Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)

A pretense theory of a given discourse is a theory that claims that we do not believe or assert the propositions expressed by the sentences we token (speak, write, and so on) when taking part in that discourse. Instead, according to pretense theory, we are speaking from within a pretense. According to pretense theories of mathematics, we engage with mathematics as we do a pretense. We do not use mathematical language to make claims that express propositions and, thus, we do (...) not use mathematical discourse to make claims that are either true or false. In this paper I make use of recent findings from cognitive neuroscience and developmental science to suggest that pretense theories of mathematics fail. 1 Introduction 2 The Autism Objection 2.1 Autism and pretense 2.2 Autistic engagement with mathematics 2.2.1 Cortical folding 2.2.2 The language of mathematics 3 The Onset of the Number Sense and the Recognition of Pretense 3.1 A difference in neurology 3.2 Young and no numbers 3.2.1 When and where is the difference? 3.2.2 Damaged HIPS without impairment to engagement with fiction 4 Concluding Remarks. (shrink)

Normal children learn tens of thousands of words, and do so quickly and efficiently, often in highly impoverished environments. In How Children Learn the Meanings of Words, I argue that word learning is the product of certain cognitive and linguistic abilities that include the ability to acquire concepts, an appreciation of syntactic cues to meaning, and a rich understanding of the mental states of other people. These capacities are powerful, early emerging, and to some extent uniquely human, but they are (...) not special to word learning. This proposal is an alternative to the view that word learning is the result of simple associative learning mechanisms, and it rejects as well the notion that children possess constraints, either innate or learned, that are specifically earmarked for word learning. This theory is extended to account for how children learn names for objects, substances, and abstract entities, pronouns and proper names, verbs, determiners, prepositions, and number words. Several related topics are also discussed, including naïve essentialism, children's understanding of representational art, the nature of numerical and spatial reasoning, and the role of words in the shaping of mental life. Key Words: cognitive development; concepts; meaning; semantics; social cognition; syntax; theory of mind; word learning. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (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)

Rousseau’s thoughts on education are being presented and then put in tension with todays educational conceptions. We aim at highlighting in how far Rousseau’s work can still contribute to conceive teaching and learning, but also how it is in tension with some contemporary educational tenets. We conclude by emphasising the need to reflect all teaching and learning taking into account the objective to allow the development of a human being bestowed with a unique potential, that of being able to become (...) autonomous and free, actively taking part in his and his society’s future. (shrink)

Abstract The typical explanation of an event or process which attracts the label ‘conspiracy theory’ is an explanation that conflicts with the account advanced by the relevant epistemic authorities. I argue that both for the layperson and for the intellectual, it is almost never rational to accept such a conspiracy theory. Knowledge is not merely shallowly social, in the manner recognized by social epistemology, it is also constitutively social: many kinds of knowledge only become accessible thanks to the agent's embedding (...) in an environment that includes other epistemic agents. Moreover, advances in knowledge typically require ongoing immersion in this social environment. But the intellectual who embraces a conspiracy theory risks cutting herself off from this environment, and therefore epistemically disabling herself. Embracing a conspiracy theory therefore places at risk the ability to engage in genuine enquiry, including the enquiry needed properly to evaluate the conspiracy theory. (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)

I shall propose five theses on de re states and attitudes. To be a de re state or attitude is to bear a peculiarly direct epistemic and representational relation to a particular referent in perception or thought. I will not dress this bare statement here. The fifth thesis tries to be less coarse. The first four explicate and restrict context- bound, singular, empirical representation, which constitutes a significant and central type of de re state or attitude.

Researchers of language origins typically try to explain how compositional communication might evolve to bridge the gap between animal communication and natural language. However, as an explanatory target, compositionality has been shown to be problematic for a gradualist approach to the evolution of language. In this article, I suggest that reflexivity provides an apt and plausible alternative target that does not succumb to the problems that compositionality faces. I further explain how protoreflexivity, which depends on functional reference, gives rise to (...) complex communication systems via modular composition. (shrink)

We propose that procedures of separation have two functions, namely first, to establish the integrity of individual parts, and second, to make previously joint entities discreet and therefore countable. This allows taking stock of available resources, including evaluating the use of individual objects, a process that is especially adaptive under conditions of threat of contagious disease and resource scarcity.