Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked (...) some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie). (shrink)

This essay takes a close look at specially selected features of the Göttingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Göttingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Göttingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation (...) of a special atmosphere that served as a model for several other important centers for mathematical research. Göttingen exemplified a dynamic new way of doing mathematics within a highly competitive community in which the spoken word often carried more weight than did information conveyed in written texts. This oral dimension of the Göttingen culture played an important, till now overlooked role in the early development of Einstein's general theory of relativity. (shrink)

Albert Einstein's most important public and private political writings are put into historical context in this firsthand view of how one of the twentieth century's greatest minds responded to the political challenges of his day.

ArgumentEinstein's initial fame came in late 1919 with a dramatic breakthrough in his general theory of relativity. Through a remarkable confluence of events and circumstances, the mass media soon projected an image of the photogenic physicist as a bold new revolutionary thinker. With his theory of relativity Einstein had overthrown outworn ideas about space and time dating back to Newton's day, no small feat. While downplaying his reputation as a revolutionary, Einstein proved he was well cast for the role of (...) mild-mannered scientific genius. Yet fame demanded its price. Surrounded by social and economic unrest in Berlin, he was caught between two worlds, one struggling to be born, another refusing to die. Far from withdrawing, he threw himself into the political fray to become a symbol for international reconciliation during the early Weimar Republic. A decade later, his public image acquired another layer when he re-emerged as a Stoic sage and selfless humanitarian, a quasi-religious figure who saw himself as a modern-day Spinoza. Focusing on events of this period and the role of the German media in portraying them, this essay highlights the scientific and political undercurrents that drew Einstein into the public eye at a critical juncture in European history. Its broader aim is to show the import of these themes within the context of the vast literature on Einstein as well as the larger historiography of science. (shrink)

This paper is primarily a response to ‘analytically-minded’ philosophers, such as Maudemarie Clark and Brian Leiter, who push for a ‘naturalistic’ interpretation of Nietzsche. In particular, this paper will consider Leiter’s (2007) discussion of Nietzsche’s chapter in Twilight of the Idols, ‘The Four Great Errors’, and argue that Leiter has misinterpreted this chapter in at least four ways. I provide a superior interpretation of this chapter, which argues that Nietzsche is using a transcendental style of argument to argue against a (...) common conception of causation. I argue that Nietzsche’s ultimate aim of this chapter is to argue for ‘the innocence of becoming’ rather than, as Leiter claims, the error of free will. I argue that this anti-naturalist methodology and conclusion are in tension with Leiter/clark’s Nietzsche, and highlights the need to pay attention to the being/becoming distinction in Nietzsche. (shrink)

This book provides an interpretation of the late nineteenth-century German philosopher Friedrich Nietzsche as holding a distinct and original metaethical position, which is to say a theory about our practice of ethics. Rowe uses this interpretation to provide some interesting and thought-provoking criticisms of themes in contemporary metaethics.

Although rarely appreciated, the collaboration that brought Felix Klein and Sophus Lie together in 1869 had mainly to do with their common interests in the new field of line geometry. As mathematicians, Klein and Lie identified with the latest currents in geometry. Not long before, Klein’s mentor Julius Plücker launched the study of first- and second-degree line complexes, which provided much inspiration for Klein and Lie, though both were busy exploring a broad range of problems and theories. Klein used invariant (...) theory and other algebraic methods to study the properties of line complexes, whereas Lie set his eyes on those aspects related to analysis and differential equations. Much later, historians and mathematicians came to treat the collaboration between Klein and Lie as a famous early chapter in the history of transformation groups, a development often identified with Klein’s “Erlangen Program” from 1872. The present detailed account of their joint work and mutual interests provides a very different picture of their early research, which had relatively little to do with group theory. This essay shows how the geometrical interests of Klein and Lie reflected contemporary trends by focusing on the central importance of quartic surfaces in line geometry. (shrink)

In this paper I argue that Nietzsche should be understood as a “thorough-going nihilist”. Rather than broaching two general projects of destroying current values and constructing new ones, I argue that Nietzsche should be understood only as a destroyer of values. I do this by looking at Nietzsche’s views on nihilism and the role played by Nietzsche’s cyclical view of time, or his doctrine of the eternal recurrence of the same. I provide a typology of nihilisms, as they are found (...) in Nietzsche—negative, reactive and radical—through a close reading of an unpublished fragment in his later notebooks, remnants of which are scattered throughout his published work. I show how the progression between the different stages of nihilism are a “necessary consequence of the ideals entertained hitherto” , with the eternal recurrence of the same playing a vital role in this progression. The last stage of nihilism—radical nihilism—is ambiguous between a life-denying, or passive, nihilism and a life-affirming, or active, one; but, I argue, both kinds of nihilism preclude a construction of new values. But there is an inherent tension within Nietzsche’s account of nihilism insofar as it relies on the eternal recurrence of the same. This tension is brought out nicely by Löwith and partially resolved by Klossowski. There are at least two meanings of the eternal recurrence of the same. In one sense, the cosmological reading, it is intended to make sense of the idea that time is infinite and matter is finite by claiming that every possible combination of matter will recur infinite times. In the other sense, the anthropological reading, it is a kind of thought experiment, analogous to Kant’s categorical imperative: “live in every moment so that you could will that moment back again over and over” . There is a tension between these readings insofar as one must will to live in such a way that they will do it again, over and over , but also that what they do will make no difference, for what one decides to do has been done innumerable times. I argue that this tension can only be resolved by considering Nietzsche as aiming at “goal-lessness as such” and placing him as an active nihilist. (shrink)

If death is a harm then it is a harm that cannot be experienced. The proponent of death’s harm must therefore provide an answer to Epicurus, when he says that ‘death, is nothing to us, since when we are, death is not present, and when death is present, then we are not’. In this paper I respond to the two main ways philosophers have attempted to answer Epicurus, regarding the subject of death’s harm: either directly or via analogy. The direct (...) way argues that there is a truth-maker (or difference-maker) for death’s harm, namely in virtue of the intrinsic value the subject’s life would have had if they had not died. The analogy argues that there are cases analogous to death, where the subject is harmed although they experience no pain as a result. I argue that both accounts beg the question against the Epicurean: the first by presupposing that one can be harmed while experiencing no displeasure as a result and the second by conflating a de re with a de dicto reading of death’s harm. Thus, I argue, until better arguments are provided, one is best to agree with Epicurus and those who follow him that death is not a harm. (shrink)

Volume 29, Issue 6, September 2024, Page 692-694.

This paper applies models of the onset of adolescent sexual intercourse using national data from Denmark and the USA. The model gave excellent fits to data on Danish Whites and a good fit to American Whites, but the model-fits for American Blacks and Hispanics were not as good. The weakness of the latter model fits may reflect either real processes that the model does not capture or problems in the reliability of adolescent sexuality data.

Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

Unlike some psychiatric illnesses, criminal lifestyles are not reproductive dead ends and may represent frequency-dependent adaptations. Sociopaths may gain reproductively from their greater relative to nonsociopaths. This mating-effort construct should be assessed directly in future studies of sociopathy. Collaboration between biologically oriented and environmentally oriented researchers is needed to investigate the biosocial basis of sociopathy.

Howe et al. have mistaken gene x environment correlations for environmental main effects. Thus, they believe that training would develop the same level of performance in anyone, when it would not. The heritability of talents indicates their dependence on variation in physiological (including neurological) capacities. Talents may be difficult to predict from early cues because tests are poorly designed, or because the skill requirements change at more advanced levels of performance. One twin study of training effects demonstrated greater heritability of (...) physical skill after than before training. In summary, talents are real. (shrink)

This paper argues that there is a heretofore unresolved tension between truthmaker-style metaphysics and a plausible version of Naturalism. At the turn of the century, George Molnar proposed four prima facie plausible principles for a realist metaphysics in order to expose truthmaker theory’s incapacity to find truthmakers for negative truths. I marshal the current plethora of attempted solutions to the problem into a crisp trilemma. Those who solve it claim that Molnar’s tetrad is consistent; those who dissolve it do away (...) with the requirement that every truth needs a truthmaker; and those who absolve it embrace a negative ontology. I argue that one is forced to absolve the problem: all other avenues undermine the truthmaker principle itself. Absolving the problem, however, does not sit well with a version of Naturalism that most would accept. We are drawn to a simple dilemma: either embrace a negative ontology, or reject truthmaker-style metaphysics. (shrink)

Spatial and mathematical abilities may be “sex-limited” traits. A sex-limited trait has the same determinants of variation within the sexes, but the genetic or environmental effects would be differentially expressed in males and females. New advances in structural equation modeling allow means and variation to be estimated simultaneously. When these statistical methods are combined with a genetically informative research design, it should be possible to demonstrate that the genes influencing spatial and mathematical abilities are sex-limited in their expression. This approach (...) would give an empirical confirmation of Geary's evolutionary speculations. (shrink)

As books about Einstein and the Relativity Revolution have continued to flood the market, many might wonder: why yet another? Part of the answer in the present case has to do with the difficult pro...

Simon Robertson's Nietzsche and Contemporary Ethics is a significant contribution to analytic-style interpretations of Nietzsche and his impact on contemporary ethics. Robertson proposes a Nietzschean-inspired ethics, which, while not committed to everything Nietzsche says, is largely consistent with Nietzsche's views. The resultant position is an error theory about contemporary morality with a positive alternative that is naturalist, internalist, irrealist, cognitivist, non-elitist, non-categorical and non-universal, but produces individualistic, normative claims on flourishing and excellence. In short, Robertson espouses a Nietzschean Individualist, Non-elitist, (...) Perfectionism.While this book does... (shrink)