Complex cognitive skills such as reading and calculation and complex cognitive achievements such as formal science and mathematics may depend on a set of building block systems that emerge early in human ontogeny and phylogeny. These core knowledge systems show characteristic limits of domain and task specificity: Each serves to represent a particular class of entities for a particular set of purposes. By combining representations from these systems, however human cognition may achieve extraordinary flexibility. Studies of cognition in human infants (...) and in nonhuman primates therefore may contribute to understanding unique features of human knowledge. 2020 APA, all rights reserved). (shrink)

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)

has a more specific role to play in the development of Of course, the conclusion to draw is not that innateness innate cognitive structure. In particular, a common claim claims are trivially false or that they cannot be character-.

In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one (...) correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis. (shrink)

Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill1,2. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations3,4, and their performance suffers if this nonsymbolic system is impaired5. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required6–10. Here (...) we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction11–15. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics. We presented children with approximate symbolic arithmetic problems in a format that parallels previous tests of non-symbolic arithmetic in preschool children8,9. In the first experiment, five- to six-year-old children were given problems such as ‘‘If you had twenty-four stickers and I gave you twenty-seven more, would you have more or less than thirty-five stickers?’’. Children performed well above chance (65.0%, t1952.77, P 5 0.012) without resorting to guessing or comparison strategies that could serve as alternatives to arithmetic. Children who have been taught no symbolic arithmetic therefore have some ability to perform symbolic addition problems. The children’s performance nevertheless fell short of performance on non-symbolic arithmetic tasks using equivalent addition problems with numbers presented as arrays of dots and with the addition operation conveyed by successive motions of the dots into a box (71.3% correct, F1,345 4.26, P 5 0.047)8.. (shrink)

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

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)

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)

The concept of innateness is a part of folk wisdom but is also used by biologists and cognitive scientists. This concept has a legitimate role to play in science only if the colloquial usage relates to a coherent body of evidence. We examine many different candidates for the post of scientific successor of the folk concept of innateness. We argue that none of these candidates is entirely satisfactory. Some of the candidates are more interesting and useful than others, but the (...) interesting candidates are not equivalent to each other and the empirical and evidential relations between them are far from clear. Researchers have treated the various scientific notions that capture some aspect of the folk concept of innateness as equivalent to each other or at least as tracking properties that are strongly correlated with each other. But whether these correlations exist is an empirical issue. This empirical issue has not been thoroughly investigated because in the attempt to create a bridge between the folk view and their theories, researchers have often assumed that the properties must somehow cluster. Rather than making further attempts to import the folk concept of innateness into the sciences, efforts should now be made to focus on the empirical questions raised by the debates and pave the way to a better way of studying the development of living organisms. Such empirical questions must be answered before it can be decided whether a good scientific successor – in the form of a concept that refers to a collection of biologically significant properties that tend to co-occur – can be identified or whether the concept of innateness deserves no place in science. (shrink)

The idea that formal geometry derives from intuitive notions of space has appeared in many guises, most notably in Kant’s argument from geometry. Kant claimed that an a priori knowledge of spatial relationships both allows and constrains formal geometry: it serves as the actual source of our cognition of principles of geometry and as a basis for its further cultural development. The development of non-Euclidean geometries, however, seemed to definitely undermine the idea that there is some privileged relationship between our (...) spatial intuitions and mathematical theory. This paper’s aim is to look at this longstanding philosophical issue through the lens of cognitive science. Drawing on recent evidence from cognitive ethology, developmental psychology, neuroscience and anthropology, I argue for an enhanced, more informed version of the argument from geometry: humans share with other species evolved, innate intuitions of space which serve as a vital precondition for geometry as a formal science. (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)

Plato's Meno and Phaedo are two of the most important works of ancient western philosophy and continue to be studied around the world. The Meno is a seminal work of epistemology. The Phaedo is a key source for Platonic metaphysics and for Plato's conception of the human soul. Together they illustrate the birth of Platonic philosophy from Plato's reflections on Socrates' life and doctrines. This edition offers new and accessible translations of both works, together with a thorough introduction that explains (...) the arguments of the two dialogues and their place in Plato's thought. (shrink)