Cities around the globe are immersed in transnational projects of place reconfiguration and attraction. Urban places, intent on competing in the globalized experience-based economy, undertake identity projects—on-going, dynamic processes through which places are produced and reproduced by conscious strategies of place making and identity building (see, for example, Nyseth and Viken 2009). In this article, I employ Henri Lefebvre’s conceptions of a “right to the city” in order to explore the right to full participation in imagining and shaping urban futures. (...) Spatial practices, such as those I term civic tinkering, may offer one way to help enable such imagining.My discussion draws from scholarship on imaginaries and place identity, as well as on my own qualitative field studies conducted in Roanoke, Virginia, in the United States, and Belfast, Northern Ireland in the United Kingdom. While my precise research questions differed in these two sites, I explored, in each instance, the processes of place identification and development centered on arts and culture, and the extent to which marginal groups and their concerns were engaged or considered in such processes. I also explore “tinkering” as a set of activities that hold potential for residents to more fully participate in the urban project byconstructing, altering, and disrupting spatial meanings. Tinkering may be any impermanent, unsanctioned, and informal activity endeavoring to positively alter a city’s identity. Henri Lefebvre described the relevance of such practices in his vision of the city as oeuvre, or ongoing project. (shrink)

In an important and widely cited paper, Zerilli, Knott, Maclaurin, and Gavaghan (2019) argue that opaque AI decision makers are at least as transparent as human decision makers and therefore the concern that opaque AI is not sufficiently transparent is mistaken. I argue that the concern about opaque AI should not be understood as the concern that such AI fails to be transparent in a way that humans are transparent. Rather, the concern is that the way in which opaque AI (...) is opaque is very different than the way in which humans are opaque. What matters is the degree to which the opaque processes of a class of decision makers are stable, uniform, and safe. The degree to which such processes have these features in humans is higher than the degree to which such processes have these features in opaque AI. And therefore we should require AI to be more transparent than humans. (shrink)

The tradition descending from Frege and Russell has typically treated theories of meaning either as theories of meanings, or as theories of truth conditions. However, propositions of the classical sort don't exist, and truth conditions can't provide all the information required by a theory of meaning. In this book, one of the world's leading philosophers of language offers a way out of this dilemma. Traditionally conceived, propositions are denizens of a "third realm" beyond mind and matter, "grasped" by mysterious Platonic (...) intuition. As conceived here, they are cognitive-event types in which agents predicate properties and relations of things--in using language, in perception, and in nonlinguistic thought. Because of this, one's acquaintance with, and knowledge of, propositions is acquaintance with, and knowledge of, events of one's cognitive life. This view also solves the problem of "the unity of the proposition" by explaining how propositions can be genuinely representational, and therefore bearers of truth. The problem, in the traditional conception, is that sentences, utterances, and mental states are representational because of the relations they bear to inherently representational Platonic complexes of universals and particulars. Since we have no way of understanding how such structures can be representational, independent of interpretations placed on them by agents, the problem is unsolvable when so conceived. However, when propositions are taken to be cognitive-event types, the order of explanation is reversed and a natural solution emerges. Propositions are representational because they are constitutively related to inherently representational cognitive acts. Strikingly original, What Is Meaning? is a major advance. (shrink)

This article critically interrogates contemporary forms of addiction medicine that are portrayed by policy-makers as providing a ‘rational’ or politically neutral approach to dealing with drug use and related social problems. In particular, it examines the historical origins of the biological facts that are today understood to provide a foundation for contemporary understandings of addiction as a ‘disease of the brain’. Drawing upon classic and contemporary work on ‘styles of thought’, it documents how, in the period between the mid-1960s and (...) the mid-1970s, such facts emerged in relation to new neurobiological styles of explaining and managing social problems associated with drug abuse, and an alliance between a relatively marginal group of researchers and American policy-makers who were launching the ‘War on Drugs’. Beyond illustrating the political and material conditions necessary for the rise of addiction neuroscience, the article highlights the productivity of neurobiological thought styles, by focusing on the new biological objects, treatments and hopes that have emerged within the field of addiction studies over the last several decades. (shrink)

An original interpretation of Merleau-Ponty on subjectivity, drawing from and challenging both the continental and analytic traditions.

It is widely believed that Perelman and Olbrechts-Tyteca’s theory of argumentation is vulnerable to the charge of relativism. This paper provides a more charitable interpretation of Perelman and Olbrechts-Tyteca’s normative views, one that properly considers the historical trajectory of their work and a wider range of texts than existing interpretations. It is argued that their views are better characterized as a form of “contrastivism about arguments” than any kind relativism. This more accurate depiction contributes to ongoing efforts to revive interest (...) in Perelman and Olbrechts-Tyteca’s work as well as build bridges with trends in contemporary argumentation theory. (shrink)

_An original interpretation of Merleau-Ponty on subjectivity, drawing from and challenging both the continental and analytic traditions._.

For anyone approaching the Encheiridion of Epictetus for the first time, this book provides a comprehensive guide to understanding a complex philosophical text. Including a full translation and clear explanatory commentaries, Epictetus's 'Encheiridion' introduces readers to a hugely influential work of Stoic philosophy. Scott Aikin and William O. Stephens unravel the core themes of Stoic ethics found within this ancient handbook. Focusing on the core themes of self-control, seeing things as they are, living according to nature, owning one's roles (...) and fulfilling the responsibilities that those roles entail, the authors elucidate the extremely challenging ideas in Epictetus's brisk chapters. Divided into five distinct parts, this book provides readers with: -/- - A new translation of the Encheiridion by William O. Stephens. - A new introduction to ancient Stoicism, its system of concepts, and the ancient figures who shaped it. - A fresh treatment of the notorious and counter-intuitive 'Stoic paradoxes'. - An accessible overview of the origin and historical context of the Encheiridion. - Detailed commentaries on each chapter of the Encheiridion that clarify its recurring themes and highlight their interconnections. - Careful attention to the presentation of the arguments embedded in Epictetus's aphoristic style. - A thoughtful discussion of serious criticisms of Epictetus's Stoicism and replies to these objections. -/- Written with clarity and authority, Epictetus's 'Encheiridion' provides a foundation from which readers can understand this important text and engage with the fundamental questions of Stoic philosophy and ethics. This guide will aid teachers of Epictetus, students encountering Stoicism for the first time, and readers seeking a greater understanding of Stoic ethics. (shrink)

Albert Einstein's bold assertion of the form-invariance of the equation of a spherical light wave with respect to inertial frames of reference became, in the space of six years, the preferred foundation of his theory of relativity. Early on, however, Einstein's universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light-ellipsoid. Drawing in part on archival sources, this paper shows how an (...) informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview. (shrink)

Canada has followed the pattern of Benelux nations by legislating sufferingSuffering as the pivotal eligibilityEligibilitycriterionCriterion for euthanasiaEuthanasia/assisted death without requiring terminal prognosis as is needed in most permissive jurisdictions. This chapter will explore the relationship between sufferingSuffering and Medical Assistance in Dying (MAID) and the ways in which sufferingSuffering is understood in the Supreme Court of Canada, the federal Criminal Code legislation and by health care assessors. Based on this analysis, we will argue that the resulting sufferingSufferingeligibilityEligibilitycriterionCriterion leaves the law (...) open to unintended forms of interpretation, thus instituting perhaps the most unbounded and risk-prone form of assisted death in the world. A review of the literature on sufferingSuffering, the wish to dieWish to die, and reasons for MAIDReasons for MAID requests found sufferingSuffering of severe illness to be frequently associated with unstable mental health, social, and existentialExistential variables that are often amenable to therapy or remediation. While sufferingSuffering remains a powerful motivating force to seek opportunities to relieve distress, its use as an eligibilityEligibilitycriterionCriterion for MAID has significant ambiguity in its’ characterization of ‘enduring’ and ‘irremediable’ and thus fails to protect against abuse for the vulnerable. (shrink)

Two important debates have characterized mainstream epistemology in recent years. The first is the debate between foundationalists and anti-foundationalists. The second is the debate over the details of a naturalized epistemology. Both debates have meant that traditional concepts of rationality and justification are now understood in a new light. Both debates have helped focus attention on the future direction of epistemology, its goals and its limitations.

An examination of the history and arguments behind W.K. Clifford and William James's landmark essays and subsequent impact on the importance of knowledge-based evidence.

I defend the view that moral properties are identical to properties that can be expressed without using moral vocabulary.

The paper is an attempt to explain what a transcendental argument is for Kant. The interpretation is based on a reading of the 'Discipline of Pure Reason', Sections 1 and 4 of the first Critique. The author first identifies several statements that Kant makes about the method of proof he followed in the 'Analytic of Principles' which seem to be inconsistent. He then tries to remove the apparent inconsistencies by focusing on the idea of instantiation and drawing a distinction between (...) the intension and the extension of a concept. Finally, the results are applied to the second 'Analogy of Experience' for the purposes of illustration. The paper should be seen as an attempt to provide an historical answer to a question that has been treated thematically in much of the recent literature. (shrink)

A new collection of essays highlighting the wide range of Buber's thought, career, and activism. Best known for I and Thou, which laid out his distinction between dialogic and monologic relations, Martin Buber (1878-1965) was also an anthologist, translator, and author of some seven hundred books and papers. Martin Buber: Creaturely Life and Social Form, edited by Sarah Scott, is a collection of nine essays that explore his thought and career. Martin Buber: Creaturely Life and Social Form shakes up (...) the legend of Buber by decentering the importance of the I-Thou dialogue in order to highlight Buber as a thinker preoccupied by the image of relationship as a geode to spiritual, social, and political change. The result is a different Buber than has hitherto been portrayed, one that is characterized primarily by aesthetics and politics rather than by epistemology or theology. Martin Buber: Creaturely Life and Social Form will serve as a guide to the entirety of Buber's thinking, career, and activism, placing his work in context and showing both the evolution of his thought and the extent to which he remained driven by a persistent set of concerns. (shrink)

Scott Yenor argues that David Hume's reputation as a skeptic is greatly exaggerated. In David Hume's Humanity, Yenor shows how Hume's skepticism is a moment leading Hume to defend a philosophy that is grounded in the inescapable assumptions of common life. Humane virtues reflect the proper reaction to the complex mixture of human faculties that define the human condition. These gentle virtues best find their home in the modern commercial republic, of which England is the leading example. Hume's defense (...) of both common life philosophy and humanity are, however, flawed by his secretly dogmatic assumptions about the nature of history and his Enlightened approach to religious teachings and psychology. This study makes the case for Hume's manner of grounding philosophy in common life is essential to any reinvigoration of the humanities. It ultimately holds that Hume's practice of that philosophy is seriously flawed, but that a more philosophic philosophy of common life is available. (shrink)

This book is a radical plea for the centrality of experience in the social and human sciences. Scott Lash argues that a large part of the output of the social sciences today is still shaped by assumptions stemming from positivism, in contrast to the tradition of interpretative social enquiry pioneered by Max Weber. These assumptions are particularly central to economics, with its emphasis on homo economicus, the utility-maximizing, instrumental actor, but they have infiltrated the other social sciences too. Lash (...) argues for a social sciences based not in positivism’s utilitarian a priori but instead in the a posteriori of grounded and embedded subjective experience. This features a politics of Hannah Arendt’s public sphere, which begins with the particular experience of Aristotle’s polis and moves - via Rome, Augustine and Kant - to a modernity that acknowledges the fragility of political worlds. Yet modernity is also a matter of technological experience and technological forms of life. Lash - starting from Aristotle’s technics and working through Turing’s and Shannon’s computer mediation – develops a novel account of technological experience, of how objects themselves experience. And here he finds a surprising convergence with Chinese cosmology’s ethos of dao, qi and li: the experience of the embedded multiplicity of the ‘ten thousand things’. This original book by a leading social and cultural theorist will be of interest to scholars and students across the social sciences, from sociology and cultural studies to anthropology and politics. (shrink)

Cognitive science proposes that we have evolved to build mental maps of the world not according to its actual, physical nature, but according to what allows us to thrive. In other words, our individual and collective realities are fictions - carefully constructed to enable us to maintain our particular perspectives. It used to be that our fictions were rooted to reasonably solid things: to people, places and memories. Today, in an age of online personas, alternative truths, constant surveillance and an (...) increasingly hysterical news cycle, our realities are becoming more flimsy and more vulnerable than ever before. Ours is now a zoomed-in perspective, where the backstage is centre stage. We are both camera person and subject, with new powers and new weaknesses. Our personal and political spheres are dangerously merging. How will the form and grammar of our feelings have to change in this over-exposed environment? Should any of our stories remain secret? How are these phenomena changing the way we live? How do we maintain a sense of reality in an increasingly fantastic world? Picnic Comma Lightning is an innovative examination of the nature of reality in the twenty-first century, one that explores the key ethical, political and neurological forces contouring our inner selves, but also the old influences of grief and desire, memory and imagination. In it, award-winning author Laurence Scott provides a lively and accessible new philosophy for this epoch in Western civilisation, one that will change the way you see the world, and your place within it."--Publisher description. (shrink)

Women and religion -- Reproductive futurism -- Political emancipation -- From the Cold War to the clash of civilizations -- Sexual emancipation.

Many fans of Diogenes of Sinope laud his parrhesia, free speech used for critique. However, Diogenes abused not only the powerful but also the socially marginalized. We argue that interpreters of Diogenes cannot explain away the undeniably troublesome things that Diogenes said about those at the margins. But we also argue that Diogenes ought nonetheless to be preserved. Some of his chreiai can be reminders of how to be courageous and fight for the downtrodden, and others can serve as reminders (...) of how easily those aspirations can be forgotten. We offer a variety of ways to interpret Diogenes, especially since the figure of Diogenes is an historical composite from centuries of sources. But we arrive at a position of loving antagonism toward Diogenes, loving Cynic commitments to autarkeia and against wealth and power, and disapproving when Cynics fell short of their commitments and critical aspirations. (shrink)

The brief, practical texts in the Essentials of Qualitative Methods series introduce social science and psychology researchers to key approaches to capturing phenomena not easily measured quantitatively, offering exciting, nimble opportunities to gather in-depth qualitative data. In this book, Scott D. Churchill introduces readers to existential phenomenological research, an approach that seeks an in-depth, embodied understanding of subjective human existence that reflects a person's values, purposes, ideals, intentions, emotions, and relationships. This method helps researchers understand the lives and needs (...) of others by helping identify and set aside theoretical and ideological prejudgments. About the Essentials of Qualitative Methods book series: Even for experienced researchers, selecting and correctly applying the right method can be challenging. In this groundbreaking series, leading experts in qualitative methods provide clear, crisp, and comprehensive descriptions of their approach, including its methodological integrity, and its benefits and limitations. Each book includes numerous examples to enable readers to quickly and thoroughly grasp how to leverage these valuable methods. (shrink)

I present a counterexample to Kirk-Giannini’s Dilemmatic Theory of gaslighting.

According to Pew Research studies, most Americans think religion always conflicts with science. The popular writings of scientists such as Richard Dawkins, Sam Harris, and Lawrence Krauss reinforce this idea, as do books by writers such as Christopher Hitchens and Daniel Dennet. Furthermore, the two versions of the enormously popular television show Cosmos, hosted by Carl Sagan in 1980 and Neil deGrasse Tyson in 2014, present a history of science in which religion has always acted as a barrier to scientific (...) development, with scientists frequently persecuted or even executed for their work. "Gods, Philosophers, and Scientists" shows that just because an idea is popular, doesn't mean it's correct. By examining the historical record from the time of the Ancient Greeks to today, readers are able to see that religion and science have been allies more often than enemies, and when conflict does occur it's too simplistic to view it as coming from something inherent to either science or religion. Instead, as with the case of Greek philosophy or the reception of Darwinian evolution, complex social forces are to blame, and in cases such as the infamous one of Galileo's conflict with the Catholic Church, clashing personalities are at least as important as those social forces. Anyone interested in the history of science or religion, who is curious about how science works, or who wants to have a better understanding of the world should read this book. (shrink)

Literary and philosophical reflections combine with true-life farm anecdotes to offer commentary on seeking the good life in the modern age.

Starting at the beginning: what's so good about being good? -- Theological ethics: where does morality come from? -- Cultural views of morality: why can't we make up our own moral rules for ourselves? -- Making ethical decisions: when I'm in a moral dilemma, what do I do? -- Abortion: how can you say that a pregnant seventeen-year-old, for whom having the baby will ruin her life, is doing something wrong by having an abortion? -- Reproductive technologies: what do you (...) say to infertile couples about the hi-tech ways to have a baby? -- Genetics and biotechnology: what do you tell couples who want to use biotechnology to produce designer children? -- Death, dying, and assisted suicide: don't people have a fundamental right to die? -- Capital punishment: isn't the death penalty a barbaric holdover from uncivilized cultures that should be done away with today? -- War and morality: in view of the Bible's teaching to love your enemies, why isn't every Christian a pacifist? -- Sexual ethics: shouldn't people be able to love and have sex with whomever they choose? -- Christian ethics, economics, and the workplace: how does my work connect to my spiritual life and my service to God? (shrink)

The life fantastic -- Bedtime stories -- The end of things -- Optical disillusions -- Double vision -- Backstage pass -- Romance languages -- Fellow-feeling -- Bolts from the blue -- Final fantasies.

Prominent atheists claim the Bible is a racist text. Yet Dr. Martin Luther King Jr. read it daily. Then again, so did many ardent segregationists. Some atheists claim religion serves to oppress the masses. Yet the classic text of the French Revolution, What is the Third Estate?, was written by a priest. On the other hand, the revolutionaries ended up banning religion. What do we make of religion's confusing role in history? And what of religion's relationship to science? Some scientists (...) claim that we have no free will. Others argue that advances in neurobiology and physics disprove determinism. As for whispering to the universe, an absurd habit say the skeptics. Yet prayer is a transformative practice for millions. This book explores the most common atheist critiques of the Bible and religion, incorporating Jewish, Christian, and Muslim voices. The result is a fresh, modern re-evaluation of religion and of atheism. (shrink)

Hermann Cohen (b. 1842, d. 1919), more than any other single figure, is responsible for founding the orthodox neo-Kantianism that dominated academic philosophy in Germany from the 1870s until the end of the First World War. Earlier German philosophers finding inspiration in Kant tended either towards speculative, metaphysical idealism, or sought to address philosophical questions with the resources of the empirical sciences, especially psychology. In contrast, Cohen’s seminal interpretation of Kant offered a vision of philosophy that decisively maintained its independence (...) from empirical psychology, without at the same time simply lapsing back into uncritical metaphysics. Cohen brought these attitudes to bear on a wide range of topics, writing systematically about epistemology, philosophy of science, ethics, law, political theory, and aesthetics. His anti-psychologism became a defining commitment not only of the Marburg School of neo-Kantianism, founded by Cohen himself, but of orthodox neo-Kantianism more generally. Indeed, that commitment ultimately defined the philosophical context from which, in the early twentieth century, both phenomenology and logical positivism emerged. No less significant than his influence on academic philosophy, Cohen was his generation’s preeminent German-Jewish public intellectual and religious philosopher. His philosophical ethics and political theory provided the foundation for a non-Marxist, Kantian democratic socialism that informed his more popular and topical writings. He argued publicly for universal suffrage and for the rights of workers to organize democratically-constituted collectives. He also saw deep points of connection between ethics and religion, and developed a view of Judaism as a fundamentally ethical system of belief and practice. He argued that monotheism was the historical source of the idea of universal ethical laws, and thus that Judaism offered the world its first model of a universalist morality. This view of Judaism’s ethical significance ultimately informed Cohen’s public defense of the Jews’ place in Germany not only against anti-Semitic attacks, but also against the arguments of early twentieth-century Zionists. However, Cohen’s influence on Jewish thought extends far beyond debates within Imperial Germany: his late religious writings inspired a broad renewal in twentieth-century Jewish ethics and philosophy of religion. (shrink)

As society becomes more aware of the rights of individuals, ethical issues become of increasing importance. Many research funders, including the research councils, increasingly emphasise research governance and ethical review in their consideration of submitted proposals. Little is known, however, about what universities do over ethical scrutiny and in order to find out the authors undertook a national study of all universities in the United Kingdom. The focus of the study was on human volunteers for research outside the remit of (...) the National Health Service. The key questions being: to what extent do universities undertake ethical scrutiny of research and, if so, how? The broad conclusion is that when this survey was carried out in the autumn of 2003, the majority of universities were aware of the need for the ethical scrutiny of research on human subjects although in many of those universities the scrutiny system was being developed at the time of completion of the questionnaire. In some cases practice appeared to lag behind awareness and whilst there were some very good examples there were also some which were below an ‘acceptable’ standard. Recommendations are made concerning structures, coverage and membership for systems of ethical scrutiny within the university sector. (shrink)

This chapter contains sections titled: Allotment Associations The Allotment Site New Relationships: Councillors and Gardeners Conclusions Notes.

Although informed consent is important in clinical research, questions persist regarding when it is necessary, what it requires, and how it should be obtained. The standard view in research ethics is that the function of informed consent is to respect individual autonomy. However, consent processes are multidimensional and serve other ethical functions as well. These functions deserve particular attention when barriers to consent exist. We argue that consent serves seven ethically important and conceptually distinct functions. The first four functions pertain (...) principally to individual participants: (1) providing transparency; (2) allowing control and authorization; (3) promoting concordance with participants' values; and (4) protecting and promoting welfare interests. Three other functions are systemic or policy focused: (5) promoting trust; (6) satisfying regulatory requirements; and (7) promoting integrity in research. Reframing consent around these functions can guide approaches to consent that are context sensitive and that maximize achievable goals. (shrink)

What is law, and why does it matter? Scott Hershovitz says that law is a moral practice-a tool for adjusting our moral relations. This claim is simple on its face, but it has stark implications for the rule of law. At once erudite and entertaining, Hershovitz's argument engages with the most important legal and political controversies of our time.

There is widespread agreement that there should be a principle requiring that artificial intelligence be ‘explicable’. Microsoft, Google, the World Economic Forum, the draft AI ethics guidelines for the EU commission, etc. all include a principle for AI that falls under the umbrella of ‘explicability’. Roughly, the principle states that “for AI to promote and not constrain human autonomy, our ‘decision about who should decide’ must be informed by knowledge of how AI would act instead of us” :689–707, 2018). There (...) is a strong intuition that if an algorithm decides, for example, whether to give someone a loan, then that algorithm should be explicable. I argue here, however, that such a principle is misdirected. The property of requiring explicability should attach to a particular action or decision rather than the entity making that decision. It is the context and the potential harm resulting from decisions that drive the moral need for explicability—not the process by which decisions are reached. Related to this is the fact that AI is used for many low-risk purposes for which it would be unnecessary to require that it be explicable. A principle requiring explicability would prevent us from reaping the benefits of AI used in these situations. Finally, the explanations given by explicable AI are only fruitful if we already know which considerations are acceptable for the decision at hand. If we already have these considerations, then there is no need to use contemporary AI algorithms because standard automation would be available. In other words, a principle of explicability for AI makes the use of AI redundant. (shrink)

This is a book about the pragmatics of reference. When we communicate through language we inevitably talk about things. Those things might be people, places or objects, or they might be thoughts, ideas, emotions or abstract concepts. To talk about things, we need to refer to things, and this book is about how we refer to things.

The chapter explores the sufferingSufferingassociated with MAIDMedical Assistance in Dying (MAID) giving special attention to assessmentAssessment and the psychological responses elicited in caregivers highlighting the need for all MAIDMedical Assistance in Dying (MAID) enquiries to activate a period of intense assessmentAssessment and the provision of detailed treatment alternatives. This chapter calls for a renewed commitment to compassionCompassion (‘sufferingSuffering together with’) as the communal dynamic to relieve and assuage such sufferingSuffering. Using the four domains of ‘total pain’ (Saunders in The management (...) of terminal malignant disease. Edward Arnold, London, UK, 1978), we summarize the evidence for the multiple opportunities available to ‘relieve often and comfort always.’ Finally, we review evidence on the impactImpactof MAIDMedical Assistance in Dying (MAID) suggesting that the overall burden of sufferingSuffering in Canada has increased since legalization. (shrink)

This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and (...) culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge. (shrink)