Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI −1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is that of a (...) particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies. (shrink)

The equivalence of Fermat's Last Theorem and the non-existence of solutions of a generalized n th order homogeneous hyperbolic partial differential equation in three dimensions and periodic boundary conditions defined in a cubic lattice is demonstrated for all positive integer, n > 2. For the case n = 2, choosing one variable as time, solutions are identified as either propagating or standing waves. Solutions are found to exist in the corresponding problem in two dimensions.

The Fermi energy at 0°K is evaluated for electrons confined to cubical and spherical rigid-walled boxes of equal volume, respectively, in the Sommerfeld approximation. Due primarily to large differences in single-particle degeneracies, Fermi energies compared for equal numbers of particles in these two configurations are found to be unequal. Approximate expressions of the Fermi energy in the large particle-number limit for the spherical case reveal that it agrees in form with the Fermi energy for the cubical configuration. The finite cylindrical (...) box is also examined and it is found that for fixed number of particles and fixed volume, the Fermi energy varies as the two characteristic lengths of the box are changed. Experimental corroboration of the theory is suggested through measurement of the work function for equal-volume micrometallic samples in the different geometries. (shrink)

In this groundbreaking work, Richard L. Velkley examines the complex philosophical relationship between Martin Heidegger and Leo Strauss. Velkley argues that both thinkers provide searching analyses of the philosophical tradition’s origins in radical questioning. For Heidegger and Strauss, the recovery of the original premises of philosophy cannot be separated from rethinking the very possibility of genuine philosophizing. Common views of the influence of Heidegger’s thought on Strauss suggest that, after being inspired early on by Heidegger’s dismantling of the philosophical (...) tradition, Strauss took a wholly separate path, spurning modernity and pursuing instead a renewal of Socratic political philosophy. Velkley rejects this reading and maintains that Strauss’s engagement with the challenges posed by Heidegger—as well as by modern philosophy in general—formed a crucial and enduring framework for his lifelong philosophical project. More than an intellectual biography or a mere charting of influence, _Heidegger, Strauss, and the Premises of Philosophy_ is a profound consideration of these two philosophers’ reflections on the roots, meaning, and fate of Western rationalism. (shrink)

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as (...) if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book. (shrink)

In Being after Rousseau, Richard L. Velkley presents Jean-Jacques Rousseau as the founder of a modern European tradition of reflection on the relation of philosophy to culture—a reflection that calls both into question.

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. He provides discussions of Gödel's views, and develops a new type of (...) platonic rationalism that requires rational intuition, called 'constituted platonism'. (shrink)

What are termed the ‘collateral legal consequences’ (or CLCs) of criminal conviction have been defended in a variety of ways. The focus in this article is on efforts to justify the burdens and restrictions they involve as nonpenal measures designed to secure public safety. Zachary Hoskins' careful defense of such public‐safety CLCs is utilized as a point of departure. Although it is granted that such measures might be defensible, the many complications and problems of ensuring that they do not amount (...) to further legal punishment and are kept within reasonable bounds are explored. I argue that the state is unlikely to deploy such public safety measures wisely and with sufficient restraint. (shrink)

Given the desert-centric character of retributive penal theory, it seems odd that its supporters rarely discuss the undeserved losses and suffering of crime victims and the state’s role in responding to them. This asymmetry in the desert-focus of retributive penal theory is examined and the likely arguments in support of it are found wanting. Particular attention is paid to the claim that offenders, rather than the state, should supply compensation to victims. Also, standard retributive accounts of why the deserving should (...) be punished are shown to support state-supplied victim compensation. (shrink)

After surveying the many practical difficulties sentencing judges must confront in determining whether the offenders who appear before them are genuinely remorseful, recent dialogical accounts of remorse-based sentence reductions are examined. These accounts depend on a morally communicative approach to legal punishment’s justification and seem to confine such communication to offenders. They contend that, in order to respect remorseful offenders, sentencing judges must reduce their sentences. Why they should do so, by how much they should do so, and whether they (...) should do so when the individuals being sentenced are recidivists, are among the questions discussed. Also examined is whether remorse should be a prominent mitigating factor in sentencing or only one among many aggravating or mitigating factors. In conclusion, it is suggested that existing sentencing practices might make more sense if we suppose judges to be looking for things other than genuine remorse in the individuals who appear before them. (shrink)

"The University of Missouri's rich record of accomplishment and service to Missouri, the nation, and the world is captured in this collection of photographs of campus landmarks, people, events, and Tiger spirit. Includes a history of the campus and timeli.

In the century between the creation of the first large, European astronomical observatory by Tycho Brahe in the 1580s and the national observatories of France and England in the 1660–1670s, astronomers constructed ever more sets of tables, derived from various geometrical and physical models, to compute planetary positions. But how were these tables to be evaluated? What level of precision or accuracy should be expected from mathematical astronomy? In 1644, the Stetin astronomer and calendar-maker Lorenz Eichstadt published a new set (...) of tables, mostly cobbled together from earlier tables, which include a running commentary on how his tables might be expected to match ‘observed’ planetary positions. His earlier works also often display a rhetoric of ‘exactitude’ and ‘error’. Eichstadt thus offers a case study of explicit discussions of ‘precision’ in mid-seventeenth astronomy. Although some tables could generate positions to arcseconds, Eichstadt argued that a regime of five arcminutes should be enough for most table users who were, presumably, computing horoscopes. (shrink)

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

This article provides a brief background of key issues in physician burnout, a significant problem in the healthcare industry. The extent and severity of burnout are not well understood, and those seeking help are often stigmatized. A number of different approaches to alleviating burnout have been suggested, but the problem lacks any single or simple solution.We posit that an ethics committee may be well positioned to help address this issue because of its unique position within an institution. An ethics committee (...) serves the entire hospital staff regardless of department. As such it may be able to identify common elements in the development of burnout, and can serve as a conduit to administration in identifying these. An ethics committee can obtain information about the extent of burnout by conducting surveys to assess the extent and severity of burnout in an institution, and serve as a central resource to help address and alleviate it.Finally, an ethics committee may be able to act as an intermediary between practitioners and the administration, in advising the administration of the extent of the problem and offer suggestions for alleviating it. (shrink)

"This book explores the religious underpinnings of psychoanalysis and examines how the tenets of Judaism and Christianity specifically influenced the theories and practices of Freud and Jung, respectively. It demonstrates that secular psychoanalysis is in large measure a revision of religious principles contained within the Judeo-Christian ethic and questions whether Freud's and Jung's approaches may best be suited to the psychological configurations of their fellow religionists." -- Back cover.

The claim that visually masked, unidentifiable words are analyzed at the level of whole word meaning has been challenged by recent findings indicating that instead, analysis occurs mainly at the subword level. The present experiments examined possible limits on subword analysis. Experiment 1 obtained semantic priming from pleasant- and unpleasant-meaning subliminal words in which no individual letter contained diagnostic information about a word’s evaluative valence; thus analysis must operate on information more complex than that contained in individual letters. Experiments 2 (...) and 3 showed that analysis must operate on information more complex than that represented by individual bigrams or trigrams . These findings suggest that while subliminal priming is driven by subword analysis, the effective units of analysis are distributed widely across at least short words. (shrink)

In a recent book, J. R. Lucas presents an argument to show that if God has infallible knowledge of the future, our will is not free. Thus, Lucas concludes, like the medieval Jewish philosopher Gersonides, that God in creating beings with genuinely free will, abdicates some of his omniscience as well as some of his omnipotence. God could, but will not, determine our choices, since such an exercise of his power would rob us of free will. Similarly, Lucas holds, God (...) could but does not foreknow our future choices since this also would rob us of free will. This argument, from so formidable a foe of determinism as Lucas, merits our most serious attention. However, I believe that there is a way to evade its conclusion, a way which Lucas considers but rejects. (shrink)

This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of (...) abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work. (shrink)

For more than a decade, American lawyers have bewailed the ethical crisis in their profession, wringing their hands about its bad image. But their response has been limited to spending money on public relations, mandating education, and endlessly revising ethical rules. In this book, Richard Abel will argue that these measures will do little or nothing to solve the problems illustrated by the six disciplinary case studies featured in this book unless the legal monopoly enjoyed by attorneys in the (...) U.S. is drastically contracted. Richard Abel examines some of the most common ethical complaints made about lawyers in Lawyers in the Dock. Using detailed records of disciplinary proceedings, he describes the actions surrounding certain cases based on three of the most common complaints: neglecting the client by failing to pursue cases diligently; overcharging of clients by mystifying billing practices; and betraying adversaries and courts out of excessive loyalty to clients or causes. In this book, Richard Abel will argue that these measures will do little or nothing to solve the problems exposed by his six disciplinary case studies unless structural changes are made to the legal monopoly in order to restore the public trust in lawyers. Lawyers in the Dock is essential reading for lawyers, law students, and potential clients who wish to restore trust and professional responsibility in the legal profession. (shrink)

Comparative case studies of lawyer deviance and discipline offer a unique perspective on how and why lawyers misbehave, how regulatory bodies respond, and the efficacy of those responses. Such studies also provide valuable pedagogic tools, opening the eyes of law students to the ways in which they, too, could transgress ethical rules. This special issue builds on my two books on misbehaving lawyers in New York and California by presenting vivid accounts of such lawyers in the UK, Canada, Australia, New (...) Zealand, and the Netherlands. (shrink)

In _Freedom and the End of Reason_, Richard L. Velkley offers an influential interpretation of the central issue of Kant’s philosophy and an evaluation of its position within modern philosophy’s larger history. He persuasively argues that the whole of Kantianism—not merely the Second Critique—focuses on a “critique of practical reason” and is a response to a problem that Kant saw as intrinsic to reason itself: the teleological problem of its goodness. Reconstructing the influence of Rousseau on Kant’s thought, Velkley (...) demonstrates that the relationship between speculative philosophy and practical philosophy in Kant is far more intimate than generally has been perceived. By stressing a Rousseau-inspired notion of reason as a provider of practical ends, he is able to offer an unusually complete account of Kant’s idea of moral culture. (shrink)

The question addressed here is whether evidence concerning defendants' past criminal records should be introduced at their trials because such evidence reveals their character and thus reveals whether they are the kinds of persons likely to have committed the crimes with which they are currently charged. I strongly caution against the introduction of such evidence for a number of reasons. First, the link between defendants' past criminal records and claims about their standing dispositions to think and act is tenuous, at (...) best. Second, noncharacter, or trace, evidence should have primacy in determining the guilt or innocence of defendants. Third, character evidence will vary in its freshness and specificity. Other things being equal, only relatively fresh and specific character evidence has probative value. Moreover, such evidence will have greater probative value in criminal cases where the issue before the court is whether a crime has been committed than in cases where the issue is whether it was the defendant who committed the crime. Finally, we might be more sanguine about the introduction of fresh and specific character evidence under conditions likely to work against its misuse or misinterpretation. However, the relevant conditions may not often be satisfied in the real world of criminal trials and defendants. (shrink)

This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's views wend (...) their way through the work, serving as a foil to Frege. Appendices give the proofs of the first 68 propositions of Begriffsschrift in modern notation. This book will be of interest to students and professionals in philosophy and linguistics. (shrink)

In a recent paper Anthony Flew gives an argument which can be outlined as follows: 1. Any attempt to give a ‘free will defence’ must be based either on a compatibilist notion of free will or a libertarian, incompatibilist, notion of free will. 2. A free will defence based on a compatibilist notion of free will must fail, for on a compatibilist view of free will, God could make creatures who were free but never chose evil. 3. A free will (...) defence based on a libertarian notion of free will might have other difficulties, but on a libertarian view of free will God could not both leave men free and bring it about that they never chose evil. 4. But a free will defence based on an incompatibilist, libertarian notion of free will can be rejected, since: It is not clear that the ordinary use of such key terms as ‘action’ and ‘choice’ carry any implications of libertarian free will. If such terms did carry the implication of libertarian free will it becomes hard to see how anyone could be in a position to know that a choice had been made or an action performed. The possession of libertarian free will by created beings seems to be incompatible with the essential theistic doctrine that all created beings are always utterly dependent on God as their sustaining cause. 5. Therefore the free will defence fails. (shrink)

One of the most difficult problems for a student of religion is the problem of how to relate different religious views of life. It is not difficult to say, ‘My religious orientation has the only truth,’ but the art of giving evidence and argument to support a view on how they should be compared is almost nonexistent. Because of this, the recent work that John Hick has done in this area deserves thoughtful consideration. Since I am working on a book (...) which is concerned with this issue, I am not only going to discuss Hick's views but also defend an alternative way of relating religious views of life. I hope this article will stimulate reactions which will be of help in my work on the book. (shrink)

The critics of Schleiermacher's hermeneutic are legion and its defenders few – due, to a great extent, to the popularity of Gadamer's Truth and Method and its attack on Schleiermacher. I believe that the critics of Schleiermacher have not understood him very well and the failure of his hermeneutics to gain very much respect lies, at least partially, to a lack of understanding of what he had to say. Besides, if we look at contemporary scholars who focus on the study (...) of language and how it functions we will find that they often have views very much like those found in Schleiermacher's discussion of hermeneutics. (shrink)

In _Freedom and the End of Reason_, Richard L. Velkley offers an influential interpretation of the central issue of Kant’s philosophy and an evaluation of its position within modern philosophy’s larger history. He persuasively argues that the whole of Kantianism—not merely the Second Critique—focuses on a “critique of practical reason” and is a response to a problem that Kant saw as intrinsic to reason itself: the teleological problem of its goodness. Reconstructing the influence of Rousseau on Kant’s thought, Velkley (...) demonstrates that the relationship between speculative philosophy and practical philosophy in Kant is far more intimate than generally has been perceived. By stressing a Rousseau-inspired notion of reason as a provider of practical ends, he is able to offer an unusually complete account of Kant’s idea of moral culture. (shrink)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Here is an in-depth look at the role myth, mortality, and religion play in J. R. R. Tolkien's works such as The Hobbit, The Lord of the Rings, and The Silmarillion -- including Tolkien's private letters and revealing opinions of his own work. Richard L. Purtill brilliantly argues that Tolkien's extraordinary ability to touch his readers' lives through his storytelling -- so unlike much modern literature -- accounts for his enormous literary success. This book demonstrates the moral depth in (...) Tolkien's work and cuts through current subjectivism and cynicism about morality. A careful reader will find a subtle religious dimension to Tolkien's work -- all the more potent because it is below the surface. Purtill reveals that the author's fantasy stories creatively incorporate profound religious and ethical ideas. For example, Purtill shows us how hobbits reflect both the pettiness of unimaginative parochial humanity and the unexpected heroism of ordinary people in crisis. Purtill effectively addresses larger issues of the place of myth, the relation of religion and morality to literature, the relation of Tolkien's work to traditional mythology, modern fantasy and science fiction, and the lessons Tolkien's work teaches that are applicable to our own lives. Book jacket. (shrink)

There is a core to the referential/attributive distinction that reveals a propositional ambiguity that is scope-related and rooted in syntax.

Upshot: Conversational conferences are difficult to design in a way that avoids the consequences that arise when participants are not experienced with or fully value the conversational mode of interaction. So, the designers of such conferences must experiment with ways to build a culture, use a structure, and facilitate participation that might mitigate some of these consequences. The potential of the experimental conference designed in the light of second-order cybernetics lies, in part, in the prospect of identifying and acquiring the (...) conversational abilities and appreciations necessary to support a participative-dialogic society. (shrink)