Henry E. Dudeney (1857-1930) was, according to pure mathematician G. H. Hardy (1877-1947), one of England’s “better makers of puzzles”. His “Perplexities” column, a regular feature in The Strand Magazine between 1910 and 1930, not only gave recreational mathematicians what they wanted – an “intellectual ‘kick’” – but also occasioned the odd sparkling display of intellect from professionals. Dudeney’s geometrical dissection puzzles are a case in point, though his ingenious solutions sometimes betray a lack of clarity about the difference (...) between a mathematical proof and an empirical procedure. His equilateral triangle to square dissection and the equally stunning regular octagon to square dissection sent to him by Hardy’s colleague G. T. Bennett (1868-1943) are both here demonstrated visually – process and result an evident unity. (shrink)

Long tradition in philosophy and in empirical psychology has it that the perceptual recovery of enduring objective size and shape proceeds through initial spatial appearance experiences—like the sensed changing visual field size of a receding car, or the shifting shape appearance of a coin as it rotates in depth. The present paper carefully frames and then critically examines such proposals. It turns out that these are contingent, empirical matters, requiring close examination of relevant research in perception science in order to (...) decide. The paper concludes with extended discussions of the empirical study of the perception of slant, size, and shape. (shrink)

An empirically based view of size and distance perceptual content and phenomenology is introduced, in which perceivers measure worldly size and distance against their bodies. Central principles of the formal, representational theory of the measurement of extensive magnitudes are then applied in framing the account in a precise way. The question of whether spatial-perceptual experience is “unit-free” is clarified. The framework is used to assess Dennis Proffitt's proposal that spatial setting is perceived in various “units,” “scales,” or “rulers”, some of (...) them non-spatial—distance in terms of calories burned to traverse and the like. The debate between Proffitt and Firestone about the commensurability of differing measurement scales held by Proffitt to be relied on by perceivers is then clarified and resolved. Finally, the measurement theory framed account of size and distance perception is used to illuminate Gibson’s famous but elusive contrasts between “geometrical optics” and “ecological optics” and between the “physical world” and the “animal environment”. (shrink)

This paper examines the discrepancy between the attitudes of many historians of mathematics to sixteenth-century geometry and those of museum curators and others interested in practical mathematics and in instruments. It argues for the need to treat past mathematical practice, not in relation to timeless criteria of mathematical worth, but according to the agenda of the period. Three examples of geometrical activity are used to illustrate this, and two particular contexts are presented in which mathematical practice localised in the (...) sixteenth century takes on a special historical significance. (shrink)

In the late sixteenth century a number of mathematicians tried to introduce geometrical methods into surveying practice, to be based on simplified astronomical instruments, angle measurement, and triangulation. A measure of success is indicated by the acceptance of the simple theodolite, but the surveyors resisted such complex instruments as the altazimuth theodolite, recipiangle, and trigonometer. Counter-proposals, in particular the plane table, threatened to undermine the geometrical programme, but by the mid-seventeenth century a stable compromise had evolved. Among other (...) things, the demise of the shadow square indicates that angle measurement was then part of surveying practice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 34.4 (2001) 292-307 [Access article in PDF] The Rhetoric of the Geometrical Method Spinoza's Double Strategy Christopher P. Long A double strategy may be apprehended in the first definitions, axioms and propositions of Spinoza's Ethics: the one is rhetorical, the other, systematic. Insofar as these opening passages constitute a geometrical argument that leads ultimately to the strict monism that lies at the heart of (...) Spinoza's philosophy, they function systematically as grounding principles. However, insofar as they are designed to uncover errors at the heart of the Cartesian system, they function rhetorically as a critique of Descartes's equivocal theory of substance. The geometrical mode of presentation lends an aura of necessity to the systematic strategy and tends to eclipse the rhetorical strategy that functions as a critique of Cartesian dualism. 1 To this extent, the systematic strategy itself functions rhetorically. On the other hand, to the extent that any seventeenth-century attempt to establish a monistic system would inevitably have had to involve a critique of Cartesian dualism, the rhetorical strategy itself functions systematically. Thus, although two distinct strategies are simultaneously discernible in the opening passages of the Ethics, the two work together, each arguing on a different front, to establish Spinoza's monism. By focusing on the rhetorical side of this double strategy, the underlying nature of Spinoza's critique of Descartes can be clarified and certain gaps in the systematic, geometrical argument for monism can be explained. Descartes's theory of substance The rhetorical strategy Spinoza employs at the outset of the Ethics involves a brilliant use of equivocation and ambiguity designed to draw a reader dedicated to Cartesian dualism into the heart of an argument designed to [End Page 292] undermine this dualism itself. The impetus behind this rhetorical critique is surely Spinoza's dissatisfaction with Descartes's theory of substance. 1. Descartes's equivocation Descartes's theory rests upon a fundamental equivocation: on the one hand, the term "substance" is meant strictly to designate that which is absolutely self-sufficient, namely, God; on the other hand, Descartes allows for a weaker understanding of substance, which pertains to those things (specifically res cogitans and res extensa) that require only the concurrence of God in order to exist (Principles I, 51-52; AT VIIIA24-25). 2 Thus, for Descartes, although God is, strictly speaking, the only substance, there remains a sense in which both res cogitans and res extensa may be understood as substances as well.Ultimately, this equivocal understanding of substance may be traced to a tension internal to Descartes between the Aristotelian notion of substance as underlying subject and the seventeenth-century mutation of that notion, which came to be defined in terms of causal self-sufficiency. 3 Jonathan Bennett traces the source of this mutation back to the view held by Aristotle that the existence of some property depends upon its being instantiated--that is, there can be no courage unless there exists someone courageous. He continues his interesting argument thus: This suggests that there is a relation of dependence running from properties to the things that have them and not conversely. The dependence would be logical: the thesis must be that "existent but uninstantiated property" is conceptually defective, not merely contrary to physics. Thus, one mark of a genuine thing, or substance, is its not being logically dependent for its existence on anything else. (Bennett 1984, 56) The development of this line of thinking leads to the conception of substance we find both in Descartes's Principles and in Spinoza's Ethics, namely, that a substance must not causally depend on anything outside of itself for its existence. 4 However, with Descartes, what emerges out of this tradition is a hybrid understanding of substance in which the term "substance" is not reserved simply for that which is utterly self-sufficient (God), but extends to those things that depend only upon the concurrence of God for their existence (rescogitans and resextensa). This bifurcated understanding of substance seems to stem from the distinction at work in [End Page 293] Aristotle... (shrink)

Objective: Based upon notions to a mental vision of the Vitruvian Man, to determine if any obvious asymmetries exist within Leonardo da Vinci’s timeless schematic—which is famous for its highly symmetrical presentation. Methods: A qualitative analysis performed upon a Vitruvian Man print (taken from the namesake Wikipedia article) to: closely examine if the man’s head is positioned to noticeably tilt toward either direction—left or right—of a dissecting line superimposed for equally splitting (vertically) the circle in the schematic; and, to closely (...) examine the man’s eyes for any artistic asymmetry therein drawn. Results: The man’s head is determined tilting toward his right half/hemisphere of the circle. Also noticeable: the man’s right eye appears being of a much brighter look relative to a darkness observable about his left eye; and, an outline to an inverted equilateral triangle is identifiably shaded surrounding his left eye, whereas a more contrastingly circular shape appears as so shaded around his right eye. Discussion: Once a certain awareness is drawn to such artistic anomalies, they can become so clearly observable that one may wonder if Leonardo da Vinci did as much intentionally. And if so, then why? This paper details a hypothesis necessarily built upon the assumption that Leonardo intentionally embedded such cues within his Vitruvian Man whereby speculations toward a hemispheric brain theory can be established of such cryptic nature, given a then-pronouncedly authoritarian Catholic Church, whereupon he may have figured it possible to receive credit posthumously if ever such notions were proven valid. Incidentally, the concerning analysis as to why the Vitruvian Man’s head tilts in such a fashion aligns with Dr. Iain McGilchrist’s peer-reviewed findings to a hemispheric hypothesis. (shrink)

A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the Banach–Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. (...) In the present paper, we consider the problem of which systems of congruences can be satisfied using open subsets of the sphere ; of course, these open sets cannot form a partition of the sphere, but they can be required to cover "most of" the sphere in the sense that their union is dense. Various versions of the problem arise, depending on whether one uses all isometries of the sphere or restricts oneself to a free group of rotations, or whether one omits the requirement that the open sets have dense union, and so on. While some cases of these problems are solved by simple geometrical dissections, others involve complicated iterative constructions and/or results from the theory of free groups. Many interesting questions remain open. (shrink)

In 1986, philosopher-bioethicist Samuel Gorovitz published an essay entitled “Baiting Bioethics,” in which he reported on various criticisms of bioethics that were “in print, or voiced in and around … the field” at that time, and set forth his assessment of their legitimacy. He gave detailed attention to what he judged to be the particularly fierce and “irresponsible attacks” on “the moral integrity” and soundness of bioethics contained in two papers: “Getting Ethics” by philosopher William Bennett and “Medical Morality Is (...) Not Bioethics,” coauthored by us. Gorovitz attributed some of the criticisms that bioethics was eliciting to the fact that this new, rapidly rising, and increasingly visible field had brought “scholars and practitioners together who otherwise would have little exposure to one another's disciplines. Their interactions are mutually enriching at times,” he declared, “but mutually baffling and even infuriating at other times.” In this latter regard, he suggested that “perhaps” Fox and Swazey's characterization of bioethics in the article he dissected “reflects a general revulsion at endeavors they see as inadequately like the social sciences or insufficiently respectful of them.” He went on to say that despite his objections to our “complaints” about bioethics—especially to our claim that “autonomy [had] been an unduly emphasized value” in the field—he had “a lingering sense” that there might be “a grain of truth” in them. Gorovitz ended his essay with an affirmation about the “benefit” that bioethics can derive from “responsible” and even from “irresponsible” criticism. “The unexamined discipline invites the philosopher's critical scrutiny no less than the unexamined life,” he aphoristically concluded. a. (shrink)

Ineffability—that which cannot be explained in words—lies at the heart of the Christian mystical tradition. It has also been part of every discussion of religious experience since the early twentieth century. Despite this centrality, ineffability is a concept that has largely been ignored by philosophers of religion. In this book, Bennett-Hunter builds on the recent work of David E. Cooper, who argues that the meaning of life can only be understood in terms of an ineffable source on which life depends, (...) and engages with the work of continental philosophers, such as Heidegger, Merleau-Ponty and Karl Jaspers. This is the first book to explore the concept of ineffability within contemporary philosophy of religion and provides a starting point for further scholarly debate. It will be of interest to scholars of philosophy of religion, theology, existentialism and phenomenology. -/- 'Bennett Hunter’s book is a timely contribution to the growing theological and philosophical literature on mystery and ineffability. Written in a lucid and elegant style, the book makes a convincing case for the ineffability of religious experience and explores its relationship to a sense that our lives are answerable to such experience.' — David E. Cooper. -/- 'Philosophers have long concentrated on linguistic forms in a way that has isolated language from the rest of life, and this isolation has increasingly obscured for them the vast range of things that cannot be spoken. Bennett-Hunter is not the first philosopher to try and map this distracted field, but he is remarkable in the width and sympathy of his approach to the highly various thinkers whom he invokes to illuminate it.' — Mary Midgley. (shrink)

Jonathan Bennett engages with the thought of six great thinkers of the early modern period: Descaretes, Spinoza, Leibniz, Locke, Berkeley, Hume. While not neglecting the historical setting of each, his chief focus is on the words they wrote. What problem is being tackled? How exactly is the solution meant to work? Does it succeed? If not, why not? What can be learned from its success or failure? For newcomers to the early modern scene, this clearly written work is an excellent (...) introduction to it. Those already in the know can learn how to argue with the great philosophers of the past, treating them as colleagues, antagonists, students, teachers. (shrink)

Jonathan Bennett engages with the thought of six great thinkers of the early modern period: Descartes, Spinoza, Leibniz, Locke, Berkeley, and Hume. While not neglecting the historical setting of each, his chief focus is on the words they wrote. What problem is being tackled? How exactly is the solution meant to work? Does it succeed? If not, why not? What can be learned from its success or failure? For newcomers to the early modern scene, this clearly written work is an (...) excellent introduction to it. Those already in the know can learn how to argue with the great philosophers of the past, treating them as colleagues, antagonists, students, teachers. In this second volume, Bennett focuses on the work of Locke, Berkeley, and Hume. (shrink)

For the dynamical hypothesis to be defended as a viable alternative to a computational perspective on natural cognition, the role of biological constraints needs to be considered. This task requires a detailed understanding of the structural organization and function of the dynamic nervous system, as well as a theoretical approach that grounds cognitive activity within the constraints of organism and ecological context.

Various researchers have suggested that below 7 years of age children do not recognize that they are the authority on knowledge about themselves, a suggestion that seems counter-intuitive because it raises the possibility that children do not appreciate their privileged first-person access to their own minds. Unlike previous research, children in the current investigation quantified knowledge and even 5-year-olds tended to assign relatively more to themselves than to an adult (Studies 1 and 2). Indeed, children's estimations were different from ratings (...) made by their mothers: Their mothers sometimes rated themselves as knowing more about their child than they rated their child as knowing (Study 2). While previous research seemed to suggest that children shift from viewing their mother to viewing themselves as the authority on knowledge about them (the children), these new findings surprisingly suggest the opposite. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:New Essays on the RationalistsSteven NadlerRocco J. Gennaro and Charles Huenemann, editors. New Essays on the Rationalists. Oxford: Oxford University Press, 1999. Pp. xvii + 391. Cloth, $60.00.Here is yet another collection of essays on early modern philosophy. The focus this time is on the Seventeenth century, in particular "the rationalists." What this apparently involves is, as the old-fashioned classification has it, Descartes, Spinoza, and Leibniz. But there (...) is no overall theme to the essays, nothing uniting them besides the fact that almost all are devoted to those three thinkers and the fact that the volume was inspired by a summer seminar run by Jonathan Bennett.What the editors mean by "the rationalists" (besides the extensional definition) is [End Page 437] thinkers "united in the belief that the intellect and human reason are powerful tools in our ability to know about the ultimate nature of mind and matter." What is supposed to separate "the rationalists" from "the empiricists" is "a belief in the power of human reason" (xv). This is a fairly weak claim; and I, for one, am skeptical that such categories are truly useful (or even valid—one would be hard-pressed to find a single issue on which Descartes, Spinoza, and Leibniz all agree and on which those who are usually called "empiricists" unanimously dissent). In the light of so much important and creative work done over the last twenty years in seventeenth-century philosophy, it would have been nice to see a volume devoted to "the rationalists" include at least one sophisticated discussion of the legitimacy and grounds of such a label.The essays in this book are divided into three categories: Matter and Substance; Freedom and Necessity; and Mind and Consciousness. The contributors are a broad mix of scholars: some established and accomplished, others new and up-and-coming. The quality of the work is consistently high. There is a lot of detailed and careful work here, both in the attention to the historical texts and in philosophical analyses. However, not all of the essays are of great scope or interest; in fact, most are not. There is a definite tendency toward the small-scale (but not brevity): a concern with micro-problems (for example, the chapter by Clarence Bonnen and Daniel Flage, "Distinctness," is devoted to the question of what the "distinctness" of an idea is for Descartes) and an emphasis on theses and arguments (such as Geoffrey Gorham's examination of the "similarity condition" for causation in Descartes, "Causation and Similarity in Descartes,"). If there is indeed an "analytical" way of doing history of philosophy, that school is well represented here.And then there are a couple of essays that stand out by transcending this narrowness of focus. The chapters by Catherine Wilson ("The Illusory Nature of Leibniz's System") and Don Garrett ("Teleology in Spinoza and Early Modern Rationalism") are, without question, the boldest and most interesting of the collection. Wilson argues that, in the light of Leibniz's changing and inconsistent views on substance, there really is no metaphysical "system" in his philosophy. Garrett, in what is, to my mind, the best essay in the book (although I think I disagree with him), defends an account of teleology in Spinoza's metaphysics, and then compares Spinoza's views on teleology with those of Aristotle, Descartes, and Leibniz; he concludes that Spinoza not only accepted teleological explanations of particular phenomena, but did so more strongly than anyone else in the modern period. Experts will, of course, disagree with the claims made by Wilson and Garrett; that is what this game is all about. But it is truly refreshing to see scholars such as these taking on large-scale issues.It is worth noting that there is also a nice, indirect dialogue between two of the essays: Charles Huenemann's interesting account of a consistent necessitarianism in Spinoza ("The Necessity of Finite Modes and Geometrical Containment in Spinoza's Metaphysics,") and Edwin Curley and Gregory Walski's argument (in "Spinoza's Necessitarianism Reconsidered,") that, when it comes to the finite modes, Spinoza is not a strong or absolute necessitarian. What is truly unfortunate about the collection, however... (shrink)

Advances in machine learning and the development of very large knowledge graphs have accompanied a proliferation of ontologies of many types and for many purposes. These ontologies are commonly developed independently, and as a result, it can be difficult to communicate about and between them. To address this difficulty of communication, ontologies and the communities they serve must agree on how their respective terminologies and formalizations relate to each other. The process of coming into accord and agreement is called “harmonization.” (...) The Ontology Summit 2021 examined the overall landscape of ontologies, the many kinds of ontology generation and harmonization, as well as the sustainability of ontologies. The Communiqué synthesizes and summarizes the findings of the summit as well as earlier summits on related issues. One of the major impediments to harmonization is the relatively poor quality of natural language definitions in many ontologies. The summit surveyed the state of the art in natural language definition development, based on lexicographic principles, as well as examples of ongoing projects that are explicitly dealing with harmonization and sustainability. (shrink)

Secular Millenialism: The Train of Aesthetics from Baumgarten and Kant to Walt Disney and Hitler by Benjamin Bennett combines the perspectives of intellectual history, literary history, and political history in order to illuminate the operation of the idea of aesthetics, and of the historical actualization of that idea, in the background of twentieth-century totalitarianism.

In lieu of an abstract, here is a brief excerpt of the content:Texts and Icons in Heidegger’s Metaphysical TraditionMichael James Bennett (bio)[End Page 26]This essay is about texts that draw attention to themselves as texts, that is, as material, graphical figures, rather than as more or less efficiently pellucid semantic relays. In other words, it is about what happens when texts behave like images. In what follows I examine a series of philosophical contexts where this question appears to be at (...) issue. I claim that one way of understanding what’s going on in these contexts is that here the image-form of a text becomes a kind of icon. I begin by reflecting on a prejudice that belongs, according to Heidegger, to the “history of metaphysics”: the notion that it would be better, clearer, and less ambiguous to replace all reliance on images with self-effacing, transparent words. My goal here is to demonstrate the existence of an alternative historical trend that defends an opposite view. I compare a defense of iconography by Byzantine patriarch Nikephoros of Constantinople, as well as the Neoplatonist Porphyry’s commentary on Aristotle’s Categories, with works by two latter-day Heideggerians, Jacques Derrida and Jean-Luc Marion, who respond to the inherited problematic of non-referential, iconic texts. These responses suggest that non-semantic image-creation, as much as non-semantic verbal play, is the pre-conceptual condition of conceptuality. This essay presents a new way of understanding the philosophical issues that connect ancient and medieval discussions about icons and images with twentieth-century concerns about language.In her study of medieval European manuscript illumination, Animating the Letter (1999), Laura Kendrick emphasizes the non-semantic character of illuminated texts. Kendrick argues that the basic distinction between text and image is fundamentally at stake in illumination, and that the distinction is inherited from the Christian church fathers who opposed text and image, privileging the former and denigrating the latter. According to this traditional view, texts are better suited than images to a consideration of the divine on account of writing’s ethereal quality, its “transparency,” which leads the reader beyond the material sign to the immaterial concept. The problem with images, on the other hand, is their materiality, which may lead viewers down a dark path toward an ultimately heretical veneration for the mere image instead of for its referent. It seems to me that we find in Kendrick’s argument an exact homology with the discourse on the icon in the Byzantine Christian church. Emperor Constantine V, for instance, at the time of the “first iconoclast crisis” (the mid-eighth century CE), expresses wariness about the potentially heterodox metaphysics underpinning iconophilia. He objects to icons on the basis that their veneration would be acceptable only if the icon were to share the essence of that of which it is an icon (God), but that this is impossible; infinite divine nature cannot be encompassed within the finite line of human composition. The Byzantine iconophile’s response to this objection is not to deny the infinite, uncircumscribable nature of God, but to affirm that the icon, bound though it is to the register of images, nevertheless does not function in the same manner as an ordinary image. That is, the icon does not refer to its model by means of resemblance alone. In the language of Nikephoros of Constantinople (758–828 CE), the character of the icon consists in consubstantiality (homoousia) prior to resemblance (homoiōsis).1 [End Page 27]The problem of the limits of reference unites the discourse on the icon and the flourishing of the illuminated text. Just as the icon does not refer in the normal way to its referent, so Kendrick contends that the “animated letter” is not reducible to its pure semantic quality, is not to be understood as if it were just a kind of significative relay through which a sublime quantity of something called “meaning” is obliged to pass. “Meaning,” conceived of in what I am inclined to call the narrowly economic sense as the cargo of material vehicles called “words,” meaning that is gambled in words and then “cashed out” again, is not always what is at stake when one writes. Something else is... (shrink)

By age 85, most adults manifest some degree of motor impairment. However, in most individuals a specific etiology for motor decline and treatment to modify its inexorable progression cannot be identified. Recent clinical-pathologic studies provide evidence that mixed-brain pathologies are commonly associated with late-life motor impairment. Yet, while nearly all older adults show some degree of accumulation of Alzheimer’s disease and related dementias pathologies, the extent to which these pathologies contribute to motor decline varies widely from person to person. Slower (...) or faster than expected motor decline in the presence of brain injury and/or pathology has been conceptualized as more or less “resilience” relative to the average person This suggests that other factors, such as lifestyles or other neurobiologic indices may offset or exacerbate the negative effects of pathologies via other molecular pathways. The mechanisms underlying neural motor resilience are just beginning to be illuminated. Unlike its cousin, cognitive resilience which is restricted to neural mechanisms above the neck, the motor system extends the total length of the CNS and beyond the CNS to reach muscle and musculoskeletal structures, all of which are crucial for motor function. Building on prior work, we propose that by isolating motor decline unrelated to neuropathologies and degeneration, investigators can identify genes and proteins that may provide neural motor resilience. Elucidating these molecular mechanisms will advance our understanding of the heterogeneity of late-life motor impairment. This approach will also provide high value therapeutic targets for drug discovery of therapies that may offset the negative motor consequences of CNS pathologies that are currently untreatable. (shrink)

We highlight a recent study exploring the hand‐off of UV damage to several key nucleotide excision repair (NER) proteins in the cascade: UV‐DDB, XPC and TFIIH. The delicate dance of DNA repair proteins is choreographed by the dynamic hand‐off of DNA damage from one recognition complex to another damage verification protein or set of proteins. These DNA transactions on chromatin are strictly chaperoned by post‐translational modifications (PTM). This new study examines the role that ubiquitylation and subsequent DDB2 degradation has during (...) this process. In total, this study suggests an intricate cellular timer mechanism that under normal conditions DDB2 helps recruit and ubiquitylate XPC, stabilizing XPC at damaged sites. If DDB2 persists at damaged sites too long, it is turned over by auto‐ubiquitylation and removed from DNA by the action of VCP/p97 for degradation in the 26S proteosome. (shrink)

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this book, making it the fullest and most authoritative treatment of the subject.

'Mr Bennett, as was to be expected, has written a first-rate book on Kant's Analytic. It is vivid, entertaining, and extremely instructive. It will be found of absorbing interest both by those who already know the Critique and by those - if there are any such - who have a developed interest in philosophy, yet no direct acquaintance with Kant. These last it will surely drive to the text and, as surely, will drive them to approach it in a truly (...) philosophical spirit. Bennett's Kant is not a giant immersed, or frozen, in time. He is a great contemporary - a little out of touch, admittedly, with recent developments in mathematics and physics - but one with whom we can all argue, against him, at his side, or obliquely to him. And so Bennett does argue, continuously, fiercely, and fruitfully; and summons to join in the argument, at appropriate moments, those older contemporaries, Locke, Leibniz, Berkeley, and Hume, and those younger contemporaries, Wittgenstein, Ryle, Ayler, Quine, Quinton, Warnock, and others. This is splendid, and a necessary corrective to that extraordinary isolation in which Kant tends to be islanded, partly indeed, by his own unique qualities, but partly by oceans of the wrong kind of respect. Bennett, continuously engaging his great antagonist, shows the right kind.'. (shrink)

The thoughts of three philosophers on three topics: meaning, causality, and objectivity, are the focus of this study.

Christopher Bennett presents a theory of punishment grounded in the practice of apology, and in particular in reactions such as feeling sorry and making amends. He argues that offenders have a 'right to be punished' - that it is part of taking an offender seriously as a member of a normatively demanding relationship that she is subject to retributive attitudes when she violates the demands of that relationship. However, while he claims that punishment and the retributive attitudes are the necessary (...) expression of moral condemnation, his account of these reactions has more in common with restorative justice than traditional retributivism. He argues that the most appropriate way to react to crime is to require the offender to make proportionate amends. His book is a rich and intriguing contribution to the debate over punishment and restorative justice. (shrink)

The philosophy of personalism inspired Martin Luther King’s dream of a better world. We still need its hopeful ideas today.

Jonathan Bennett's analysis of the second half of Kant's Critique of Pure Reason, in which Kant concerns himself with topics such as substance, the nature of the self, the cosmos, freedom and the existence of God, continues to be an engaging and accessible exploration of Kant's major work. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Karl Ameriks, illuminating its enduring importance and relevance to philosophical enquiry, this influential work has been revived for (...) a new generation of readers. (shrink)

We frequently speak of certain things or phenomena being built out of or based in others. Making Things Up concerns these relations, which connect more fundamental things to less fundamental things: Karen Bennett calls these 'building relations'. She aims to illuminate what it means to say that one thing is more fundamental than another.

In _Death in Documentaries: The Memento Mori Experience_, Benjamin Bennett-Carpenter suggests that documentaries are an especially apt form of contemporary _memento mori_; that is, documentaries offer transformative experiences for a viewer to renew one’s consciousness of mortality.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 12.1 (2004) 4-16 [Access article in PDF] Once More With Feeling Reconciling Discrepant Accounts of Musical Affect Bennett Reimer Northwestern University When I was sixteen, a junior in high school in Brooklyn, I auditioned for the All-City High School Band of New York and was placed as first chair clarinet. At the first rehearsal, a piece we played (I don't remember what it was (...) except that it was new to me) had a long, melodic clarinet solo, with accompaniment. When I finished playing it the director stopped the band and said, "Very nice, first clarinet. Let's do it again, this time with more feeling." Then he said, "Letter C," and we started again.I could not have known, then, that I was to spend much of my life in pursuit of some sort of clarification of what transpired in that episode, as in this paper, where I deal once more with feeling. I had no idea that his apparently simple instruction to me raised issues so complex that many of humankind's most important thinkers had struggled with them in search of a resolution, as I, infinitely more modestly, was also to do. I was unaware that philosophical blood, sweat, and tears had been spilled through the centuries in various contentions as to the relation, if any, of musical feeling to feeling outside musical experience. I knew nothing of metaphor, [End Page 4] of effability and ineffability, of embodiment and designation, of issues of authenticity of feeling, and semantic density, significant form, semiotics, the relation of feeling to emotion, to gender, to meaning, and on and on with seemingly endless and intractable debates centered on how and why and when music is related to feeling.Being unencumbered with any of this (how one longs, sometimes, to return to one's philosophical Garden of Eden), and having to play that solo again immediately, I did what my novice performer's instincts told me to do-the only thing I knew how to do-I placed more emphasis on what the notes of that melody seemed to want to do, where they seemed to want to go and how they got there. Feeling their melodic tendencies more concentratedly and making them more apparent by the way I sounded them, I felt in myself a deeper sense of union-of the music as part of my undergoing-than I had the first time. When I finished the director stopped the band again, looked at me for several seconds, and said, "Lovely, first clarinet. Very musical. Let's go on."I would not have been able at the time that event occurred to describe, as I just did, what I did and how I felt. I did not have the conceptual apparatus to do so, although I did have, luckily for me, enough intuitive musicianship to have survived that test. My description, or perhaps interpretation, of how I reacted and how I experienced it can only reflect who I am now, with the cognitive structure allowing me to understand what happened as I reflect about it. Nevertheless I believe that several important matters relating to musical feeling can be clarified in relation to how I now interpret what I experienced as a youth in that band.I am aware now that I did what I did in ignorance of the fact that I was not the first to have played that solo. If I had known about and studied previous performances by a variety of clarinetists I would have, without doubt, been influenced by their solutions to the challenge of expressive interpretation it presented. Especially if I had been guided by a sensitive teacher, I would have reflected those influences in my own sounding. Perhaps I would have imitated what seemed to me the most musical rendition. If I had done so, I am now aware, that would have been regarded, in my culture at any rate, as a sign of my novice status, a more mature stage of musicianship requiring that I both reflect... (shrink)

In _Vibrant Matter_ the political theorist Jane Bennett, renowned for her work on nature, ethics, and affect, shifts her focus from the human experience of things to things themselves. Bennett argues that political theory needs to do a better job of recognizing the active participation of nonhuman forces in events. Toward that end, she theorizes a “vital materiality” that runs through and across bodies, both human and nonhuman. Bennett explores how political analyses of public events might change were we to (...) acknowledge that agency always emerges as the_ _effect of ad hoc configurations of human and nonhuman forces. She suggests that recognizing that agency is distributed this way, and is not solely the province of humans, might spur the cultivation of a more responsible, ecologically sound politics: a politics less devoted to blaming and condemning individuals than to discerning the web of forces affecting situations and events. Bennett examines the political and theoretical implications of vital materialism through extended discussions of commonplace things and physical phenomena including stem cells, fish oils, electricity, metal, and trash. She reflects on the vital power of material formations such as landfills, which generate lively streams of chemicals, and omega-3 fatty acids, which can transform brain chemistry and mood. Along the way, she engages with the concepts and claims of Spinoza, Nietzsche, Thoreau, Darwin, Adorno, and Deleuze, disclosing a long history of thinking about vibrant matter in Western philosophy, including attempts by Kant, Bergson, and the embryologist Hans Driesch to name the “vital force” inherent in material forms. Bennett concludes by sketching the contours of a “green materialist” ecophilosophy. (shrink)

In this paper I consider whether traditional behaviors of animals, like traditions of humans, are transmitted by imitation learning. Review of the literature on problem solving by captive primates, and detailed consideration of two widely cited instances of purported learning by imitation and of culture in free-living primates (sweet-potato washing by Japanese macaques and termite fishing by chimpanzees), suggests that nonhuman primates do not learn to solve problems by imitation. It may, therefore, be misleading to treat animal traditions and human (...) culture as homologous (rather than analogous) and to refer to animal traditions as cultural. (shrink)

In this study of events and their places in our language and thought, Bennett propounds and defends views about what kind of item an event is, how the language of events works, and about how these two themes are interrelated. He argues that most of the supposedly metaphysical literature is really about the semantics of their names, and that the true metaphysic of events--known by Leibniz and rediscovered by Kim--has not been universally accepted because it has been tarred with the (...) brush of a false semantic theory. (shrink)

How can we motivate ourselves to do what we think we ought? How can we deliberate about personal values and priorities? Bennett Helm argues that standard philosophical answers to these questions presuppose a sharp distinction between cognition and conation that undermines an adequate understanding of values and their connection to motivation and deliberation. Rejecting this distinction, Helm argues that emotions are fundamental to any account of value and motivation, and he develops a detailed alternative theory both of emotions, desires and (...) evaluative judgements and of their rational interconnections. The result is an innovative theory of practical rationality and of how we can control not only what we do but also what we value and who we are as persons. (shrink)

Talks collected from lectures given by Bennett with Gurdjieff's approval, to help people understand All and Everything: Beelzebub's Tales to His Grandson. Bennett regarded Gurdjieff's All and Everything as a work of superhuman genius.

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Lighten up about mathematics! Have fun. If you read this book, you will have to endure bad math puns and jokes and out-of-date pop culture references. You'll learn some really cool mathematics to boot. In the process, you will immerse yourself in living, thinking, and breathing logical reasoning. We like to call this proofs, which to some is a bogey word, but to us it is a boogie word. You will learn how to solve problems, real and imagined. After all, (...) math is a game where, although the rules are pretty much set, we are left to our imaginations to create. Think of this book as blueprints, but you are the architect of what structures you want to build. Make sure you lay a good foundation, for otherwise your buildings might fall down. To help you through this, we guide you to think and plan carefully. Our playground consists of basic math, with a loving emphasis on number theory. We will encounter the known and the unknown. Ancient and modern inquirers left us with elementary-sounding mathematical puzzles that are unsolved to this day. You will learn induction, logic, set theory, arithmetic, and algebra, and you may one day solve one of these puzzles. (shrink)

Let us introduce two antithetical terms in order to avoid certain elementary confusions: To the question “How do you know that so‐and‐so is the case?”, we sometimes answer by giving ‘criteria’ and sometimes by giving ‘symptoms. If medical science calls angina an inflammation caused by a particular bacillus, and we ask in a particular case “Why do you say this man has got angina?” then the answer “I have found the bacillus so‐and‐so in his blood” gives us the criterion, or (...) what we may call the defining criterion of angina. If on the other hand the answer was, “His throat is inflamed”, this might give us a symptom of angina, I call “sympton” a phenomenon of which experience has taught us that it coincided, in some way or other, with the phenomenon which is our defining criterion, Then to say “A man has angina if this bacillus is found in him” is a tautology or it is a loose way of stating the definition of “angina”. But to say, “A man has angina whenever he has an inflamed throat” is to make a hypothesis. (BB, pp. 24–25)1. (shrink)

Should arts education have a more significant place in our schools? An emphatic "Yes" comes from the editors and other contributors to this provocative volume. They build their case by drawing upon recent developments in cognitive theory and, in particular, upon contemporary thought regarding aesthetic knowing. They contend that aesthetic knowing constitutes a "special mode of cognition" and they see aesthetic learning as vital to intellectual growth and development. They argue that the arts should "constitute a foundational school subject." An (...) opening chapter reviews past practices in education in the arts, thus providing a needed historical context within which current thinking about aesthetic learning can be viewed. The following chapters elaborate on the idea and value of aesthetic knowing from various perspectives to buttress the case for its importance in education. Developmental issues are explored to deepen understanding of the nature of aesthetic growth. Studies reveal that children's art products have not changed over the years. But how has a cognitive perspective changed the way in which child art is interpreted? Can phases in general aesthetic development be identified? Or are such phases specific to each art form? What pedagogical issues arise in education in the arts? How are conceptual learnings important to the development of aesthetic understanding? Does the study of fine arts enrich the quality of life and shape human personality in positive ways. Given the long history of arts education as a peripheral matter in schools, is it now possible to envision a greater recognition of what study of the arts can accomplish by a proper focus on aesthetic knowing? These are some of the questions addressed in a volume that provides stimulating reading not only for arts educators but for all who are genuinely concerned about education. (shrink)

Researchers have studied non-human primate cognition along different paths, including social cognition, planning and causal knowledge, spatial cognition and memory, and gestural communication, as well as comparative studies with humans. This volume describes how primate cognition is studied in labs, zoos, sanctuaries, and in the field, bringing together researchers examining similar issues in all of these settings and showing how each benefits from the others. Readers will discover how lab-based concepts play out in the real world of free primates. This (...) book tackles pressing issues such as replicability, research ethics, and open science. With contributors from a broad range of comparative, cognitive, neuroscience, developmental, ecological, and ethological perspectives, the volume provides a state-of-the-art review pointing to new avenues for integrative research. (shrink)