A Transition to Advanced Mathematics promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence to theoretical upper-level mathematics courses. The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics.

This article by Curtis Wilson is an account of the origin of Hansen’s powerful systematic method for finding contributions of higher order perturbations in celestial mechanics. Hansen’s method was developed in the course of improving on Laplace’s treatment of the mutual perturbations of Jupiter and Saturn. This method, an entirely new way of doing celestial mechanics when it first appeared, later made possible the successful treatment of the complicated motions of our moon (see Wilson 2010). In this paper Wilson (...) gives a brief historical introduction followed by an account of relevant technical details of the Laplacian background, an account illustrating technical details in Hansen’s initial development in his Disquisitions of 1829, and a treatment illustrating details contributing to the achievement of Hansen’s more refined development in his Untersuchung of 1831. These details include conditional equations Hansen provides for checking the accuracy of calculations. Wilson also includes a detailed assessment showing the extraordinary improvement in empirical accuracy of Hansen’s treatment over the best earlier treatment of the Jupiter-Saturn interactions. (shrink)

Liberal democracy needs a clear-eyed, robust defense to deal with the increasingly complex challenges it faces in the twenty-first century. Unfortunately much of contemporary liberal theory has rejected this endeavor for fear of appearing culturally hegemonic. Instead, liberal theorists have sought to gut liberalism of its ethical substance in order to render it more tolerant of non-liberal ways of life. This theoretical effort is misguided, however, because successful liberal democracy is an ethically demanding political regime that requires its citizenry to (...) display certain virtues and habits of mind. Against the grain of contemporary theory, philosopher Richard Rorty blends American pragmatism and romanticism to produce a comprehensive vision of liberal modernity that features a virtue-based conception of liberal democracy. In doing so, Rorty defends his pragmatic liberalism against a host of notable interlocutors, including Charles Taylor, Nancy Fraser, Hilary Putnam, Richard J. Bernstein, and Jean Bethke Elshtain. (shrink)

Called the “greatest philosophical essayist of his time,” Rorty is both famous and notorious in academic philosophy for his uniquely engaging writing style. While his fellow analytic philosophers look askance at his flamboyant prose, suspicious that it lacks the care and precision that their discipline demands, literary intellectuals who champion the essay genre can have their qualms about Rorty as well: his work is too professional and specialized to be properly called essays. I argue not only that Rorty's work fits (...) into the essay genre, but also that his use of the essay form is integral to his rhetorical project of advancing his ideal of pragmatic liberalism. Rorty writes essays because the essay is a pragmatic literary genre: it is anti‐essentialist, conversational, and experimentalist and provocatively aims at “breaking the crust of convention,” in Dewey's phrase. Using the essay, Rorty “joshes” us to becoming more pragmatic and, therefore, better liberals. (shrink)

The first systematic study of the aesthetic evaluations that scientists pass on their theories.

The confounding effects of heterogeneity in biological psychiatry and psychiatric genetics have been widely discussed in the literature. We suggest an approach in which heterogeneity may be put to use in hypothesis testing, and may find application in evaluation of the Crespi & Badcock (C&B) imprinting hypothesis. Here we consider three potential sources of etiologic subtypes for analysis.

The target article by Charney on behavior genetics/genomics discusses how numerous molecular factors can inform heritability estimations and genetic association studies. These factors find application in the search for genes for behavioral phenotypes, including neuropsychiatric disorders. We elaborate upon how single causal factors can generate multiple phenotypes, and discuss how multiple causal factors may converge on common neurodevelopmental mechanisms.

Rosa Calcaterra has written an extremely learned and thoughtful book about Richard Rorty’s controversial neopragmatism. It is a worthy addition to the growing number of works that offer a more generous and balanced assessment of Rorty’s thought, in contrast to the scores of highly critical treatments it received during his career. But, as Calcaterra insists, her book is “not an apology for Rorty” (Calcaterra 2019: ix); she critically approaches what she calls Rorty’s philosophical “provocatio...

Virtue liberalism holds that the success of liberal politics and society depends on the citizenry possessing a set of liberal virtues, including traits like open-mindedness, toleration, and individual autonomy. Virtue liberalism is thus an ethically demanding conception of liberalism that is at odds with conceptions, like Rawlsian political liberalism andmodus vivendiliberalism, that attempt to minimize liberalism’s ethical impact in order to accommodate a greater range of ethical pluralism. Although he claims to be a Rawlsian political liberal, Richard Rorty’s pragmatic liberalism (...) is best understood as a version of virtue liberalism that, in particular, recommends a controversial civic virtue of irony for good liberal citizenship. Indeed, Rorty ultimately joins Dewey in conceiving of liberal democracy as a “way of life,” rather than merely a set of political relations that have a minimal effect on our characters or on the shape of our private commitments and projects. (shrink)

Eschewing conventional candidates, like Plato's Republic or Machiavelli's Prince, Richard Rorty praises Aldous Huxley's Brave New World as "the best introduction to political philosophy," because it shows us "what sort of human future would be produced by a naturalism untempered by historicist Romanticism, and by a politics aimed merely at alleviating mammalian pain."1 Huxley's celebrated dystopia is thus a poignant warning to our modern utilitarian political projects. Yet Rorty also suggests that utopian literature can play a positive and inspirational role (...) for liberal politics, and even dubs his own political ideal, "liberal utopia." Rorty's liberal utopia is not an impossible society bereft of political .. (shrink)

Virtue liberalism requires democratic citizens to possess certain ethical character traits, like open-mindedness, toleration, and autonomy. This puts it at odds with theories, like Rawlsian political liberalism, that seek to minimize liberalism’s ethical demands to accommodate a greater range of ethical pluralism. Although Rorty endorses Rawls’s theory, his pragmatic liberalism is best understood as a version of virtue liberalism that, in particular, recommends a controversial civic virtue of irony for good citizenship. Indeed, in contrast to Rawls, Rorty joins Dewey in (...) conceiving of liberal democracy as a “way of life” that deeply affects our characters and our private commitments and projects. (shrink)

Charles Taylor and John Gray offer competing liberal responses to the contemporary challenge of pluralism. Gray's morally minimal 'modus vivendi liberalism' aims at peaceful coexistence between plural ways of life. It is, in Judith Shklar's phrase, a 'liberalism of fear' that is skeptical of attempts to harmonize clashing values. In contrast, Taylor's 'hermeneutic liberalism' is based on dialogical engagement with difference and holds out the possibility that incompatible values and traditions can be reconciled without oppression or distortion. Although Taylor's theory (...) is superior to Gray's because it recognizes that dialogue is crucial for respecting pluralism, both theories fail to fully articulate the ethical ideal of citizenship that they imply. Citizens who are able to dialogically engage with pluralism must be cultivated through liberal education to possess certain ethical traits, and this requirement inevitably limits the range of pluralism liberal societies can accommodate. The theoretical overemphasis on pluralism in recent liberal theory serves to obscure this point. (shrink)

First published in 1876, this classic work of philosophy by William Curtis Swabey provides a detailed analysis of the ideas and theories of the French philosopher Nicolas Malebranche. Drawing on the latest scholarship of the time, Swabey examines Malebranche's ideas on the nature of knowledge, the relationship between the mind and body, and more. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This (...) work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Can scientific evidence outstretch what scientists have mentally entertained, or could ever entertain? This article focuses on the plausibility and consequences of an affirmative answer in a special case. Specifically, it discusses how we may treat automated scientific data-gathering systems—especially AI systems used to make predictions or to generate novel theories—from the point of view of confirmation theory. It uses AlphaFold2 as a case study.

SummaryIn this article I argue that Darwin was the author, quite contrary to his original intentions, of a fundamental revolution in the theory of scientific knowledge. In 1838, in order to meet the anti-evolutionist challenge of his professional colleague, William Whewell, he began to sketch a transmutationist theory of the origin of human ideas which would explain the success of inductive science: its discovery of what Whewell and his contemporaries thought were necessary and certain truths. But though it explained (...) how scientific ideas originated, Darwin's theory implied also that theoretical certainty in science was impossible. Thus Darwin's evolutionism when combined with Whewell's a priorism led to a thorough-going fallibilism. This was worked out in detail by W. K. Clifford, a Cambridge evolutionist, Kantian and fallibilist. (shrink)