Sometimes we learn through the use of imagination. The epistemology of imagination asks how this is possible. One barrier to progress on this question has been a lack of agreement on how to characterize imagination; for example, is imagination a mental state, ability, character trait, or cognitive process? This paper argues that we should characterize imagination as a cognitive ability, exercises of which are cognitive processes. Following dual process theories of cognition developed in cognitive science, the set of imaginative processes (...) is then divided into two kinds: one that is unconscious, uncontrolled, and effortless, and another that is conscious, controlled, and effortful. This paper outlines the different epistemological strengths and weaknesses of the two kinds of imaginative process, and argues that a dual process model of imagination helpfully resolves or clarifies issues in the epistemology of imagination and the closely related epistemology of thought experiments. (shrink)

If education is to make a difference it is widely acknowledged that we must aim to educate for understanding, but this means being clear about what we mean by understanding. This paper argues for a concept of personal understanding, recognising both the commonality and individuality of each pupil's understandings, and the relationship between understanding and interpretation, analysis and synopsis, and the quest for meaning. In supporting this view, the paper advocates an emergentist notion of person‐hood, and considers the neurophysiological reasons (...) for asserting the individuality of human minds, brains, and the creation of personal meanings. The notion of personal meanings would, however, seem to run counter to the post‐modern denial of the autonomous self, and the tradition in philosophy, most recently stemming from Wittgenstein, that insists that meanings and understandings are essentially social, and not personal—a view also advocated by John White in regard to education. In contrast, this paper argues that meanings and understandings are both social and personal. Once we reinstate the notion of personal minds and personal understandings, alongside the social, we may see more clearly what it means to educate for understanding, and why this might begin to make a difference. (shrink)

This article addresses the question of the coherence of enactivism as a research perspective by making a case study of enactivism in mathematics education research. Main theoretical directions in mathematics education are reviewed and the history of adoption of concepts from enactivism is described. It is concluded that enactivism offers a ‘grand theory’ that can be brought to bear on most of the phenomena of interest in mathematics education research, and so it provides a sufficient theoretical framework. It has particular (...) strength in describing interactions between cognitive systems, including human beings, human conversations and larger human social systems. Some apparent incoherencies of enactivism in mathematics education and in other fields come from the adoption of parts of enactivism that are then grafted onto incompatible theories. However, another significant source of incoherence is the inadequacy of Maturana’s definition of a social system and the lack of a generally agreed upon alternative. (shrink)

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, (...) I summarize Clark’s notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited. (shrink)

This paper outlines the process of verbal communication of emotion as this occurs through the phases of the referential process, including arousal of an emotion schema; detailed and specific descriptions of images and episodes that are exemplars of emotion schemas; and reflection and reorganization, which may include emotion labels and other types of categorical terms. The concepts of emotion schemas and the referential process are defined in the theoretical framework of multiple code theory which includes subsymbolic sensory, visceral and motoric (...) processes, symbolic images and words. Emotion schemas are defined as clusters of representations of events incorporating similar bodily, sensory and motoric processes activated in relation to different people in different contexts. Through the referential process subsymbolic components of a schema that have been activated in a speaker or writer and that may be connected only partially to words may be evoked in a listener or reader. The concept of the emotion schemas is examined in relation to current work in emotion theory and neuroscience. The unique effects of detailed descriptions of episodes in conveying complex aspects of emotional experience are discussed, as recognized by writers, and as demonstrated in empirical research. Computerized measures of the phases of the referential process are presented, focusing particularly on the central measure, the Weighted Referential Activity Dictionary which identifies points of narrative and imagery. The operation of the function words that dominate the WRAD are examined in relation to the structure of narrative expression underlying the verbal representation of emotion schemas. (shrink)

What role does the imagination play in scientific progress? After examining several studies in cognitive science, I argue that one thing the imagination does is help to increase scientific understanding, which is itself indispensable for scientific progress. Then, I sketch a transcendental justification of the role of imagination in this process.

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held (...) since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in the mathematics classroom, with fallibilist and social constructivist perspectives arguably being most conducive for conceiving of creativity as a type of action for all students. Thus, this paper proposes a framework of creative mathematical action that is based in these epistemologies and explains key aspects of the framework by drawing connections between it and research in the field of creativity. (shrink)