This chapter provides an overview of Thomas Hobbes's materialistic philosophy of mathematics. Hobbes's mathematical ontology rejects the seventeenth century's received view of the subject and his proposed first principles departed quite significantly from the tradition. Hobbes's understanding of geometry as a generalized science of material bodies puts him at odds with the traditional notion that the objects of geometrical investigation are radically distinct from the realm of material things. Hobbes's methodology holds that demonstrative knowledge must be based on definitions that (...) identify the causes of things. Hobbes was quite hostile to the algebraic methods characteristic of Descartes's analytic geometry, and he found fault with some presentations of the “method of indivisibles” that is an important precursor to the calculus. Hobbes approved of Bonaventura Cavalieri's method while dismissing John Wallis's approach as incoherent. The chapter investigates Hobbes's controversy with Wallis. Any discussion of Hobbes's mathematics takes place against the background of his controversy with Wallis. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Infinitesimal Differences: Controversies between Leibniz and his ContemporariesFrançoise Monnoyeur-BroitmanUrsula Goldenbaum and Douglas Jesseph, editors. Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Berlin-New York: Walter de Gruyter, 2008. Pp. vi + 327. Cloth, $109.00.Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected (...) to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt.Many of us know and probably have used the Leibnizian formula: to calculate the area under a curve; this book considers the origin, nature, method, and metaphysics of this formula. The most fascinating question discussed in it is the fiction introduced to define the infinitesimal calculation: in his mature period, Leibniz himself referred to his calculus as “a well-founded fiction.” We learn that he gradually gave up the idea of an actual infinite in favor of describing infinitely small quantities. As a result, the quantities became fictive and finite or indefinite instead of real and infinite, and the process of calculation shifted towards mathematics rather than metaphysics.In the first essay, Richard Arthur compares the calculus of Leibniz and Newton and demonstrates how it was based for both on the development of continuously varying quantity. He also shows how the understanding of this quantity derived from the Archimedean axiom that excludes the existence of actual infinite quantity. Ursula Goldenbaum next demonstrates how Hobbes, with his conatus considered as point and instant, had a direct impact on the Leibnizian conception of continuity; to confirm her interpretation, she includes at the end of her article the “Marginalia or Leibniz comments” on Hobbes. Samuel Levey establishes a connection between the notion of the infinitesimal as a “well-founded fiction” and the law of continuity, arguing that the law of continuity, understood as an extension of Archimedes’ principle, gives a finite foundation to the infinitesimal calculation. O. Bradley Bassler discusses the idea of the differential in terms of infinitely small quantities and the use of proportions between infinitely small and finite quantities in order to measure [End Page 527] the infinitely small; here, differentials are also presented as fictions. Fritz Nagel discusses the methodological sophistication of the calculus and its opponents. His main questions concern the different grades of infinity, quantities regarded as zero, and the infinitesimal as a fiction that can be calculated. Douglas Jesseph considers the reality of the infinitesimal and the “well-founded fiction,” showing how Leibniz methodically constructs infinitesimal quantities without reality by returning to Hobbes’ notion of conatus. Hobbes is, for Jesseph, the initiator of these infinitely small quantities without existence.A second group of essays examines the connection between algebra and geometry in the calculus. Philip Beeley demonstrates how John Wallis, on the path of Cavalieri’s method of the indivisibles, found a way to transform geometric problems into sums of arithmetic sequences. Siegmund Probst expresses the different phases in the discovery of the Leibnizian method. He mentions that Leibniz coined the term ‘infinitesimal’ in 1673, and points out that he did not need the method of indivisibles to find a curve from its given arc, but only a series expansion using differences of higher order. Emily Grosholz looks at how, thanks to his algebraic and geometrical notations of curves, Leibniz could formulate the equation of his infinitesimal calculus. According to Grosholz, Leibniz exploits the ambiguity of notations in order to express the geometrical and dynamical aspect of the calculus. Herbert Breger underlines the novelty and abstract nature of Leibniz’s new method of calculation, showing how the theory of infinitesimals became an algebraic calculus independent of geometry.A final group of articles studies the relationship between the calculus and Leibniz’s physics. François Duchesneau shows how the differential and integral calculus provided a model for the integrative laws of Leibniz’s... (shrink)

What reasons can a physicist have to reject the principle of a mathematical method, which he nonetheless uses and which he used frequently in his unpublished works? We are concerned here with Galileo’s doubts and objections against Cavalieri’s “geometry of indivisibles.” One may be astonished by Galileo’s behaviour: Cavalieri’s principle is implied by the Galilean mathematization of naturally accelerated motion; some Galilean demonstrations in fact hinge on it. Yet, in the Discorsi Galileo seems to be opposed to this principle. (...) e fundamental reason of Galileo’s reluctance with respect to Cavalieri’s geometry is to be sought in Galileo’s ideal of intelligibility. It is true that Galilean physics, and more particularly Galileo’s theories of motion and matter, faces deep paradoxes, which Cavalieri’s geometry succeeds to avoid, thanks to a clear determination of the concept of “aggregatum.” But while avoiding these difficulties, Cavalieri does not furnish any solution for the problems raised by Galilean physics. (shrink)

Hobbes intended and expected De Corpore to secure his place among the foremost mathematicians of his era. This is evident from the content of Part III of the work, which contains putative solutions to the most eagerly sought mathematical results of the seventeenth century. It is well known that Hobbes failed abysmally in his attempts to solve problems of this sort, but it is not generally understood that the mathematics of De Corpore is closely connected with the work of some (...) of seventeenth-century Europe’s most important mathematicians. This paper investigates the connection between the main mathematical chapters of De Corpore and the work of Galileo Galilei, Bonaventura Cavalieri, and Gilles Personne de Roberval. I show that Hobbes’s approach in Chapter 16 borrows heavily from Galileo’s Two New Sciences, while his treatment of “deficient figures’ in Chapter 17 is nearly identical in method to Cavalieri’s Exercitationes Geometricae Sex. Further, I argue that Hobbes’s attempt to determine the arc length of the parabola in Chapter 18 is intended to use Roberval’s methods to generate a more general result than one that Roberval himself had achieved in the 1640s. I claim Hobbes was convinced that his first principles had led him to discover a “method of motion” that he mistakenly thought could solve any geometric problem with elementary constructions. (shrink)

Critical discussion of J.M.E. Moravcsik's paper on Plato's method of division.

How much do animals matter--morally? Can we keep considering them as second class beings, to be used merely for our benefit? Or, should we offer them some form of moral egalitarianism? Inserting itself into the passionate debate over animal rights, this fascinating, provocative work by renowned scholar Paola Cavalieri advances a radical proposal: that we extend basic human rights to the nonhuman animals we currently treat as "things." Cavalieri first goes back in time, tracing the roots of the debate from (...) the 1970s, then explores not only the ethical but also the scientific viewpoints, examining the debate's precedents in mainstream Western philosophy. She considers the main proposals of reform that recently have been advanced within the framework of today's prevailing ethical perspectives. Are these proposals satisfying? Cavalieri says no, claiming that it is necessary to go beyond the traditional opposition between utilitarianism and Kantianism and focus on the question of fundamental moral protection. In the case of human beings, such protection is granted within the widely shared moral doctrine of universal human rights' theory. Cavalieri argues that if we examine closely this theory, we will discover that its very logic extends to nonhuman animals as beings who are owed basic moral and legal rights and that, as a result, human rights are not human after all. (shrink)

"This book provides new interpretations of Heidegger's philosophical method in light of 20th-century postmodernism and 21st-century speculative realism. In doing so, it raises important questions about philosophical method in the age of global warming and climate change. Vincent Blok addresses topics that have yet to be extensively discussed in Heidegger scholarship, including Heidegger's method of questioning, the religious character of Heidegger's philosophical method and Heidegger's conceptualization of philosophical method as explorative confrontation. He is also critical (...) of Heidegger's conceptuality and develops a post-Heideggerian concept of philosophical method, which provides a new perspective on the role of willing, poetry and earth-interest in contemporary philosophy. This earth-interest turns out to be particularly important to consider and leads to critical reflections on Heidegger's concept of Earth, the necessity of Earth-interest in contemporary philosophy and a post-Heideggerian concept of the Earth. Heidegger's Concept of Philosophical Method will be of interest primarily to Heidegger scholars and graduate students, but its discussion of philosophical method and environmental philosophy will also appeal to scholars in other disciplines and areas of philosophy"--. (shrink)

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

Descartes’s Method: The Formation of the Subject of Science provides a systematic interpretation of Descartes’s method in Rules for the Direction of the Mind and related texts. The book reconstructs Descartes’s method in its entirety and concretely demonstrates both the efficacy of the method in the sciences as well as the unity of the method from Rules for the Direction of the Mind (1620s) to Principles of Philosophy (1644). The principal thesis of the book is (...) that Descartes’s method is a problem-solving cognitive disposition (or habitus) that can be actualized in a variety of well-defined ways, depending always on the nature of problem. The book divides into five parts and eleven chapters. Parts I–II (Chapters 1–4) develop an interpretation of the historical and conceptual foundations of Descartes’s method (its operations and acquisition), while the remainder of the book (Parts III–V, which include Chapters 5–11) demonstrates the fruits of the method in solutions to problems in the sciences (above all, mathematics and optics). (shrink)

Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to explain, but (...) also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progress toward Laplace's ideal limit of a final theory of everything, and is not threatened by the classic argument against convergent realism. Newton's method endorses the radical theoretical transformation from his theory to Einstein's. Harper argues that it is strikingly realized in the development and application of testing frameworks for relativistic theories of gravity, and very much at work in cosmology today. (shrink)

The purpose of this study was to illuminate the ethically difficult situations experienced by care providers working in a nursing home. Individual interviews using a narrative approach were conducted. A phenomenological-hermeneutic method developed for researching life experience was applied in the analysis. The findings showed that care providers experience ethical challenges in their everyday work. The informants in this study found the balance between the ideal, autonomy and dignity to be a daily problem. They defined the culture they work (...) in as not supportive. They also thought they were not being seen and heard in situations where they disagree with the basic values of the organization. The results are discussed in terms of Habermas’s understanding of modern society. Care settings for elderly people obviously present ethical challenges, particularly in the case of those suffering from dementia. The care provider participants in this study expressed frustration and feelings of powerlessness. It is possible to understand their experiences in terms of Habermas’s theory of modern society and the concept of the system’s colonization of the life world. (shrink)

ABSTRACTThis paper argues that Machiavelli's method, his inductive and comparative use of history and experience for political analysis, and his fashioning of historical-political analysis as ‘science’, played an important and still unrecognised role in his reception in the sixteenth century. It makes the case that Machiavelli's inductive reasoning and stress on historia and experientia offered a model for scientific method that open-minded sixteenth-century scholars, eager to understand, organise and augment human knowledge, could fit to their own epistemology. By (...) focusing on the question of method—a crucial issue for sixteenth-century contemporaries—the paper offers more than a key to the understanding of Machiavelli's positive reception. It also helps in apprehending the crucial importance of Lucretius to Machiavelli's scholarship; the role of the late Renaissance fascination with historia in his reception; and the breadth of appropriation of his method exactly in the decades when anti-Machiavellianism became official politics all over Europe. These claims are sustained through the cases of Machiavelli's early translators and promulgators; the French legal humanists and historiographers; the Swiss, Italian and French scholars engaging with medicine, Paracelsism and astronomy; the authors of political maxims from all over Europe; and finally Francis Bacon. (shrink)

Introduction:To meet and take care of people with dementia implicate professional and moral challenges for caregivers. Using force happens daily. However, staff also encounter challenges with the management in the units. Managing the caretaking function is also significant in how caretakers experience working in dementia care.Purpose:The purpose of this study is to explore the caregiver’s experiences with ethical challenges in dementia care settings and the significance of professional leadership in this context.Method:The design is qualitative, and data appear through narrative (...) interviews. A total of 23 caretakers participated in the study. The transcribed interviews were subjected to a phenomenological-hermeneutical interpretation.Ethical considerations:The respondents signed an informed consent for participation prior to the interviews. They were assured anonymity and confidentiality in the publication of the data. Ricoeur’s method for interpretation ensures anonymity as the researcher relates to the data as one collective text. The study is part of a larger research project in ethics, in its entirety approved in line with the Helsinki Convention.Results:The findings show that the caretakers experienced inadequacy. Some of them described a negative work atmosphere where they experienced that their leaders did not take them seriously. Because of this, informal negative sub-groups functioned as an exclusive debriefing arena. Some of the informants described the opposite experience where the leaders actively supported them.Discussion:The analyses of the findings are discussed in light of the concepts of trust and mistrust in leadership.Conclusion:There is a correlation between the leadership and the caregivers’ experience of being in difficult situations. (shrink)

One staple of living in our information society is having access to the web. Web-connected devices interpret our queries and retrieve information from the web in response. Today’s web devices even purport to answer our queries directly without requiring us to comb through search results in order to find the information we want. How do we know whether a web device is trustworthy? One way to know is to learn why the device is trustworthy by inspecting its inner workings, 156–170 (...) 1995; Humphreys 2004, Episteme, 6, 221–229 2009). But ordinary users of web devices cannot inspect their inner workings because of their scale, complexity, and the corporate secrecy which enshrouds both the procedures by which the devices operate and the companies that make them. Further piling on this predicament, authors have criticized web technology on the grounds that the invisibility of the web devices’ inner workings prevents users from critically assessing the procedures that produce a given output, in some cases, barring users from fulfilling their epistemic responsibilities, 343–355 2010; Miller and Record Episteme, 10, 117–134 2013). I consider four broad kinds of reasons which we can acquire without inspecting the inner workings of black-boxed technology: individual understanding, expert testimony, testing through experience, and social vetting; and show how each is a viable method of appraising black-boxed technology. By deploying these methods, we can remain responsible inquirers while nonetheless benefitting from today’s epistemic resources on the web. (shrink)

The scope of this study is both ambitious and modest. One of its ambitions is to reintegrate Hegel's theory of knowledge into main stream epist~ology. Hegel's views were formed in consideration of Classical Skepticism and Modern epistemology, and he frequently presupposes great familiarity with other views and the difficulties they face. Setting Hegel's discussion in the context of both traditional and contemporary epistemology is therefore necessary for correctly interpreting his issues, arguments, and views. Accordingly, this is an issues-oriented study. I (...) analyze Hegel's problematic and method by placing them in the context of Sextus Empiricus, Descartes, Kant, Carnap, and William Alston. I discuss Carnap, rather than a Modern empiricist such as Locke or Hume, for several reasons. One is that Hegel himself refutes a fundamental presupposition of Modern empiricism, the doctrine of "knowledge by acquaintance," in the first chapter of the Phenomenology, a chapter that cannot be reconstructed within the bounds of this study. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means of both (...) manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics. (shrink)

For most commentators, the universality of Descartes’s method goes hand in hand with the uniformity with which it must be applied to any problem in any science. I will henceforth refer to this as the Uniformity Thesis. Finding themselves unable to identify such a uniformly applied method in any of Descartes’s extant treatises, many readers of Descartes have been led to conclude that Descartes’s method played little or no role in Cartesian science. My principle argument will be (...) that Descartes did not, in fact, accept the Uniformity Thesis, and that the relevant textual evidence strongly suggests that he denied it. For Descartes, the method is universal, and can be employed to discover scientia, not because it can or ought to be uniformly applied to any problem in any science, but rather because practice in the method habituates the human ingenium to be sensitive to diff erent kinds of problem, such that the procedure for constructing and resolving a problem can, within definable limits, vary from application to application. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Method and Politics in Plato’s Statesman by M. S. LaneFrancisco J. GonzalezM. S. Lane. Method and Politics in Plato’s Statesman. Cambridge: Cambridge University Press, 1998. Pp. xiii + 229. Cloth, $59.95.This rewarding book not only is another sign of growing interest in the Statesman, but also does much to justify this interest. The reasons for the dialogue’s relative neglect until recently are easily stated: readers have (...) been puzzled by the amount of space devoted to method in a dialogue ostensibly about politics; furthermore, they have found both the method and the politics highly unsatisfactory. Lane addresses each of these concerns. She continually draws our attention to the unity of method and politics in the dialogue: the limitations of the Stranger’s initial divisions are shown to be equally methodological and political (44–5); the cosmic story is shown to be flawed by a political prejudice (the traditional model of king as shepherd), which turns into a methodological prejudice (the telling of a story too long to be profitably used as an example; 9–10, 121–3); the capacities ultimately shown to be necessary for a successful inquiry (division, exemplification, and finding the mean) also prove to be essential requirements of political knowledge (143–4, 202).Lane’s major contribution to our understanding of the dialogue’s method is her demonstration of the central role played by example (paradeigma). Lane expresses a common objection to the method of division: “But how to choose just which apparently similar things or names to investigate? Similarities are ubiquitous; there is some respect in which everything is similar to everything else. What is more, it is usually on the basis of prejudice and preconceived ideas … that similarities are distinguished” (75–6). Lane sees example as the solution, since it is precisely the task of an example to fix on those similarities relevant to the aim of the inquiry (76, 86–7).This is a very appealing solution, but one must wonder if it does not simply postpone the problem. To choose the right example, must we not make assumptions about which similarities are relevant to defining the object of inquiry and therefore about the nature of this object? And may not these assumptions be no more than prejudices or preconceived ideas? While the Stranger indeed develops his own example of weaving to an extent unparalleled in other dialogues (93), that there are essential similarities between statecraft and weaving appears to be more assumed than demonstrated by the example.With regard to politics, Lane provides a very illuminating account of the dialogue’s characterization of political expertise as certain knowledge of the good in a temporal context, or the kairos. She shows in what way this “knowledge of timing” (142) both is distinct from, and rules over, other contenders for the title of statecraft (such as rhetoric and strategy).Since, however, the existence of a statesman possessing such political expertise is, from the dialogue’s perspective, “a logical but unlikely possibility” (111) and, “from a [End Page 159] modern perspective,” seemingly impossible (4–5), the practical value of the Stranger’s political theory depends on his claim that the regimes which do exist can ‘imitate’ this ideal (300e11–301a3). But how? Even the second-best regimes are characterized by strict adherence to laws based on nothing more than persuasion, experiment and majority consensus (300b1–6), while in the ideal regime a knowledgeable statesman creates laws only as “memoranda” which he is entitled to revise or revoke at any time. According to Lane there is nevertheless one similarity that allows the second-best regimes to be called “second-order imitations” (see 109–111) of the ideal: both will not change laws without expert advice (158–9). This assumes that the second-best regimes acknowledge the authority of a political expert to change the laws, should one appear, an assumption that Lane reiterates throughout the book (11, 111, 114, 139, 147).Yet it is precisely this assumption that appears to be refuted by the thought-experiment at 298a–299e. The Stranger describes a city in which the practice of medicine, navigation and the other technai must adhere strictly to laws... (shrink)

Virginia Held, in How Terrorism Is Wrong: Morality and Political Violence, proposes a method by which moral theories can be "tested" by moral experience. Building on her previous work, she considers here how to utilize this method in the moral assessment of terrorism. Held's method is morally pluralistic; it encompasses a variety of moral theories and principles, including care ethics. Held's evolving account of how to test moral theories in terms of real-world moral experience remains an important (...) and welcome contribution of hers to moral theory. Anyone who thinks rational intuition is not enough to determine which moral principles are justified, or who distrusts the moral "tests" that involve bizarre hypothetical examples devised by philosophers in armchairs, should consider Held's experiential moral method. If daily lived experience really matters to moral theorizing—and how could it not?—then we need an account of how to interpret our experiences morally, how to "test" moral judgments in terms of those experiences, and how best to revise our moral convictions in light of further experiences. (shrink)

What, then, is the method of Hegel's PhG if it is not dialectical? Insofar as it can be characterized in a word, it is descriptive. The study of a science, in Hegel's sense, requires that the student, through a tremendous effort of restraint, give himself completely over to the structural development of that science itself. This, I take it, is what Hegel means by the famous phrase "die Anstrengung des Begriffs". The true philosopher must strenuously avoid the temptation of (...) interrupting the immanent development of the subject-matter by the introjection of interpretive models; he must rather give up this instinctively felt prerogative or "freedom" and "instead of being the arbitrarily moving principle of the content," his task is "to submerge this freedom in the content and let the content be moved through its own nature, i.e., through the self as the self of the content, and to observe this movement". (shrink)

Errol Harris talks about a crypto-dialectic method that lies behind the geometrical disguise of Spinoza'sEthics.Spinoza's method, he argues, is not the linear formal deduction of traditional logic but a crypto-dialectical development of the structural implications of a systematic whole. Substance differentiates itself into infinite attributes and infinite modes. Each attribute is self-differentiated into a hierarchy of modes ranging from the most complex to the simplest. Harris calls this a dialectical scale or a crypto-dialectical development of the structural implications (...) of a systematic whole. The self-specification of the whole into attributes and modes provides the framework for a dialectical system. Spinoza's hypotheses are implications dialectically derived from his concept of substance, a concept of a whole which differentiates itself into infinite attributes and modes. Substance is not a hypothesis but is a postulate which s i absolutely certain. Everything follows from substance with dialectical necessity. Substance is the origin of all things and ideas. (shrink)

Summary A famous debate between John Ray, Joseph Pitton de Tournefort and Augustus Quirinus Rivinus at the end of the seventeenth century has often been referred to as signalling the beginning of a rift between classificatory methods relying on logical division and classificatory methods relying on empirical grouping. Interestingly, a couple of decades later, Linnaeus showed very little excitement in reviewing this debate, and this although he was the first to introduce the terminological distinction of artificial vs. natural methods. In (...) this paper, I will explain Linnaeus's indifference by the fact that earlier debates were revolving around problems of plant diagnosis rather than classification. From Linnaeus's perspective, they were therefore concerned with what he called artificial methods alone ? diagnostic tools, that is, which were artificial no matter which characters were taken into account. The natural method Linnaeus proposed, on the other hand, was not about diagnosis, but about relations of equivalence which played a vital, although largely implicit role in the practices of specimen exchange on which naturalists relied to acquire knowledge of the natural world. (shrink)

Abstract Christopher Gauker has argued that a cause?effect analysis of the acquisition of communication skills in chimpanzees is adequate to describe the data reported in our work at the Language Research Center. I agree that the cause?effect approach to language function is the only viable method of analyzing language. Language must be studied as a process that functions to organize behavior between two or more individuals. However, the problem of language understanding is not addressed satisfactorily by the perspective offered (...) by Gauker. Some more recent work, particularly with the pygmy chimpanzee ?Kanzi?, is now beginning to explicate a cause?effect analysis of language comprehension. It is argued that in the young chimpanzee, as with children, language comprehension is the driving force underlying the language acquisition process. It is further argued that the transition from comprehension to production is made possible by the capacity for goal?directed observational imitation. (shrink)

On the method of Saint Giovanni Bosco, 1815-1888, in guidance and counselling.

The 2017 Commission on Public Relations Education report found new professionals are not meeting employers’ expectations regarding ethics knowledge, skills and abilities. This mixed-method s...

The article addresses some aspects of Gava’s book, highlighting two main points: (1) the notion of philosophy in a cosmic sense; (2) its connection with the meaning of the concept of method. Regarding (1) I show how Gava’s interpretation of the systematic concept of philosophy does not account adequately for the scholastic concept. This has consequences for the notion of philosophy in a cosmic sense itself; its nature as an objective archetype and its personification in the ideal of a (...) master of wisdom are not properly emphasized. These features are closely related to Kant’s claim that philosophy cannot be learned, which is connected with Kant’s peculiar idea of method. Regarding (2), I argue that ‘method’ for Kant does not concern only the construction of scientific systems, but also the establishment of a way of thinking, a stance embracing thought and action. The meaning of the postulates and the notion of ‘faith’ thus acquire a ‘weaker’ connotation, as an attitude, habitus, aimed at the establishment and promotion of a ‘life-structuring’ rationality, and not as an alternative route to a theoretical ‘commitment’. (shrink)

A new method was devised to test object permanence in young infants. Fivemonth-old infants were habituated to a screen that moved back and forth through a 180-degree arc, in the manner of a drawbridge. After infants reached habituation, a box was centered behind the screen. Infants were shown two test events: a possible event and an impossible event. In the possible event, the screen stopped when it reached the occluded box; in the impossible event, the screen moved through the (...) space occupied by the box. The results indicated that infants looked reliably longer at the impossible than at the possible event. This hnding suggested that infants (1) understood that the box continued to exist, in its same location, after it was occluded by the screen, and (2) expected the screen to stop against the occluded box and were surprised, or puzzled, when it failed to do so. A control experiment in which the box was placed next to the screen provided support for this interpretation of the results. Together, the results of these experiments indicate that, contrary to Piaget’s (1954) claims, infants as young as 5 months of age understand that objects continue to exist when occluded. The results, also indicate that 5-month-old infants realize that solid objects do not move through the space occupied by other solid objects. (shrink)

Since the publication of Wahrheit und Methode in 1960 (Tfibingen), Gadamer's hermeneutics has called forth a varied and fruitful response from the Continent, without receiving anything near the same attention from the English-speaking world. Though E. D. Hirsch thought Gadamer sufficiently important in 1965 to merit an early rebuttal and rehabilitation (Validity in Interpretation [New Haven, Conn., 1967], pp. 245-64), Wahrheit und Methode remained unread in England and America, partly because a translation was not available until 1975 (Truth and (...) class='Hi'>Method, ed. Garrett Barden and John Cumming [New York]). Even after that date, Gadamer's influence on Anglo-American debate has been largely secondhand, filtering in through such figures as Paul Ricoeur and Jiurgen Habermas. But a renewed interest in the question of what we are to make of tradition, no doubt spurred in large measure by deconstruction's effort to unmake it, has lent Gadamer a new pertinence. One sign that his stock is on the rise is the publication of Joel Weinsheimer's Gadamer's Hermeneutics, a much needed and admirably written introduction to Truth and Method that should push its value even higher. -- JSTOR (June 12, 2012.). (shrink)

This volume is presented in honour of Heinz Post, who founded a distinc tive and distinguished school of philosophy of science at Chelsea College, University of London. The 'Chelsea tradition' in philosophy of science takes the content of science seriously, as exemplified by the papers presented here. The unifying theme of this work is that of 'Correspondence, Invariance and Heuristics', after the title of a classic and seminal paper by Heinz Post, published in 1971, which is reproduced in this volume (...) with the kind permission of the editors and publishers of Studies in History and Philosophy of Science. Described by Paul Feyerabend in Against Method as "brilliant" and " . . . a partial antidote against the view which I try to defend" (1975, p. 61, fn. 17), this paper, peppered with illustrative examples from the history of science, brings to the fore some of Heinz Post's central concerns: the heuristic criteria used by scientists in constructing their theories, the intertheoretic relationships which these criteria reflect and, in particular, the nature of the correspondence that holds between a theory and its predecessors (and its suc cessors). The appearance of this volume more than twenty years later is an indica tion of the fruitfulness of Post's contribution: philosophers of science continue to explore the issues raised in his 1971 paper. (shrink)

In this paper, I would like to examine the method that Bacon proposes in Novum organum II.1-20 and illustrates with the example of the procedure for discovering the form of heat. One might think of a scientific method as a general schema for research into nature, one that can, in principle, be used independently of the particular conception of the natural world which one adopts, and independently of the particular scientific domain with which one is concerned. Indeed, Bacon (...) himself suggested that as with logic, his method, or as he calls it there his “system of interpreting” is widely applicable to any domain, and not just to natural philosophy. [Novum organum I.127] Now, recent studies of Bacon have emphasized his own natural philosophical commitments, and the underlying conception of nature that runs through his writings. In my essay I argue that the method Bacon illustrates in Novum organum II is deeply connected to this underlying view of nature: far from being a neutral procedure for decoding nature, Bacon’s method is a tool for filling out the details of a natural philosophy built along the broad outlines of the Baconian world view. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Vessel of Honor: The Virgin Birth and the Ecclesiology of Vatican II by Brian A. GraebeAaron Pidel S.J.Vessel of Honor: The Virgin Birth and the Ecclesiology of Vatican II. By Brian A. Graebe (Steubenville, OH: Emmaus Academic, 2021), 351 pp.Though Mary's undiminished virginity in giving birth (virginitas in partu) was long understood to be an event as miraculous and a teaching as authoritative as her virginity in conceiving (...) (virginitas ante partum), virginitas in partu underwent a kind of existential reinterpretation in the middle of the twentieth century. Authors such as Albert Mitterer and Karl Rahner suggested that, physically speaking, Jesus's birth might have happened like any other, rupturing the hymen, distending the birth canal, and causing Mary pain, albeit not in the spiritually disintegrating way common to postlapsarian humanity. These arguments effectively "unsettled" the traditional understanding of virginitas in partu, leading theologians of the highest stature to distinguish between the doctrine itself and the anatomical aspects attached to it over time. Fr. Brian Graebe has written a fine book arguing that the bodily dimensions of the virgin birth, including the physical "seal" of virginity, belong to the substance of the doctrine. This more inclusive understanding not only does better justice to the data of tradition, he argues, but illuminates the ecclesiology of the Second Vatican Council. The book impresses by its theologically reflective method, its clarity of exposition, [End Page 1106] and its depth of research—especially into the archival and antepreparatory sources of Vatican II.Vessel of Honor responds in effect to Rahner's argument that physical intactness is peripheral to the dogmatic core of Mary's virginity in partu. To show otherwise, Rahner contended, one would need to show that such a doctrine can be found directly in the apostolic teaching, or that it, "being implicitly contained therein, has grown out of the apostolic doctrine, by a legitimate historical, logical, and theological process, as its authentic development" (68–69). If the bodily aspects of this doctrine really belonged to the deposit of faith, in other words, one would need to show how they are implied in the traditio divino-apostolica, as well as how they cohere organically with the rest of the deposit. The two major parts of Vessel of Honor respond in turn to each aspect of Rahner's challenge.The first three chapters argue that Mary's bodily integrity in parturition belongs at least implicitly to the traditio divino-apostolica. Turning first to the postapostolic tradition, Fr. Graebe shows that—apart from the early exceptions of Origen and Tertullian—patristic sources either affirm or strongly imply a miraculous delivery. This constant witness culminates in the Lateran Council (649 AD), which, while not itself an ecumenical council, was received into the magisterium of Pope Martin and affirmed by the Third Council of Constantinople (680 AD). Its teaching that Mary "gave birth without corruption" (incorruptibiliter... genuisse) would be defended by Paschasius, Ratramnus, Thomas Aquinas, and others. This consensus remained undisturbed until the eve of Vatican II.Even at Vatican II, Fr. Graebe argues in the next chapter, the Council Fathers intended to reaffirm the more inclusive idea of virginitas in partu against those who would marginalize its bodily dimensions. Here he really breaks new ground, delving deep into the antepreparatory, preparatory, and conciliar drafting history. He shows convincingly that many of the chief drafters of the final formula—"Our Lord, who did not diminish his mother's virginal integrity but sanctified it..." (Lumen Gentium §57)—saw it as excluding Rahner's and Mitterer's minimalizing interpretations. Drawing on material from the Vatican Apostolic Archives, Fr. Graebe shows that some of the very theologians who voted to omit the pointed phrase "in the birth itself" (in ipsomet partu) did so for tonal rather than substantive reasons.The third chapter argues that Mary's physical integrity in birth is to be believed with divine and Catholic faith, despite the ongoing confusion introduced by Rahner and others. Admittedly, Vatican II did not define but merely reaffirmed the traditional understanding of virginitas in partu. But there are other reasons for including it in the traditio divino-apostolica. [End Page 1107] Drawing heavily... (shrink)

In this paper we describe an experimental test of the validity of the Pauli Exclusion Principle (for electrons) which is based on a straightforward idea put forward a few years ago by Ramberg and Snow (Phys. Lett. B 238:438, 1990). We perform a very accurate search of X-rays from the Pauli-forbidden atomic transitions of electrons in the already filled 1S shells of copper atoms. Although the experiment has a very simple structure, it poses deep conceptual and interpretational problems. Here we (...) describe the experimental method and recent experimental results, which we interpret in the framework of quon theory. We also present future plans to upgrade the experimental apparatus using Silicon Drift Detectors. (shrink)

A physician and spokesman for the French Ideologues, Pierre-JeanGeorges Cabanis (1757-1808) stands at the crossroads of several influential developments in modern culture--Enlightenment optimism about human perfectibility, the clinical method in medicine, and the formation and adaptation of liberal social ideals in the French Revolution. This first major study of Cabanis in English traces the influences of these developments on his thought and career. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available (...) previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

A prevailing view in the literature on Hegel’s dialectical method is that employing it involves advancing a false account and then modifying it to be closer to the truth. I will call this the Modification View. In this essay, I argue that the Modification View is incorrect. Hegel’s insight, I show, is that one can only explain the objective validity of a form of thought through employing that very form. Consequently, the dialectical method cannot relate to its subject (...) matter as something given to it, and so cannot involve advancing and then correcting errors in one’s account. (shrink)

Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to explain, but (...) also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically, by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progress toward Laplace's ideal limit of a final theory of everything, and is not threatened by the classic argument against convergent realism. Newton's method endorses the radical theoretical transformation from his theory to Einstein's. Harper argues that it is strikingly realized in the development and application of testing frameworks for relativistic theories of gravity, and very much at work in cosmology today. (shrink)

A problem is posed: Is pleasure choiceworthy, or not? The answerer claims that yes, it is. The questioner must refute him by asking questions—by offering him premises to accept or reject. The questioner succeeds if he forces the answerer to accept a proposition contrary to the one he undertook to defend, and fails if the answerer always accepts or rejects premises in a way consistent with that proposition. To a first approximation, dialectic is the distinctive method of Aristotelian philosophy. (...) At the heart of dialectic is the dialectical deduction. This article discusses Aristotle's philosophical method, focusing on dialectical premises, endoxa, and aporiai. It also examines the uses of dialectic in intellectual training, ordinary discussion, and the philosophical sciences, as well as in regard to scientific starting points or first principles. The article concludes by returning to dialectic and philosophy and an important difference between them. (shrink)

Following our [6], though with somewhat different methods here, further variants of Goodstein sequences are introduced in terms of parameterized Ackermann–Péter functions. Each of the sequences is shown to terminate, and the proof-theoretic strengths of these facts are calibrated by means of ordinal assignments, yielding independence results for a range of theories: PRA, PA,$\Sigma ^1_1$-DC$_0$, ATR$_0$, up to ID$_1$. The key is the so-called “Hardy hierarchy” of proof-theoretic bounding finctions, providing a uniform method for associating Goodstein-type sequences with parameterized (...) normal form representations of positive integers. (shrink)