This paper is a combination of a grandfather's musings over his grandson's drawings, combined with a reconsideration of hermeneutics as an early childhood educational theory.

Thus, Meyers provides a valuable account, not only of current medical attitudes, but also of relevant case and statute law as it stands at present.

Abstractabstract:Ursula K. Le Guin’s classic work of anarchist literature, The Dispossessed (1974), is preoccupied with the issue of imprisonment. This is hardly surprising given anarchism’s longstanding critical engagement with the prison as state apparatus. For classical anarchists, the prison represents one of the most vile and visible examples of state repression. However, while the abolition of prisons constitutes one of the fundamental goals of anarchism, the alternatives put forth by classical anarchist thinkers risk perpetuating the underlying power relations of carceral (...) justice by encouraging social shaming and the policing of norms. The anarchist society of The Dispossessed uses these techniques to discourage the accumulation of power in order to create an egalitarian society. Unfortunately, these same techniques encourage a conformity that hinders other anarchist values, such as creativity and individual self-determination. In essence, the anarchist society depicted in the novel replaces the literal prison with a different form of imprisonment—the social prison, which continues the repressive function of the state through different means. By creating an “ambiguous” anarchist utopia, Le Guin anticipates the critiques of classical anarchism formulated by poststructural and postmodern anarchist theorists. These critiques are most evident in the theme of imprisonment that threads throughout the novel. (shrink)

Abstract:Spirituality is an undeniable human need and is thus the subject of increasing interest among management scholars and practitioners. In this article, we propose using archetypal psychology as a framework for understanding the human need for spirituality more clearly because it provides important insights into spirituality and organizational life. Because most spiritual needs reside in the deepest aspects of the self, an archetypal approach helps us recognize not only that we have spiritual needs but alsowhywe have them. We present three (...) common archetypes and their implications in a management context. That is followed by an application of the archetypal approach to some of the more spiritually corrosive aspects of organizational life and a discussion of the implications of archetypes as a source of motivation. (shrink)

This book explores the way that human symbolic abilities have precipitated the colonisation and replacement of the natural world by the industrial order, transforming human character and experience.

This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that (...) are grasped through geometrical or intelligible intuition. -/- Accordingly, this study classifies Fichte’s philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or “mathesis of the mind.” -/- “This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched.” Professor Dr. Marco Ivaldo -/- “This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious.” Professor Dr. Emmanuel Cattin. (shrink)

It has been suggested that we turn to solar geoengineering to counter global warming, which would consequently transform the relationship of terrestrial plant-life to the sun. This is an article not about geoengineering as such, but instead what is called photosynethics, or, thinking about our moral relationship to the light – in particular, as it is mediated by plants. Working from within but then extending the idea of responsibility found in the work of Emmanuel Levinas, it is argued here that, (...) since the plant cultivates the conditions of life on earth by photosynthesis, its relationship to the sun is then a relation of giving to others that is properly moral. The plant’s existence is an exposure so out of kilter with human ways of understanding existence that it interrupts our own and brings us into a relation of responsibility. It is concluded that rather than redirecting the sun’s radiation, we should turn to plants to reconsider how we live with the light on a heating planet. This first means separating moral responsibility from human vision so that we might encounter light on its own terms, and not simply as an element of rationality or sentiment or discipline. (shrink)

Fichte-Studien, volume 49 (Leiden: Brill/Rodopi Publishers, 8 April 2021), edited by David W. Wood, 471pp. -/- Presenting new critical perspectives on J.G. Fichte’s Wissenschaftslehre, this volume of articles in English by an international group of scholars addresses the topic of first principles in Fichte’s writings. Especially discussed are the central text of his Jena period, the 1794/95 Grundlage der gesammten Wissenschaftslehre, as well as later versions like the Wissenschaftslehre nova methodo (1796-99) and the presentations of 1804 and 1805. Also (...) included are new studies on the first principles of the particular sub-disciplines of Fichte’s system, such as the doctrines of aesthetics, nature, right, ethics, and history. The volume also contains a number of miscellaneous essays on Fichte research, as well as several book reviews. (shrink)

Mother and Fetus: Rights in Conflict A. INTRODUCTION After fertilization of the female egg (ovum) with male sperm the resulting zygote may implant ...

David Miller elegantly and provocatively reformulates critical rationalism—the revolutionary approach to epistemology advocated by Karl Popper—by answering its most important critics. He argues for an approach to rationality freed from the debilitating authoritarian dependence on reasons and justification. "Miller presents a particularly useful and stimulating account of critical rationalism. His work is both interesting and controversial... of interest to anyone with concerns in epistemology or the philosophy of science." —Canadian Philosophical Reviews.

David Miller is the foremost exponent of the purist critical rationalist doctrine and here presents his mature views, discussing the role that logic and argument play in the growth of knowledge, criticizing the common understanding of argument as an instrument of justification, persuasion or discovery and instead advocating the critical rationalist view that only criticism matters. Miller patiently and thoroughly undoes the damage done by those writers who attack critical rationalism by invoking the sterile mythology of induction and justification (...) that it seeks to sweep away. In addition his new material on the debate on verisimilitude is essential reading for all working in this field. (shrink)

In her book Specifications Grading, Linda B. Nilson advocates for a grading regimen she claims will save faculty time, increase student motivation, and improve the quality and rigor of student work. If she is right, there is a strong case for many faculty to adopt some version of the system she recommends. In this paper, we argue that she is mostly right and recommend that faculty move away from traditional grading. We begin by rehearsing the central features of specifications grading (...) and providing two examples of how to implement it in philosophy classes. In light of the examples, we argue that specifications grading fulfills two of Nilson’s central desiderata but not the third. Since specifications grading generates two benefits that when combined increase student learning, without adding or increasing burdens, we conclude that student learning increases when courses are revised to include aspects of specifications grading. (shrink)

Evolution is frequently concentrated in bursts of rapid morphological change and speciation followed by long‐term stasis. We propose that this pattern of punctuated equilibria results from an evolutionary tug‐of‐war between host genomes and transposable elements (TEs) mediated through the epigenome. According to this hypothesis, epigenetic regulatory mechanisms (RNA interference, DNA methylation and histone modifications) maintain stasis by suppressing TE mobilization. However, physiological stress, induced by climate change or invasion of new habitats, disrupts epigenetic regulation and unleashes TEs. With their capacity (...) to drive non‐adaptive host evolution, mobilized TEs can restructure the genome and displace populations from adaptive peaks, thus providing an escape from stasis and generating genetic innovations required for rapid diversification. This “epi‐transposon hypothesis” can not only explain macroevolutionary tempo and mode, but may also resolve other long‐standing controversies, such as Wright's shifting balance theory, Mayr's peripheral isolates model, and McClintock's view of genome restructuring as an adaptive response to challenge. (shrink)

This paper articulates and defends a noncognitive, care-based view of identification, of what privileged psychic subset provides the source of self-determination in actions and attitudes. The author provides an extended analysis of "caring," and then applies it to debates between Frankfurtians, on the one hand, and Watsonians, on the other, about the nature of identification, then defends the view against objections.

This essay points to parallel criticisms made by Charles Peirce and Polanyi against the “critical method”or “method of doubt.” In an early set of essays (1868–1869) and in later work, Peirce claimed that the Cartesian method of doubt is both philosophically bankrupt and useless because practitioners do not apply the method upon the criteria of doubting itself. Likewise, in his 1952 essay “The Stability of Beliefs” and in Personal Knowledge, Polanyi charges practitioners of the critical method with a failure to (...) apply the method rigorously enough. Polanyi contends that “critical” philosophers apply the method of doubt only to beliefs they find distasteful and rarely ever to the tacit beliefs that make doubt possible. (shrink)

Many philosophers have taken there to be an important relation between personal identity and several of our practical concerns (among them moral responsibility, compensation, and self-concern). I articulate four natural methodological assumptions made by those wanting to construct a theory of the relation between identity and practical concerns, and I point out powerful objections to each assumption, objections constituting serious methodological obstacles to the overall project. I then attempt to offer replies to each general objection in a way that leaves (...) the project intact, albeit significantly changed. Perhaps the most important change stems from the recognition that the practical concerns motivating investigation into personal identity turn out to be not univocal, as is typically thought, such that each of the different practical concerns may actually be related to personal identity in very different ways. (shrink)

While a number of classical pragmatists crafted their philosophies in conjunction with a careful study of Hegel's works, others saw their philosophies emerge in antagonism with proponents of Hegel. In this paper, we offer an instance of the latter case. Namely, we show that the impetus for Charles S. Peirce's early articulation and avowal of realism (the claim that some generals are real) was William Torrey Harris's claim that the formal laws of logic lacked universal validity. According to Harris, the (...) leading representative of Hegelism in the United States, the universal validity of the laws of logic rested on a nominalistic metaphysics that a Hegelian-realism showed to be false. In response to this charge, we articulate how Peirce's attempt to prove the universal validity of the laws of logic resulted in avowing a realism that differed from both nominalism and Harris's Hegelian-realism. (shrink)

In this paper, I attempt to show that the moral/conventional distinction simply cannot bear the sort of weight many theorists have placed on it for determining the moral and criminal responsibility of psychopaths. After revealing the fractured nature of the distinction, I go on to suggest how one aspect of it may remain relevant—in a way that has previously been unappreciated—to discussions of the responsibility of psychopaths. In particular, after offering an alternative explanation of the available data on psychopaths and (...) their judgments of various sorts of norm transgressions, I put forward a hybrid theory of their responsibility, suggesting how they might be criminally responsible, while nevertheless failing to meet the conditions for an important arena of moral responsibility. (shrink)

[Open access] In this book symposium the author takes up questions from phenomenology, hermeneutics, ethical theory, and intellectual history raised by a group of scholarly interlocutors from a range of backgrounds. In the course of engaging with these issues, he discusses, inter alia, McDowell’s realism, Jonathon Lear’s work on the end of a world, Michael Oakeshott’s view of selfhood, Heidegger’s conception of Jemeinigkeit, Uexküll’s notion of Umwelt, and Gadamer’s hermeneutic conception of truth.

In birds and frogs, species pairs retain the capacity to produce viable hybrids for tens of millions of years, an order of magnitude longer than mammals. What accounts for these differences in relative rates of pre- and postzygotic isolation? We propose that reproductive mode is a critically important but previously overlooked factor in the speciation process. Viviparity creates a post-fertilization arena for genomic conflicts absent in egg-laying species. With viviparity, conflict can arise between: mothers and embryos; sibling embryos in the (...) womb, and maternal and paternal genomes within individual embryos. Such intra- and intergenomic conflicts result in perpetual antagonistic coevolution, thereby accelerating interpopulation postzygotic isolation. In addition, by generating intrapopulation genetic incompatibility, viviparity-driven conflict favors polyandry and limits the potential for precopulatory divergence. Mammalian diversification is characterized by rapid evolution of incompatible feto-maternal interactions, asymmetrical postzygotic isolation, disproportionate effects of genomically-imprinted genes, and “F2 hybrid enhancement.” The viviparity-driven conflict hypothesis provides a parsimonious explanation for these patterns in mammalian evolution. BioEssays 22:938–946, 2000. © 2000 John Wiley & Sons, Inc. (shrink)

"In the first study of its kind, David W. Johnson's "Watsuji on Nature" reconstructs the astonishing philosophy of nature of Watsuji Tetsurō (1889-1960), situating it in relation both to his reception of the thought of Heidegger and to his renewal of core ontological positions in classical Confucian and Buddhist philosophy. Johnson shows that for Watsuji we have our being in the lived experience of nature, one in which nature and culture compose a tightly interwoven texture called "fūdo". By fully (...) unfolding Watsuji's novel and radical claim that this is a setting that is neither fully external to human subjectivity nor merely a product of it, this book also sets out what still remains unthought in this concept, as well as in the relational structure that underwrites it. Johnson argues that what remains unarticulated is nothing less than the recovery of a reenchanted conception of nature and an elucidation of the wide-ranging implications of a relational conception of the self for questions about the disclosive character of experience, the distinction between fact and value, and the possibility of a place-based ecological ethics. In an engagingly lucid and deft analysis, "Watsuji on Nature" radically expands our appreciation of twentieth-century Japanese philosophy and shows what it has to offer to a global philosophical conversation"--Provided by publisher. (shrink)

In our age of globalization, we need a theory of global management consistent with our common human nature. The place to begin in developing such a theory is the philosophy of traditional cultures. The article focuses on African philosophy and its fruitfulness for contributing to a theory of management consistent with African traditional cultures. It also looks briefly at the Confucian and Platonic-Aristotelian traditions and notes points of agreement with African traditions. It concludes that the needed theory of global management (...) should regard the firm as a community, not a collection of individuals, and should understand the purpose of management as promoting the common good. (shrink)

In lieu of an abstract, here is the first paragraph: Paksi and Héder’s Guide to Personal Knowledge (hereafter GPK and Guide) is, as the title suggests, a guide of the most important and original ideas of Michael Polanyi’s book Personal Knowledge: Towards a Post-Critical Philosophy (1958, hereafter PK). Is a guide to Personal Knowledge needed? I think the answer is a resounding “yes” for many new readers. To see why, let’s briefly review two common complaints about PK.

Before the early 1990s, accounts of classical American philosophy paid relatively little attention to the work and intellectual contributions of women philosophers. However, as early as 1991, a number of contemporary feminist philosophers and historians began to devote more focused attention to women philosophers whose intellectual achievements had been marginalized or forgotten. One woman philosopher whose contributions have still gone unnoticed is that of American logician, mathematician, and color theorist Christine Ladd-Franklin. This paper argues that Ladd-Franklin's feminist efforts to increase (...) the opportunities for women in professional academia were influenced not only by her work as a woman scientist and her reading of feminist literature but also by her understanding of pragmatism and her interaction with Charles Peirce. Specifically, Ladd-Franklin's arguments to increase academic research positions for women and her criticisms of male-only scientific societies point out how discrimination on the basis of gender violates Peirce's first rule of reason that one ought not block the road to inquiry and expose the unscientific nature of gender discrimination by contrasting the pragmatic meaning of acquiring a doctorate with the institutional practice of barring women from making intellectual contributions by denying them professorial positions. (shrink)

One dimension of a comprehensive semantic and semiotic theory is its explanation of how a wide-variety of linguistic expressions designate singular objects. The bulk of scholarship on Peirce's theory of proper names has aligned his theory with the so called new theory of reference by drawing connections between proper names qua rhematic indexical legisigns and various aspects of Kripke's theory of names.2 Recent scholarship has navigated away from indexing Kripke-Peirce affinities and has begun the process of articulating a semiotic or (...) pragmatic theory of names that is distinctly Peircean. For example.. (shrink)

David Hume's writings on history, politics and philosophy have shaped thought to this day. His bold scepticism ranged from common notions of the 'self' to criticism of standard theistic proofs. He insisted on grounding understandings of popular religious beliefs in human psychology rather than divine revelation, and he aimed to disentangle philosophy from religion in order to allow the former to pursue its own ends. In this book, Professors David W Purdie and Peter S Fosl decipher some of (...) Hume's most challenging texts for the modern reader, while preserving the sharp intellect and undaunted nerve for which Hume is famous. Hume's spirit is brought alive for contemporary times and his writing is made accessible for its intended audience: the general public."-- Back cover. (shrink)

Scholarship on borderline vagueness pinpoints Russell's 1923 essay titled “Vagueness” as the starting point for rigorous analysis. The importance of Russell's work over and above discussions of indeterminacy in antiquity and in the modern period is that Russell isolated borderline vagueness from indeterminacies that do not threaten classical logic. This paper argues that historical propriety concerning the analysis of borderline vagueness belongs to Peirce since he was the first to show that borderline vagueness is distinct from other forms of indeterminacy (...) (e.g., generality, unspecificity, and uninformativeness) and that the application of vague predicates to borderline cases involves an intrinsic uncertainty. (shrink)

This paper assesses a recent criticism of Michael Polanyi’s account of the origin of complex entities by Alicia Juarrero. According to Juarrero, Polanyi took higher-level complex entities like machines and organisms to come into existence through the imposition of external, top-down forces. This paper argues that while Polanyi took the emergence of machines to come about in such a way, Polanyi’s reading of 19th and early 20th-Century experimental embryology indicates his position is more sophisticated. Polanyi appears to have thought a (...) synthesis was possible between reductive-mechanical and holistic-vitalistic approaches in embryology and he appears to have relied on this synthesis in his account of the origin of complex organisms. While I argue that this synthesis is unclear, it suggests that Polanyi conceived of the emergence of organisms as the result of internal, complex, and non-deterministic processes. (shrink)

Take a hypothetical sequence of human beings ordered by height from tallest to shortest. Make sure there is no more than a difference of a millimeter between each person and make sure the tallest person is clearly tall and the shortest person is clearly not tall. Now consider the following argument: P1 A person of height n is tall ; P2 For any height n, if n is tall, then n–1mm is tall ; C Therefore, a person of height n (...) = 1mm is tall. P1 and P2 are intuitively true, C is intuitively false, yet the argument is deductively valid (the conclusion follows... (shrink)

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

This essay presents the use-first-and-investigate-later (UFAIL) approach to technological use through two case studies: the atomic bomb in World War II and chemical defoliants during the Vietnam War. The methodology of UFAIL is as follows: despite limited understanding of an array of potential effects (medical, environmental, etc.), technology users employ a commitment to ex post facto investigations of these effects. In generalizing these cases, the essay argues (a) that failure to check rapid technological uptake will result in continued disaster and (...) (b) the abatement of the negative consequences of UFAIL is a more tempered approach to the infiltration of technologies into society by rigorous and preemptive investigation into the potential effects of a technology. (shrink)

This is a comment on Tihamér Margitay’s “From Epistemology to Ontology,” where he criticizes Polanyi’s claim that there is a systematic correspondence between the levels of ontology and the levels of tacit knowing. Margitay contends that Polanyi supports this correspondence by appealing to a “purely ontological argument,” one which concludes that it is impossible to reduce machines to a singular, chemical-physical type, and criticizes this claim by pointing to industrial standards (machines that do reduce to singular physical-chemical type). I respond (...) to Margitay’s claim by distinguishing two different “purely ontological arguments” in Polanyi’s thought (one relying on the multi-realizability of a machine in different physical-chemical types, the other pointing to the inability of a purely physical-chemical ontology to account for the artificial shaping and functioning of machines). With these two arguments clarified, Margitay’s criticism by appealing to industrial standards loses much of its initial force. (shrink)

This is a comment on Tihamér Margitay’s “From Epistemology to Ontology,” where he criticizes Polanyi’s claim that there is a systematic correspondence between the levels of ontology and the levels of tacit knowing. Margitay contends that Polanyi supports this correspondence by appealing to a “purely ontological argument,” one which concludes that it is impossible to reduce machines to a singular, chemical-physical type, and criticizes this claim by pointing to industrial standards (machines that do reduce to singular physical-chemical type). I respond (...) to Margitay’s claim by distinguishing two different “purely ontological arguments” in Polanyi’s thought (one relying on the multi-realizability of a machine in different physical-chemical types, the other pointing to the inability of a purely physical-chemical ontology to account for the artificial shaping and functioning of machines). With these two arguments clarified, Margitay’s criticism by appealing to industrial standards loses much of its initial force. (shrink)

The purpose of this paper is to explore an hypothesis rather than draw any unassailable conclusions. I argue that there is a fundamental tension between the sub-Christian account of the “Three Stages” presented in the earlier pseudonymous writings and the explicitly Christian account presented in the Anti-Climacean and later acknowledged writings. The earlier version is that of a progress from spiritless “immediacy” toward more complete integrations of the self, culminating in authentic religious faith; while the later is that of a (...) regress from lesser to ever greater forms of spiritual peril, culminating in a disordered religiosity that vainly seeks to overthrow the established ecclesiastical order. Tracing the conflict between these two perspectives also enhances our understanding of the purpose underlying Kierkegaard’s project by suggesting the possibility that the authorship constitutes a literary confession of Kierkegaard’s own spiritual regress. (shrink)

The purpose of this paper is to explore an hypothesis rather than draw any unassailable conclusions. I argue that there is a fundamental tension between the sub-Christian account of the “Three Stages” presented in the earlier pseudonymous writings and the explicitly Christian account presented in the Anti-Climacean and later acknowledged writings. The earlier version is that of a progress from spiritless “immediacy” toward more complete integrations of the self, culminating in authentic religious faith; while the later is that of a (...) regress from lesser to ever greater forms of spiritual peril, culminating in a disordered religiosity that vainly seeks to overthrow the established ecclesiastical order. Tracing the conflict between these two perspectives also enhances our understanding of the purpose underlying Kierkegaard’s project by suggesting the possibility that the authorship constitutes a literary confession of Kierkegaard’s own spiritual regress. (shrink)

This paper attempts to reconcile two ideas that seem fundamentally opposed to one another: the reality of the self and the doctrine of no-self. Buddhism offers a form of spiritual equanimity that turns on the denial of a self. Nonetheless, there seem to be good reasons to hold onto the reality of the self. The existence of a self enables us to account for praise and blame, the hopes for oneself that motivate actions, and attachments to the selves of others (...) in bonds of love and affection. I show how it may be possible to reconcile the reality of the self with a particular interpretation of the no-self doctrine by engaging with the work of thinkers from the phenomenological tradition such as Merleau-Ponty, Zahavi, Gallagher, and Petitmengin. (shrink)

Sir Austin Bradford Hill’s ‘aspects of causation’ represent some of the most influential thoughts on the subject of proximate causation in health and disease. Hill compiled a list of features that, when present and known, indicate an increasing likelihood that exposure to a factor causes—or contributes to the causation of—a disease. The items of Hill’s list were not labelled ‘criteria’, as this would have inferred every item being necessary for causation. Hence, criteria that are necessary for causation in health, disease (...) and intervention processes, whether known, knowable, or not, remain undetermined and deserve exploration. To move beyond this position, this paper aims to explore factors that are necessary in the constitution of causative relationships between health, disease processes, and intervention. To this end, disease is viewed as a causative pathway through the often overlapping stages of aetiology, pathology and patho-physiology. Intervention is viewed as a second, independent causative pathway, capable of causing changes in health for benefit or harm. For the natural course of a disease pathway to change, we argue that intervention must not only occupy the same time and space, but must also share a common form; the point at which the two pathways converge and interact. This improved conceptualisation may be used to facilitate the interpretation of clinical observations and inform future research, particularly enabling predictions of the mechanistic relationship between health, disease and intervention. (shrink)

Attacks nothing less than the currently prevailing worldphilosophy--humanism, which the author feels is exceedingly dangerous in itshidden assumptions.

In this paper we study abstract elementary classes using infinitary logics and prove a number of results relating them. For example, if is an a.e.c. with Löwenheim–Skolem number κ then is closed under L∞,κ+-elementary equivalence. If κ=ω and has finite character then is closed under L∞,ω-elementary equivalence. Analogous results are established for . Galois types, saturation, and categoricity are also studied. We prove, for example, that if is finitary and λ-categorical for some infinite λ then there is some σLω1,ω such (...) that and contain precisely the same models of cardinality at least λ. (shrink)

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we (...) hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed. (shrink)