The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in (...) 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics. (shrink)

This article looks at Vesto Slipher’s work on nebular spectroscopy between 1912 and 1922as well as related research by other astronomers of the period, and it examines the dissem-ination of their results more widely. Slipher’s observations are viewed as marking the di-viding line between speculation about the universe in traditional astronomy and theadvent of modern cosmology and the theory of an expanding universe. The intent is todocument the dissemination of Slipher’s results in the period leading up to the publicationof studies (...) of relativistic cosmology by Willem de Sitter in 1917 and Alexander Friedmannin 1922. Themes touched on in the article include the unprecedented character ofSlipher’sfindings and the interaction of observation and theory in modern cosmology.A prominent concern is the role of technology in astronomical science over the past cen-tury and a half. Here reference is made to the writings of Paul Forman on historical shiftsthat have taken place in our understanding of the relationship of science and technology. (shrink)

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques (...) for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

Harry C. Boyte. Craig Calhoun. Geoff Eley. Nancy Fraser. Nicholas Garnham. JürgenHabermas. Peter Hohendahl. Lloyd Kramer. Benjamin Lee. Thomas McCarthy. Moishe Postone. Mary P.Ryan. Michael Schudson. Michael Warner. David Zaret.

Which factors influence the folk application of the concept of causation? Knobe has argued that causal judgments are primarily influenced by the moral valence of the behavior under consideration. Whereas Driver has pointed out that the data Knobe relies on can also be used to support the claim that it is the atypicality of the agent's behavior that influences our willingness to assign causality to that agent. While Knobe and Fraser have provided a further study to address the cogency of (...) this alternative explanation, we argue that they have not provided a complete analysis. We present a variation on this study that addresses the relation between atypical and moral considerations as they contribute to the application of the concept causation. Our results indicate that atypicality cannot be ignored in an analysis of the folk concept of causation. That is, Knobe and Fraser's response to Driver is inadequate. (shrink)

Shannon Sullivan has criticized Richard Rorty for the discrepancy in his treatments of Cornel West and Marilyn Frye's prophetic philosophies, which Sullivan reads to indicate a racial bias on Rorty's part. This article defends Rorty from this criticism, first clarifying his view of the discontinuous relation of philosophy to politics, then, on the basis of this clarification, arguing that Rorty's different treatments of West and Frye do not reveal a racial bias as Sullivan claims. Finally, revisiting Rorty's exchange with Nancy (...) Fraser, it is argued that although Rorty has no philosophy of race, he does offer a strong antiracist politics. (shrink)

Targeting injustices that cut across borders, they are making the scale of justice an object of explicit struggle.Inspired by these efforts, Nancy Fraser asks: ...

What does it mean to think critically about politics at a time when inequality is increasing worldwide, when struggles for the recognition of difference are eclipsing struggles for social equality, and when we lack any credible vision of an alternative to the present order? Philosopher Nancy Fraser claims that the key is to overcome the false oppositions of "postsocialist" commonsense. Refuting the view that we must choose between "the politics of recognition" and the "politics of redistribution," Fraser argues for an (...) integrative approach that encompasses the best aspects of both. (shrink)

What is the connection between philosophy as studied in universities and those general views of man and reality which are commonly considered "philosophy"? Through his attempt to rediscover this connection, Craig offers a view of philosophy and its history since the early 17th century. Craig discusses the two contrary visions of man's essential nature that dominated this period--one portraying man as made in the image of God and required to resemble him as closely as possible, the other depicting (...) man as the autonomous creator of his own environment and values--and uses this context to clarify previously opaque textual detail. Illustrating how general concepts embodied by philosophical thought can be embodied in other media--especially literary--the author brings together disparate disciplines; he also reveals striking similarities between Anglo-American and certain 20th-century continental European lines of thought. (shrink)

Best known for having declared the death of God, Nietzsche was a thinker thoroughly absorbed in the Christian tradition in which he was born and raised. Yet while the atheist Nietzsche is well known, the pious Nietzsche is seldom recognised and rarely understood. Redeeming Nietzsche examines the residual theologian in the most vociferous of atheists. Fraser demonstrates that although Nietzsche rejected God, he remained obsessed with the question of human salvation. Examining his accounts of art, truth, morality and eternity, Nietzsche's (...) thought is revealed to be a series of experiments in redemption. (shrink)

Until recently, struggles for justice proceeded against the background of a taken-for-granted frame: the bounded territorial state. With that "Westphalian" picture of political space assumed by default, the scope of justice was rarely subject to open dispute. Today, however, human-rights activists and international feminists join critics of structural adjustment and the World Trade Organization in challenging the view that justice can only be a domestic relation among fellow citizens. Targeting injustices that cut across borders, they are making the scale of (...) justice an object of explicit struggle. Inspired by these efforts, Nancy Fraser asks: What is the proper frame for theorizing justice? Faced with a plurality of competing scales, how do we know which one is truly just? In exploring these questions, Fraser revises her widely discussed theory of redistribution and recognition. She introduces a third, "political" dimension of justice—representation—and elaborates a new, reflexive type of critical theory that foregrounds injustices of "misframing." Engaging with thinkers such as Jürgen Habermas, John Rawls, Michel Foucault, and Hannah Arendt, she envisions a "postwestphalian" mapping of political space that accommodates transnational solidarity, transborder publicity, and democratic frame-setting, as well as emancipatory projects that cross borders. The result is a sustained reflection on who should count with respect to what in a globalizing world. (shrink)

Increasingly, metaphors are the target of political critique: Jewish groups condemn Holocaust imagery; mental health organizations, the metaphorical exploitation of psychosis; and feminists, “rape metaphors.” I develop a novel model for making sense of such critiques of metaphor.

A framework for pragmatic analysis is proposed which treats discourse as a game, with context as a scoreboard organized around the questions under discussion by the interlocutors. The framework is intended to be coordinated with a dynamic compositional semantics. Accordingly, the context of utterance is modeled as a tuple of different types of information, and the questions therein — modeled, as is usual in formal semantics, as alternative sets of propositions — constrain the felicitous flow of discourse. A requirement of (...) Relevance is satisfied by an utterance (whether an assertion, a question or a suggestion) iff it addresses the question under discussion. Finally, it is argued that the prosodic focus of an utterance canonically serves to reflect the question under discussion (at least in English), placing additional constraints on felicity in context. (shrink)

A priori reflection, common sense and intuition have proved unreliable sources of information about the world outside of us. So the justification for a theory of the categories must derive from the empirical support of the scientific theories whose descriptions it unifies and clarifies. We don’t have reliable information about the de re modal profiles of external things either because the overwhelming proportion of our knowledge of the external world is theoretical—knowledge by description rather than knowledge by acquaintance. This undermines (...) the traditional idea that to be an object of category C is to be an object with such- and-such characteristic possibilities of combination. But this is no loss because de re modal thought lacks utility for creatures like us. (shrink)

How can we talk meaningfully about the past if it does not exist to be talked about? What gives time its direction? Is time travel possible? This defence of presentism - the view that only the present exists - makes an original contribution to a fast growing and exciting debate.