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)

Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.

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)

Pointing is a cornerstone of human communication, but does it take the same form in all cultures? Manual pointing with the index finger appears to be used universally, and it is often assumed to be universally preferred over other forms. Non-manual pointing with the head and face has also been widely attested, but it is usually considered of marginal significance, both empirically and theoretically. Here, we challenge this assumed marginality. Using a novel communication task, we investigated pointing preferences in the (...) Yupno of Papua New Guinea and in U.S. undergraduates. Speakers in both groups pointed at similar rates, but form preferences differed starkly: The Yupno participants used non-manual pointing numerically more often than manual pointing, whereas the U.S. participants stuck unwaveringly to index-finger pointing. The findings raise questions about why groups differ in their pointing preferences and, more broadly, about why humans communicate in the ways they do. (shrink)

The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...) universalist/particularist dichotomy. In place of strictly innatist perspectives on mathematical cognition, a model is proposed that invokes domain-specific and notationally-specific constraints to explain patterns in numerical notations. The analysis of exceptions to cross-cultural generalizations makes the study of near-universals highly productive theoretically. The cross-cultural study of patterns in written numbers thus provides a rich complement to the cognitive analysis of writing systems. (shrink)

The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...) universalist/particularist dichotomy. In place of strictly innatist perspectives on mathematical cognition, a model is proposed that invokes domain-specific and notationally-specific constraints to explain patterns in numerical notations. The analysis of exceptions to cross-cultural generalizations makes the study of near-universals highly productive theoretically. The cross-cultural study of patterns in written numbers thus provides a rich complement to the cognitive analysis of writing systems. (shrink)

Why Theories of Concepts Should Not Ignore the Problem of Acquisition.

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)

A theory of conceptual development must provide an account of the innate representational repertoire, must characterize how these initial representations differ from the adult state, and must provide an account of the processes that transform the initial into mature representations. In Carey, 2009 (The Origin of Concepts), I defend three theses: 1) the initial state includes rich conceptual representations, 2) nonetheless, there are radical discontinuities between early and later developing conceptual systems, 3) Quinean bootstrapping is one learning mechanism that underlies (...) the creation of new representational resources, enabling such discontinuity. I also claim that the theory of conceptual development developed in The Origin of Concepts addresses two of Fodor's challenges to cognitive science; namely, to show how learning could possibly lead to an increase in expressive power and to defeat Mad Dog Nativism, the thesis that all concepts lexicalized as mono-morphemic words are innate. A recent article by Georges Rey (Mind & Language, 29.2, 2014) argues that my responses to Fodor's challenges fail, because, he says, I fail to distinguish concept possession from manifestation and I do not confront Goodman's new riddle of induction. My response is to show that, and how, new primitives in a language of thought can be learned, that there are easy routes and hard ones to doing so, and that characterizing the learning mechanisms involved is the key to understanding both concept possession and constraints on induction. (shrink)

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)

Mathematical cognition has become an interesting case study for wider theories of cognition. Menary :1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal (...) with exact numbers of arbitrary size. I then argue that the system underlying our grasp of small numbers is an unhelpful case study for Menary; it doesn’t support an argument for externalism over internalism. The system for large numbers, on the other hand, clearly displays important interactions between public numeral systems and our cognitive processes. I argue that the large number system supports an argument against internalist theories of arithmetical cognition, but that one cannot conclude that the Hypothesis of Extended Cognition is correct. In other words, the large number case doesn’t decide between the Hypothesis of Extended Cognition and the Hypothesis of EMbedded Cognition. (shrink)

Can concepts be acquired by testing hypotheses about these concepts? Fodor famously argued that this is not possible. Testing the correct hypothesis would require already possessing the concept. I argue that this does not generally hold for mathematical concepts. I discuss specific, empirically motivated, hypotheses for number concepts that can be tested without needing to possess the relevant number concepts. I also argue that one can test hypotheses about the identity conditions of other mathematical concepts, and then fix the application (...) conditions based on those hypotheses—under the assumption that the neo‐logicist view on abstraction principles is correct. (shrink)

We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behaviour as a neutral element and finally its role as a truth-value in logic.

Disagreement remains about whether particular human socio-cognitive traits arose primarily as a result of biological adaptations, or because of changing cultural practices. Heyes argues that uniquely human traits, including imitation and theory of mind, are the product of cultural learning. In contrast, Tomasello argues that they are, in key respects, part of a suite of adaptations for ‘shared intentionality’. We consider how such disagreements might be resolved. We show that the kinds of consideration often used to adjudicate questions about trait (...) origins are insufficient to settle origin questions. Furthermore, humankind’s immersion in culture undermines the prospect that cross-cultural and developmental studies could resolve origin questions. Nonetheless we argue that, when cautiously interpreted, currently neglected studies of enculturated great apes (i.e. apes raised in human environments) can shed new light on trait origins, and inform mechanistic accounts of cognitive development. While acknowledging the shortcomings of enculturation research, we argue that it deserves renewed attention. (shrink)

The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems—general and object-specific ones—that were in parallel (...) use in several Oceanic languages. The analysis indicates that the object-specific systems outperform the general systems with respect to counting and mental arithmetic, largely due to their regular and more compact representation. What these findings reveal on cognitive diversity, how the conjectures involved speak to more general issues in cognitive science, and how the approach taken here might help to bridge the gap between anthropology and other cognitive sciences is discussed in the conclusion. (shrink)

An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine).

This thesis is intended to analyze a mental phenomenon widely neglected in current philosophical discussions: personal memories. The first part presents a general framework to better understand what personal memories are, how we access our personal past and what we access about our personal past. Chapter 1 introduces traditional theories of memory: direct realism and representationalism in their different versions, as well as some objections. I defend here a particular form of representationalism that is based on the distinction between content, (...) intentional object and ontological object. Chapter 2 explores the possible contents of our personal memories, which prove to be heterogeneous, whereas chapter 3 analyses their possible intentional objects, with a special focus on past events. The second part of the thesis explores an aspect of our personal memories that was omitted in the first part: the senses in which our personal past is apprehended as personal. Chapter 4 examines the way in which the “self” intervenes in the construction of our personal memories. Chapters 5 and 6 focus on the analysis of what seems to be the most subjective aspect of our memories, that is, the emotions and feelings of our past experiences. In these last two chapters, I analyze the different interactions that can take place between memories and emotions and defend the idea that there can be emotional memories that are reducible neither to a propositional memory nor an occurrent and present emotion. The overall intention of this thesis is twofold. First, I aim to show to the philosophical community that there is still a lot to be said and discussed about memory as a mental phenomenon. And second, I intend to emphasize the importance of bringing into the philosophical discussions about the mind ideas coming from different philosophical traditions as well as ideas and empirical data coming from scientific research. (shrink)

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...) claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework. (shrink)

One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) as it is exercised by ordinary people. I do so by looking at the different theories that have been put forward in the recent debate, and showing for each of these that they are unable to account for the mathematical practices of ordinary people. In order to show that these practices do need to be accounted for, I also argue that ordinary people are doing mathematics, i.e. that they engage in properly mathematical practices. Because these practices are properly mathematical, they should be accounted for by any philosophy of mathematics. The conclusion of my thesis, then, is that current theories fail to do something that they should do, while remaining neutral on how well they perform when it comes to accounting for the practices of professional mathematicians. (shrink)

My dissertation establishes the basis for a systematic outlook on the role language plays in human cognition. It is an investigation based on a cognitive conception of language, as opposed to communicative conceptions, viz. those that suppose that language plays no role in cognition. I focus, in Chapter 2, on three paradigmatic theories adopting this perspective, each offering different views on how language contributes to or changes cognition. -/- In Chapter 3, I criticize current views held by dual-process theorists, and (...) I develop a picture of the complex interaction between language and cognition that I deem more plausible by using resources from the literature on the evolution of the faculty of language. Rather than trying to find one general explanation for all cognitive processes, I take seriously the idea that our mind is composed of many subsystems, and that language can interact and modify each in different ways. There is no reason offered in the empirical literature—besides maybe parsimony—that suggest that language has to interact in the same ways with all cognitive processes. Yet, this is seemingly taken for granted, especially within dual-process approaches. -/- On my view, it is a central requirement for a theory of the role of language in cognition to explain how language might have effects, at once, on and within various parts of cognition. In Chapter 4, I explore how this framework can modify how we think about some experiments in psychology, specifically in research on categorization. My idea is that language, once it evolved, changed how some cognitive capacities worked and interacted with each other, but did so in more than one or two ways. Cognitive systems are changed in very different ways—sometimes the transformation is very subtle, such as our way of forming categories by using how similar objects are, while other times it is deep and changes the very way the system works. (shrink)

The aim of this dissertation is to create a naturalistic philosophical picture of creative capacities that are specific to our species, focusing on artistic ability, religious reflection, and scientific study. By integrating data from diverse domains within a philosophical anthropological framework, I have presented a cognitive and evolutionary approach to the question of why humans, but not other animals engage in such activities. Through an application of cognitive and evolutionary perspectives to the study of these behaviors, I have sought to (...) provide a more solid footing for philosophical anthropological discussions of uniquely human behavior. In particular, I have argued that art, religion and science, which are usually seen as achievements that are quite remote from ordinary modes of reasoning, are subserved by evolved cognitive processes that serve functions in everyday cognitive tasks, that arise early and spontaneously in cognitive development, that are shared cross-culturally, and that have evolved in response to selective pressures in our ancestral past. These mundane cognitive processes provide a measuring rod with which we can assess a diversity of cultural phenomena; they form a unified explanatory framework to approach human culture. I have argued that we can explain uncommon thoughts in terms of interactions between common minds. This dissertation is subdivided into four parts. Part I outlines the problem of human uniqueness, examining theories on how humans conceptualize the world, and what their mental tool box looks like. Part II discusses the evolutionary and cognitive origins of human artistic behavior. Part III focuses on the cognitive science of religion, especially on how it can be applied to the reasoning of theologians and philosophers of religion. Part IV considers the cognitive basis of scientific practice. (shrink)

Linguistic structures have recently started to attract attention from economists as determinants of economic phenomena. This paper provides the first comprehensive review of this nascent literature and its achievements so far. First, we explore the complex connections between language, culture, thought and behaviour. Then, we summarize the empirical evidence on the relationship between linguistic structures and economic and social outcomes. We follow up with a discussion of data, empirical design and identification. The paper concludes by discussing implications for future research (...) and policy. (shrink)