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)

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.

Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

Arithmetical cognition is the result of enculturation. On a personal level of analysis, enculturation is a process of structured cultural learning that leads to the acquisition of evolutionarily recent, socio-culturally shaped arithmetical practices. On a sub-personal level, enculturation is realized by learning driven plasticity and learning driven bodily adaptability, which leads to the emergence of new neural circuitry and bodily action patterns. While learning driven plasticity in the case of arithmetical practices is not consistent with modularist theories of mental architecture, (...) it can be enriched by the theory of neural reuse. According to neural reuse, cerebral regions are reused to contribute to multiple neural circuits in functionally constrained ways throughout ontogeny. By hypothesis, learning driven plasticity is complemented by learning driven bodily adaptability, which suggests that there is an interesting functional relationship between finger gnosis, finger counting, and arithmetical practices. The emerging perspective on enculturated arithmetical cognition will be complemented by considerations on associated developmental and acquired disorders, namely developmental dyscalculia and acquired acalculia. The upshot is that we need to take the cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturation into account in order to arrive at a better understanding of the phylogenetic and ontogenetic conditions of arithmetical cognition. (shrink)

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...) effectiveness of mathematics in natural science. (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)

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)

In a previous issue of Tijdschrift voor Filosofie, Filip Buekens argues that evolutionary psychology (EP), or some interpretations thereof, have a corrosive impact on our ‘manifest self-image’. Buekens wants to defend and protect the global adequacy of this manifest self-image in the face of what he calls evolutionary revisionism. Although we largely agree with Buekens’ central argument, we criticize his analysis on several accounts, making some constructive proposals to strengthen his case. First, Buekens’ argument fails to target EP, because his (...) notion of the ‘constitutive conditions’ of our attitudes is too wide and too extensive. Second, his defense of the global adequacy of our attitudes does not allow for sufficient differentiation to analyze the problem of potential self-refutation with respect to EP. Third, his account of knowledge about constitutive conditions, and its impact on our self-image, is problematic. We provide a more detailed explanation for the pervasiveness of evolutionary revisionism and other misconceptions about EP. Finally, we consider in what sense EP may legitimately affect our self-image, and whether it can truly inspire corrections of our view of human nature. (shrink)