Research on the capacity to understand others' minds has tended to focus on representations ofbeliefs,which are widely taken to be among the most central and basic theory of mind representations. Representations ofknowledge, by contrast, have received comparatively little attention and have often been understood as depending on prior representations of belief. After all, how could one represent someone as knowing something if one does not even represent them as believing it? Drawing on a wide range of methods across cognitive science, (...) we ask whether belief or knowledge is the more basic kind of representation. The evidence indicates that nonhuman primates attribute knowledge but not belief, that knowledge representations arise earlier in human development than belief representations, that the capacity to represent knowledge may remain intact in patient populations even when belief representation is disrupted, that knowledge (but not belief) attributions are likely automatic, and that explicit knowledge attributions are made more quickly than equivalent belief attributions. Critically, the theory of mind representations uncovered by these various methods exhibits a set of signature features clearly indicative of knowledge: they are not modality-specific, they are factive, they are not just true belief, and they allow for representations of egocentric ignorance. We argue that these signature features elucidate the primary function of knowledge representation: facilitating learning from others about the external world. This suggests a new way of understanding theory of mind – one that is focused on understanding others' minds in relation to the actual world, rather than independent from it. (shrink)

The lack of consensus on how to characterize humans’ capacity for belief reasoning has been brought into sharp focus by recent research. Children fail critical tests of belief reasoning before 3 to 4 years (Wellman, Cross, & Watson, 2001; Wimmer & Perner, 1983), yet infants apparently pass false belief tasks at 13 or 15 months (Onishi & Baillargeon, 2005; Surian, Caldi, & Sperber, 2007). Non-human animals also fail critical tests of belief reasoning but can show very complex social behaviour (e.g., (...) Call & Tomasello, 2005). Fluent social interaction in adult humans implies efficient processing of beliefs, yet direct tests suggest that belief reasoning is cognitively demanding, even for adults (e.g., Apperly, Samson & Humphreys, 2005). We interpret these findings by drawing an analogy with the domain of number cognition, where similarly contrasting results have been observed. We propose that the success of infants and non-human animals on some belief reasoning tasks may be best explained by a cognitively efficient but inflexible capacity for tracking belief-like states. In humans this capacity persists in parallel with later-developing, more flexible but more cognitively demanding theory of mind abilities. (shrink)

Working memory limits are best defined in terms of the complexity of the relations that can be processed in parallel. Complexity is defined as the number of related dimensions or sources of variation. A unary relation has one argument and one source of variation; its argument can be instantiated in only one way at a time. A binary relation has two arguments, two sources of variation, and two instantiations, and so on. Dimensionality is related to the number of chunks, because (...) both attributes on dimensions and chunks are independent units of information of arbitrary size. Studies of working memory limits suggest that there is a soft limit corresponding to the parallel processing of one quaternary relation. More complex concepts are processed by or In segmentation, tasks are broken into components that do not exceed processing capacity and can be processed serially. In conceptual chunking, representations are to reduce their dimensionality and hence their processing load, but at the cost of making some relational information inaccessible. Neural net models of relational representations show that relations with more arguments have a higher computational cost that coincides with experimental findings on higher processing loads in humans. Relational complexity is related to processing load in reasoning and sentence comprehension and can distinguish between the capacities of higher species. The complexity of relations processed by children increases with age. Implications for neural net models and theories of cognition and cognitive development are discussed. (shrink)

How do minds emerge from developing brains? According to the representational features of cortex are built from the dynamic interaction between neural growth mechanisms and environmentally derived neural activity. Contrary to popular selectionist models that emphasize regressive mechanisms, the neurobiological evidence suggests that this growth is a progressive increase in the representational properties of cortex. The interaction between the environment and neural growth results in a flexible type of learning: minimizes the need for prespecification in accordance with recent neurobiological evidence (...) that the developing cerebral cortex is largely free of domain-specific structure. Instead, the representational properties of cortex are built by the nature of the problem domain confronting it. This uniquely powerful and general learning strategy undermines the central assumption of classical learnability theory, that the learning properties of a system can be deduced from a fixed computational architecture. Neural constructivism suggests that the evolutionary emergence of neocortex in mammals is a progression toward more flexible representational structures, in contrast to the popular view of cortical evolution as an increase in innate, specialized circuits. Human cortical postnatal development is also more extensive and protracted than generally supposed, suggesting that cortex has evolved so as to maximize the capacity of environmental structure to shape its structure and function through constructive learning. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

What makes an object the same persisting individual over time? Philosophers and psychologists have both grappled with this question, but from different perspectives—philosophers conceptually analyzing the criteria for object persistence, and psychologists exploring the mental mechanisms that lead us to experience the world in terms of persisting objects. It is striking that the same themes populate explorations of persistence in these two very different fields—e.g. the roles of spatiotemporal continuity, persistence through property change, and cohesion violations. Such similarities may reflect (...) an underlying connection, in that psychological mechanisms of object persistence (especially relevant parts of mid-level visual object processing) may serve to underlie the intuitions about persistence that fuel metaphysical theories. This would be a way for cognitive science to join these two disparate fields, helping to explain the possible origins and reliability of some metaphysical intuitions, and perhaps leading to philosophical progress. (shrink)

Though nativist hypotheses have played a pivotal role in the development of cognitive science, it remains exceedingly obscure how they—and the debates in which they figure—ought to be understood. The central aim of this paper is to provide an account which addresses this concern and in so doing: a) makes sense of the roles that nativist theorizing plays in cognitive science and, moreover, b), explains why it really matters to the contemporary study of cognition. I conclude by outlining a range (...) of further implications of this account for current debate in cognitive science. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...) facie favor a realist account of numbers. (shrink)

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...) knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology. (shrink)

According to proper functionalist theories of warrant, a belief is warranted only if it is formed by cognitive faculties that are properly functioning according to a good, truth-aimed design plan, one that is often thought to be specified either by intentional design or by natural selection. A formidable challenge to proper functionalist theories is the Swampman objection, according to which there are scenarios involving creatures who have warranted beliefs but whose cognitive faculties are not properly functioning, or are poorly designed, (...) or are not aimed at truth. In this paper, we draw lessons from cognitive science in order to develop a novel argument for the conclusion that the Swampman objection fails against proper functionalist theories of warrant. Our argument not only shows that the underlying, central intuition motivating Swampman-like scenarios is false but also motivates proper function as a necessary condition for warrant, thereby lending support to the claim that any theory of knowledge that lacks a proper function requirement is false. (shrink)

Much evidence has accumulated in favor of such a dual view of reasoning. There is however some vagueness in the way the two systems are characterized. Instead of a principled distinction, we are presented with a bundle of contrasting features - slow/fast, automatic/controlled, explicit/implicit, associationist/rule based, modular/central - that, depending on the specific dual process theory, are attributed more or less exclusively to one of the two systems. As Evans states in a recent review, “it would then be helpful to (...) have some clear basis for this distinction”; he also suggests that “we might be better off talking about type 1 and type 2 processes” rather than systems. We share the intuitions that drove the development of dual system theories. Our goal here is to propose in the same spirit a principled distinction between two types of inferences: ‘intuitive inference’ and ‘reflective inference’. We ground this distinction in a massively modular view of the human mind where metarepresentational modules play an important role in explaining the peculiarities of human psychological evolution. We defend the hypothesis that the main function of reflective inference is to produce and evaluate arguments occurring in interpersonal communication. This function, we claim, helps explain important aspects of reasoning. We review some of the existing evidence and argue that it gives support to this approach. (shrink)

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...) few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature (...) from across the cognitive sciences and describe how the evidence reported in these works supports the hypothesis that numerical cognitive processing is modular. I outline the properties that would suffice for deeming a certain processing system a modular processing system. Subsequently, I use behavioral, neuropsychological, philosophical, and anthropological evidence to show that the number module is domain specific, informationally encapsulated, neurally localizable, subject to specific pathological breakdowns, mandatory, fast, and inaccessible at the person level; in other words, I use the evidence to demonstrate that some of our numerical capacity is housed in modular casing. (shrink)

There has been a call for a potentially revolutionary change to our existing understanding of the psychological concept of personal identity. Apparently, people can psychologically represent people, including themselves, as multiple individuals at the same time. Here we ask whether the intransitive judgments found in these studies truly reflect the operation of an intransitive concept of personal identity. We manipulate several factors that arbitrate between transitivity and intransitivity and find most support for transitivity: in contrast to prior work, most participants (...) do not make intransitive judgments when there is any reason to favor one individual over another. People change which single individual they personally identify with, depending on which individual competes more strongly or weakly for identity, rather than identifying with both individuals. Even when two individuals are identical and therefore both entitled to be the same person, we find that people make more transitive judgments once they understand the practical commitments of their responses (Experiment 4), and report not being able to actually imagine two perspectives simultaneously when reasoning about the scenario (Experiment 5). In short, we suggest that while people may make intransitive judgments, these do not reflect that they psychologically represent identity in an intransitive manner. (shrink)

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

Experimental studies indicate that nonhuman animals and infants represent numerosities above three or four approximately and that their mental number line is logarithmic rather than linear. In contrast, human children from most cultures gradually acquire the capacity to denote exact cardinal values. To explain this difference, I take an extended mind perspective, arguing that the distinctly human ability to use external representations as a complement for internal cognitive operations enables us to represent natural numbers. Reviewing neuroscientific, developmental, and anthropological evidence, (...) I argue that the use of external media that represent natural numbers (like number words, body parts, tokens or numerals) influences the functional architecture of the brain, which suggests a two-way traffic between the brain and cultural public representations. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific (...) structure and consequently that there is no domain-general alternative to an innate domain-specific small number system. (shrink)

One of the most important abilities we have as humans is the ability to think about number. In this chapter, we examine the question of whether there is an essential connection between language and number. We provide a careful examination of two prominent theories according to which concepts of the positive integers are dependent on language. The first of these claims that language creates the positive integers on the basis of an innate capacity to represent real numbers. The second claims (...) that language’s function is to integrate contents from modules that humans share with other animals. We argue that neither model is successful. (shrink)

How is knowledge of geometry developed and acquired? This central question in the philosophy of mathematics has received very different answers. Spelke and colleagues argue for a “core cognitivist”, nativist, view according to which geometric cognition is in an important way shaped by genetically determined abilities for shape recognition and orientation. Against the nativist position, Ferreirós and García-Pérez have argued for a “culturalist” account that takes geometric cognition to be fundamentally a culturally developed phenomenon. In this paper, I argue that (...) when understood as moderate versions supported by the state-of-the-art research, the nativist and culturalist views are in fact possible to reconcile. While Ferreirós and García-Pérez present the work of Spelke and colleagues as implying that geometric cognition is genetically determined, I argue that they fail to appreciate the role that Spelke and colleagues see for cultural factors. On this basis, I provide theoretical and terminological clarifications and show that moderate versions of the nativist and culturalist view are in fact consistent with each other. I then propose a unifying theoretical framework for future study that can integrate the two accounts in ontogeny by moving beyond the crude nature (nativism) vs. nurture (culturalism) dichotomy. (shrink)

While research on object individuation assumes that even very young children are able to perceive objects as particulars, we argue that the results of relevant studies can be explained in terms of feature discrimination. We propose that children start out navigating the world with a feature‐based ontology and only later become able to individuate objects spatiotemporally. Furthermore, object individuation is a cognitively demanding achievement resting on a uniquely human form of enculturation, namely the acquisition of deictic demonstratives. We conclude by (...) outlining empirical expectations for operationalizations of our proposal. (shrink)

In Pantsar (2014), an outline for an empirically feasible epistemological theory of arithmetic is presented. According to that theory, arithmetical knowledge is based on biological primitives but in the resulting empirical context develops an essentially a priori character. Such contextual a priori theory of arithmetical knowledge can explain two of the three characteristics that are usually associated with mathematical knowledge: that it appears to be a priori and objective. In this paper it is argued that it can also explain the (...) ... (shrink)

Children show increasing control of emotions and behavior during their early years. Our studies suggest a shift in control from the brain’s orienting network in infancy to the executive network by the age of 3—4 years. Our longitudinal study indicates that orienting influences both positive and negative affect, as measured by parent report in infancy. At 3—4 years of age, the dominant control of affect rests in a frontal brain network that involves the anterior cingulate gyrus. Connectivity of brain structures (...) also changes from infancy to toddlerhood. Early connectivity of parietal and frontal areas is important in orienting; later connectivity involves midfrontal and anterior cingulate areas related to executive attention and self-regulation. (shrink)

Epistemology has recently witnessed a number of efforts to rehabilitate rationalism, to defend the existence and importance of a priori knowledge or warrant construed as the product of rational insight or apprehension (Bealer 1987; Bigelow 1992; BonJour 1992, 1998; Burge 1998; Butchvarov 1970; Katz 1998; Plantinga 1993). This effort has sometimes been coupled with an attack on naturalistic epistemology, especially in BonJour 1994 and Katz 1998. Such coupling is not surprising, because naturalistic epistemology is often associated with thoroughgoing empiricism and (...) the rejection of the a priori. In this paper, however, I shall present a conception of naturalistic epistemology that is entirely compatible with a priori justification or knowledge. The resulting conception, I claim, gives us a better appreciation of the respective merits of the rational and the empirical, as well as a better understanding of how moderate epistemological naturalism comports, at least in principle, with moderate rationalism. This paper defends moderate rationalism; but it does not defend everything rationalists have often wanted, only what it is reasonable to grant them. (shrink)

A tradition of work in cognitive science indicates that much of our mental lives is not available to introspection . Though the researchers often present these results as surprising, little has been done to explore the degree to which people presume introspective access to their mental events. In this paper, we distinguish two dimensions of introspective access: the power of access, i.e. whether people believe they can unfailingly or only typically introspect mental events; and the domain of access, i.e. what (...) types of mental events people believe they are able to introspect. We report five experiments carried out to discover where lay beliefs about introspection fall on these dimensions. In our experiments, people did not presume universal introspective access, but they did overestimate the amount of access they actually have, particularly in the case of decisions. (shrink)

This article focuses on how young children acquire concepts for exact, cardinal numbers. I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey. In this framework, the (...) counting list and the counting routine form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information that they had no way of representing before. (shrink)

In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formal mathematical concepts and methods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist (...) hypothesis? Second, granting that infants have some elementary mathematical skills, does this mean that such skills play an important role in the development of mathematical knowledge? (shrink)

What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...) arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education. (shrink)

Macphail’s “null hypothesis,” that there are no differences in intelligence, qualitative, or quantitative, between non-human vertebrates has been controversial. This controversy can be useful if it encourages interest in acquiring a detailed understanding of how non-human animals express flexible problem-solving capacity (“intelligence”), but limiting the discussion to vertebrates is too arbitrary. As an example, we focus here on Portia, a spider with an especially intricate predatory strategy and a preference for other spiders as prey. We review research on pre-planned detours, (...) expectancy violation, and a capacity to solve confinement problems where, in each of these three contexts, there is experimental evidence of innate cognitive capacities and reliance on internal representation. These cognitive capacities are related to, but not identical to, intelligence. When discussing intelligence, as when discussing cognition, it is more useful to envisage a continuum instead of something that is simply present or not; in other words, a continuum pertaining to flexible problem-solving capacity for “intelligence” and a continuum pertaining to reliance on internal representation for “cognition.” When envisaging a continuum pertaining to intelligence, Daniel Dennett’s notion of four Creatures (Darwinian, Skinnerian, Popperian, and Gregorian) is of interest, with the distinction between Skinnerian and Popperian Creatures being especially relevant when considering Portia. When we consider these distinctions, a case can be made for Portia being a Popperian Creature. Like Skinnerian Creatures, Popperian Creatures express flexible problem solving capacity, but the manner in which this capacity is expressed by Popperian Creatures is more distinctively cognitive. (shrink)

This chapter explores a way in which visual processing may involve innate constraints and attempts to show how such processing overcomes one enduring challenge to nativism. In particular, many challenges to nativist theories in other areas of cognitive psychology have focused on the later development of such abilities, and have argued that such development is in conflict with innate origins. Innateness, in these contexts, is seen as antidevelopmental, associated instead with static processes and principles. In contrast, certain perceptual models demonstrate (...) how the very same mental processes can both be innately specified and yet develop richly in response to experience with the environment. This process is entirely unmysterious, as shown in certain formal theories of visual perception, including those that appeal to spontaneous endogenous stimulation and those based on Bayesian inference. (shrink)