Evidence and theory ranging from traditional philosophy to contemporary cognitive research support the hypothesis that consciousness has a two-part structure: a focused region of articulated experience surrounded by a field of relatively unarticulated, vague experience.William James developed an especially useful phenomenological analysis of this "fringe" of consciousness, but its relation to, and potential value for, the study of cognition has not been explored. I propose strengthening James′ work on the fringe with a functional analysis: fringe experiences work to radically condense (...) context information in consciousness; are vague because a more explicit representation of context information would overwhelm consciousness′ limited articulation capacity; help mediate retrieval functions in consciousness; and contain a subset of monitoring and control experiences that cannot be elaborated in focal attention and are "ineffable." In general, the phenomenology of the fringe is a consequence of its cognitive functions, constrained by consciousness′ limited articulation capacity. Crucial to monitoring and control is the feeling of "rightness." Rightness functions as a summary index of cognitive integration, representing, in the fringe, the degree of positive fit between a given conscious content and its parallel, unconsciously encoded context. Rightness appears analogous to the connectionist metric of global network integration, known variously as goodness-of-fit, harmony, or minimum energy. (shrink)

The essays in this book discuss the originally proposed Baldwin effect, how it was modified over time, and its possible contribution to contemporary empirical...

The current paper synthesizes theory and data from the field of life history (LH) evolution to advance a new developmental theory of variation in human LH strategies. The theory posits that clusters of correlated LH traits (e.g., timing of puberty, age at sexual debut and first birth, parental investment strategies) lie on a slow-to-fast continuum; that harshness (externally caused levels of morbidity-mortality) and unpredictability (spatial-temporal variation in harshness) are the most fundamental environmental influences on the evolution and development of LH (...) strategies; and that these influences depend on population densities and related levels of intraspecific competition and resource scarcity, on age schedules of mortality, on the sensitivity of morbidity-mortality to the organism’s resource-allocation decisions, and on the extent to which environmental fluctuations affect individuals versus populations over short versus long timescales. These interrelated factors operate at evolutionary and developmental levels and should be distinguished because they exert distinctive effects on LH traits and are hierarchically operative in terms of primacy of influence. Although converging lines of evidence support core assumptions of the theory, many questions remain unanswered. This review demonstrates the value of applying a multilevel evolutionary-developmental approach to the analysis of a central feature of human phenotypic variation: LH strategy. (shrink)

James Sterba has constructed a powerful argument for there being a conflict between the presence of evil in the world and the existence of God. I contend that Sterba’s argument depends on a crucial assumption, namely, that God has an obligation to act according to the principle of meticulous providence. I suggest that two of his analogies confirm his dependence on this requirement. Of course, his argument does not rest on either of these analogies, but they are illustrative of the (...) role that meticulous providence plays in his argument. I then investigate the ethical principles Sterba invokes in his use of meticulous providence and suggest that not only do we often not predicate goodness of human persons based on these principles of obligation, but that these principles are much too stringent to function to determine moral obligations and moral goodness. From there, I contend that to think that God has a similar obligation regarding meticulous providence in order to be good encounters several serious problems, especially with respect to the soul-building Sterba wants to preserve. I conclude by considering Sterba’s reply in terms of a limited application of meticulous providence. (shrink)

“Clinical ethics consultants” have been practicing in the United States for about 50 years. Most of the earliest consultants—the “pioneers”—were “outsiders” when they first appeared at patients' bedsides and in the clinic. However, if they were outsiders initially, they acclimated to the clinical setting and became “insiders” very quickly. Moreover, there was some tension between traditional academics and those doing applied ethics about whether there was sufficient “critical distance” for appropriate reflection about the complex medical ethics dilemmas of the day (...) if one were involved in the decision making. Again, the pioneers deflected concerns by identifying and instituting safeguards to assure professional objectivity in clinical ethics consultation services. One might suggest that in moving inside and establishing normative practices, the pioneer clinical ethics consultants anticipated adoption of their routines and professionalization of the field. (shrink)

Current debate on business ethics in Australia continues apace as the excesses of the 1980s are exposed. Codes of Ethics have been a high profile instrument in the American business scene. A survey of Australia''s largest business corporations reveals a different situation. Codes are not as commonly used, tend to refer to legal requirements and do not have as high a profile within the corporation. Given the changing legal framework in Australia a greater role for Codes of Ethics may emerge.

Rightness, not familiarity, is the feeling of knowing. Rightness and familiarity are distinct at both the functional and phenomenological levels of analysis. In problem solving, for example, an unfamiliar solution can still feel right. Rightness is the fringe experience permeating all cases of felt meaning in consciousness, and can occur even when the retrieval of specific content is for whatever reason blocked (e.g., in a tip of the tongue experience). For the most extensive published treatment of rightness and fringe experience, (...) see Mangan (2003): "The conscious 'fringe': Bringing William James up to date" in Essential Sources in the Scientific Study of Consciousness, MIT press. (shrink)

Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia’s second (...) law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. (shrink)

The alleged conflict between religion and science most pointedly focuses on what it is to be human. Western philosophical thought regarding this has progressed through three broad stages: mind/body dualism, Neo-Darwinism, and most recently strong artificial intelligence (AI). I trace these views with respect to their relation to Christian views of humans, suggesting that while the first two might be compatible with Christian thought, strong AI presents serious challenges to a Christian understanding of personhood, including our freedom to choose, moral (...) choice itself, self-consciousness, and the relevance of God to our beginning, being, and ending. (shrink)

The Great Psychotherapy Debate: Models, Methods, and Findings comprehensively reviews the research on psychotherapy to dispute the commonly held view that the benefits of psychotherapy are derived from the specific ingredients contained in a given treatment (medical model). The author reviews the literature related to the absolute efficacy of psychotherapy, the relative efficacy of various treatments, the specificity of ingredients contained in established therapies, effects due to common factors, such as the working alliance, adherence and allegiance to the therapeutic protocol, (...) and effects that are produced by different therapists. In each case, the evidence convincingly corroborates the contextual model and disconfirms the prevailing medical model. (shrink)

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center'' – we describe two serious flaws in the Principia's argument (...) for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given'' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.''. (shrink)

Center for Humans and Nature, 109 West 77th Street, Suite 2, New York, NY 10024, USA. Tel.: 212 362 7170; Fax: 212 362 9592; Email: brucejennings{at}humansandnature.org ' + u + '@' + d + ' '//--> . Abstract A fundamental question for the ethical foundations of public health concerns the moral justification for limiting or overriding individual liberty. What might justify overriding the individual moral claim to non-interference or to self-realization? This paper argues that the libertarian justification for limiting individual (...) liberty known as the ‘harm principle’ or the ‘Millian paradigm’ is inadequate as a basis of public health ethics and policy. But simply pitting some collectivist value or utilitarian criterion over against individual liberty is not theoretically satisfactory, either. John Stuart Mill himself was not a Millian, in this sense, and his utilitarianism does not pit itself against individual liberty as a situation of balancing conflicting values. A reconsideration of Mill, particularly in light of the later work of Berlin on liberty, points toward a conception of relational liberty that is crucial for public health ethics because it contains within itself the basis for its own moral limitation. CiteULike Connotea Del.icio.us What's this? (shrink)

I argue that the atheological claim that the existence of pain and suffering either contradicts or makes improbable God's existence or his possession of certain critical properties cannot be sustained. The construction of a theodicy for both moral and natural evils is the focus of the central part of the book. In the final chapters I analyze the concept of the best possible world and the properties of goodness and omnipotence insofar as they are predicated of God.

This book is an important contribution to the philosophy of music. Whereas most books in this field focus on the creation and reproduction of music, Bruce Benson's concern is the phenomenology of music making as an activity. He offers the radical thesis that it is improvisation that is primary in the moment of music making. Succinct and lucid, the book brings together a wide range of musical examples from classical music, jazz, early music and other genres. It offers a (...) rich tapestry incorporating both analytic and continental philosophy, musicology and performance-practice issues. It will be a provocative read for philosophers of art and musicologists and, because it eschews technicality, should appeal to general readers, especially those who perform. (shrink)

We ask God to involve himself providentially in our lives, yet we cherish our freedom to choose and act. Employing both theological reflection and philosophical analysis, the author explores how to resolve the interesting and provocative puzzles arising from these seemingly conflicting desires. He inquires what sovereignty means and how sovereigns balance their power and prerogatives with the free responses of their subjects. Since we are physically embodied in a physical world, we also need to ask how this is compatible (...) with our being free agents. Providence raises questions about God's fundamental attributes. The author considers what it means to affirm God's goodness as logically contingent, how being almighty interfaces with God's self-limitation, and the persistent problems that arise from claiming that God foreknows the future. Discussion of these divine properties spills over into the related issues of why God allows, or even causes, pain and suffering; why, if God is all-knowing, we need to petition God repeatedly and encounter so many unanswered prayers; and how miracles, as ways God acts in the world, are possible and knowable. Throughout, the author looks at Scripture and attends to how providence deepens our understanding of God and enriches our lives. (shrink)

In this paper I consider several versions of the argument from evil against the existence of a God who is omniscient, omnipotent and wholly good and raise some objections to them. Then I offer my own version of the argument from evil that says that if God exists, nothing happens that he should have prevented from happening and that he should have prevented the brutal rape and murder of a certain little girl if he exists. Since it was not prevented, (...) God does not exist. My conclusion rests on the claim that no outweighing good was served by allowing that murder, or any other instance of comparable evil, to occur. I take up the objection that my argument moves illicitly from apparently pointless suffering to the claim that there is reason to believe that there is pointless suffering. I offer an example to show that the existence of apparently pointless suffering counts to some extent against the existence of God and to show that no basic belief that God exists that rests on certain sorts of grounds can remain justified in the face of apparently pointless suffering. (shrink)

Innovation is fundamental to cumulative culture, allowing progressive modification of existing technology. The authors define innovation as an asocial process, uninfluenced by social information. We argue that innovation is inherently social – innovation is frequently the product of modifying others' outputs, and successful innovations are acquired by others. Research should target examination of the cognitive underpinnings of socially-mediated innovations.

It is a truism that where one starts from and the direction one goes determines where one ends up. This is no less true in philosophy than elsewhere, and certainly no less true in matters dealing with the relationship between God’s foreknowledge and human free actions. In what follows I will argue that the incompatibilist view that Fischer and others stalwartly defend results from the particular starting point they choose, and that if one adopts a different starting point about divine (...) knowledge the logical incompatibility they envision and philosophically anguish over evaporates. (shrink)

This essay examines the goals of care and the exercise of guardianship authority in the long-term care of persons with Alzheimer's disease and other forms of chronic, progressive dementia. It counters philosophical views that deny both agency and personhood to individuals with Alzheimer's on definitional or analytic conceptual grounds. It develops a specific conception of the quality of life and offers a critique of hedonic conceptions of quality of life and models of guardianship that are based on a hedonic legal (...) standard of “best interests.” As an alternative, it proposes a conception of quality of life based on the notions of “semantic agency” and “memorial personhood.”. (shrink)

How do the arts inform and cultivate our service to God? In this addition to an award-winning series, distinguished philosopher Bruce Ellis Benson rethinks what it means to be artistic. Rather than viewing art as practiced by the few, he recovers the ancient Christian idea of presenting ourselves to God as works of art, reenvisioning art as the very core of our being: God calls us to improvise as living works of art. Benson also examines the nature of liturgy (...) and connects art and liturgy in a new way. This book will appeal to philosophy, worship/liturgy, art, music, and theology students as well as readers interested in engaging issues of worship and aesthetics in a postmodern context, including Christian artists and worship leaders. (shrink)

Abstract.As an undergraduate at Cambridge, Newton entered into his ‘Waste Book’ an assumption that we have named the Equivalence Assumption (The Younger): ‘‘ If a body move progressively in some crooked line [about a center of motion]..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent.’’ In this assumption, Newton somewhat imprecisely describes two (...) mathematical models, a ‘‘polygonal limit model’’ and a ‘‘tangent deflected model,’’ for ‘‘one-body motion,’’ that is, for the motion of a ‘‘body in orbit about a fixed center,’’ and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton’s work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz’s ‘‘polygonal model’’ of one-body motion; then to repair Newton’s argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in ‘‘De motu’’ and the Principia. (shrink)

Introduction: Philosophy-in-place -- Tradition in the periphery -- Questioning reason -- Wisdom is actually thought -- Culture and the problem of universality -- Listening to language -- Practicality : African philosophy's debts and duties -- Locating African philosophy.

The book's key questions concern whether we have a right to believe whatever we choose and whether we have significant control over our beliefs. After exploring four case studies in which the question of a right to believe arises and querying what epistemic obligations are, we consider how epistemic obligations might be grounded, whether in prudence, morality, or human virtues. Some argue that epistemic excellence is less concerned with our obligations to believe the truth and avoid falsehood than with seeing (...) that the beliefs we hold are justified. We argue that our epistemic responsibility is best fulfilled somewhere in between the strict objectivist and strict subjectivist views. We proceed to defend the thesis that we have not only indirect but direct control over our beliefs. We then examine the nature of belief, contending for belief as both disposition and an action. In the final chapter we discuss the relation between epistemic obligations and moral accountability. (shrink)

Attempts to resolve the problem of evil often appeal to a greater good, according to which God’s permission of moral and natural evil is justified because (and just in case) the evil that is permitted is necessary for the realization of some greater good. In the extensive litany of greater good theodicies and defenses, the appeal to the greater good of an afterlife of infinite reward or pleasure has played a minor role in Christian thought but a more important role (...) in Islamic thought. In a recent article, Seyyed Jaaber Mousavirad invites us to reconsider a greater good theodicy of compensation. He contends that not only are all evils justified in that God compensates the sufferer in an afterlife, but because evils experienced produce some good, God has reason for bringing about or allowing evils in the first place (Mousavirad 211). In what follows I argue that this modified compensation theodicy is flawed in its premises, faces serious problems about its concept of justice, treats people as means only and not as intrinsically valuable, and ultimately fails to show that an afterlife compensation, along with some good produced here and now by evil, justify God bringing about or allowing evil. (shrink)

The language of propositional modal logic is extended by the introduction of sequents. Validity of a modal sequent on a frame is defined, and modal sequent-axiomatic classes of frames are introduced. Through the use of modal algebras and general frames, a study of the properties of such classes is begun.

Physicists and historians of science have always held that Isaac Newton should receive credit for the first proof that inverse-square orbits must be conics. This conviction derives from a brief argument, regarded as essentially correct, given by Newton in the Principia. Recently, however, it has been contended that this outline or sketch contains irreparable logical flaws. Here, the logical structure of this outline of Newton's, as well as the details that this outline omits, are carefully examined. We find that whilst (...) his argument does indeed contain a flaw, it is a minor omission rather than a serious logical error. Having rectified this omission, we show how Newton's outline expands into a convincing proof that inverse-square orbits must be conics. (shrink)

argues that correlated interactions are necessary for group selection. His argument turns on a particular procedure for measuring the strength of selection, and employs a restricted conception of correlated interaction. It is here shown that the procedure in question is unreliable, and that while related procedures are reliable in special contexts, they do not require correlated interactions for group selection to occur. It is also shown that none of these procedures, all of which employ partial regression methods, are reliable when (...) correlated interactions of a specific kind arise, and it is argued that such correlated interactions will likely be ubiquitous in natural populations. Introduction Process and Product Fitness, Mean Fitness, and Phenotypic Change Correlated Interactions Causation Implications CiteULike Connotea Del.icio.us What's this? (shrink)

After preparing the way with comments on evanescent quantities and then Newton’s interpretation of his second law, this study of Proposition II (Book I)— Proposition II Every body that moves in some curved line described in a plane and, by a radius drawn to a point, either unmoving or moving uniformly forward with a rectilinear motion, describes areas around that point proportional to the times, is urged by a centripetal force tending toward that same point. —asks and answers the following (...) questions: When does a version of Proposition II first appear in Newton’s work? What revisions bring that initial version to the final form in the 1726 Principia? What, exactly, does this proposition assert? In particular, what does Newton mean by the motion of a body “urged by a centripetal force”? Does it assert a true mathematical claim? If not, what revision makes it true? Does the demonstration of Proposition II persuade? Is it as convincing, for example, as the most convincing arguments of the Principia? If not, what revisions would make the demonstration more persuasive? What is the importance of Proposition II, to the physics of Book III and the mathematics of Book I? (shrink)

Over the course of his work, Graham Oppy developed numerous important criticisms of versions of the cosmological argument. Here I am not concerned with his specific criticisms of cosmological arguments but rather with his claim that cosmological arguments per se are not good arguments, for they provide no persuasive reason for believing the conclusion that God exists and are embedded in theories that already affirm the conclusion. I explore what he believes makes an argument good, contend that cosmological arguments can (...) have functions within worldviews other than persuasion, and consider his recent modifications of the discussion that address competing worldviews. (shrink)

Experts play an important role in society, but there has been little investigation about the nature of expertise. I argue that there are two kinds of experts: those whose expertise is a function of what theyknow (epistemic expertise), or what theydo (performative expertise). Epistemic expertise is the capacity to provide strong justifications for a range of propositions in a domain, while performative expertise is the capacity to perform a skill well according to the rules and virtues of a practice. Both (...) epistemic and performative experts may legitimately disagree with one another, and the two senses are conceptually and logically distinct. (shrink)

The design argument was rebutted by David Hume. He argued that the world and its contents (such as organisms) were not analogous to human artifacts. Hume further suggested that there were equally plausible alternatives to design to explain the organized complexity of the cosmos, such as random processes in multiple universes, or that matter could have inherent properties to self-organize, absent any external crafting. William Paley, writing after Hume, argued that the functional complexity of living beings, however, defied naturalistic explanations. (...) In effect he dared anyone to come up with an alternative to his inference to design, and hence a designer, outside of nature. Charles Darwin explained the apparent design of functional complexity by his theory of natural selection. Asa Gray, however, in essays as well as in correspondence with Darwin argued that natural selection allowed for a type of ' evolutionary teleology' in which design at most could be considered the result of universal principles. F. E. Hicks updated Hume by specifically objecting to the use of design arguments by Paley. Hicks argued that the apparent design seen in nature reflected order at a deep level in nature. The design argument was briefly revived by Lawrence Henderson early in the twentieth century but he ultimately concluded that design and teleology were not necessarily mutually entailing and he retracted his design argument in favor of one that he termed ' natural teleology'. The current claims of ' intelligent design' have the same logical problems that have beset previous design arguments. If design is divorced from teleology and its discontents put behind us, then there is a possibility that the latter can have a place in the development of theories to explain the phenomena of emergent complexity. (shrink)

I first discuss the Buddhist concept of the self as lying between nihilism and substantialism, understood in terms of sets of skandhas and later momentariness. I then discuss the role of karma as a causal nexus that brings the skandhas into a state of co-ordination and whether this role is subjective or objective. Finally, I discuss the import of this view that there is no substantial self but only momentary events of various discrete sorts on the meaning and possibility of (...) life after death and the rootedness of the law of karma in justice. Finally, I consider the implications of this for rebirth and nirvana. (shrink)

The development of atomic bombs under the auspices of the U.S. Army's Manhattan Project during World War II is considered to be the outstanding news story of the twentieth century. In this book, a physicist and expert on the history of the Project presents a comprehensive overview of this momentous achievement. The first three chapters cover the history of nuclear physics from the discovery of radioactivity to the discovery of fission, and would be ideal for instructors of a sophomore-level "Modern (...) Physics" course. Student-level exercises at the ends of the chapters are accompanied by answers. Chapter 7 covers the physics of first-generation fission weapons at a similar level, again accompanied by exercises and answers. For the interested layman and for non-science students and instructors, the book includes extensive qualitative material on the history, organization, implementation, and results of the Manhattan Project and the Hiroshima and Nagasaki bombing missions. The reader also learns about the legacy of the Project as reflected in the current world stockpiles of nuclear weapons. This second edition contains important revisions and additions, including a new chapter on the German atomic bomb program and new sections on British and Canadian contributions to the Manhattan project and on feed materials. Several other sections have been expanded; reader feedback has been helpful in introducing minor corrections and improved explanations; and, last but not least, the second edition includes a detailed index. (shrink)

The paper reaches two main conclusions: Firstly, even if there are one or more possible worlds than which there are none better, God cannot actualise any of them. Secondly, if there are possible worlds which God can actualise, and than which God can actualise none better, then God must actualise one of them. The paper is neutral between compatibilist and libertarian views of creaturely freedom. The paper's main ideas have been used, with modifications, in my book "God, the Best, and (...) Evil" (OUP 2008). (shrink)

Two main questions are addressed: (1) What standard defines the nonmoral good for humans, the prudentially rational life? (2) How is this standard applied in guiding and in assessing lives? The standard presented is “The Worthwhileness Principle,” which asserts that if one’s life situation is sufficiently fortunate, the aim is to maximize worthwhileness, the net balance of benefits over costs; but if one’s life situation is chronically, and substantially unfortunate, the aim is to minimize nonworthwhileness, the net balance of costs (...) over benefits. The principle is based on a two-sided, positivity and negativity, or cost-and-benefit-centered viewpoint, rather than a one-sided, good-centered viewpoint. Specifically, it includes negative ends, harms to be avoided, negative means, resource costs to be minimized, and negative luck, misfortune, unfortunate lives.Regarding the second question, the standard is applied prospectively in guiding lives and activities by means of prudential deliberation, prudential habits, and prudential spontaneity. It is applied retrospectively in assessing whole or partial lives using the Worthwhileness Scale. (shrink)

Principia (Book 1, Sect. 6), Newton's Lemma 28 on the algebraic nonintegrability of ovals has had an unusually mixed reception. Beginning in 1691 with Jakob Bernoulli (who accepted the lemma) and Huygens and Leibniz (who rejected it and offered counterexamples), Lemma 28 has a history of eliciting seemingly contradictory reactions. In more recent times, D.T. Whiteside in 1974 gave an “unchallengeable counterexample,” while the mathematician V.I. Arnol'd in 1987 sided with Bernoulli and called Newton's argument an “astonishingly modern topological proof.” (...) This disagreement mostly stems, we argue, from Newton's vague statement of the lemma. Indeed, we identify several different interpretations of Lemma 28, any one of which Newton may have been intending to assert, and we then test a number of proposed counterexamples to see which, if any, are true counterexamples to one or more of these versions of the lemma. Following this, we study Newton's argument for the lemma to see whether and where it fails to be convincing. In the end, our study of Newton's Lemma 28 provides an answer to the question, Who is right: Huygens, Leibniz, Whiteside and the others who reject the lemma, or Bernoulli, Arnol'd, and the others who accept it? (shrink)