Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create and (...) compare approximate summary values that include information about mean and variance, with no evidence of explicit calculation. Accuracy and confidence increased, while the number of fixations decreased as sets became more distinct , demonstrating that the statistical properties of datasets were highly related to comparisons. The discussion includes a model proposing how reasoners summarize and compare datasets within the architecture for approximate number representation. (shrink)

A new framework for the study of the human moral faculty is currently receiving much attention: the so-called ‘universal moral grammar' framework. It is based on an intriguing analogy, first pointed out by Rawls, between the study of the human moral sense and Chomsky's research program into the human language faculty. In order to assess UMG, we ask: is moral competence modular? Does it have an underlying hierarchical grammatical structure? Does moral diversity rest on culture-dependent parameters? We review evidence that (...) supports negative answers and argue that formal grammatical concepts are of limited value for the study of moral judgments, moral development and moral diversity. (shrink)

In quantity discrimination tasks, adults, infants and animals have been sometimes observed to process number only after all continuous variables, such as area or density, have been controlled for. This has been taken as evidence that processing number may be more cognitively demanding than processing continuous variables. We tested this hypothesis by training mosquitofish to discriminate two items from three in three different conditions. In one condition, continuous variables were controlled while numerical information was available; in another, the number was (...) kept constant and information relating to continuous variables was available; in the third condition, stimuli differed for both number and continuous quantities. Fish learned to discriminate more quickly when both number and continuous information were available compared to when they could use continuous information only or number only; there was no difference in the learning rate between the two latter conditions. Our results do not support the hypothesis that processing numbers imposes a higher cognitive load than processing continuous variables. Rather, they suggest that availability of multiple information sources may facilitate discrimination learning. (shrink)

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...) express mathematical concepts—they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition. (shrink)

In this paper I will argue that this entire dialectic is somewhat misguided. The mental states which are generally assumed to fall under the category of ‘intuition’ likely comprise a highly heterogeneous group; from the point of view of psychology or of neuroscience, in fact, ‘intuitions’ appear to be generated by several fundamentally different sorts of mental processes. If this is correct, then the term ‘intuition’ may simply carve things too broadly. I will argue that it is a mistake to (...) focus on the ‘reliability of intuition’; empirical evidence suggests that the reliability of one type of intuition may tell us next to nothing about the reliability of other types. Rather than debating the evidential status of intuition as a whole, philosophers interested in methodology would do well to focus their investigations much more narrowly. (shrink)

Recent research has suggested that the Pirahã, an Amazonian tribe with a number-less language, are able to match quantities > 3 if the matching task does not require recall or spatial transposition. This finding contravenes previous work among the Pirahã. In this study, we re-tested the Pirahãs’ performance in the crucial one-to-one matching task utilized in the two previous studies on their numerical cognition, as well as in control tasks requiring recall and mental transposition. We also conducted a novel quantity (...) recognition task. Speakers were unable to consistently match quantities > 3, even when no recall or transposition was involved. We provide a plausible motivation for the disparate results previously obtained among the Pirahã. Our findings are consistent with the suggestion that the exact recognition of quantities > 3 requires number terminology. (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)

Despite tremendous advances in neuroscience, the topic “brain, sex and gender” remains a matter of misleading interpretations, that go well beyond the bounds of science. In the 19th century, the difference in brain sizes was a major argument to explain the hierarchy between men and women, and was supposed to reflect innate differences in mental capacity. Nowadays, our understanding of the human brain has progressed dramatically with the demonstration of cerebral plasticity. The new brain imaging techniques have revealed the role (...) of the environment in continually re-shaping our brain all along our lifetimes as it goes through new experiences and acquires new knowledge. However, the idea that biology is a major determining factor for cognition and behavioral gender differentiation, is still very much alive. The media are far from being the only guilty party. Some scientific circles actively promote the idea of an innate origin of a gender difference in mental capacities. Experimental data from brain imaging, cognitive tests or genetics are often distorted to serve deterministic ideas. Such abuse of “scientific discourses” have to be counteracted by effective communication of clear and unbiased information to the citizens. This paper presents a critical analysis of selected examples which emphasize sex differences in three fields e.g. skills in language and mathematics, testosterone and financial risk-taking behavior, moral cognition. To shed light on the data and the methods used in some papers, we can now—with today’s knowledge on cerebral plasticity—challenge even more strongly, many false interpretations. Our goal here is double: we want to provide evidence against archaic beliefs about the biological determinism of sex differences but also promote a positive image of scientific research. (shrink)

This paper proposes an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence S is semantically associated with a canonical procedure for determining whether S is true; while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from a psycholinguistic experiment examining adult judgments (...) concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves unsettled, e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|{x: Dot(x) & ~Blue(x)}|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|{x: Dot(x)}| – |{x: Dot(x) & Blue(x)}|’; or in some other way. Psycholinguistic evidence and psychophysical modeling support the second hypothesis. (shrink)

Inspired by the success of generative linguistics and transformational grammar, proponents of the linguistic analogy (LA) in moral psychology hypothesize that careful attention to folk-moral judgments is likely to reveal a small set of implicit rules and structures responsible for the ubiquitous and apparently unbounded capacity for making moral judgments. As a theoretical hypothesis, LA thus requires a rich description of the computational structures that underlie mature moral judgments, an account of the acquisition and development of these structures, and an (...) analysis of those components of the moral system that are uniquely human and uniquely moral. In this paper we present the theoretical motivations for adopting LA in the study of moral cognition: (a) the distinction between competence and performance, (b) poverty of stimulus considerations, and (c) adopting the computational level as the proper level of analysis for the empirical study of moral judgment. With these motivations in hand, we review recent empirical findings that have been inspired by LA and which provide evidence for at least two predictions of LA: (a) the computational processes responsible for folk-moral judgment operate over structured representations of actions and events, as well as coding for features of agency and outcomes; and (b) folk-moral judgments are the output of a dedicated moral faculty and are largely immune to the effects of context. In addition, we highlight the complexity of the interfaces between the moral faculty and other cognitive systems external to it (e.g., number systems). We conclude by reviewing the potential utility of the theoretical and empirical tools of LA for future research in moral psychology. (shrink)

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)

I introduce "nomic-role nonreductionism" as an alternative to traditional causal-role functionalism in the philosophy of mind. Rather than identify mental properties by a theory that describes their intra-level causal roles via types of inputs, internal states, and outputs, I suggest that one identify mental properties by a more comprehensive theory that also describes inter-level realization roles via types of lower-level engineering, internal mental states, and still higher-level states generated by them. I defend this position on grounds that mental properties should (...) be understood by our best scientific theories, which at present include informatioin about mental engineering. I further defend this claim by a "parity of reasons" argument. Causal-role functionalists are justified to include sensory stimuli in their theory of mind as opposed to, say, the remote causes of sensory stimuli because the former but not the latter are items of direct mental production. But ditto for the system's physical realizations. They too directly produce mental states, only not by "causing" them but by "realizing" them. Engineering realizations and their input triggering conditions work in tandem. In addition, I tell a related but more general metaphysical story about property identity, namely, that the traditional causal theory should be replaced by a more comprehensive nomic theory that individuates properties by their intra-level causal powers as well as their inter-level realization capacities. (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)

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)

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...) exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers. (shrink)

I argue that analogue mental representations possess a canonical decomposition into privileged constituents from which they compose. I motivate this suggestion, and rebut arguments to the contrary, through reflection on the approximate number system, whose representations are widely expected to have an analogue format. I then argue that arguments for the compositionality and constituent structure of these analogue representations generalize to other analogue mental representations posited in the human mind, such as those in early vision and visual imagery.

A science of prelinguistic infant cognition must take seriously the language-of-thought (LoT) hypothesis. I show how the LoT framework enables us to identify the representational and computational capacities of infant minds and the developmental factors that act on these capacities, and explain how Quilty-Dunn et al.'s take on LoT has important upshots for developmental theory-building.

We compare the predictions of two important proposals made by De Neys to findings in the anchoring effect literature. Evidence for an anchoring-and-adjustment heuristic supports his proposal that system 1 and system 2 are non-exclusive. The relationship between psychophysical noise and anchoring effects, however, challenges his proposal that epistemic uncertainty determines the involvement of system 2 corrective processes in judgment.

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic‐like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function‐like structure, like symbolic arithmetic. Children (n = 74 4‐ to ‐8‐year‐olds in Experiment 1; n = 52 7‐ to 8‐year‐olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and (...) asked children which of the two derived solutions should be added to the smaller of the two sets to make them “about the same.” We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge. (shrink)

Whereas most commentators agree about the centrality of narratives in decision-making, the commentaries revealed little consensus about the nature of radical uncertainty. Here we consider thirteen objections to our views, including our characterization of the uncertain decision environment and associated cognitive, affective, and social processes. We conclude that under radical uncertainty, narratives rather than probabilities are the currency of thought.

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...) two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens’s distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens’s distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness. (shrink)

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created (...) yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical. (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)

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.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

Contemporary research in compositional, truth-conditional semantics often takes judgments of the relative unacceptability of certain phrasal combinations as evidence for lexical semantics. For example, observing that completely full sounds perfectly natural whereas completely tall does not has been used to motivate a distinction whereby the lexical entry for full but not for tall specifies a scalar endpoint. So far, such inferences seem unobjectionable. In general, however, applying this methodology can lead to dubious conclusions. For example, observing that slightly bent is (...) natural but slightly cheap is not (that is, not without a “too cheap” interpretation) leads researchers to suggest that the interpretation of bent involves a scalar minimum but cheap does not, contra intuition—after all, one would think that what is minimally cheap is (just) free. Such claims, found in sufficient abundance, raise the question of how we can support semantic theories that posit properties of entities that those entities appear to lack. This paper argues, using theories of adjectival scale structure as a test case, that the (un)acceptability data recruited in semantic explanations reveals properties of a two-stage system of semantic interpretation that can support divergences between our semantic and metaphysical intuitions. (shrink)

Philosophical Issues, Volume 30, Issue 1, Page 273-292, October 2020.

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)

On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – and show that none succeed. (...) We then highlight positive reasons for thinking that the ANS genuinely represents numbers. The upshot is that proponents of the orthodox view should not feel troubled by recent critiques of their position. (shrink)

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...) (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map‐like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism. (shrink)

The book is addressed to all readers interested in cognitive science, and especially in research combining a logical analysis with psychological, linguistic and neurobiological approaches. The publication is the result of a collaboration between the Department of Cognitive Science at University of Lodz and the Department of Cognitive Science at Lund University. It is intended to provide a comprehensive presentation of the key research issues undertaken in both Departments, including considerations on meaning, natural language and reasoning, linguistic as well as (...) numerical competence, the theory of decision making, modelling of conceptual representations, cognitive and game theoretic approach to social interactions. (shrink)

Research on theory of mind has primarily focused on demonstrating and understanding the ability to represent others' non‐factive mental states, for example, others' beliefs in the false‐belief task. This requirement confuses the ability to represent a particular kind of non‐factive content (e.g., a false belief) with the more general capacity to represent others' understanding of the world even when it differs from one's own. We provide a way of correcting this. We first offer a simple and theoretically motivated account on (...) which tracking another agent's understanding of the world and keeping that representation separate from one's own are the essential features of a capacity for theory of mind. We then show how these criteria can be operationalized in a new experimental paradigm: the “diverse‐knowledge task.”. (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)

What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...) beliefs more susceptible to a contingency challenge from evolution compared to mathematical beliefs, and indicates that mathematical beliefs might be less vulnerable to evolutionary debunking arguments. I will then examine to what extent INC can be used to flesh out a positive case for mathematical realism. Finally, I will review two forms of mathematical realism that are promising in the light of the evolutionary evidence about numerical cognition, ante rem structuralism and Millean empiricism. (shrink)

The paper offers a solution to the generality problem for a reliabilist epistemology, by developing an “algorithm and parameters” scheme for type-individuating cognitive processes. Algorithms are detailed procedures for mapping inputs to outputs. Parameters are psychological variables that systematically affect processing. The relevant process type for a given token is given by the complete algorithmic characterization of the token, along with the values of all the causally relevant parameters. The typing that results is far removed from the typings of folk (...) psychology, and from much of the epistemology literature. But it is principled and empirically grounded, and shows good prospects for yielding the desired epistemological verdicts. The paper articulates and elaborates the theory, drawing out some of its consequences. Toward the end, the fleshed-out theory is applied to two important case studies: hallucination and cognitive penetration of perception. (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.

Current theory-of-mind research faces the challenge of reconciling two sets of seemingly incompatible findings: Whereas children come to solve explicit verbal false belief tasks from around 4years of age, recent studies with various less explicit measures such as looking time, anticipatory looking, and spontaneous behavior suggest that even infants can succeed on some FB tasks. In response to this tension, two-systems theories propose to distinguish between an early-developing system, tracking simple forms of mental states, and a later-developing system, based on (...) fully developed concepts of belief and other propositional attitudes. One prediction of such theories is that the early-developing system has signature limits concerning aspectuality. We tested this prediction in two experiments. The first experiment showed that 2- and 3-year-olds take into account a protagonist's true or false belief about the location of an object in their active helping behavior. In contrast, toddlers' helping behavior did not differentiate between true and false belief conditions when the protagonist's belief essentially involved aspectuality. Experiment 2 replicated these findings with a more stringent method designed to rule out more parsimonious explanations. Taken together, the current findings are compatible with the possibility that early theory-of-mind reasoning is subject to signature limits as predicted by the two-systems account. (shrink)

Intuitions play an important role in contemporary epistemology. Over the last decade, however, experimental philosophers have published a number of studies suggesting that epistemic intuitions may vary in ways that challenge the widespread reliance on intuitions in epistemology. In a recent paper, Jennifer Nagel offers a pair of arguments aimed at showing that epistemic intuitions do not, in fact, vary in problematic ways. One of these arguments relies on a number of claims defended by appeal to the psychological literature on (...) intuitive judgment and on mental state attribution (also known as “theory of mind”, “mindreading” and “folk psychology”). I call this the "theoretical argument". The other argument relies on recent experimental work carried out by Nagel and her collaborators. It is my contention that in setting out her theoretical argument, Nagel offers an account of the relevant scientific literature that is, in crucial respects, flawed and misleading. My main goal in this paper is to rectify these errors and to make it clear that, once this is done, Nagel’s theoretical argument collapses. Since Nagel’s experimental work has not yet been published, and available details are very sketchy, I do not discuss this work in detail. However, in the final section of the paper I offer some critical observations about Nagel’s strategy for dealing with empirical data that does not support her view – both other people’s and her own. (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)