4E cognition (embodied, embedded, enactive, and extended) is a relatively young and
thriving field of interdisciplinary research. It assumes that cognition is shaped and structured …

In this paper we tentatively propose that one of the feral cognitive bases for modern symbolic
thinking may be numerosity, that is, the ability to appreciate and understand numbers. We …

In recent years, philosophical work directly concerned with the practice of mathematics has
intensified, giving rise to a movement known as the philosophy of mathematical practice. In …

Peirce considered the principal business of logic to be the analysis of reasoning. He argued
that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries …

This paper offers a framework for a mathematics lesson design that is consistent with the
way we learn about, and discover, most things in life. In addition, the framework provides a …

The aim of this article is to explain why knot diagrams are an effective notation in topology.
Their cognitive features and epistemic roles will be assessed. First, it will be argued that …

This paper describes a framework for a mathematics lesson design called ELPSA. It is
comprised of five learning components, namely: Experience, Language, Pictorial, Symbolic …

On the basis of a wide range of historical examples various features of axioms are discussed
in relation to their use in mathematical practice. A very general framework for this discussion …

This collection of new essays written by an international team of scholars is a
groundbreaking examination of the problem of divine hiddenness, one of the most dynamic …

If cognition is fundamentally interactive how did it come to be so? The cognitive integration
framework provides an answer: phylogenetically early forms of cognition, in humans, involve …