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 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)

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)

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)

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)

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)

The second edition of The Great Psychotherapy Debate has been updated and revised to include a history of healing practices, medicine, and psychotherapy, an expanded theoretical presentation of the contextual model, an examination of therapist effects, and a thorough review of the research on common factors such as the alliance, expectations, and empathy.

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)

Mass literacy, mass communication, and the Internet have all increased the amount of information available. But false knowledge still abounds. Taking cues from Sir Thomas Browne, the English Renaissance skeptic, this title examines a host of contemporary errors in thinking and offers a powerful explanation of why they occur.

Micheline Sauvage of the French National Scientific Research Centre traces for us the story of this great Athenian and great philosopher, as seen both by his contemporaries and by the European philosophers who followed after him.

The city of Cork experienced a political odyssey between Easter 1916 and the end of 1918. Wartime policies conceived in London manifested themselves unexpectedly in Cork--The Defence of the Realm Act was used to repress political speech; deficit spending generated massive inflation; mandatory arbitration encouraged workers to join trade unions; food rationing panicked a country scarred by the Potato Famine; and military conscription generated virtual rebellion. As a result, the Cork public increasingly turned against the war. The book examines the (...) political situation in Cork prior to the Easter Rising; local reactions to the rebellion; the rapid creation of the Republican mass movement; the dramatic decline of the Irish Party; the explosion of anti-authority street rioting; the mobilization of women in the independence struggle; disturbances against venereal disease treatments and visiting American sailors; the emergence of radical trade unionism; agitation over the retention of local food supplies; the nationalist mobilization during the Conscription Crisis; and Sinn Féin's triumph in the 1918 General Election. (shrink)

A study of Philo and Paul and the first-century sophistic movement.

Offers a compelling vision of how to achieve and conduct a liberal but democratic society through the ideal of Neutrality--between people and ideas of the good--and using the tool of Neutral dialogue.

The article investigates the mathematical and philosophical backdrop of the digital ocean as contemporary model, moving from the digitalized ocean of Georg Cantor’s set theory to that of Alan Turing’s computation theory. It examines in Cantor what is arguably the most rigorous historical attempt to think the structural essence of the continuum, in order to clarify what disappears from the computational paradigm once Turing begins to advocate for the structural irrelevance of this ancient ground.

Since the introduction of mathematical population genetics, its machinery has shaped our fundamental understanding of natural selection. Selection is taken to occur when differential fitnesses produce differential rates of reproductive success, where fitnesses are understood as parameters in a population genetics model. To understand selection is to understand what these parameter values measure and how differences in them lead to frequency changes. I argue that this traditional view is mistaken. The descriptions of natural selection rendered by population genetics models are (...) in general neither predictive nor explanatory and introduce avoidable conceptual confusions. I conclude that a correct understanding of natural selection requires explicitly causal models of reproductive success. *Received May 2006; revised December 2006. †To contact the author, please write to: Department of Philosophy, Kansas State University, 201 Dickens Hall, Manhattan, KS 66506; e‐mail: [email protected] . (shrink)

Contemporary thought has been profoundly shaped by the early-twentieth-century turn toward synchronic models of explanation, which analyze phenomena as they appear at a single moment, rather than diachronically as they develop through time. But the relationship between time and system remains unexplained by the standard account of this shift. Through a new history of systematic thinking across the humanities and sciences, The Writing of Spirit argues that nineteenth-century historicism wasn't simply replaced by a more modern synchronic perspective. The structuralist revolution (...) consisted rather in a turn toward time's absolutely minimal conditions, and thus also toward a new theory of diachrony. Pourciau arrives at this surprising and powerful conclusion through an analysis of language-scientific theories over the course of two centuries, associated with thinkers from Jacob Grimm and Richard Wagner to the Russian Futurists, in domains as disparate as historical linguistics, phonology, acoustics, opera theory, philosophy, poetics, and psychology. The result is a novel contribution to a pressing contemporary question--namely, what role history should play in the interpretation of the present. (shrink)

Editors provide a substantive introduction to the history and theories of perfectionism and neutrality, expertly contextualizing the essays and making the collection accessible.

Voting Institutions Justifications Notes.

I hope to persuade Charles Fried to think again about his developing views on distributive justice. Since I live at a certain remove from Cambridge, the best I can offer is a hypothetical dialogue with an imaginary person whose views seem, to me at least, of a Friedian inspiration. My central question deals with the way Fried establishes his rights to things he candidly concedes he does not deserve. To present my problems, I shall begin with a simpler case than (...) those – involving kidneys and talents – that Fried makes central to his discussion. Rather than starting with these rather special goods, I find it clarifying to focus first on more garden variety commodities – which, to emphasize their character, I shall call apples. (shrink)

This study investigates financial correlates of corporate philanthropy in Fortune 1000 companies using structural equation modeling. The results suggest that cash flow (one of the most discretionary types of organizational slack) has a significant impact on a firm’s cash donations to charitable causes, but monetary donations do not affect firm financial performance. These findings support the accepted view of corporate philanthropy as a discretionary social responsibility and the traditional thinking about firm giving in the business and society literature—that doing well (...) enables doing good. Contrary to some contemporary thinking, the findings imply no significant effect on profits from corporate generosity. (shrink)

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.

This volume for the first time brings the scholarly discipline of comparative religious ethics into constructive collaboration with the community of interreligious dialogue. Its design is premised on two important insights. First, interreligious dialogue offers to comparative religious ethics a new, more persuasive rationale, agenda of issues, and practical orientation. Second, comparative religious ethics offers to interreligious dialogue an arsenal of critical tools and methods which will enhance the sophistication of its practical work. In this way, both theory (a dominant (...) concern and strength of comparative religious ethics) and praxis (a dominant concern and strength of interreligious moral dialogue) are joined together in mutual effort, each contributing to the benefit of the other.The volume’s contributors share this vision of collaboration, drawing explicitly from both communities of discourse in a manner that crosses disciplinary and professional boundaries to deal creatively and constructively with important methodological and global moral issue. Although theory and practice cannot easily be separated in such a collaborative project, for the purpose of clarity, the volume is divided into two main parts. The first specifically engages questions of method, theory, and the social role of the public intellectual; the second, on substantive moral themes and issues, many of which were raised at the 1993 Parliament. Taken together, the volume’s essays articulate and illustrate new ways of approaching contemporary moral concerns cross-culturally yet with a rigor appropriate to our complex and pluralistic world. (shrink)

Philosophy long sought to set knowledge on a firm foundation, through derivation of indubitable truths by infallible rules. For want of such truths and rules, the enterprise foundered. Nevertheless, foundationalism's heirs continue their forbears' quest, seeking security against epistemic misfortune, while their detractors typically espouse unbridled coherentism or facile relativism. Maintaining that neither stance is tenable, Catherine Elgin devises a via media between the absolute and the arbitrary, reconceiving the nature, goals, and methods of epistemology. In Considered Judgment, she argues (...) for a reconception that takes reflective equilibrium as the standard of rational acceptability. A system of thought is in reflective equilibrium when its components are reasonable in light of one another, and the account they comprise is reasonable in light of our antecedent convictions about the subject it concerns.Many epistemologists now concede that certainty is a chimerical goal. But they continue to accept the traditional conception of epistemology's problematic. Elgin suggests that in abandoning the quest for certainty we gain opportunities for a broader epistemological purview--one that comprehends the arts and does justice to the sciences. She contends that metaphor, fiction, emotion, and exemplification often advance understanding in science as well as in art. The range of epistemology is broader and more variegated than is usually recognized. Tenable systems of thought are neither absolute nor arbitrary. Although they afford no guarantees, they are good in the way of belief. (shrink)

Since its publication in 1982, _Beyond Positivism _has become established as one of the definitive statements on economic methodology. The book’s rejection of positivism and its advocacy of pluralism were to have a profound influence in the flowering of work methodology that has taken place in economics in the decade since its publication. This edition contains a new preface outlining the major developments in the area since the book’s first appearance. The book provides the first comprehensive treatment of twentieth century (...) philosophy of science which emphasizes the issues relevant to economics. It proceeds to demonstrate this relevance by reviewing some of the key debates in the area. Having concluded that positivism has to be rejected, the author examines possible alternative bases for economic methodology. Arguing that there is no best method, he advocates methodological pluralism. (shrink)

I present a general theory for the initial domestication of plants and animals that is based on niche construction theory and incorporates several behavioral ecological concepts, including central-place provisioning, resource catchment, resource ownership and defensibility, and traditional ecological knowledge. This theory provides an alternative to, and replacement for, current explanations, including diet breadth models of optimal foraging theory, that are based on an outmoded concept of asymmetrical adaptation and that attempt to explain domestication as an adaptive response to resource imbalance (...) resulting from either environmental decline or human population growth. The small-scale human societies that first domesticated plants and animals share a number of basic interrelated attributes that when considered as an integrated and coherent set of behaviors provide the context for explaining initial domestication not as an adaptive response to an adverse environmental shift or to human population growth or packing but rather as the result of deliberate human enhancement of resource-rich environments in situations where evidence of resource imbalance is absent. (shrink)

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)

In Inhabiting the Earth Foltz undertakes the first sustained analysis of how Heidegger's thought can contribute to environmental ethics and to the more broadly conceived field of environmental philosophy. Through a comprehensive study of the status of "nature" and related concepts such as "earth" in the thought of Martin Heidegger, Foltz attempts to show how Heidegger's understanding of the natural environment and our relation to it offer a more promising basis for environmental philosophy than others that have so far been (...) put forward. Indeed, Dr. Foltz finds that to ecofeminism and social ecology, whose prescriptions are based on historically oriented etiologies of domination and oppression, Heidegger's work offers what is arguably the first comprehensive and nonreductive philosophy of history since Hegel that can embrace both nature and humanity in one narrative, and the first since Augustine that can do this while granting to nature a messure of selfstanding. But it is probably for the environmental philosophies of deep ecology, bioregionalism, and ecological holism that Heidegger's work has the most immediate, as well as the most extensive implications, because it is to them that it has the most affinity. Finally, as a corrective and a major challenge to deep ecology, which has tended to valorize the scientific approach to nature, Heidegger's work provides a sophisticated basis for showing the primacy of the poetic in the task of learning to inhabit the earth rightly. (shrink)

Many of our inherited civic institutions are dead or dying. We need an ambitious reform program to revive democratic life. This essay advances a four-pronged “citizenship agenda”: a campaign finance initiative granting each voter fifty “patriot dollars” to fund candidates and political parties of his or her choice; a proposal for a new national holiday, Deliberation Day, held before each national election, enabling citizens to deliberate on the merits of rival candidates; a system of federally financed electronic news-vouchers to permit (...) professional journalism to survive the destruction of its traditional business model; and a new form of citizenship inheritance, which provides $80,000 to all Americans as they start off life as adults. Working with collaborators, I have developed each of these initiatives at book length. This essay suggests how the “citizenship agenda” yields a whole that is larger than the sum of its parts. (shrink)