Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up (...) on lexicality, problems of the same kind remain. (shrink)

Many of Dworkin’s interlocutors saw his ‘one-system view’, according to which law is a branch of morality, as a radical shift. I argue that it is better seen as a different way of expressing his longstanding view that legal theory is an inherently normative endeavor. Dworkin emphasizes that fact and value are separate domains, and one cannot ground claims of one sort in the other domain. On this view, legal philosophy can only answer questions from within either (...) domain. We cannot ask metaphysical questions about which domain law ‘properly’ belongs in; these would be archimedean, and Dworkin has long argued against archimedeanism. The one-system view, then, is best understood as an invitation to join Dworkin in asking moral questions from within the domain of value. Finally, I argue that Dworkin’s view can be understood as a version of ‘eliminativism’, a growing trend in legal philosophy. (shrink)

Face perception and emotion categorization are widely investigated under laboratory conditions that are devoid of real social interaction. Using mobile eye-tracking glasses in a standardized diagnostic setting while applying the Autism Diagnostic Observation Schedule, we had the opportunity to record gaze behavior of children and adolescents with and without Autism Spectrum Conditions during social interaction. The objective was to investigate differences in eye-gaze behavior between three groups of children and adolescents either with ASC or with unconfirmed diagnosis of ASC or (...) with neurotypical development during social interaction with an adult interviewer in a diagnostic standard situation using the ADOS-2. In a case control study, we used mobile eye-tracking glasses in an ecologically valid and highly standardized diagnostic interview to investigate suspected cases of ASC. After completion of the ASC diagnostic gold standard including the ADOS-2, the participants were assigned to two groups based on their diagnosis and compared with a matched group of neurotypically developed controls. The primary outcome measure is the percentage of total dwell times assessed for different areas of interest with regard to the face and body of a diagnostic interviewer and the surrounding space. Overall, 65 children and adolescents within an age range of 8.3–17.9 years were included in the study. The data revealed significant group differences, especially in the central-face area. Previous investigations under laboratory conditions gave preferential attention to the eye region during face perception to describe differences between ASC and NTD. In this study – using an ecologically valid setting within a standard diagnostic procedure – the results indicate that neurotypically developed controls seem to process faces and facial expressions in a holistic manner originating from the central-face region. Conversely, participants on the Autism Spectrum seem to avoid the central-face region and show unsystematic gaze behavior, not using the preferred landing position in the central-face region as the Archimedean point of face perception. This study uses a new approach, and it will be important to replicate these preliminary findings in future research. (shrink)

Non-Archimedean population axiologies – also known as lexical views – claim (i) that a sufficient number of lives at a very high positive welfare level would be better than any number of lives at a very low positive welfare level and/or (ii) that a sufficient number of lives at a very low negative welfare level would be worse than any number of lives at a very high negative welfare level. Such axiologies are popular because they can avoid the (Negative) (...) Repugnant Conclusion and satisfy the adequacy conditions given in the central impossibility result in population axiology due to Gustaf Arrhenius. I provide a novel argument against them which appeals to the way that good and bad lives can intuitively outweigh one other. (shrink)

According to the orthodox account of meaning and translation in the literature, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well-known skeptical conclusions about translation, objectivity, meaning and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a TEXT-TYPE that does conform to our best (...) translational practices. With their semantic function in view, text-types are Archimedean points for their respective disciplines. The text-type of philosophy is no exception. Culture-transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text-types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy. (shrink)

In A Theory of Justice, John Rawls defines a hypothetical contract situation and argues rational people will agree on reflection it is fair to contractors. He solves the rational choice problem it poses by deriving two lexically-ordered principles of justice and suggests the derivation justifies the principles. Its soundness aside, just what justificatory force does such a derivation have?On one view, there is no justificatory force because the contract is rigged specifically to yield principles which match our pre-contract moral (...) judgments. Rawls provides ammunition for this claim: “By going back and forth, sometimes altering the conditions of the contractual circumstances, at others withdrawing our judgments [about what is just] and conforming them to principle, I assume that eventually we shall find a description of the initial situation that both expresses reasonable conditions and yields principles which match our considered judgments duly pruned and adjusted.”. (shrink)

In this contribution I discuss Hannah Arendt's philosophy of culture in three rounds. First I give an account of my view on Hannah Arendt's main work The Human Condition. In this frame of reference I distance myself from the importance attached to Hannah Arendt as a political philosopher and hold a warm plea for her as a philosopher of culture (I and II). Second I pay attention to her view on science and technology in their cultural meaning, expressed (...) in the last chapter of The Human Condition. This part consists in a summary of her thoughts as I read them (III, IV, and V). After these two rounds I make some critical remarks on Hannah Arendt's interpretation of science and technology. The viewpoint of ?eccentricity? will be discussed as a frame of reference for her philosophy of culture (VI). (shrink)

“The Archimedean point for moral life” discussed in this article refers to the starting point of one's moral reasoning and what ultimately makes moral life possible. The article intends to show that Mengzi's doctrine of the Four Beginnings may throw some light on our search for such an Archimedean point. More specifically, it argues for the following: Mengzi's doctrine of the Four Beginnings actually takes moral sentiments as the Archimedean point for moral life; Mengzi's view of (...) the starting point of moral reasoning and the ultimate ground for moral life not only can be empirically supported to a great extent, but also logically plausible. (shrink)

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, imposes (...) the integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

Critical thinking (CT) is frequently mentioned as a key competence in sustainability curricula. In this context our era is often diagnosed as being ‘post-truth’, indicating an epistemic concern. However, emerging ‘post-sustainable’ views in education indicate that environmental crises are posing increasingly existential concerns, which might partly explain why simple consciousness-raising sometimes faces denial or fails to promote sustainable action. To overcome this challenge, we undertake a philosophical critique of modern (individual, rational, autonomous) subjectivity assumed in CT and much of curricular (...) thinking. We follow the ‘ontological turn’ where criticality means self-reflective questioning of one’s own being-in-the-world. One acute question concerns energy, especially fossil fuels, which constitute much of the autonomous experience of modern, critical subjectivity, while simultaneously endangering the future horizon of that same subjectivity. Climate strikes at schools and the yellow vest movements indicate, in their own ways, how ecologically problematic fossil fuels are bending modern rationality into unpredicted directions. Metaphoric Archimedes and his ‘circles in the sand’ demonstrate the vulnerability of critical thought facing post-sustainability. This vulnerability should be addressed in curriculum theory, since it is interdependent persons—rather than independent subjects—who are open to sustainable transformation and action. (shrink)

Barry Stroud’s book _The Quest for Reality_1 is, I think, the most substantial study of colour realism that has yet been written. It subjects to fundamental criticism a tradition that found its classic expression in Descartes and Locke and which in many ways remains standard today; it argues to be flawed not only the traditional rejection of colours as mere ideas or features of ideas in the mind, but also the view that colours are dispositions or powers in objects (...) to produce ideas in us—which in other quarters sometimes passes as a form of colour realism. Stroud rejects subjectivism, dispositionalism, relativism, and reductionism; but he is deliberately reticent about offering any positive account of what we believe to exist when believe colours to exist (after all, he says, in quiet allusion to Butler, everything is what it is and not another thing). And he is resolute in denying that we can give a philosophical argument to establish such belief as true. Stroud’s general conclusion can be seen as occupying a middle ground between what we might call dogmatic anti-realism and dogmatic realism. He argues (in Ch. 7) that anti-realism (or what Stroud calls the ‘unmasking’ of colours) is a view that cannot be affirmed without a kind of self-refutation—for ‘no one could abandon all beliefs about the colours of things and still _understand_ the colour terms’ (168, my emphasis). On the other hand (in Ch. 9), it remains in some sense a ‘possibility’ (204) that everyday colour beliefs might actually all be false. Stroud’s final judgment is not that we shall or should abandon the ‘Quest for Reality’, though he has expressed many reservations about it.2 The. (shrink)

This paper is divided into two parts. In the first one I distinguish between weak and strong Anti-Archimedeanisms, the latter being the view that metaethics, just as any other discipline attempting to work out a second-order conceptual, metaphysical non-committed discourse about the first-order discourse composing normative practices, is conceptually impossible or otherwise incoherent. I deal in particular with Ronald Dworkin’s famous exposition of the view. I argue that strong Anti-Archimedeanism constitutes an untenable philosophical stance, therefore making logical space (...) for the practice of a discipline such as metaethics—conceived as ethically neutral. This makes space, concurrently, for neutral conceptual jurisprudence. In the second part of the article, I attempt to show two things. On the one hand, that Dworkin’s widely discussed ‘challenge of disagreements’ to legal positivism is founded upon strong Anti-Archimedeanism. On the other hand, that having rejected strong Anti-Archimedeanism we should consequently reject the challenge as a serious challenge to positivism. This move, of course, does not thereby imply that accounting for legal disagreements is not an important jurisprudential task. But it marks—contra Dworkin—that there is no principled or a priori impossibility of doing so within a positivist framework. (shrink)

The central argument of The Quest for Reality is that of Ch. 7, to show that an anti-realist rejection of colours could never be asserted without a kind of self-refutation; that view is consequently ‘no threat’ to everyday colour beliefs. There are people these arguments have not convinced; but my present interest lies in a turn which occurs later in the book, where Stroud insists it remains in some sense a ‘possibility’ that our everyday colour beliefs might still be (...) false: there might ‘really’ be no colours. Stroud emerges therefore in a middle ground between what we might call dogmatic anti-realism and dogmatic realism. His position might even be called a form of reluctant scepticism—though on the ancient model more than the modern, recommending that we ‘live by appearances’ and abandon dogma: we know in any ordinary way that grass is green and tomatoes red, but ‘the metaphysical question about the reality of colour’ remains unsettled—indeed, it seems, permanently beyond us. The ‘scepticism’ about colour here, I think, bears comparison with the limited scepticism about material objects in Stroud’s earlier book The Significance of Philosophical Scepticism. However, I shall argue that even in the case of material objects, such scepticism seems compulsory only because another option is simply passed over; and in the case of colour, the scepticism is one degree less coherent than in the case of material objects. (shrink)

The central argument of The Quest for Reality is that of Ch. 7, to show that an anti-realist rejection of colours could never be asserted without a kind of self-refutation; that view is consequently ‘no threat’ to everyday colour beliefs. There are people these arguments have not convinced; but my present interest lies in a turn which occurs later in the book, where Stroud insists it remains in some sense a ‘possibility’ that our everyday colour beliefs might still be (...) false: there might ‘really’ be no colours. Stroud emerges therefore in a middle ground between what we might call dogmatic anti-realism and dogmatic realism. His position might even be called a form of reluctant scepticism—though on the ancient model more than the modern, recommending that we ‘live by appearances’ and abandon dogma: we know in any ordinary way that grass is green and tomatoes red, but ‘the metaphysical question about the reality of colour’ remains unsettled—indeed, it seems, permanently beyond us. The ‘scepticism’ about colour here, I think, bears comparison with the limited scepticism about material objects in Stroud’s earlier book The Significance of Philosophical Scepticism. However, I shall argue that even in the case of material objects, such scepticism seems compulsory only because another option is simply passed over; and in the case of colour, the scepticism is one degree less coherent than in the case of material objects. (shrink)

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, (...) or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

This thesis consists of a series of papers in population ethics: a subfield of normative ethics concerned with the distinctive issues that arise in cases where our actions can affect the identities or number of people of who ever exist. Each paper can be read independently of the others. In Chapter 1, I present a dilemma for Archimedean views in population axiology: roughly, those views on which adding enough good lives to a population can make that population better than (...) any other. In Chapter 2, I extend Gustaf Arrhenius’s famous impossibility theorems in population axiology into the domain of choices under risk. My risky impossibility theorems dispense with the assumption that welfare levels are finitely fine-grained, and so tell against lexical views in population axiology. In Chapter 3, I present objections to critical-level and critical-range views in population axiology. I then sketch out what I call the ‘Imprecise Exchange Rates View’ and argue that it is an attractive alternative. In Chapter 4, I address critical-level and critical-range views again. This time, I note that they are vulnerable to objections from biographical identity: identity between lives. I suggest that these objections give us reason to reject critical-level and critical-range views and embrace the Total View. In Chapter 5, I argue that objections of the same form – objections from personal identity – tell against person-affecting views in population ethics. In Chapter 6, I draw out some counterintuitive implications of two recent complaints-based theories of the procreation asymmetry. (shrink)

Zuckerberg almost always tells users that change is hard, often referring back to the early days of Facebook when it had barely any of the features people know and love today. He says sharing and a more open and connected world are had barely any of the features people know and love today. He says sharing and a more open and connected world are good, and often he says he appreciates all the feedback.

This paper investigates what choices teachers made and what rationales they offered related to the inclusion and exclusion of primary source photographs for a hypothetical unit about the U.S. Civil...

The paper contrasts Kant's conception of original common possession of the earth with Hugo Grotius's superficially similar notion. The aim is not only to elucidate how much Kant departs from his natural law predecessors—given that Grotius's needs-based framework very much lines in with contemporary theorists’ tendency to reduce issues of global concern to questions of how to divide the world up, it also seeks to advocate Kant's global thinking as an alternative for current debates. Crucially, it is Kant's radical shift (...) in perspective—from an Archimedean ’view from nowhere‘, to a first-personal standpoint through which agents reflexively recognise their systematic interdependence in a world of limited space—that provides him with the more thorough and ultimately convincing global standpoint. This standpoint does not come with ready-made solutions to shared global problems, but provides a promising perspective from which to theorise them. (shrink)

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile (...) Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

The paper contrasts Kant's conception of original common possession of the earth with Hugo Grotius's superficially similar notion. The aim is not only to elucidate how much Kant departs from his natural law predecessors—given that Grotius's needs-based framework very much lines in with contemporary theorists’ tendency to reduce issues of global concern to questions of how to divide the world up, it also seeks to advocate Kant's global thinking as an alternative for current debates. Crucially, it is Kant's radical shift (...) in perspective—from an Archimedean ’view from nowhere‘, to a first-personal standpoint through which agents reflexively recognise their systematic interdependence in a world of limited space—that provides him with the more thorough and ultimately convincing global standpoint. This standpoint does not come with ready-made solutions to shared global problems, but provides a promising perspective from which to theorise them. (shrink)

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where the (...) equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolò Fontana, better known as Tartaglia (1500?-1557), wrote the treatise Quesiti et inventioni diverse (1546). This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia's lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle on the Sources of the Ethical Life by Sylvia BerrymanElizabeth C. Shaw and Staff*BERRYMAN, Sylvia. Aristotle on the Sources of the Ethical Life. Oxford: Oxford University Press, 2019. vii + 220 pp. Cloth, $70.00—Berryman’s goals in Aristotle on the Sources of the Ethical Life are threefold: to establish that Aristotle practiced what contemporary philosophers call metaethics; to refute the idea that Aristotle justified those ethics by recourse (...) to human nature, understood as an “external point” for “establishing substantial ethical truths from a value-neutral perspective”; and to demonstrate that, for Aristotle, the source and justification for ethical demands is human practical reason.Locating the source of normativity in practical reason does not mean that there are no “standards of truth other than human beings as a species.” Positioning Aristotle against both “Archimedean” naturalisms as well as relativisms and subjectivisms, Berryman sees Aristotle’s appeals to nature as delimiting “the kinds of normative positions that could guide practical reason,” and practical reason as responsive to biological constraints. Still, nature is no fulcrum. It does not mandate the contents of the life we should live. All of this together makes Berryman’s Aristotle a “constitutive constructivist,” which is to say, a nonskeptical, cognitivist nonfoundationalist.Chapter 1’s “Introduction” sets the stage for the book’s metaethical project. Chapters 2 and 3 argue against two versions of the claim that “Aristotle was not reflective on the sources and justifications for his ethical views.” Chapter 2 places “Aristotle in the Ethics Wars” of the twentieth and twenty-first centuries, challenging the historicist view that “the kind of metaethical reflection about the sources of normativity” that preoccupies modern philosophy in response to “‘disenchantment’ of the modern world picture” would not have been available to Aristotle. Chapter 3, “Nature and the Sources of Normativity,” positions itself against scholars who maintain that Aristotle was complacent about the values of his own society and/or “too philosophically naïve to even reflect on the sources and justifications of ethical claims.” Inhabiting Aristotle’s social and intellectual milieu, it shows how the epistemological questions, commitments to materialist-scientific worldviews, as well as challenges to divine authority posed by fifth-century sophists, Plato, and fourth-century [End Page 381] hedonists meant that “a philosopher in Aristotle’s position could hardly avoid being reflective on questions of the status of ethics.”After establishing in chapter 3 that Aristotle could have grounded ethical claims in his natural philosophy, chapters 4 through 6 make the case that he did not. Exploring the philosophical work done by Aristotle’s appeals to nature, chapter 4, “Is Aristotle an Archimedean Naturalist?”, focuses on the apparent directionality of human development as well as references to “natural justice” and “natural virtue” in Aristotle’s ethical writings, while chapter 5, “Naturalism in Aristotle’s Politics,” scrutinizes the “naturalness of the polis” and “natural slavery” in Politics 1. Finding “only very minimal appeal to human nature” in the ethical treatises, Berryman sees Aristotle’s recourse to nature in Politics 1 as “the main anomaly” for which her refutation of Archimedean naturalism must account. Based on internal evidence in the Politics and comparison with Aristotle’s biological writings, Berryman concludes that Aristotle wrote the Politics before he “developed his more detailed biological theories.” Rather than evidence of naturalism, Aristotle’s appeals to nature in Politics 1, Berryman argues, are an early reflection of the “nomos-phusis distinction found in sophistic controversies” and a “kind of rhetorical move” based on thorough “prejudice and not reasoned inference.” Concluding “The Case Against a Naturalist Reading,” chapter 6 sets the stage for Berryman’s resourcing of Aristotle’s metaethics away from nature by exploring the inadequacies of the instrumental and theoretical rule-guiding reasoning implicit in naturalist accounts of Aristotelian practical reason.Chapters 7 and 8 offer the book’s positive account. After elaborating Aristotle’s rejection of “metaphysical abstractions” as action-guiding, chapter 7, “Aristotle’s Metaethics,” recovers from the Eudemian Ethics human agency as the source of normativity in Aristotle. Action “carries with it an implicit commitment to the norms of practical reasoning,” and “Aristotle’s insight,” Berryman writes, “is the metaethical recognition that the practical... (shrink)

This article argues that a pragmatist ambition to transcendence undergirds Richard Rorty’s metaphilosophy. That transcendence might play a positive role in Rorty’s work might seem implausible given his well-known rejection of the idea that human practices are accountable to some external, Archimedean standpoint, and his endorsement of the historicist view that standards of rationality are products of time and chance. It is true that Rorty’s contributions to epistemology, philosophy of mind and metaphysics have this anti-transcendentalist character. But in (...) his metaphilosophy, Rorty shows great respect for pre-philosophical impulses aimed at transcendence of some kind, in particular the romantic (and indeed religious) experience of awe at something greater than oneself, and the utopian striving for a radically better world. These impulses do not disappear in Rorty’s metaphilosophy but are reshaped in a pragmatist iteration of transcendence which, we argue, can be characterised as horizontal (rather than vertical) and weak (rather strong). We use this characterization to distinguish Rorty’s metaphilosophy from other accounts that share a postmetaphysical ambition to transcendence. (shrink)

Newton and Leibniz had profound disagreements concerning metaphysics and the relationship of mathematics to natural philosophy, as well as deeply opposed attitudes towards analysis. Nevertheless, or so I shall argue, despite these deeply held and distracting differences in their background assumptions and metaphysical views, there was a considerable consilience in their positions on the status of infinitesimals. In this paper I compare the foundation Newton provides in his Method Of First and Ultimate Ratios (sketched at some time between 1671 and (...) 1684, and published in the Principia of 1687) with that provided independently by Leibniz in his unpublished manuscript De quadratura arithmetica (1675-6) as well as in later writings. I argue that both appeal to a version of the Archimedean Axiom to underwrite their use of infinitesimal techniques, which must be interpreted as a shorthand for rigorously finitist methods. (shrink)

The development of empirical research methods in both the social and the natural sciences has had a deep impact on the self-conception of philosophy. Jürgen Habermas aims to strike a balance between two ways of understanding the relationship between philosophy and the sciences: between a conception of philosophy as an Archimedean point from which to view the human condition and a conception of philosophy as a mere artefact of Western culturally embedded assumptions. Against the first, Habermas aims to (...) integrate the resources and methods of the social sciences into philosophy and to deny that philosophy can proceed outside of historical and social contexts. On his view, philosophical knowledge is produced communicatively, through socially embedded dialogue. Against the second, Habermas claims fundamental questions about the human condition cannot be answered by purely social or natural scientific approaches. His “postmetaphysical” methodology aims to integrate empirical resources into philosophy without losing sight of what is unique to philosophy: namely, its ability to step back from the empirical data in order to reconstruct in a systematic way underlying universal truths about us, our societies and our place in the world. (shrink)

The nature of state governance in consolidated liberal democracies has important implications for the ideal theory debate. The states of these societies are polycentric. Decision-making power within them is disaggregated across multiple sites. This rules out one major justification for ideal theory. On this influential view, the ideal furnishes a blueprint of the morally perfect society that we should strive to realise. This justification is not viable in consolidated liberal democracies because their states lack an Archimedean point from (...) which the institutional structure as a whole can be designed to accord with the true ideal – whichever it might be. However, knowledge of the ideal can still aid agents in those societies to determine the worth of more modest political objectives other than the ideal itself. (shrink)

The primary purpose of this paper is to analyze the relationship between the familiar non-Archimedean field of hyperreals from Abraham Robinson’s nonstandard analysis and Paolo Giordano’s ring extension of the real numbers containing nilpotents. There is an interesting nontrivial homomorphism from the limited hyperreals into the Giordano ring, whereas the only nontrivial homomorphism from the Giordano ring to the hyperreals is the standard part function, namely, the function that maps a value to its real part. We interpret this asymmetry (...) to mean that the nilpotent infinitesimal values of Giordano’s ring are “smaller” than the hyperreal infinitesimals. By viewing things from the “point of view” of the hyperreals, all nilpotents are zero, whereas by viewing things from the “point of view” of Giordano’s ring, nonnilpotent, nonzero infinitesimals register as nonzero infinitesimals. This suggests that Giordano’s infinitesimals are more fine-grained. (shrink)

In the latter half of the twentieth century, some prominent ethicists turned to the history of philosophy to challenge the prevailing trend toward subjectivism or noncognitivism. G. E. M. Anscombe offered the first of several historical narratives challenging the world picture that undergirded this prevalence, narratives in which Aristotelian ethics is presented as a possible alternative. It is striking, however, how differently these narratives characterize the ancient–modern divide and how differently Aristotle is interpreted, particularly on the issue of his appeal (...) to naturalism in ethics. The tendency to view Philippa Foot as Anscombe’s best interpreter might leave us with the unfortunate supposition that Aristotelian ethics is saddled with an implausible Archimedean naturalism. The author suggests that there is another way to read Anscombe’s message, which does not fetter it to a kind of metaphysical biology that we have no reason to accept. (shrink)

This book presents a historical and scientific analysis as historical epistemology of the science of weights and mechanics in the sixteenth century, particularly as developed by Tartaglia in his Quesiti et inventioni diverse, Book VII and Book VIII (1546; 1554). -/- In the early 16th century mechanics was concerned mainly with what is now called statics and was referred to as the Scientia de ponderibus, generally pursued by two very different approaches. The first was usually referred to as Aristotelian, where (...) the equilibrium of bodies was set as a balance of opposite tendencies to motion. The second, usually referred to as Archimedean, identified statics with centrobarica, the theory of centres of gravity based on symmetry considerations. In between the two traditions the Italian scholar Niccolò Fontana, better known as Tartaglia (1500?–1557), wrote the treatise Quesiti et inventioni diverse (1546). -/- This volume consists of three main parts. In the first, a historical excursus regarding Tartaglia’s lifetime, his scientific production and the Scientia de ponderibus in the Arabic-Islamic culture, and from the Middle Ages to the Renaissance, is presented. Secondly, all the propositions of Books VII and VIII, by relating them with the Problemata mechanica by the Aristotelian school and Iordani opvsculvm de ponderositate by Jordanus de Nemore are examined within the history and historical epistemology of science. The last part is relative to the original texts and critical transcriptions into Italian and Latin and an English translation. -/- This work gathers and re-evaluates the current thinking on this subject. It brings together contributions from two distinguished experts in the history and historical epistemology of science, within the fields of physics, mathematics and engineering. It also gives much-needed insight into the subject from historical and scientific points of view. The volume composition makes for absorbing reading for historians, epistemologists, philosophers and scientists. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge Companion to Galileo ed. by Peter MachamerMartin CurdPeter Machamer, editor. The Cambridge Companion to Galileo. Cambridge: Cambridge University Press, 1998. Pp xii + 462. Cloth, $59.95. Paper, $19.95.The contributions fall into three main areas: Galileo’s work on mechanics, his defense of Copernicus, and his relationship with the church. The relative number of pages devoted to these topics is unusual: the ratio is roughly 3 to 1 (...) to 3.The papers on Galileo’s mechanics and physics are by William Wallace, Peter Machamer, Rivka Feldhay, Wallace Hooper, and Pietro Redondi. Wallace concentrates on unpublished manuscripts from Galileo’s early period, arguing that they reveal Galileo’s intense involvement with Aristotelian philosophy. As in his other writings, Wallace emphasizes the importance of the demonstrative regressus argument for Galileo’s thought, especially for Galileo’s later claim in the Dialogue to have demonstrated the earth’s motion from the phenomenon of the tides. Machamer offers an “Archimedean” [End Page 364] interpretation of Galileo, stressing the Galileo’s use of simple machines, especially the balance, as a model of intelligibility throughout his scientific work. According to Machamer, these machines functioned as something like a Kuhnian exemplar for Galileo, providing the element of necessity and picturability that Galileo deemed essential for scientific explanation. Feldhay explores the role of mathematics in Galileo’s science, arguing that Galileo began to diverge from the Jesuit-Aristotelian tradition once he gave up trying to understand the causes of accelerated motion and focused instead on its geometrical analysis in terms of degrees of velocity. In a useful discussion, Hooper follows the development of Galileo’s inertial mechanics, concluding that even in the Discourses (1638) it is unclear whether Galileo abandoned his pre-Newtonian notion of impetus as the sustaining cause of motion. Redondi examines the relationship of Galileo’s physics to his theology. While Redondi’s conclusion is clear—“Galileo’s physics required God”—his argument is hard to follow, ranging as it does over Galileo’s views on time, atomism, macroscopic and microscopic physics, and cosmogony.Only two articles are directly about Galileo and the Copernican theory but those two pieces, by William Shea and Noel Swerdlow, are models of clarity. Swerdlow focuses on Galileo’s telescopic discoveries 1610–13 while Shea covers the entire period up to the Dialogue of 1632. Unfortunately, this involves repetition of the material about the telescopic discoveries, including some diagrams and illustrations. Tighter editorial control might have avoided this duplication and allowed Shea to devote more time to the fascinating arguments in the Dialogue. What we have is fine, but more would have been better.On Galileo and the church, there are contributions from Ernan McMullin, Richard Blackwell and Marcello Pera. McMullin argues that the seeds of Galileo’s downfall in 1633 were sown in his Letter to the Grand Duchess Christina (1615) in which Galileo endorsed a theory of scriptural interpretation remarkably similar to that contained in Augustine’s commentary on Genesis. McMullin finds a tension in that theory between regarding Scripture and natural science as mutually irrelevant while at the same time giving science priority over the literal reading of Scripture if and only if a demonstration has been provided. Once the demonstration principle was adopted, Galileo’s task of defending the earth’s motion against biblical literalism in the Dialogue became hopeless. Blackwell asks whether there could be another Galileo case in light of the Vatican’s admission of error in 1992. His answer is “Yes.” Blackwell reminds us that while in 1616 it was the Copernican theory that been tried and found heretical, in 1633 the sole issue was Galileo’s obedience to church authority. In Blackwell’s view, there remains the potential for conflict between the church’s “logic of centralized authority” and the democratic, pluralistic methods that give legitimacy to science. Pera, too, concludes that the possibility of conflict remains as long as the church insists that there are truths of faith, necessary for salvation, and those doctrines also have a factual content amenable, at least in principle, to scientific investigation.The book concludes with two pieces: a survey by Michael Segre of the evolution of Galileo’s... (shrink)

Legal philosophers share the same phenomenology of legal practice. Yet, they differ in its explanation. For normativists, descriptivists got it wrong and vice versa. This controversy between normativists and descriptivists will be called “the methodological problem” in legal theory. Normativists such as Dworkin and Perry argue that descriptivists need evaluation. By contrast, descriptivists such as Coleman argue that normativists need the methods of descriptivism such as conceptual analysis and therefore might be committed to descriptivism. The paper shows that the responses (...) of Perry and Coleman to the methodological problem are not free from difficulties. The article also advances a reinterpretation of normativism in terms of two tenets: 1. the semantic sting argument, and 2. the ametaphysical thesis argument. If the latter argument is sound, normativism is unavoidable, because if there cannot be an external point of view or Archimedean perspective, then we can only resort to our moral convictions or substantive claims. The first tenet has been criticized in previous work and the paper focuses on a criticism of the second tenet. (shrink)

Human Reason and Its Enemies is the result of a two-year research project under a National Fellowship of the Indian Council of Philosophical Research. The book is an uncompromising expose of postmodernism-a philosophy which seeks to destroy philosophy; challenges and objectivity, universality and impartiality of reason; and whcih swears by 'situated' knowledge. The views of many postmoderns, particularly those of Cohen, Foucault, Lyotard, MacIntyre and Taylor, are shown to be superficial, sophistical, confused, fallacious and even ridiculous. Postmodernism believes truth to (...) be culture-relative and therefore believes that intercultural comparison and critical appraisal must require an 'Archimedean point' to make this possible. Since, they say, there is no such point, cultures are incommensurable. This argument, as well as the incommensurability thesis, are shown to be based on messy thinking and prejudice. The postmodern reliance on the concept of 'language games' and its love hate relationship to Western science, are examined in depth. The pronouncements of thinkers like Feyerabend and Kuhn are thoroughly exposed as mistaken and even laughable. An attempt is made to disclose the true nature and salient features of human reason and thinking. A full chapter is devoted to the arch-postmodern, Richard Rorty, and another to feminist writers like Fox Keller, Harding, Irigary and Tiles, who are powerfully drawn to postmodern ideas. (shrink)

Both “optimists” and “sceptics” in regard to extraterrestrial intelligence tend to hold the view that we are entitled to an epistemically clear position: either there will be a signal, in the sufficiently general sense, proving the existence of extraterrestrial intelligence, or no such signal is forthcoming. The distinction, I wish to argue here, is not at all so clear-cut. On the contrary, there are arguments, intrinsic to the subject matter, to the effect that the detection of ETI will be (...) a protracted affair characterized by uncertainty at every step. Such view of SETI discovery mandates different policies from those conventionally discussed in the literature. We should not gear our expectations and publicly promote the view that the Contact will be a clear-cut, Archimedean “Eureka!”-style discovery. In contrast, the tempo and mode of the process of discovery might significantly influence societal and political reactions to the discovery. We should be prepared for such a protracted unfolding of events. (shrink)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the (...) continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

This paper is the second part of our recent paper ‘Historical and Epistemological Reflections on the Culture of Machines around the Renaissance: How Science and Technique Work’. In the first paper—which discussed some aspects of the relations between science and technology from Antiquity to the Renaissance—we highlighted the differences between the Aristotelian/Euclidean tradition and the Archimedean tradition. We also pointed out the way in which the two traditions were perceived around the Renaissance. The Archimedean tradition is connected with (...) machines: its relationship with science and construction of machines should be made clear. It is enough to think that Archimedes mainly dealt with three machines: lever, pulley and screw. As underlined in the first part, our thesis is that many machines were constructed by people who ignored theory, even though, in other cases, the knowledge of the Archimedean tradition was a precious help in order to build machines. Hence, an a priori idea as to the relations between the Archimedean tradition and construction of machines cannot exist. In this second part we offer some examples of functioning machines constructed by people who ignored any physical theory, whereas, in other cases, the ignorance of some principles—such as the impossibility of a perpetuum mobile—induced the attempt to construct impossible machines. What is very interesting is that these machines did not function, of course, as a perpetuum mobile, but anyway had their functioning and were useful for certain aims, although they were constructed on an idea which is completely wrong from a theoretical point of view. We mainly focus on the Renaissance and early modern period, but we also provide examples of machines built before and after this period. We have followed a chronological order in both parts, starting from the analysis of the situation in ancient Greece. Therefore, in the first part, we have examined the relations between the Aristotelian/Euclidean and Archimedean traditions from ancient Greece to the early modern age. In this second part, we analyse the relations of Archimedean tradition/ construction of machines from ancient Greece to the 19th century, focusing on the mentioned period. We remind the reader that our aim is to prove an epistemological thesis, not to provide a complete historical endeavour. As a correlated article, the reader will find three previous paragraphs in the first above-mentioned article. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 29.2 (2005) 379-393 [Access article in PDF] Love, Self-Deception, and the Moral "Must" Randy Ramal Claremont Graduate University I One significant impact that conceptual relativism has had on current discussions in moral philosophy is the denial of intelligibility to discourses that affirm moral absolutism. The denial is typically based on two allied arguments. The first argument entails that the justification of absolute moral laws and values (...) presupposes the existence of an Archimedean standpoint, but since such viewpoint is unintelligible, a "view from nowhere" as it has been called, then affirming moral absolutism could only be the result of a confused temptation for metaphysical universality and objectivity. The second argument states that since all moral values and concepts are the products of particular cultural-linguistic contexts, it would not make sense to speak of absolute values that have application in other cultural-linguistic contexts.I sympathize with the critical spirit in which this dual argument is made. The unintelligibility of a neutral standpoint and the obvious contextuality of all moral discourses render meaningless any attempt to affirm metaphysically-based moral absolutes. But what this argument fails to acknowledge is that the ordinary language of moral absoluteness is not only infinitely distant from the metaphysical claims to Olympian grounds but also internally related to the absolute moral judgments and principles it invokes. Furthermore, it is doubtful that one could speak at all of moral discourse as needing metaphysical justification. It would not make sense to speak of moral discourse as either needing or not needing metaphysical backing because both notions ignore the ordinary contexts of moral discourse, where the issue of philosophical justification does not arise. The point here is not simply to reject the [End Page 379] metaphysical need for justifying moral discourse but to question the intelligibility of the attempt itself.1In what follows I argue that the ordinary claims to moral absoluteness, be it to give moral advice, to justify personal beliefs and actions, or to judge and criticize the conduct of other people, are perfectly intelligible practices that embody ordinary moral judgments and values. I elucidate the intelligibility of these moral claims by discussing Leo Tolstoy's "The Death of Ivan Ilych," Proust's Remembrance of Things Past, and Ann Beattie's "Learning to Fall." These works, I argue, portray an ethical notion of "need" that expresses natural, and intelligible, affirmations of moral necessity. The context of this affirmation concerns the ethical call to end all self-deception about one's love life.Traditionally, the relationship between love and self-deception has been interpreted to suggest that people often deceive themselves about love in order to fulfill a deep need in them to give meaning to their lives. This interpretation is often invoked to explain, on the one hand, why people who are in love might claim otherwise and, on the other hand, why those who are not in love at all convince themselves of the opposite. Although this interpretation is not philosophical in nature and does not necessarily entail the denial of all discourses of moral necessity, the idea that self-deception fulfils a deep need in people is often invoked as a philosophical explanation of the notion of "need." One example of such philosophical explanation is Martha Nussbaum's Love's Knowledge, where she endorses the traditional interpretation of the relation between love and self-deception through a discussion, among other works, of the above mentioned works by Proust and Beattie.There is no doubt that self-deception, whether in regards to one's love life or other aspects of it, could sometimes arise as a result of a need in people to give their existence some meaningful stability. But this interpretation cannot apply to all cases of love and self deception because the radical plurality of our notions of love prevents such explanatory reductionism. The insistence on this type of reductionism, it seems to me, rests on a common tendency among moral philosophers, Nussbaum included, to read into literature personal ethical views that are not intended by it. The task of the moral philosopher... (shrink)

The twelfth century was a period of transmission and absorption of Arabic learning though it filtered outside of the Arabic world as early as the second half of the tenth century. In general, the lure of Spain began to act only in the twelfth century, and the active impulse toward the spread of Arabic mathematics came from beyond the Pyrenees and from men of diverse origins. The chief names are Adelard of Bath, Robert of Chester, Hermann of Carinthia and Gerard (...) of Cremona. In this time the Latin world became acquainted with the Hindu numerals, the Arabic Algebra and Euclid'sElements. However, not only Spain, but also the Norman kingdom of southern Italy and Sicily occupies a position of peculiar importance, though the works of the translators did not become very influential. There were made direct translations from Greek into Latin. One had to wait a century more to obtain a translation from Greek into Latin of the chief Archimedean scientific and mathematical treatises by William of Moerbeke. In the thirteenth century Fibonacci and Jordanus Nemorarius stand at the threshold of European mathematics. Not only was Fibonacci the first to explain Arabic arithmetic, but his works, especially his later ones, contain many original ideas. Jordanus continued the Greco-Roman tradition rather than the Greco-Arabic one, but he did so with much independence. To Nicole Oresme (fourteenth century) was due a broadened view of proportionality, a geometric proof to determine the summation of convergent infinite series and the proof, evidently the first in the history of mathematics, that the harmonic series is divergent. The Configuration Doctrine was treated by Merton College authors and by Oresme. In the fifteenth century theDe triangulis omnimodis of Regiomontan, a systematic account of the methods for solving triangles, marked the rebirth of trigonometry. (shrink)

French theorists have recently proposed a theory which describes all literature in terms of the probable, the vraisemblable.6 This poetics of the probable commences with a purely relativistic claim. What is probable not only changes in accordance with the audience’s concept of reality but also changes in accordance with the needs of the story and with the narrative possibilities open to various genres. It includes all of the norms and models making a given text understandable to the reader, however outlandish (...) and eccentric it may be. Various levels of the vraisemblable are distinguished from each other, and the vraisemblable based upon models of the world or the world view prevalent in a given culture is scrupulously separated from types of the vraisemblable that are based upon literary, generic models. However, as Tzvetan Todorov gladly admits, “the two notions tend to melt into each other.”7 He and other theorists see the literary genre itself as one of the models “probabilizing” a given text, at times in direct contradiction with “natural” models of the world. Still others see the world, or the prevalent world view, as the universal text which probabilizes other texts.[…]Rather than how this new concept of the vraisemblable, of probability, fares in relation to farce in films, theater, and literature, I prefer to ask how farce fares in relation to it. I think that it doesn’t do well. Farce shows that it is a mistake to unify the possibilities for understanding a text and the possibilities for understanding its fictional world within a single integrated concept. It is a further mistake to term such a concept “probability.” When dealing with the fantastic or the marvelous, for instance, probabilizing the text and probabilizing the work’s fictional world may legitimately be unified under a single principle or concept. If we agree to change or suspend a fundamental belief about the world, we will be able to perceive as logical and probable not only the texts but also the fictional worlds of such works. Coleridge’s “willing suspension of disbelief” excellently fits works that are written in these genres. Such works require that we temporarily forget a certain general belief about the world. After we’ve agreed, as a result of this suspension, to include certain elements in the world , we may then rebuild the fictional world while using the rest of our beliefs along with this new assumption. Farce’s incredibility creates a different situation. Before we have even begun to recover from an attack upon one probability principle, another is undermined. In farce the rules of probability are not neutralized in one specific realm of reality; their inversion operates constantly on all of reality’s realms. The image of a seemingly real world, reminding us of our own world and of our own set of probabilities, is all we need to be constantly astonished by farce’s persistently novel deviations from predictable probability. Here, in direct opposition to the marvelous, the new deviations must keep on coming from unexpected directions, because farce won’t allow its incredibilities to consolidate and become new rules of probability. The fictional world of overt farce lacks a specific factor, the one that would have probabilized all of the other factors of this world. Such an Archimedean center might seem to be located in the genre’s definition—this genre, however, does not probabilize the incredible. Farce’s definition does not make farce’s world more intelligible in any sense of that word. At the very most, farce allows us to forgo such intelligibility without transgressing the established boundaries of art.6. For an excellent presentation of their views, see Jonathan Culler, Structuralist Poetics: Structuralism, Linguistics, and the Study of Literature , pp. 131-60.7. Tzvetan Todorov, The Poetics of Prose, trans. Richard Howard , p. 83. See also his introduction to Communications 11 : 2. (shrink)