simulation is the process whereby we envision a situation that is not factually the case. Whenever we mentally simulate an event, we must be able to prevent our representation of the imaginary, simulated, or hypothetical situation to become confused with our representation of the real world (otherwise we would no longer know what is real and simulated). Therefore, we need to decouple our representation of the real world from the representation of the simulated event. This decoupling process enables mental simulation. Both go hand in hand (and presumably this is why [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF], have listed them as one single defining feature).

At a general descriptive level, this characterization is again making good sense. Few scholars would disagree with the claim that deliberate thinking will often involve a process whereby we envisage alternative possibilities and hypotheses (i.e., "hypothetical thinking") and decouple representations (e.g., dissociating semantic beliefs and the underlying logical structure of a statement). However, the problem is that if we put this characterization forward as the defining feature that qualitatively differentiates deliberation and intuition, we need a much more specific processing specification. [START_REF] Stanovich | Rationality and the reflective mind[END_REF] has gone to great length to characterize and describe the cognitive decoupling and simulation process. However, to date this theorizing has not clarified how we can operationally measure whether a mental simulation process has occurred or not. The available empirical evidence focuses on measuring correlated features such as the effortful, cognitively demanding nature of mental simulation (e.g., the fact that it will be less likely among people lower in cognitive capacity or under cognitive load, e.g., [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Stanovich | Rationality and the reflective mind[END_REF][START_REF] Stanovich | Individual differences in reasoning: Implications for the rationality debate[END_REF].

At this point it might be worthwhile to clarify some potential confusion with respect to the specification of multiple defining features. As I noted, in theory, a dual process model only requires that there is a qualitative difference along a single dimension. Hence, one single defining feature may suffice. Alternatively, one can also argue that multiple defining features need to be present. For example, a process will need to both engage working memory and involve mental simulation before it can be classified as a deliberate one. This is the position that [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF] seem to be taking. Hence, the two defining features they identified are necessary conditions for a process to be classified as deliberate; they need to co-occur. This is not trivial because as soon as one posits multiple defining features, there might be cases of non-alignment between the defining features. That is, a process might require mental simulation but not engage working memory. One clear example involves cases in which we experience regret. Imagine we hear a story about someone who usually drives their son to school. One day they very exceptionally decide to walk to school and the boy gets overrun by a truck. Here we typically engage in counterfactual thinking (i.e., "If only they had taken the car …"). We readily start envisaging alternative states of affairs. This process involves mental simulation but it is not cognitively demanding. Experimental studies show that people still engage in it when their attentional resources are burdened with a secondary task [START_REF] Goldinger | Blaming the victim" under memory load[END_REF]. Indeed, it is precisely refraining from engaging in this counterfactual reasoning process that seems to be demanding. Hence, there can be cases in which the two defining features will be dissociated [START_REF] Osman | A case study: Dual-process theories of higher cognition-Commentary on Evans & Stanovich[END_REF]. In and of itself this is not a problem. If we define a deliberate process as requiring both features, a process that has only one of the features will simply not be considered a deliberate process. At a practical level, it does become clear that this further complicates the issues that plague each defining feature in isolation. To falsify whether the alleged qualitatively different intuitive and deliberate processing occurs, we need to conjointly measure not only one, but two imprecisely defined concepts.

Autonomy

Dual process theorists have also pointed to the autonomy of intuitive processes as a critical defining feature [START_REF] Pennycook | A perspective on the theoretical foundation of dual-process models[END_REF][START_REF] Thompson | Why it matters: The implications of autonomous processes for dual process theories-Commentary on Evans & Stanovich[END_REF]. In general, autonomous processes are conceived as those processes whose execution is mandatory when their triggering stimuli are encountered. Whenever the stimulus is perceived, the response will be executed, irrespective of the intent of the reasoner. In other words, whenever an autonomous process is initiated it will run to completion whether or not we want it; the outcome is not under control of the reasoner (e.g., [START_REF] Braem | Getting a grip on cognitive flexibility[END_REF][START_REF] Diamond | Executive functions[END_REF].

Note that [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF] characterized autonomous processes as the opposite of processes that require mental simulation. However, this this does not need to be the case. As [START_REF] Thompson | Why it matters: The implications of autonomous processes for dual process theories-Commentary on Evans & Stanovich[END_REF] argued, one can define intuitive processes as being autonomous and deliberate processes as non-autonomous processes without making any further assumptions about the nature of the non-autonomous processing (i.e., whether it involves a mental simulation process or not).

A popular example to illustrate the difference between an autonomous and non-autonomous process is the difference between algebraic problems such as: A) "I + I = ?" and B) "236 * 42 = ?". When faced with problem A, any educated adult cannot help but think of the answer "2". The "2" instantly pops into mind whether or not we want to. With problem B this is not the case. Merely encountering it does not suffice to think of the answer (i.e., 9912), the reasoner will need time and effort to compute it. Clearly, even if we want to, we might not always manage to arrive at the answer. However, the point is that we can actively decide to refrain from computing it. With problem A we do not have this choice; the outcome is not under our control.

As with the other defining features I reviewed, it will be clear that at a general, descriptive level, the autonomy suggestion is far from unreasonable. From a phenomenological point of view, few would disagree that problem A and B above indeed feel quite different. However, whenever we move to a more precise operationalization it becomes readily clear that the autonomy concept also remains too vague.

A key issue is that we are always surrounded by gazillion potential stimuli. Sound, light, and pressure waves constantly hit our retinas, ear drums, and skin. Only a fraction of these are consciously perceived and attended to. Hence, encountering the stimulus per se is not sufficient to define autonomy. We need to attend to the stimulus and consider it relevant in our current processing context. To illustrate, consider the inattentional blindness phenomenon (e.g., the famous "invisible gorilla" studies, [START_REF] Simons | Gorillas in our midst: Sustained inattentional blindness for dynamic events[END_REF]. Imagine you are watching a group of people who are passing a basketball to each other. Your job is to count the number of times the ball is being passed. Unbeknown to you, at a certain point the experimenters will let a man dressed in a gorilla suit run through the court. Most laypeople expect that they would readily notice and attend to such a weird event. However, the experimental data show they do not. The vast majority of participants simply fail to notice the gorilla. Because our attention is focused on the passes-counting task, we are blind to any non-task relevant stimuli. Hence, autonomy is never absolute or universal but always contingent on the context (e.g., our task goals).

To illustrate the point further, imagine you are shown a number of matchsticks in vertical position (e.g., "I") and are asked to mentally rotate them horizontally (e.g., "͟ ") and "glue" them together. You are then asked to estimate how long the resulting summed horizontal line is. You get items such as in Figure 1. After doing a couple dozen of these you presumably will get pretty good at the task. Imagine now that at a certain point you are given the item in Figure 1d. This is physically the exact same stimulus as the stimulus to which you answered "2" in the algebraic task above. However, during the line estimation task you will not readily think of the Arabic numeral "2" but rather of the image "͟ ͟ ͟ ". The point is that there are no universally autonomous processes. Whether or not a stimulus X will mandatorily lead to response Y depends on the current task or "goal" context. Hence, if one wants to use autonomy as a defining feature, one also needs to pinpoint how attention and goal selection are operationalized. Imagine a dual process theorist makes claims about a critical autonomous process that cannot be intentionally controlled. Upon testing we find that the process can be controlled. In this case the dual process theorists can always argue that the subject did not construe the proper goal context. Hence, if we want to make falsifiable autonomy claims, we need to have an independent test to establish the goal context. Putting forward autonomy as a defining feature necessitates specifying an attention and goal selection mechanism. This is far from straightforward. Currently, no dual process theorist has provided such a specification.

Note that my discussion of defining features relied heavily on the arguments put forward in [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]. [START_REF] Evans | Dual Process Theories: Perspectives and problems[END_REF][START_REF] Evans | Reflections on reflection: the nature and function of Type 2 processes in dual-process theories of reasoning[END_REF] has since updated his views. [START_REF] Evans | Dual Process Theories: Perspectives and problems[END_REF][START_REF] Evans | Reflections on reflection: the nature and function of Type 2 processes in dual-process theories of reasoning[END_REF] key point is that a defining feature such as "autonomy" is too broad as defining feature for intuitive thinking. Since many low-level perceptive or digestive processes might in theory operate autonomously, they would also need to be classified as intuitive reasoning processes-which Evans conceives as problematic. Hence, Evans has proposed additional criteria to characterize intuitive thinking. In addition to being autonomous, we are typically also conscious of the output of prototypical intuitive reasoning processes. For example, if you are asked "How much is 2 + 2?" the answer will be accompanied by a subjective feeling of correctness (or rightness, e.g., Thompson, Prowse Turner, & Pennycook, 2011). As Evans (2019) puts it, intuitive thought processes do not require working memory for their operation but they do post their products into working memory in a way that other autonomous processes of the brain do not. Hence, according to the narrower updated definition, the defining feature of intuitive thinking is that it is autonomous and posts it output into working memory.

This framework is an interesting attempt at a more detailed processing specification of intuitive thinking. It allows us to differentiate between different types of intuitive processes (and different types of deliberate processes, see Evans, 2019, for that matter). Unfortunately, however, it does not help to settle the fundamental single vs dual process model debate. Indeed, by positing an additional criterion we again need to measure two imprecisely established concepts. We need to determine whether a process is autonomous and whether its output (and only its output) is posted in working memory. The problems I highlighted for each individual traditional defining feature in isolation are back in full swing here.

Defining feature conclusion

Taken together, the defining features arguments and evidence that dual process proponents have put forward do not suffice to support the claim that intuition and deliberation are qualitatively different. The general problem is that the features are not well-defined and do not allow us to establish a precise threshold at which a continuous feature gives rise to a qualitatively different processing. To avoid confusion, as [START_REF] Keren | A tale of two systems: A scientific advance or a theoretical stone soup? Commentary on Evans & Stanovich[END_REF] noted, this does not imply that there is no such threshold and there are no qualitative differences. The point is that it is extremely hard to establish the threshold empirically and dual process proponents have failed to provide clear evidence for it.

Criterion S

People can sometimes hold simultaneous contradictory beliefs. At the same time we might be convinced that X and not-X are both the case. Consider for example, superstitious beliefs [START_REF] Risen | Believing what we do not believe: Acquiescence to superstitious beliefs and other powerful intuitions[END_REF]. Sport fans might be very well aware that it is physically impossible that the shirt they are wearing affects the performance of their favorite football team, but they might nevertheless be convinced that their team will lose if they don't wear their team jersey while watching the game.

Contradictory beliefs can also occur during reasoning. Consider, for example, the ratio bias problem (Denes-Ray [START_REF] Epstein | Integration of the cognitive and the psychodynamic unconscious[END_REF]. Imagine you're being presented with a small and large tray containing red and white jelly beans. In the small tray there are 1 white and 9 red jelly beans. In the large tray there are 9 white jelly beans and 91 red jelly beans. You can draw one jelly bean from one of the trays (without looking). If you draw a white jelly bean you win $10. Which tray should you draw from to maximize your chances of winning? Logically speaking, you should obviously pick the small tray. The probability of drawing a white jelly bean is 10% (1/10) for the small tray and only 9% (9/100) for the large tray. Nevertheless, many people prefer to draw from the large tray [START_REF] Epstein | Integration of the cognitive and the psychodynamic unconscious[END_REF]. Intuitively, people tend to focus on the absolute number of white beans. Because there are more white beans in the large tray, people intuitively feel it is more likely they'll end up with a white bean. Interestingly, when questioned, participants sometimes indicate they realize their preference is illogical. They report they "know" the odds are against them but nevertheless "feel" that the large tray is giving them a better chance of winning (Denes-Ray & Epstein, 1994;[START_REF] Epstein | Integration of the cognitive and the psychodynamic unconscious[END_REF].

In an influential paper, [START_REF] Sloman | The empirical case for two systems of reasoning[END_REF] argued that the observation of simultaneously held contradictory beliefs (i.e., "criterion S") supports the dual process model. Sloman reasoned that any qualitatively homogeneous reasoning system 2 can provide but a single response at one time. Hence, if we observe two conflicting responses at the same time, they must have been generated by two qualitatively different reasoning systems. This argument has been repeatedly criticized [START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF]Gigerenzer & Regier, 1996;[START_REF] Osman | An evaluation of dual-process theories of reasoning[END_REF] but keeps on being used to justify dual process models [START_REF] Hoerl | Thinking in and about time: A dual systems perspective on temporal cognition[END_REF].

It should be clear that the basic deductive logic of Sloman's argument is sound. If we posit by definition that a system cannot provide but a single response at one time, then criterion S entails we need dual reasoning systems. However, the problem is that the assumption can be questioned. There is no empirical evidence that indicates that simultaneous contradictory responses necessarily result from two qualitatively different reasoning processes [START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF]. That is, one and the same qualitative system can also produce simultaneous contradictory responses [START_REF] Kelso | The Complementary Nature[END_REF]. Hence, we should be able to empirically determine whether two responses are generated simultaneously 3 . However, the key point is that the claim that such co-occurrence results from two qualitatively different processes does not itself rely on empirical data and can be questioned.

Parsimony

The previous subsections indicated that it is hard to decide the single vs dual process debate based on empirical data. The evidence does not suffice to conclude that there are qualitative differences but we cannot exclude it either. Given the empirical ambivalence, one may also try to decide the debate with more theoretical arguments. For example, some scholars have argued in favor of a single process account on the basis of parsimony (e.g., [START_REF] Hammond | Human judgment and social policy[END_REF][START_REF] Hayes | The dimensionality of reasoning: Evidence for a single process account of inductive and deductive inference[END_REF]; see also [START_REF] Gawronski | Dual-process theories[END_REF].

The principle of parsimony or "Occam's razor" posits that when two hypotheses are equally well (or badly, if you wish) supported by the data, we should favor the hypothesis that makes the least assumptions. Put differently, simpler models are more likely to be true. The dual process model assumes there are two qualitatively different types of reasoning; the single process account only postulates one single process. Since one is less than two, parsimony might seem to force us to favor the single model account. However, although this argument might be appealing in its simplicity, it is fallacious. An easily overlooked aspect of parsimony is that it 2 There is a long and muddled discussion about what constitutes a reasoning "system" (e.g., [START_REF] Keren | Two is not always better than one: A critical evaluation of two-system theories[END_REF][START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF]. By all means, "dual system" and "dual process" can be used as synonyms here. A dual system model posits two qualitatively different processes (see Nomenclature section 1.2).

3 More generally, in discussions concerning the criterion S argument there might be some confusion between the quality and time-course of mental processes. If at the exact same point in time, two conflicting responses become available, most scholars will presumably agree that one may claim that the two responses are computed by different processes. One process might be more intuitive, the other more deliberate. Hence, this indicates that in this case the intuitive and deliberate processes run in parallel (i.e., simultaneously) rather than serially (i.e., one after the other). However, this does not imply that both processes are qualitatively different. In a single process model, intuitive and deliberate processing might be activated at the same time too [START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF]. Hence, the quality and time-course question are orthogonal. Criterion S or the empirical observation of simultaneous contradictory beliefs might inform us about the time-course of different processes, but it does not allow us to argue in favor or against the existence of qualitative differences.

refers to the total number of theoretical assumptions that are required to explain a given finding [START_REF] Gawronski | Dual-process theories[END_REF][START_REF] Gawronski | Two of what? A conceptual analysis of dual-process theories[END_REF]. That is, single process models make additional assumptions beyond the simple claim that there is no qualitative difference between intuitive and deliberate processing. For example, Kruglanski's single process models [START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF][START_REF] Kruglanski | On parametric continuities in the world of binary either ors[END_REF] feature numerous parameters that will modify the activation within the model. Without these parameters the empirical findings cannot be fully accounted for. Any contrast between a single and dual process model needs to take the full range of assumptions or parameters into account. Consequently, the fact that a dual process model postulates two qualitatively different processes does not make it less parsimonious per se.

Since the parsimony argument is often misapplied it is worthwhile to clarify the point with an illustrative example. Imagine we have a single process model. Intuitive and deliberate processing are conceived as opposite ends of one and the same scale. In and of itself, this model is not very useful. If the model wants to have any predictive and explanatory value it will need to make additional assumptions and propose further specifications. For example, can reasoners engage in both types of processing simultaneously (i.e., can more intuitive and deliberate processes run in parallel)? Are the amount of simultaneous intuitive and deliberate processing independent of each other (e.g., can we engage in full blown intuitive and deliberate processing at the same time or does more intuitive reasoning necessarily implies less deliberate processing?). Imagine that we have a single process model in which intuitive and deliberate thinking are posited to be fully interdependent. The amount of activation at one level is the complement of the activation at the other level. So if we are at 70% of maximum intuitive processing, we're necessarily at 30% of maximum deliberate processing. In this model a single parameter would suffice to model the activation state of the reasoner. But we can also envisage an alternative single process model in which the activation levels are independent. Intuitive activation might be at 60% and deliberate processing at, say, 5% of their maximum activation. In this case, even though we assume that there is no qualitative difference between intuition and deliberation, our single process model would still need two independent parameters to track the activation state of the reasoner.

At the other end of the spectrum, in theory, we can also construct dual process models with independent and interdependent activation 4,5 . The interdependent dual process model would assume that there are qualitative differences between intuition and deliberation but that their activation is linked. In this case, a single parameter 4 Some might want to equate single process models with a dependent activation assumption and dual process models with an independent one. Under this specific operationalization, a single process model would necessarily be defined as an activation dependent model (and vice versa). However, whether intuition and deliberation are qualitatively different and whether their activation is interdependent are two orthogonal questions [START_REF] Gilbert | What the mind's not[END_REF][START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF].

5 There can also be some confusion here because of a possible misunderstanding concerning the interdependency of intuitive and deliberate processing. As noted, some may tend to spontaneously equate a dual process model with an independent activation model. If two processes are qualitatively different, people assume that their activation levels cannot depend on each other. However, this assumption is not correct. It can be helpful to illustrate the point with an example. Imagine we have two machines. One is powered by steam power. Water flows from a water tank in a boiler, gets heated, the resulting steam moves a piston and drives the machine. The second machine is driven by muscle power. The machine is connected to the sprocketwheel of a stationary bike on which a human is pedalling. Most scholars will presumably agree that we can say that both machines are being powered by qualitatively different mechanisms. However, clearly, in order to keep on pedalling, the cyclist needs to stay hydrated and drink. Imagine the cyclist is being hydrated with water from the same tank the steam engine is being fed with. The harder the cyclist pedals, the more water they will need, and the less water will be available for the steam engine. Hence, although the machines are driven by a qualitatively different type of engine, their activation might show some (minimal) dependency. The same conceptual point can be made about cognitive processes. Ultimately, these are instantiated in the brain. Imagine that intuitive and deliberate processing are qualitatively different and instantiated by two different brain regions X and Y. Because both regions need oxygen to function, depending on the specific wiring of the two regions, it might be that increased activation in region X necessarily results in a lower activation in region Y. Clearly, these are hypothetical examples. I do not want to make claims about the localization of intuitive and deliberate processing or their neural instantiation. The point is simply to illustrate that assuming that processes are qualitatively different does not necessarily imply that their activation level cannot be interdependent to some extent. can suffice to represent the activation state of a dual process model. Alternatively, a dual process model might also posit independent activation and-just as its single process independent activation cousin-it would require two parameters.

In sum, the parsimony of our models is determined by the specific processing assumptions they make, not simply by the fact whether we posit qualitative or quantitative differences. Processing assumptions such as the activation dependency question can be tested empirically (see further 3.2), but they do not allow us to decide between a single and dual process view per se.

Scientific misinformation argument

Another popular practical argument that is often used against dual process models is that they are bound to lead to misinformation and halt scientific progress (e.g., Cokely, 2009;[START_REF] Melnikoff | The mythical number two[END_REF][START_REF] Osman | An evaluation of dual-process theories of reasoning[END_REF][START_REF] Osman | Persistent Maladies: The Case of Two-Mind Syndrome[END_REF]. The argument goes that because intuition and deliberation are subjectively experienced as quite different, people are readily tempted to conclude that they are qualitatively different. Although there is no factual evidence for the duality, because of its simplicity, it is bound to slip into scientists' mind and-through science communication-into popular culture. Hence, the unsupported dichotomization will distort scientists' conceptualizations and misinform the general public. Since a single process model does not posit a duality it would fare better in this respect.

There are various points to make against this argument. First, the scientific sound conclusion is that there is currently no empirical evidence to decide between a single or dual process model view. Hence, logically speaking, one might indeed argue that a dual process model misrepresents the scientific knowledge by positing that there is a qualitative difference between intuition and deliberation. But obviously, by the same logic, a single process model equally misrepresents the scientific knowledge by positing that there is no qualitative difference.

Second, any scientific claim can be misinterpreted [START_REF] Chater | Is the Type 1/Type 2 Distinction Important for Behavioral Policy?[END_REF]. It is indeed not hard to envisage how the dual process duality might distort some people's judgment [START_REF] Melnikoff | The mythical number two[END_REF]. But the same is true for the single model view. For example, in a single process model people might be tempted to infer that if intuition and deliberation are not really different, it does not matter whether we do one or the other. Hence, this might give people the perfect excuse to refrain from engaging in demanding deliberation altogether. To date, there is no systematic comparative empirical data that speaks to the issue. The claim that a dual process model is more dangerous than a single process model when it comes to misinforming the public (or vice versa) relies on personal opinion and anecdotes. In the absence of hard data, scientists should refrain from making strong claims here.

Third, the strong general claim that the dual process conceptualization halts scientific progress per se is easily disproven in practice. One example is work on conflict detection during reasoning (e.g., [START_REF] Bonner | In conflict with ourselves? An investigation of heuristic and analytic processes in decision making[END_REF][START_REF] De Neys | Conflict monitoring in dual process theories of thinking[END_REF][START_REF] Gangemi | Feelings of error in reasoning-in search of a phenomenon[END_REF][START_REF] Mata | Seeing the conflict: an attentional account of reasoning errors[END_REF][START_REF] Pennycook | Base rates: Both neglected and intuitive[END_REF][START_REF] Stupple | When logic and belief collide: Individual differences in reasoning times support a selective processing model[END_REF][START_REF] Swan | To detect or not to detect: A replication and extension of the threestage model[END_REF][START_REF] Travers | The time course of conflict on the Cognitive Reflection Test[END_REF]. At least since the 1960s it is well established in the reasoning and decision-making literature that people's intuitions can cue so-called "heuristic" answers that can lead them to violate logical principles [START_REF] Evans | Logic and human reasoning: An assessment of the deduction paradigm[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. Traditionally, it was assumed that this "bias" results from a failure to detect that our intuitions conflict with more logical considerations (Morewedge & Kaheman, 2010). In the last decade, empirical studies on conflict or bias detection have forced scholars to revise the view. Response latency, confidence, and brain-activation data obtained with new experimental paradigms indicated that biased reasoners often show some minimal sensitivity to their errors (for review and discussion see De [START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF][START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF].

Interestingly, the vast majority of the work on conflict detection has used a dual process conceptualization (e.g., [START_REF] Bago | The smart System 1: Evidence for the intuitive nature of correct responding on the bat-and-ball problem[END_REF][START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF][START_REF] De Neys | Conflict monitoring in dual process theories of thinking[END_REF][START_REF] Pennycook | Base rates: Both neglected and intuitive[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF][START_REF] Swan | To detect or not to detect: A replication and extension of the threestage model[END_REF][START_REF] Thompson | Conflict, metacognition, and analytic thinking[END_REF][START_REF] Travers | The time course of conflict on the Cognitive Reflection Test[END_REF]. Indeed, the findings have been critical in the development of revised dual process models (for review see De [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF][START_REF] De Neys | Logic, fast and slow: Advances in dual-process theorizing[END_REF]. To avoid confusion, the point I am making here is not that the conflict detection work supports the dual process view per se. One could readily present a single model variant to account for the findings. Arguably, one might say that the dual process framework in research and theorizing on conflict detection has been used as a communicative tool. It has been a handy vehicle to conceptualize key points and facilitate communication among scholars. However, the point is that the use of the dual process lingo per se has not prevented scholars from making advances in answering outstanding questions. We know more about the conflict detection process than we did a decade ago. The work has resulted in new empirical findings, the development of new methodology, and theoretical advances [START_REF] De Neys | Logic, fast and slow: Advances in dual-process theorizing[END_REF]. This presents a clear counterexample against the claim that adopting a dual process framework is necessarily bound to block scientific progress.

In conclusion, whether scholars adopt a dual or single process model, they obviously need to make sure that people are not misinformed about the scientific findings and their implications. One might question whether dual process theorists have done enough to avoid possible misinterpretation of their ideas in the past [START_REF] Melnikoff | The mythical number two[END_REF]. But in and of itself, the claim that the mere adoption of a dual (vs single) process view endangers scientific advances or misinforms the public is unsupported. There is no ground to favor a single over a dual process model (or vice versa) on the basis of this argument.

An Irrelevant Debate

The first part of this paper clarified that after 30 years of debate, there is currently no good evidence that would allow us to decide between the single and dual process model view. Therefore, some might be tempted to conclude that we need to increase our efforts to find such empirical evidence. Much to the contrary, I believe that we should move on and let the debate lie. As I clarify in this section, first, it can be questioned whether the debate can ever be solved. Second, and more critically, even if it can be solved, the debate will not advance our psychological understanding of human thinking.

A non-empirical debate

Can the single vs dual process debate ever be solved? I already highlighted the complexity involved in specifying a defining feature, determining a feature threshold, and testing whether processing above and below the threshold is qualitatively different. At the very least this indicates that it is far from clear how one would go about to set up an experiment to address these issues. However, more generally, one can also argue that it is-by definition-impossible to settle the debate with empirical data.

As [START_REF] Gawronski | Two of what? A conceptual analysis of dual-process theories[END_REF] have noted, there is a long tradition in philosophy that argues that existence claims-such as the question as to how many reasoning processes (one, two, …) there "really" are-are metaphysical in nature and cannot be tested empirically (e.g., [START_REF] Popper | The logic of scientific discovery[END_REF][START_REF] Quine | Word and object[END_REF]. Philosophers such as [START_REF] Whitehead | Process and Reality[END_REF] have long pointed to the limitations of language in these discussions. For example, one may argue that semantically speaking, there is a point at which a mere quantitative difference becomes qualitative. To illustrate, think, for example, of a game of basketball. I can call some friends; we can go to a court, make two teams, and start passing and shooting. In one sense, there is no qualitative difference between what my friends and I are doing on the court and what professional teams such as the LA Lakers and Golden State Warriors do when they play each other. It is not the case that my friends and I are playing ice-hockey and the Lakers and Warriors are playing football. Both of us can be playing a game of basketball. However, in another sense, one may argue that the mere quantitative difference in physical, technical, and tactical skills can be so extreme that the two games become qualitatively different. In that sense, LeBron James and I are playing a different game.

To illustrate further, think of one and the same person at different life stages, say, at age 10 and age 40. In one sense, this individual is qualitatively the same and changes are merely quantitative in nature. We might be taller and smarter at age 40 than at age 10, but it is not the case that at age 10 we are insects and at age 40 we are horses. However, at the same time, one can argue that our accumulated experiences result in a qualitative difference in the way we perceive the world at the two life stages. In this sense, we are not the same person at age 10 and age 40. These examples illustrate how debates about qualitative and quantitative differences are intertwined with semantic discussions in which empirical data will be of little avail.

A trivial debate

The dual vs single process debate has not yet been settled and it can be questioned whether we'll ever manage to decide it. Is this a problem for the psychological study of intuitive and deliberate thinking? I believe not. To illustrate, consider what we would learn if we were to find that intuition and deliberation are qualitatively different or not. How would this knowledge advance our theorizing? The goal of any psychological theory of thinking is to identify the operating principles and mechanisms that allow us to think. We need to know how intuition and deliberation work and how they interact. My point is that merely knowing that intuition and deliberation are qualitatively rather than quantitatively different does not allow us to make a single prediction in this respect. This is readily clarified by looking at some of the key outstanding questions in the field.

For example, one critical question concerns what we can do at the more intuitive vs deliberate end of the processing spectrum. Irrespective of whether intuition and deliberation are qualitatively different, what can we accomplish when we intuit or deliberate? Are certain behaviors and decisions affected by the fact that we deliberate more or less? For example, if we want to arrive at sound logical conclusions do we need to deliberate more or less (e.g., [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF], 2019;[START_REF] Evans | Reflections on reflection: the nature and function of Type 2 processes in dual-process theories of reasoning[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF][START_REF] Gigerenzer | Heuristics: The foundations of adaptive behavior[END_REF]? Do intuition and deliberation tend to cue different types of moral decisions (e.g., [START_REF] Greene | The rise of moral cognition[END_REF]? Do we behave more altruistically when we intuit more or less (e.g., [START_REF] Rand | Spontaneous Giving and Calculated[END_REF]? Are we more or less susceptible to fake news when we deliberate more (e.g., Bago et al., 2020)?

Second, how do we decide to engage more/less deliberation (e.g., [START_REF] Kruglanski | Intuitive and deliberate judgments are based on common principles[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF][START_REF] Thompson | Intuition, reason, and metacognition[END_REF][START_REF] Stanovich | Miserliness in human cognition: the interaction of detection, override and mindware[END_REF]? If there are things we do better (or more) at each end of the intuition vs deliberation end, how do we know we need to switch from one to the other? Do we make these decisions randomly? Which cues or mechanisms do we use to detect we need to deliberate more or less?

Third, what is the time course of intuitive and deliberate thinking? Can we do both at the same time (e.g. [START_REF] Evans | On the resolution of conflict in dual process theories of reasoning[END_REF][START_REF] Gilbert | What the mind's not[END_REF][START_REF] Handley | Dual processes and the interplay between knowledge and structure: A new parallel processing model[END_REF]? Is the amount of intuitive processing inversely proportional to the amount of deliberate processing? Are both completely independent?

Fourth, can we optimize people's reasoning? How do we get people to intuit more or less whenever it is useful to do so (e.g., [START_REF] Morewedge | Debiasing decisions: Improved decision making with a single training intervention[END_REF]?

It will be clear that knowing whether intuition and deliberation are qualitatively different per se, does not bring us a single step closer to formulating an answer to these critical questions. Whether intuition and deliberation are qualitatively or merely quantitatively different does not tell us what we can still do when we minimize deliberation, how we switch from one to the other, etc. Hence, whether the difference between intuition and deliberation is conceived as quantitative or qualitative in nature has no further restrictions on our psychological theory development. It is in this sense that the single vs dual process model debate is irrelevant. The debate does not inform or restrict our theorizing about the underlying psychological processing mechanisms.

Our key outstanding questions are orthogonal to the question as to whether the difference between the postulated intuitive and deliberate processes is qualitative or quantitative in nature.

An example might be helpful to illustrate the basic point. Consider the outstanding question with respect to the optimization of people's reasoning. Imagine that in a specific task we find that deliberation leads to more optimal performance than intuitive thinking. Assume that we would know that there is a qualitative difference between intuition and deliberation in that deliberation loads working memory whereas intuition does not. One hypothetical intervention approach would be to train people's working memory since this would allow them to deliberate better. Now assume that there is a mere quantitative difference between intuition and deliberation. Intuition requires but a minimal amount of working memory whereas deliberation taxes it heavily. Obviously, in this case too it will be beneficial to train people's working memory. Given deliberation's quantitatively higher demands on working memory, the larger your resource pool, the better you will manage to deliberate. Hence, there is no unique connection between our answer to the quantity vs quality question and choice of intervention. One does not inform the other. It is in this regard that I perceive the quality vs quantity debate to be irrelevant.

Time to Move On

The dual vs single process model debate has not been resolved, it can be questioned whether the debate can be resolved, and even if it were to be resolved, it will not inform our theory development about the critical processing mechanism underlying human thinking. This implies that the debate is irrelevant for the empirical study of thinking. In a sense the choice between a single and dual process model boils-quite literally-down to a choice between two different religions. Scholars can (and may) have different personal beliefs and preferences as to which model serves their conceptualizing and communicative goals best. However, what they cannot do is claim there are good empirical or theoretical scientific arguments to favor one over the other.

I do not contest that the single vs dual process model debate might have been useful in the past. For example, the relentless critique of single process proponents helped to discard the erroneous perfect feature alignment view. Likewise, the work of Evans and Stanovich in trying to pinpoint defining features was helpful to start sketching the descriptive building blocks of the mental simulation and cognitive decoupling process. Hence, I do believe that the debate has had some positive by-products.

To avoid confusion, I also do not argue that the study of intuitive and deliberate thinking per se is pointless. Much to the contrary, I believe this is one of the most fascinating and important challenges for psychological scientists. Above I pointed to critical outstanding questions for the field. These questions can be addressed with empirical research and critical advances have been made over the last decades. But my argument is precisely that the answer to these questions is orthogonal to the question as to whether intuition and deliberation differ qualitatively or not. Hence, my claim is that trying to answer the core single vs dual process model debate is pointless for empirical scientists. This does not imply that we cannot or should stop studying intuitive and deliberate thinking.

The ultimate problem is that researchers have but limited time and resources. Time and resources spent arguing about qualitative or quantitative differences are not spent on the other, more pressing outstanding issues. In terms of opportunity costs, continuing this debate is not warranted. It is high time for the field to move on and focus our energy on more critical questions concerning the nature of intuitive and deliberate thinking.

Figure 1 .

 1 Figure 1. Illustration of the line length estimation task

Table 1

 1 Features often attributed to intuitive and deliberate thinking

	Intuitive ("System 1")	Deliberate ("System 2")
	Fast	Slow
	Effortless	Effortful
	Independent of cognitive ability	Correlated with cognitive ability
	Automatic	Controlled
	Does not require working memory	Requires working memory
	Autonomous	Cognitive decoupling and mental simulation
	Unconscious	Conscious
	Biased responses	Correct, normative responses
	Contextualized	Abstract
	Associative	Rule-based
	Affective	Logical
	Implicit knowledge	Explicit knowledge
	Evolutionary old	Evolutionary recent
	Shared with other animals	Distinctively human

I am using these as illustrative, descriptive or phenomenological level examples. I fully realize that quantum physicists and biologists can readily argue that even in these cases there can be mixed states and the examples are consequently not fully discrete. This strengthens the point that determining an exact splitting point is highly problematic.

Acknowledgments

I would like to thank the Agence Nationale de la Recherche for their support (ANR-16-CE28-0010-01). I also thank David Melnikoff for a stimulating twitter discussion concerning Criterion S.