This book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level - including geometry, (...) algebra, calculus, complex analysis and more - Norton unlocks students' personal power to construct mathematical objects based on their own mental activity, and illustrates the power of mathematics in organizing the world as we know it. Including reflections and activities designed to inspire awareness of the mental actions and processes coordinated in practicing mathematics, the book is geared towards current and future secondary and elementary mathematics teachers who will empower the next generation of mathematicians and STEM majors. Those interested in the history and philosophy that underpins mathematics will also benefit from this book, as well as those informed and curious minds attentive to the human experience more generally. Anderson Norton is Professor in the Department of Mathematics at Virginia Tech, USA, where he has been teaching mathematics courses for future teachers for 15 years. He is the editor of Constructing Number, and the co-author of Developing Fractions Knowledge and Numeracy for All Learners. (shrink)

Constructivist and embodied theories of learning each focus on action as the basis for cognition. However, in restricting action to sensorimotor activity, some embodied perspectives eschew ….

The COVID-19 pandemic has impacted data collection for longitudinal studies in developmental sciences to an immeasurable extent. Restrictions on conducting in-person standardized assessments have led to disruptive innovation, in which novel methods are applied to increase participant engagement. Here, we focus on remote administration of behavioral assessment. We argue that these innovations in remote assessment should become part of the new standard protocol in developmental sciences to facilitate data collection in populations that may be hard to reach or engage due (...) to burdensome requirements. We present a series of adaptations to developmental assessments and a detailed discussion of data analytic approaches to be applied in the less-than-ideal circumstances encountered during the pandemic-related shutdown. Ultimately, these remote approaches actually strengthen the ability to gain insight into developmental populations and foster pragmatic innovation that should result in enduring change. (shrink)

Nicholas Rescher’s way of understanding process philosophy reflects the ambitions of his own philosophical project and commits him to a conceptually ideal interpretation of process. Process becomes a transcendental idea of reflection that can always be predicated of our knowledge of the world and of the world qua known, but not necessarily of reality an sich. Rescher’s own taxonomy of process thinking implies that it has other variants. While Rescher’s approach to process philosophy makes it intelligible and appealing to mainstream (...) analytic philosophy, it leaves behind the more daring ideas of Bergson, James, and Whitehead, all of whom envisioned the primordial reality of process in a radical ontology of becoming. This variant of process thought can be construed as coherent and self-consistent, but not without relinquishing the correspondence theory of truth and embracing challenging ideas that bring us in close proximity to existentialism, apophatic theology, and Buddhism. (shrink)

Tuberculosis (TB) is a potentially fatal infectious disease that, in Aotearoa New Zealand (NZ), inequitably affects Asian, Pacific, Middle Eastern, Latin American, and African (MELAA), and Māori people. Medical research involving genome sequencing of TB samples enables more nuanced understanding of disease strains and their transmission. This could inform highly specific health interventions. However, the collection and management of TB isolate samples for research are currently informed by monocultural biomedical models often lacking key ethical considerations. Drawing on a qualitative kaupapa (...) Māori–consistent study, this paper reports on preliminary discussions with groups of Māori, Pacific, and Afghan people in NZ, whose communities have been harmed by TB and TB stigma. Participants’ discussions highlight key concerns and meanings that ought to inform the development of guidelines and a more robust consultative process for the governance of how TB isolate samples are collected and used both retrospectively and in future research. We argue for ethical processes to be culturally nuanced and community-generated, flexible and meaningful, and situated in relation to the physical and symbolic effects of TB. We discuss the significance of Indigenous data sovereignty, rights, and kāwanatanga (governorship) in shaping a multicultural data sovereignty model. (shrink)

The essays in this volume represent the first steps by philosophers and artificial intelligence researchers toward explaining why it is necessary to add an ...

Is there progress in philosophy? If so, how much? Philosophers have recently argued for a wide range of answers to these questions, from the view that there is no progress whatsoever to the view that philosophy has provided answers to all the big philosophical questions. However, these views are difficult to compare and evaluate, because they rest on very different assumptions about the conditions under which philosophy would make progress. This paper looks to the comparatively mature debate about scientific progress (...) for inspiration on how to formulate four distinct accounts of philosophical progress, in terms of truthlikeness, problem-solving, knowledge, and understanding. Equally importantly, the paper outlines a common framework for how to understand and evaluate these accounts. We distill a series of lessons from this exercise, to help pave the way for a more fruitful discussion about philosophical progress in the future. (shrink)

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

The assumption that environmental ethics must be nonanthropocentric in order to be adequate is mistaken. There are two forms of anthropocentrism, weak and strong, and weak anthropocentrism is adequate to support an environmental ethic. Environmental ethics is, however, distinctive vis-a-vis standard British and American ethical systems because, in order to be adequate, it must be nonindividualistic.Environmental ethics involves decisions on two levels, one kind of which differs from usual decisions affecting individual fairness while the other does not. The latter, called (...) allocational decisions, are not reducible to the former and govern the use of resources across extended time. Weak anthropocentrism provides a basis for criticizing individual, consumptive needs and can provide the basis for adjudicatingbetween these levels, thereby providing an adequate basis for environmental ethics without the questionable ontological commitments made by nonanthropocentrists in attributing intrinsie value to nature. (shrink)

Roots presents articles on major discoveries that laid the basis for contemporary molecular and cellular biology. In this article, Norton D. Zinder reviews the first findings about the single‐stranded DNA‐containing bacteriophages and what is known today about the genetics and molecular biology of these phages.

Mathias Frisch has argued that the requirement that electromagnetic dispersion processes are causal adds empirical content not found in electrodynamic theory. I urge that this attempt to reconstitute a local principle of causality in physics fails. An independent principle is not needed to recover the results of dispersion theory. The use of ‘causality conditions’ proves to be the mere adding of causal labels to an already presumed fact. If instead one seeks a broader, independently formulated grounding for the conditions, that (...) grounding either fails or dissolves into vagueness and ambiguity, as has traditionally been the fate of candidate principles of causality. 1. Introduction2. Scattering in Classical Electrodynamics3. Sufficiency of the Physics4. Failure of the Principle of Causality Proposed 4.1. A sometimes principle4.2. The conditions of applicability are obscure4.3. Effects can come before their causes4.4. Vagueness of the relata and of the notion of causal process5. Conclusion. (shrink)

Thought experiments in science are merely picturesque argumentation. I support this view in various ways, including the claim that it follows from the fact that thought experiments can err but can still be used reliably. The view is defended against alternatives proposed by my cosymposiasts.

Twenty years ago, Australian biomedical researchers took the first steps along a pathway toward common ground with opponents of the use of animals in science. Leaders of Australian medical research at that time saw the necessity of established science facing the ethical and political challenges that a revived antivivisectionist movement was mounting in the late 1970s and the 1980s.

Use of the word "Counter-Enlightenment" has become increasingly frequent in scholarly and journalistic writing. The word was almost certainly invented by the late Sir Isaiah Berlin, and it is owing to his enormous prestige and on-going influence that it has gained its current familiarity. In Berlin's view, two of the most important sources of the supposed Counter-Enlightenment are J. G. Hamann and J. G. Herder. But as I show, Berlin's numerous accounts of their thought are profoundly flawed and reflect not (...) Herder's or Hamann's own thought, but rather that of late nineteenth- and early twentieth-century German historians, who wished to legitimate their own anti-democratic, and hence anti-Enlightenment, ideology through the construction of a false historical genealogy. (shrink)

David Hume is, arguably, the most important philosopher ever to have written in English. Although best known for his contributions to epistemology, metaphysics, and the philosophy of religion, Hume also made substantial and influential contributions to psychology and the philosophy of mind, ethics, the philosophy of science, political and economic theory, political and social history, and, to a lesser extent, aesthetic and literary theory. All facets of Hume's output are discussed in this volume, the first genuinely comprehensive overview of his (...) work. The picture that emerges is of a thinker who, though critical to the point of scepticism, was nonetheless able to build on that scepticism a profoundly important, and still viable, constructive philosophy. (shrink)

In this paper we provide a psychological explanation for ‘grounding observations’—observations that are thought to provide evidence that there exists a relation of ground. Our explanation does not appeal to the presence of any such relation. Instead, it appeals to certain evolved cognitive mechanisms, along with the traditional modal relations of supervenience, necessitation and entailment. We then consider what, if any, metaphysical conclusions we can draw from the obtaining of such an explanation, and, in particular, if it tells us anything (...) about whether we ought to posit a relation of ground. (shrink)

Religious Pluralism Religious pluralism, broadly construed, is a response to the diversity of religious beliefs, practices, and traditions that exist both in the contemporary world and throughout history. The terms “pluralism” and “pluralist” can, depending on context or intended use, signify anything from the mere fact of religious diversity to a particular kind of philosophical … Continue reading Pluralism, Religious →.

Seeing Wittgenstein Anew is a collection which examines Ludwig Wittgenstein's remarks on the concept of aspect-seeing, showing that it was not simply one more topic of investigation in Wittgenstein's later writings but rather a pervasive and guiding concept in his efforts to turn philosophy's attention to the actual conditions of our common life in language. The essays in this 2010 volume open up novel paths across familiar fields of thought: the objectivity of interpretation, the fixity of the past, the acquisition (...) of language, and the nature of human consciousness. Significantly, they exemplify how continuing consideration of the interrelated phenomena of aspect-seeing might produce a fruitful way of doing philosophy in a new century. (shrink)

David and Mary Norton present the definitive scholarly edition of Hume's Treatise, one of the greatest philosophical works ever written. This set comprises the two volumes of texts and editorial material, which are also available for purchase separately. -/- David Hume (1711 - 1776) is one of the greatest of philosophers. Today he probably ranks highest of all British philosophers in terms of influence and philosophical standing. His philosophical work ranges across morals, the mind, metaphysics, epistemology, religion, and aesthetics; (...) he had broad interests not only in philosophy as it is now conceived but in history, politics, economics, religion, and the arts. He was a master of English prose. -/- The Clarendon Hume Edition will include all of his works except his History of England and minor historical writings. It is the only thorough critical edition, and will provide a far more extensive scholarly treatment than any previous editions. This edition (which has been in preparation since the 1970s) offers authoritative annotation, bibliographical information, and indexes, and draws upon the major advances in textual scholarship that have been made since the publication of earlier editions - advances both in the understanding of editorial principle and practice and in knowledge of the history of Hume's own texts. (shrink)

The underdetermination argument establishes that scientists may use political values to guide inquiry, without providing criteria for distinguishing legitimate from illegitimate guidance. This paper supplies such criteria. Analysis of the confused arguments against value-laden science reveals the fundamental criterion of illegitimate guidance: when value judgments operate to drive inquiry to a predetermined conclusion. A case study of feminist research on divorce reveals numerous legitimate ways that values can guide science without violating this standard.

Using Asimov’s “Bicentennial Man” as a springboard, a number of metaethical issues concerning the emerging field of machine ethics are discussed. Although the ultimate goal of machine ethics is to create autonomous ethical machines, this presents a number of challenges. A good way to begin the task of making ethics computable is to create a program that enables a machine to act an ethical advisor to human beings. This project, unlike creating an autonomous ethical machine, will not require that we (...) make a judgment about the ethical status of the machine itself, a judgment that will be particularly difficult to make. Finally, it is argued that Asimov’s “three laws of robotics” are an unsatisfactory basis for machine ethics, regardless of the status of the machine. (shrink)

Reply to Steven Lestition's article, "Countering, Transposing, or Negating the Enlightenment? A Response to Robert Norton," published in the Journal of the History of Ideas(2007), pp. 659-81.

In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities (...) and I argue that in it these expectations give no grounds for a decision to swap since that decision must be based on a summation of all the expectations. But this sum yields a non‐convergent series that has no meaningful value. The conflicting recommendations – that it is to one or the other player's advantage to swap – arise from different ways of grouping terms in the sum that yield an illusion of convergence. I describe a generalized exchange paradox, explore some of its properties and display another example. (shrink)

If environmentalists are to combat effectively the continuing environmental decay resulting from more and more intense human exploitation of nature, they need a plausible and coherent rationale for preserving sensitive areas and other species. This need is illustrated by reference to two examples of controversies concerning large public projects in wilderness areas. Analyses of costs and benefits to presently existing human beings and the utilitarian theory which supports such theories are inadequate to provide such a rationale, as other writers have (...) shown. A number of environmentalists have suggested that ascriptions of rights to nonhuman animals, plants, and other natural objects may provide the necessary rationale. I argue that such ascriptions can only be effective if they are supported by a general theory of rights. Although no such general theory is developed, I state four minimal conditions which must be fulfilled by all rights holders as entailments of the concept of a right and, hence, as necessary conditions on rights holding, regardless of the general theory of rights espoused. I then argue that no appeals to rights of nonhumans can simultaneously fulfill these four minimal conditions and, on the other hand, satisfy the need for a coherent rationale for environmental preservation. In the central argument of the essay I exploit the distinction between the concern of vegetarians and antivivisectionists who rest their case for animal rights on the analogy ofanimal suffering to human suffering and the concern of environmentalists to protect the integrity of holistic ecosystems. I then conclude that even if the case for nonhuman rights can be made convincingly, the rights defended are insufficient for the development of a complete and coherent rationale for environmental preservation. (shrink)

Several recent authors have recommended that “sense of place” should become an important concept in our evaluation of environmental policies. In this paper, we explore aspects of this concept, arguing that it may provide the basis for a new, “place-based” approach to environmental values. This approach is based on an empirical hypothesis that place orientation is a feature of all people’s experience of their environment. We argue that place orientation requires, in addition to a home perspective, a sense of the (...) space around the home place and that this dual aspect can be modeled using a “hierarchical” methodology. We propose a “triscalar,” place-oriented system for the analysis of environmental values, explore the characteristics of place-orientation through several examples, and employ these characteristics to distinguish acceptable and unacceptable aspects of the NIMBY (not-in-my-backyard) idea. (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer (...) scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...) result precludes many possible inductive logics, including versions of hypothetico-deductivism. (shrink)

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

Eternalists believe that there is no ontological difference between the past, present and future. Thus, a challenge arises: in virtue of what does time have a direction? Some eternalists, Oaklander and Tegtmeier ) argue that the direction of time is primitive. A natural response to positing primitive directionality is the suspicion that said posit is too mysterious to do any explanatory work. The aim of this paper is to relieve primitive directionality of some of its mystery by offering a novel (...) way to understand the phenomenon in terms of the recently popularised notion of grounding. (shrink)

In Democratic Authority, David Estlund (2008) presents a major new defense of democracy, called epistemic proceduralism. The theory claims that democracy exercises legitimate authority in virtue of possessing a modest epistemic power: its decisions are the product of procedures that tend to produce just laws at a better than chance rate, and better than any other type of government that is justifiable within the terms of public reason. The balance Estlund strikes between epistemic and non-epistemic justifications of democracy is open (...) to question, both for its neglect of the roles of non-epistemic values of equality and collective autonomy in democracy, and for the ways his use of the public reason standard overshadows empirically based epistemic arguments for democracy. Nevertheless, Estlund presents telling critiques of rival theories and develops a sophisticated alternative that illuminates some central normative features of democracy. (shrink)

Many think that sentences about what metaphysically explains what are true iff there exist grounding relations. This suggests that sceptics about grounding should be error theorists about metaphysical explanation. We think there is a better option: a theory of metaphysical explanation which offers truth conditions for claims about what metaphysically explains what that are not couched in terms of grounding relations, but are instead couched in terms of, inter alia, psychological facts. We do not argue that our account is superior (...) to grounding-based accounts. Rather, we offer it to those already ill-disposed towards grounding. (shrink)

A distinctive feature of modern capitalist societies is the tendency of the market to take over the production, maintenance, and distribution of goods that were previously produced, maintained, and distributed by nonmarket means. Yet, there is a wide range of disagreement regarding the proper extent of the market in providing many goods. Labor has been treated as a commodity since the advent of capitalism, but not without significant and continuing challenges to this arrangement. Other goods whose production for and distribution (...) on the market are currently the subject of dispute include sexual intercourse, human blood, and human body parts such as kidneys. How can we determine which goods are properly subjects of market transactions and which are not? The purpose of this article is to propose a theory of what makes economic goods differ from other kinds of goods, which can help to answer this question. (shrink)