It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to mathematics pedagogy. The main conclusion is (...) that a fallibilist view of mathematics is assumed in the Standards and that most of its pedagogical assumptions and approaches are based on this philosophy. (shrink)

The dissertation criticizes two analogical applications of Darwinism to the spheres of mind and culture: the Darwinian approach to creativity and memetics. These theories rely on three basic analogies: the ontological analogy states that the basic ontological units of culture are so-called memes, which are replicators like genes; the origination analogy states that novelty in human creativity emerges in a "blind" Darwinian manner; and the explanatory units of selection analogy states that memes are "egoistic" and that they can spread independently (...) of our mind. The detailed philosophical analysis offered in the dissertation shows that these three analogies rely on either wrong or trivial statements: they provide either wrong or no new descriptions or explanations of the phenomena at hand. In Chapter One, I introduce the diverse ways, in which contemporary Darwinism is used today outside of evolutionary biology. Chapter Two explains what it means to claim that something evolves in a Darwinian manner. Chapter Three to Five address each of the three analogies separately. Darwinism applied to culture and mind, at least in the way discussed in this study, is not a dangerous idea. It leads either to wrong claims or to a re-telling in Darwinian terms of what we have already known. (shrink)

Explores the science and creative process behind Poe’s cosmological treatise. Silver Winner for Philosophy, 2017 Foreword INDIES Book of the Year Awards In 1848, almost a year and a half before Edgar Allan Poe died at the age of forty, his book Eureka was published. In it, he weaved together his scientific speculations about the universe with his own literary theory, theology, and philosophy of science. Although Poe himself considered it to be his magnum opus, Eureka has mostly been overlooked (...) or underappreciated, sometimes even to the point of being thought an elaborate hoax. Remarkably, however, in Eureka Poe anticipated at least nine major theories and developments in twentieth-century science, including the Big Bang theory, multiverse theory, and the solution to Olbers’ paradox. In this book—the first devoted specifically to Poe’s science side—David N. Stamos, a philosopher of science, combines scientific background with analysis of Poe’s life and work to highlight the creative and scientific achievements of this text. He examines Poe’s literary theory, theology, and intellectual development, and then compares Poe’s understanding of science with that of scientists and philosophers from his own time to the present. Next, Stamos pieces together and clarifies Poe’s theory of scientific imagination, which he then attempts to update and defend by providing numerous case studies of eureka moments in modern science and by seeking insights from comparative biography and psychology, cognitive science, neuroscience, and evolution. David N. Stamos teaches philosophy at York University in Toronto. He is the author of several books, including Darwin and the Nature of Species, also published by SUNY Press. (shrink)

The concept of creativity is a central one in folk psychological explanation and has long been prominent in philosophical debates about the nature of art, genius, and the imagination. The scientific investigation of creativity in humans is also well established, and there has been increasing interest in the question of whether the concept can be rigorously applied to non-human animals. In this paper, I argue that such applications face serious challenges of both a conceptual and methodological character, reflecting deep controversies (...) within both philosophy and psychology concerning how to define and apply the concept of creativity. After providing a brief review of some of the leading theories of creativity and discussing some of the strongest putative cases of creative intelligence in non-human animals, I examine some of the more worrisome difficulties faced by attempts to use these theories to answer the question of whether animals are truly creative. I conclude by examining how we might overcome them, and suggest that one approach worth taking seriously is to adopt what I term a Strong Rejectionist view of creativity, eschewing use of the term entirely in the scientific study of comparative cognition. (shrink)

In his paper “Explaining Deductive Inference” Prawitz states what he calls «a fundamental problem of logic and the philosophy of logic»: the problem of explaining «Why do certain inferences have the epistemic power to confer evidence on the conclusion when applied to premisses for which there is evidence already?». In this paper I suggest a way of articulating, and partly modifying, the intuitionistic answer to this problem in such a way as to both answer Prawitz’s problem and satisfy a requirement (...) I argue to be crucial for any epistemic theory of the meaning of the logical constants: the requirement that evidence is epistemically transparent. (shrink)

Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...) Monistto uphold disciplinary standards ofgeometrical reasoning, authors opposed tonon-Euclidean geometry aligned theirreasoning with practical applications, universal know-how, and nonhierarchicaldemocracy. As one contributorinquired,“How isthe professional expert betterfit-ted to see more lucidly in dealing with the elements of geometry than any otherperson of good geometric faculty?”. (shrink)

Do artists have control over their ideas for new artworks? This is often treated as a question about spontaneity, or the experience of control: does the event of having an idea for a new artwork occur unexpectedly and without foresight? I suggest another way of interpreting the question—one that has mostly been neglected by philosophers, and that is not settled by claims about spontaneity. According to that interpretation, the question is about agency: are the events of having ideas for new (...) artworks exercises of mental agency? I argue that the answer is no. I apply the results of this argument to questions about what is and is not intentional in the creative process. I conclude by examining another type of control artists might exercise over their creative mental events, which I call ‘facilitation’. (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)

The present work was intended originally as a chapter for my January 2006 Ph.D dissertation, but now is essentially a 'working paper.' As is well known, economists make a number of abstract and unrealistic assumptions, such as for example characterising the economic agent as a rational maximiser. The present paper is concerned with assessing the methodological status of every-day common-sense observations in relation to such abstract and unrealistic assumptions. Following Popper and Hume, I propose a theoretical framework in which to (...) understand 'common sense.' I then argue that common-sense acts as a 'guide' assessing the value of theoretical work, that theoretical contributions that are based on premises or arrive at conclusions that diverge to a greater degree should require a higher level of justification, and that any common-sense observation about the real world should be admissable as a starting point for theoretical investigation and elaboration and any successful theory should be accountable to common-sense observations. (shrink)

Up until 1980 seismology was focused entirely upon data collection, the long-term study of tectonic processes, and limited surface-level measurements. Formal research on earthquakes was almost at a standstill despite the urgent need to discover reliable and measurable precursors in support of a system for short-term prediction. In the period 1975–1978 the author chose to interview eight intuitive experts who had proven their abilities in domains other than seismology. He asked them identical questions about the physical process involved in earthquake-triggering (...) and associated precursors, and then compiled their consistent responses into a consensus. The accounts agreed well with one another and offered a number of insightful and possibly new directions for seismological research. Re-examination of these intuitive findings thirty years later, in the light of the many subsequent discoveries reported in mainstream geophysics journals, revealed that the expert intuitives had provided novel, significant, and strikingly correct information on earthquake-triggering and related precursors. This exemplary result suggests that skillfully applied intuitive inquiry could play a significant role in future seismological and geophysical studies, as well as in scientific research generally. Keywords: earthquakes—intuition—intuitive consensus—expert intuitives—earth-quake triggering—seismology—geophysics—prediction—verification—nuclear activity—precursors—tectonic plates —atmospheric electricity—electromagnetism—faults—earthquake lights—solar wind—thermal anomalies—solar activity—magnetosphere—ground gases—earth tides—planets—atmosphere—weather changes—animal behavior—human-caused earthquakes. (shrink)

The Greeks had a ready answer for what happens when the mind suddenly finds the answer to a question for which it had been searching: insight was regarded as a gift of the Muses, its origins were divine. It served to highlight the Greeks'' belief that there are some things which are not meant to be scientifically explained. The essence of insight is that it comes from some supernatural source: unpredicted and unfettered. In other words, the origins of insight are (...) unconscious, and hence, unexplainable. Wittgenstein felt that, as long as there continues to be a noun expression like to have a moment of insight which functions in the same way as the expression to have a hunger pang, thereby inducing us to treat moment of insight as the name of an experience, then people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. To the founders of AI, this argument reeked of obscurantism. The moment of insight, they felt, is indeed a mystery, but it is one that begs to be explained in causal terms. Indeed, the problem of insight served as one of the leading problems in the evolution of AI. Hence anyone interested in the foundations of AI is compelled to examine the manner in which the early pioneers of the field sought to explain the eureka experience. In this paper I will look at some of the key conceptual developments which paved the way for Newell and Simon''s theory of GPS: the fundamental changes in the notion of the unconscious — the emergence of the cognitive unconscious — which took place in the nineteenth- and early twentieth-century. In so doing, I hope to clarify what Wittgenstein may have had in mind in his strictures against mechanist attempts to analyse the nature of insight. (shrink)

Classical theories of harmony have been used to explain phenomena like beauty, happiness, health, virtue, pleasure, peace, and even ecological sustainability. With the intent of making these theories more accessible to designers, this article reviews the conception of harmony from about 500 BCE to the present. It begins with a brief overview of harmony in classical Chinese and Greek philosophy. Then it examines the role of harmony in the renaissance, the scientific revolution, and the early modern period across topics in (...) aesthetics, ethics, physics, politics, and economics. Finally, turning to the 20th century, this article highlights the conceptual function of harmony in psychology, neuroscience, computer science, and design. This synthesis concludes with a review of applications and implications for contemporary designers. An essential conclusion of this article is that harmony involves the integration of diversity into a greater whole; harmony is not pure agreement or “sameness.” Overall, we suggest that classical principles of harmony might serve as a theoretical framework to help designers develop a more sustainable and vibrant vision of the future. (shrink)

Memoires by eminently creative people often describe architectural spaces and qualities they believe instrumental for their creativity. However, places designed to encourage creativity have had mixed results, with some found to decrease creative productivity for users. This may be due, in part, to lack of suitable empirical theory or model to guide design strategies. Relationships between creative cognition and features of the physical environment remain largely uninvestigated in the scientific literature, despite general agreement among researchers that human cognition is physically (...) and socially situated. This paper investigates what role architectural settings may play in creative processes by examining documented first person and biographical accounts of creativity with respect to three central theories of situated cognition. First, the embodied thesis argues that cognition encompasses both the mind and the body. Second, the embedded thesis maintains that people exploit features of the physical and social environment to increase their cognitive capabilities. Third, the enaction thesis describes cognition as dependent upon a person’s interactions with the world. Common themes inform three propositions, illustrated in a new theoretical framework describing relationships between people and their architectural settings with respect to different cognitive processes of creativity. The framework is intended as a starting point toward an ecological model of creativity, which may be used to guide future creative process research and architectural design strategies to support user creative productivity. (shrink)