This article argues that certain philosophically devised quality control parameters should guide approaches to interdisciplinary education. We sketch the kind of reflections we think are necessary in order to produce epistemologically responsible curricula. We suggest that the two overarching epistemic dimensions of levels of analysis and basic viewpoints go a long way towards clarifying the structure of interdisciplinary validity claims. Through a discussion of how best to teach basic ideas about numeracy in Mind, Brain, and Education, we discuss what it (...) means for an interdisciplinary curriculum to respect both the minds of students and the complexity of the subject matter. (shrink)

Physics explores a universe of wonderful order, expressed in terms of beautiful mathematical equations. Mathematics itself is understood to be the exploration of a realm of noetic reality. Science describes matter in terms of concepts with mind-like qualities. The psychosomatic nature of human persons is best understood in terms of a dual-aspect monism, in which matter and mind are complementary aspects of a unitary being. The new science of complexity theory, with its dualities of parts/whole and energy/information, offers modest resources (...) for the speculative exploration of this idea. The intrinsic unpredictabilities present in nature afford the metaphysical opportunity to consider dissipative systems as exhibiting top–down causality. (shrink)

We discuss the nature of reality in the ontological context of Penrose’s math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent views. Some physicists (...) believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches. (shrink)

‘Number sense’ is a short‐hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain‐specific, biologically‐determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)

A number of examples of studies from the field ‘The Philosophy of Mathematical Practice’ (PMP) are given. To characterise this new field, three different strands are identified: an agent-based, a historical, and an epistemological PMP. These differ in how they understand ‘practice’ and which assumptions lie at the core of their investigations. In the last part a general framework, capturing some overall structure of the field, is proposed.

Human knowledge is a phenomenon whose roots extend from the cultural, through the neural and the biological and finally all the way down into the Precambrian “primordial soup.” The present paper reports an attempt at understanding this Greater System of Knowledge (GSK) as a hierarchical nested set of selection processes acting concurrently on several different scales of time and space. To this end, a general selection theory extending mainly from the work of Hull and Campbell is introduced. The perhaps most (...) drastic change from previous similar theories is that replication is revealed as a composite function consisting of what is referred to as memory and synthesis. This move is argued to drastically improve the fit between theory and human-related knowledge systems. The introduced theory is then used to interpret the subsystems of the GSK and their interrelations. This is done to the end of demonstrating some of the new perspectives offered by this view. (shrink)