Julian Cole argues that mathematical domains are the products of social construction. This view has an initial appeal in that it seems to salvage much that is good about traditional platonistic realism without taking on the ontological baggage. However, it also has problems. After a brief sketch of social constructivist theories and Cole’s philosophy of mathematics, I evaluate the arguments in favor of social constructivism. I also discuss two substantial problems with the theory. I argue that unless and until social (...) constructivists can address the two concerns, we have reason to be skeptical about social constructivism in the philosophy of mathematics. (shrink)

In behavioral ecology some authors regard the innateness concept as irretrievably confused whilst others take it to refer to adaptations. In cognitive psychology, however, whether traits are 'innate' is regarded as a significant question and is often the subject of heated debate. Several philosophers have tried to define innateness with the intention of making sense of its use in cognitive psychology. In contrast, I argue that the concept is irretrievably confused. The vernacular innateness concept represents a key aspect of 'folkbiology', (...) namely, the explanatory strategy that psychologists and cognitive anthropologists have labeled 'folk essentialism'. Folk essentialism is inimical to Darwinism, and both Darwin and the founders of the modern synthesis struggled to overcome this way of thinking about living systems. Because the vernacular concept of innateness is part of folkbiology, attempts to define it more adequately are unlikely to succeed, making it preferable to introduce new, neutral terms for the various, related notions that are needed to understand cognitive development. (shrink)

The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.

In Reading in the Brain, Stanislas Dehaene presents a compelling account of how the brain learns to read. Central to this account is his neuronal recycling hypothesis: neural circuitry is capable of being ‘recycled’ or converted to a different function that is cultural in nature. The original function of the circuitry is not entirely lost and constrains what the brain can learn. It is argued that the neural niche co-evolves with the environmental niche in a way that does not undermine (...) the core ideas of neuronal recycling, but which is quite different from the models of cognitive and cultural evolution provided by evolutionary psychology and epidemiology. Dehaene contrasts neuronal recycling with a naïve model of the brain as a general learning device that is unconstrained in what it can learn. Consequently a tension develops in Dehaene's account of the role of plasticity in the acquisition of language. It is argued that the functional and structural changes in the brain that Dehaene documents in great detail are driven by learning and that this learning-driven plasticity does not commit us to a naïve model of the brain. (shrink)

Intersubjectivity refers to the variety of possible relations between perspectives. It is indispensable for understanding human social behaviour. While theoretical work on intersubjectivity is relatively sophisticated, methodological approaches to studying intersubjectivity lag behind. Most methodologies assume that individuals are the unit of analysis. In order to research intersubjectivity, however, methodologies are needed that take relationships as the unit of analysis. The first aim of this article is to review existing methodologies for studying intersubjectivity. Four methodological approaches are reviewed: comparative self-report, (...) observing behaviour, analysing talk and ethnographic engagement. The second aim of the article is to introduce and contribute to the development of a dialogical method of analysis. The dialogical approach enables the study of intersubjectivity at different levels, as both implicit and explicit, and both within and between individuals and groups. The article concludes with suggestions for using the proposed method for researching intersubjectivity both within individuals and between individuals and groups. (shrink)

According to Carey (2009), humans construct new concepts by abstracting structural relations among sets of partly unspecified symbols, and then analogically mapping those symbol structures onto the target domain. Using the development of integer concepts as an example, I give reasons to doubt this account and to consider other ways in which language and symbol learning foster conceptual development.

This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (shrink)

I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)