The commentators raised issues relevant to all three important theses of The Origin of Concepts (henceforth TOOC). Some questioned the very existence of innate representational primitives, and others questioned my claims about their richness and whether they should be thought of as concepts. Some questioned the existence of conceptual discontinuity in the course of knowledge acquisition and others argued that discontinuity is much more common than was portrayed in TOOC. Some raised issues with my characterization of Quinian bootstrapping, and others (...) questioned the dual factor theory of concepts motivated by my picture of conceptual development. (shrink)

The last couple of years have seen a rapid growth of interest in the study of crossmodal correspondences – the tendency for our brains to preferentially associate certain features or dimensions of stimuli across the senses. By now, robust empirical evidence supports the existence of numerous crossmodal correspondences, affecting people’s performance across a wide range of psychological tasks – in everything from the redundant target effect paradigm through to studies of the Implicit Association Test, and from speeded discrimination/classification tasks through (...) to unspeeded spatial localisation and temporal order judgment tasks. However, one question that has yet to receive a satisfactory answer is whether crossmodal correspondences automatically affect people’s performance , as opposed to reflecting more of a strategic, or top-down, phenomenon. Here, we review the latest research on the topic of crossmodal correspondences to have addressed this issue. We argue that answering the question will require researchers to be more precise in terms of defining what exactly automaticity entails. Furthermore, one’s answer to the automaticity question may also hinge on the answer to a second question: Namely, whether crossmodal correspondences are all ‘of a kind’, or whether instead there may be several different kinds of crossmodal mapping . Different answers to the automaticity question may then be revealed depending on the type of correspondence under consideration. We make a number of suggestions for future research that might help to determine just how automatic crossmodal correspondences really are. (shrink)

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a (...) numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection. (shrink)

This article discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.

What is the relationship between space and time in the human mind? Studies in adults show an asymmetric relationship between mental representations of these basic dimensions of experience: Representations of time depend on space more than representations of space depend on time. Here we investigated the relationship between space and time in the developing mind. Native Greek‐speaking children watched movies of two animals traveling along parallel paths for different distances or durations and judged the spatial and temporal aspects of these (...) events (e.g., Which animal went for a longer distance, or a longer time?). Results showed a reliable cross‐dimensional asymmetry. For the same stimuli, spatial information influenced temporal judgments more than temporal information influenced spatial judgments. This pattern was robust to variations in the age of the participants and the type of linguistic framing used to elicit responses. This finding demonstrates a continuity between space‐time representations in children and adults, and informs theories of analog magnitude representation. (shrink)

A theory of conceptual development must specify the innate representational primitives, must characterize the ways in which the initial state differs from the adult state, and must characterize the processes through which one is transformed into the other. The Origin of Concepts (henceforth TOOC) defends three theses. With respect to the initial state, the innate stock of primitives is not limited to sensory, perceptual, or sensorimotor representations; rather, there are also innate conceptual representations. With respect to developmental change, conceptual development (...) consists of episodes of qualitative change, resulting in systems of representation that are more powerful than, and sometimes incommensurable with, those from which they are built. With respect to a learning mechanism that achieves conceptual discontinuity, I offer Quinian bootstrapping. TOOC concludes with a discussion of how an understanding of conceptual development constrains a theory of concepts. (shrink)

According to the Generality Constraint, mental states with conceptual content must be capable of recombining in certain systematic ways. Drawing on empirical evidence from cognitive science, I argue that so-called analogue magnitude states violate this recombinability condition and thus have nonconceptual content. I further argue that this result has two significant consequences: it demonstrates that nonconceptual content seeps beyond perception and infiltrates cognition; and it shows that whether mental states have nonconceptual content is largely an empirical matter determined by the (...) structure of the neural representations underlying them. (shrink)

Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).

We present a theory of decision by sampling (DbS) in which, in contrast with traditional models, there are no underlying psychoeconomic scales. Instead, we assume that an attribute’s subjective value is constructed from a series of binary, ordinal comparisons to a sample of attribute values drawn from memory and is its rank within the sample. We assume that the sample reflects both the immediate distribution of attribute values from the current decision’s context and also the background, real-world distribution of attribute (...) values. DbS accounts for concave utility functions; losses looming larger than gains; hyperbolic temporal discounting; and the overestimation of small probabilities and the underestimation of large probabilities. Ó 2005 Elsevier Inc. All rights reserved. (shrink)

We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

Recent research has suggested that not all grapheme-colour synaesthetes are alike. One suggestion is that they can be divided, phenomenologically, in terms of whether the colours are experienced in external or internal space. Another suggestion is that they can be divided according to whether it is the perceptual or conceptual attributes of a stimulus that is critical. This study compares the behavioural performance of 7 projector and 7 associator synaesthetes. We demonstrate that this distinction does not map on to behavioural (...) traits expected from the higher–lower distinction. We replicate previous research showing that projectors are faster at naming their synaesthetic colours than veridical colours, and that associators show the reverse profile. Synaesthetes who project colours into external space but not on to the surface of the grapheme behave like associators on this task. In a second task, graphemes presented briefly in the periphery are more likely to elicit reports of colour in projectors than associators, but the colours only tend to be accurate when the grapheme itself is also accurately identified. We propose an alternative model of individual differences in grapheme-colour synaesthesia that emphasises the role of different spatial reference frames in synaesthetic perception. In doing so, we attempt to bring the synaesthesia literature closer to current models of non-synaesthetic perception, attention and binding. (shrink)

The traditional view of cognition as detached from emotions is recently being questioned. This study aimed to investigate the influence of emotional valence on the accuracy and bias in the representation of numbers on the mental number line (MNL). The study included 164 participants who were randomly assigned into two groups with induced positive and negative emotional valence using matched arousal film clips. Participants performed a computerised number-to-position (CNP) task to estimate the position of numbers on a horizontal line. The (...) results showed that participants in the positive valence group exhibited a rightward bias, while those in the negative valence group showed an opposite pattern. The analysis of mean absolute error revealed that the negative valence group had higher error rates compared to the positive valence group. Furthermore, the MNL estimation pattern analysis indicated that a two-cycle cyclic power model (CPM) best explained the data for both groups. These findings suggest that emotional valence influences the spatial representation of numbers on the MNL and affects accuracy in numerical estimations. Our findings are finally discussed in terms of body-specificity and the Brain’s Asymmetric Frequency Tuning (BAFT) theories. The study provides new insights into the interplay between emotions and numerical cognition. (shrink)

People can represent temporal stimuli (e.g., pictures depicting past and future events) as spatially connoted dimensions arranged along the three main axes (horizontal, sagittal, and vertical). For example, past and future events are generally represented, from the perspective of the individuals, as being placed behind and in front of them, respectively. Here, we report that such a 3D representation can also emerge for facial stimuli of different ages. In three experiments, participants classified a central target face, representing an individual at (...) different age stages, as younger or older than the reference face of 40 years. Manual responses were provided with two keys placed along the horizontal axis (Experiment 1), the sagittal axis (Experiment 2), and the vertical axis (Experiment 3). The results indicated that the younger faces were represented on the left/back/top side of the space, whereas the older faces were represented on the right/forward/bottom side of the space. Furthermore, in all experiments, the latencies decreased with the absolute difference between the age of the target face and that of the reference face (i.e., a distance effect). Overall, this work suggests that the spatial representation of time includes social features of the human face. (shrink)

The notion of domain specificity plays a central role in some of the most important debates in cognitive science. Yet, despite the widespread reliance on domain specificity in recent theorizing in cognitive science, this notion remains elusive. Critics have claimed that the notion of domain specificity can't bear the theoretical weight that has been put on it and that it should be abandoned. Even its most steadfast proponents have highlighted puzzles and tensions that arise once one tries to go beyond (...) an initial intuitive sketch of what domain specificity involves. In this paper, we address these concerns head on by developing an account of what it means for a cognitive mechanism to be domain specific that overcomes the obstacles that have made domain specificity seem so problematic. We then apply this understanding of domain specificity to one of the key debates that it has figured prominently in—the rationalism-empiricism debate concerning the origins of cognitive traits—and introduce several related theoretical notions that work alongside domain specificity in helping to clarify what makes a view more (or less) rationalist. This example illustrates how the notion of domain specificity can, and should, continue to play a central role in ongoing debates in cognitive science. (shrink)

Research on the Spatial Quantity Association of Response Codes (SQUARC) has documented associations between spatial position and mental representations of quantity. Large quantities are associated with right and top, small quantities are associated with left and bottom. Resulting compatibility effects have largely been documented for response speed and judgment accuracy. Recently, employing luminance as quantity, Löffler et al. (2022) generalised such SQUARC compatibility effects to affective judgments, showing that horizontally SQUARC-compatible stimulus arrangements (i.e. bright on the right, dark on the (...) left side) are liked more than SQUARC-incompatible arrangements. The present Experiment 1 (N = 296) replicated this horizontal compatibility effect, dz =.18, and generalised it to vertical luminance SQUARC compatibility (i.e. bright on the top, dark on the bottom), dz =.22. Experiments 2a-b (total N = 259; Experiment 2b preregistered) employed stimulus arrangements tilted by 45° to manipulate horizontal and vertical (in)compatibility simultaneously within the same stimulus, finding robust horizontal compatibility effects, but mixed evidence regarding vertical compatibility. (shrink)

There is a noticeable gap between results of cognitive neuroscientific research into basic mathematical abilities and philosophical and empirical investigations of mathematics as a distinct intellectual activity. The paper explores the relevance of a Wittgensteinian framework for dealing with this discrepancy.

The literatures on bounded and ecological rationality are built on adaptationism—and its associated modular, cognitivist and computational paradigm—that does not address or explain the evolutionary origins of rationality. We argue that the adaptive mechanisms of evolution are not sufficient for explaining human rationality, and we posit that human rationality presents exaptive origins, where exaptations are traits evolved for other functions or no function at all, and later co-opted for new uses. We propose an embodied reconceptualization of rationality—embodied rationality—based on the (...) reuse of the perception-action system, where many neural processes involved in the control of the sensory-motor system, salient in ancestral environments have been later co-opted to create—by tinkering—high-level reasoning processes, employed in civilized niches. (shrink)

According to proponents of the generalized magnitude system proposal (GMS), SNARC-like effects index spatial mappings of magnitude and provide crucial evidence for the existence of a GMS. Casasanto and Pitt (2019) have argued that these effects, instead, reflect mappings of ordinality, which people compute on the basis of differences among stimuli that vary either qualitatively (e.g., musical pitches) or quantitatively (e.g., dots of different sizes). In response to our paper, Prpic et al. (2021) argued that both magnitude and ordinality play (...) a role in SNARC-like effects. Here, we address each of their arguments and conclude that magnitude is relevant to these effects only insofar as it serves as a basis for ordinality. For this reason and others, SNARC or SNARC-like effects cannot provide evidence for the putative generalized magnitude system. (shrink)

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate (...) on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition. (shrink)

While we perceive events in our environment through multiple sensory systems, we nevertheless perceive all of these events as occupying a single unified timeline. Time, as we perceive it, is unified. I argue that existing accounts of the perceived unity of time fail. Instead, the perceived unity of time must be constructed by integrating our initially fragmented timekeeping capacities. However, existing accounts of multimodal integration do not tell us how this might occur. Something new is needed. I finish the paper (...) by articulating the hurdles that must be overcome to provide an account of the perceived unity of time. (shrink)

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

This paper refines a controversial proposal: that core systems belong to a perceptual kind, marked out by the format of its representational outputs. Following Susan Carey, this proposal has been understood in terms of core representations having an iconic format, like certain paradigmatically perceptual outputs. I argue that they don’t, but suggest that the proposal may be better formulated in terms of a broader analogue format type. Formulated in this way, the proposal accommodates the existence of genuine icons in perception, (...) and avoids otherwise troubling objections. (shrink)

The Whorfian hypothesis has received support from recent findings in psychology, linguistics, and anthropology. This evidence has been interpreted as supporting the view that language modulates all stages of perception and cognition, in accordance with Whorf’s original proposal. In light of a much broader body of evidence on time perception, I propose to evaluate these findings with respect to their scope. When assessed collectively, the entire body of evidence on time perception shows that the Whorfian hypothesis has a limited scope (...) and that it does not affect early stages of time perception. In particular, all the available evidence shows that the scope of language modulation is limited in the case of time perception, and that the most important mechanisms for time perception are cognitive clocks and simultaneity windows, which we use to perceive the temporal properties of events. Language modulation has distorting effects, but only at later stages of processing or with respect to specific categorization tasks. The paper explains what is the role of these effects in the context of all the available evidence on time cognition and perception. (shrink)

Neurosciences and cognitive sciences provide us with myriad empirical findings that shed light on hypothesised primitive numerical processes in the brain and in the mind. Yet, the hypotheses on which the experiments are based, and hence the results, depend strongly on sophisticated abstract models used to describe and explain neural data or cognitive representations that supposedly are the empirical roots of primary arithmetical activity. I will question the foundational role of such models. I will even cast doubt upon the search (...) for a general and unified philosophical foundation of an empirical science. First, it seems to me hard to draw a global and coherent view from the innumerable and piecemeal neuropsychological experiments and their variable, and sometimes uneasily compatible or fully divergent interpretations. Secondly, I think that the aim of empirical research is to describe dynamical processes, establishing correlations between different sets of data, without meaning to fix an origin or to point to a cause, let alone to a ground. From the very scientific and philosophical point of view it is essential to distinguish between explanations, which provide correlations or, at best, causal mechanisms, and grounding, which involves a claim to some form of determinism. (shrink)

Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, (...) but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section. (shrink)

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception. This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events (...) and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed. (shrink)

Dustin Stokes argues for the existence of orectic penetration, a phenomenon in which a desire-like state penetrates our perceptual experience. His candidate for a case of orectic penetration is the most convincing candidate presented thus far. It is argued here that his candidate and his further arguments for the existence of orectic penetration do not support the claim that orectic penetration takes place. As a result, it is concluded that there are no convincing cases of desire-like states penetrating perceptual experience.