The concept of self-motion is not only fundamental in Aristotle's argument for the Prime Mover and in ancient and medieval theories of nature, but it is also central to many theories of human agency and moral responsibility. In this collection of mostly new essays, scholars of classical, Hellenistic, medieval, and early modern philosophy and science explore the question of whether or not there are such things as self-movers, and if so, what their self-motion consists in. They trace the development of (...) the concept of self-motion from its formulation in Aristotle's metaphysics, cosmology, and philosophy of nature through two millennia of philosophical, religious, and scientific thought. This volume contains "Self-Movers" (David Furley), "Aristotle on Self-Motion" (Mary Louise Gill), "Aristotle on Perception, Appetition, and Self-Motion" (Cynthia Freeland), "Self-Movement and External Causation" (Susan Sauvé Meyer), "Aristotle on the Mind's Self-Motion" (Michael Wedin), "Mind and Motion in Aristotle" (Christopher Shields), "Aristotle's Prime Mover" (Aryeh Kosman), "The Transcendence of the Prime Mover" (Lindsay Judson), "Self-Motion in Stoic Philosophy" (David Hahm), "Duns Scotus on the Reality of Self-Change" (Peter King), "Ockham, Self-Motion, and the Will" (Calvin Normore), and "Natural Motion and Its Causes: Newton on the 'Vis Insita' of Bodies" (J. E. McGuire). Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

If dominating functions in ω ω are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every well-ordered unbounded family of increasing functions is a scale, and the splitting number s (and hence the distributivity number h) remains at ω 1.

We study the I-ultrafilters on ω, where I is a collection of subsets of a set X, usually R or ω 1 . The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.

We study the $I$-ultrafilters on $\omega$, where $I$ is a collection of subsets of a set $X$, usually $\mathbb{R}$ or $\omega_1$. The $I$-ultrafilters usually contain the $P$-points, often as a small proper subset. We study relations between $I$-ultrafilters for various $I$, and closure of $I$-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether $I$-ultrafilters always exist.

Among the reasons that Whitehead is such an interesting philosopher is that his work resonates across philosophical traditions. This collection develops connections between Whiteheadian concepts and recent European thinkers. The purpose is not simply to compare, however, but, as editor Jeremy Fackenthal suggests, to develop a Whiteheadian thinking “in tandem” with European philosophers in order to create disruptions or “dislocations” in thought that can engender creative approaches to contemporary problems.One general feature of the book deserves mention at the outset, though (...) I will return to it later in the review: although phenomenology and hermeneutics are each represented in the volume, roughly half of the essays focus on the work of Gilles Deleuze (if we group these together with essays focused on “new materialism,” which is connected with Deleuze, the proportion is more like two-thirds). This will be no surprise, since Deleuze is the European philosopher who was most appreciative of Whitehead. And yet, the result is that the conversation with “continental philosophy” is highly selective.The book is organized into three parts, each comprised of three essays. In part 1, “Technological and Systematic Dislocations,” William S. Hamrick brings Whitehead into conversation with Maurice Merleau-Ponty's concept of “the flesh” to suggest an ecological ontology capable of overcoming the instrumentalization of nature. Hamrick's strategy is to read Whitehead and Merleau-Ponty as contributing to an “ontological foundation” for a sustainable civilization (18). Bo Eberle writes about the “quantified self” suggested in new, wearable self-monitoring technologies. Drawing on Whitehead's notion of causal efficacy, Eberle argues that devices such as Fitbit give us access to bodily states that bypasses the standard ways we are aware of ourselves (i.e., through consciousness). He goes further to argue that, like all ways of knowing, wearable technologies are selective, and that the selection reflects the interests of the manufacturers and promotes a certain kind of subjectivity (in the case of Fitbit, a subjectivity that is oriented toward “getting your steps in”). Whitehead's epistemology thus enables the critic of wearable technologies to understand how contemporary experience and self-understanding is shaped not simply by recent technological mediations but by the material interests embedded in them. J.R. Hustwit and Carl Dyke take on what they call “activist” uses of Whitehead that naively (in their judgment) suggest that a non-relational substance metaphysics is to blame for most of our social ills. They employ the theory of complex adaptive systems in conversation with Whitehead and Antonio Gramsci to show that, in fact, achieving significant social change is far more difficult and even unpredictable than mere insertion of better ideas into public discourse. Dominant hegemonies have ways of adapting and absorbing attempts to undermine them. Here Hustwit and Dyke draw on the philosophy of Paul Ricoeur to suggest that resistance to the dominant hegemony is nevertheless always possible because of the vagueness of discourse, allowing a plurality of competing interpretations and thus fractures in the dominant hegemony. However, even this kind of resistance is impossible to control and its effects incapable of being entirely predicted. To the essay's titular question, “Can Whitehead save the world?” the authors answer, “No.”In part 2, “Animal/Human Dislocations,” Jeremy Fackenthal draws on the new materialism of Rosi Braidotti (and Deleuze) along with Whitehead to argue for a “process-relational” nomadism that culminates in a “becoming-imperceptible.” His reading together of Whitehead and Braidotti creates the opportunity to recast the former's concept of objective immortality in such a way that it does not refer to death so much as to being diffused into a relational network. The satisfaction of an actual occasion may be taken as its translation into its effects among its relations. Fackenthal argues that this becoming-imperceptible makes possible a sustainable presence within a fragile network of life. Deena M. Lin uses Whitehead, Braidotti, and Judith Butler to lay out a vision of human life as precarious and deserving attention, care, and solidarity. She presses this vision as a direct moral assault on US (Trump's) policy toward Syrian refugees. Going further, she draws on Braidotti's posthuman account of zoe to argue for universal connection and solidarity with all life that should foster, as the title of her essay puts it, “Welcoming of Syrian Life.” Tano Posteraro offers an intriguing essay drawing on Jakob von Uexküll's account of animal experience. Posteraro argues that Uexküll's notion of an animal's Umwelt, shaped by its distinctive perceptual apparatus, needs to be supplemented by Whitehead's notion of prehension to account for the active dimension of animal perception. Rather than a passive registering of animal environments, Posteraro argues that the latter are constructed, and that concepts (or conceptual prehensions) should be understood as tools with which such environments are constructed.In part 3, “Time, the World, and Abstraction,” three essays probe ways that Whiteheadian and Deleuzian themes may resonate critically and constructively. Kris Klotz brings the thought of Whitehead and Deleuze together to inquire about how alternatives to present social forms are envisioned. He argues that, for Whitehead, every actual occasion involves a selection of some features of the past, and, further, that every selection is also an abstraction from the concrete welter of influences impinging on it. For Whitehead, then, to envision alternatives involves a critique of abstractions, a reinstatement of the concrete plurality of possibilities. This, for Whitehead, is what rationality does: it works at restoring the concrete, and, with it, a series of alternatives that have been eclipsed. To this Whiteheadian analysis, Klotz adds Deleuze and Guattari's critique of “opinion.” For Deleuze and Guattari, opinion is not an idiosyncrasy but a consensus to which differences of experience are subjected. Philosophy, for Deleuze and Guattari, must always struggle against opinion in order to bring alternatives to light. These conceptions of reason/philosophy, Klotz argues, represent useful ways to critique inequalities and other social wrongs that are embedded in the social forms that are routinely taken for granted. Elijah Prewitt-Davis uses a scene from Buffy the Vampire Slayer, along with philosophical innovations of Foucault, Deleuze, and Whitehead, to offer a distinctive account of power. Prewitt-Davis calls attention to Deleuze's important book on Leibniz, The Fold, and to how Whitehead's concept of prehension lies at its center. The upshot is that power is not reduced to dominance but, instead, is at work wherever any occasion of experience persists amid the onslaught of the influence of other occasions. Power, as Deleuze wrote, is the capacity to be affected—and to decide how to constitute oneself anew. Keith Robinson offers a detailed account of Whitehead's epistemology along with a reading of Deleuze's analysis of temporality to suggest that there is a common trajectory that seeks to undermine what the title of the essay describes as the “Bifurcation of Nature” (i.e., the separation of natural phenomena and human experience) within the dominant Western philosophical tradition.There is much of value in the volume as a whole. Aside from staging what Spinoza might have called good encounters between Whitehead and a number of continental philosophers, enhancing the conceptual power of each, the contributors are able to make a case that these philosophical trajectories, when read together, have much to contribute to our understanding of and response to the pressing issues of the day. In addition, readers who are interested in the relationship between Whitehead and the new materialism will find this volume to be a helpful resource, stocked with fine examples of how to sharpen new materialist thinking with Whitehead and how to read contemporary contexts through these lenses. On the other hand, this book is not a handbook nor a comprehensive reference. The organizational logic behind its division into sections is murky and the amount of attention given to particular continental philosophers as opposed to others appears somewhat arbitrary: there are recent continental philosophers who get little to no attention at (Derrida, Malabou, Žižek, Agamben, Latour, Nancy, for example), several of whom might prove to be quite interesting to read “in tandem” with Whitehead. Perhaps that is just to say that there are many more essays to be written. (shrink)

Several canonical partition theorems are obtained, including a simultaneous generalization of Neumer's lemma and the Erdos-Rado theorem. The canonical partition relation for infinite cardinals is completely determined, answering a question of Erdos and Rado. Counterexamples are given showing that in several ways these results cannot be improved.

Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ + -saturated, i.e., are there κ + stationary subsets of κ with pairwise intersections nonstationary? Our first observation is: Theorem. NS is κ + -saturated iff for every normal ideal J on κ there is a stationary set $A \subseteq \kappa$ such that $J = NS \mid A = \{X \subseteq (...) \kappa:X \cap A \in NS\}$ . Turning our attention to large cardinals, we extend the usual (weak) Mahlo hierarchy to define "greatly Mahlo" cardinals and obtain the following: Theorem. If κ is greatly Mahlo then NS is not κ + -saturated. Theorem. If κ is ordinal Π 1 1 -indescribable (e.g., weakly compact), ethereal (e.g., subtle), or carries a κ-saturated ideal, then κ is greatly Mahlo. Moreover, there is a stationary set of greatly Mahlo cardinals below any ordinal Π 1 1 -indescribable cardinal. These methods apply to other normal ideals as well; e.g., the subtle ideal on an ineffable cardinal κ is not κ + -saturated. (shrink)

One of the contemporary results of Germany’s memorial conundrum is the rise of its “counter-monuments”: brazen, painfully self-conscious memorial spaces conceived to challenge the very premises of their being. On the former site of Hamburg’s greatest synagogue, at Bornplatz, Margrit Kahl has assembled an intricate mosaic tracing the complex lines of the synagogue’s roof construction: a palimpsest for a building and community that no longer exist. Norbert Radermacher bathes a guilty landscape in Berlin’s Neukölln neighborhood with the inscribed light of (...) its past. Alfred Hrdlicka began a monument in Hamburg to counter—and thereby neutralize—an indestructible Nazi monument nearby. In a suburb of Hamburg, Jochen Gerz and Esther Shalev-Gerz have erected a black pillar against fascism and for peace designed to disappear altogether over time. The very heart of Berlin, former site of the gestapo headquarters, remains a great, gaping wound as politicians, artists, and various committees forever debate the most appropriate memorial for this site.4 4. The long-burning debate surrounding projected memorials, to the Gestapo-Gelände in particular, continues to exemplify both the German memorial conundrum and the state’s painstaking attempts to articulate it. For an excellent documentation of the process, see Topographie des Terrors: Gestapo, SS und Reichssicherheitshauptamt auf dem “Prinz-Albrecht-Gelände,” ed. Reinhard Rürup . For a shorter account, see James E. Young, “The Topography of German Memory,” The Journal of Art 1 : 30. James E. Young is assistant professor of English and Judaic studies at the University of Massachusetts, Amherst. He is the author of Writing and Rewriting the Holocaust: Narrative and the Consequences of Interpretation and The Texture of Memory: Holocaust Memorials and Meaning in Europe, Israel, and America , from which this essay is drawn. He is also the curator of “The Art of Memory,” an exhibition at the Jewish Museum of New York. (shrink)

We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large (...) class of Easton-like forcings applied to ω1-Erdös cardinals. A class of reverse-Easton forcings preserving α-Erdösness is also described, with special attention to the establishment of □-principles. Article Outline. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue (...) for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

It is shown that for any cardinal $\kappa, \dbinom{(2^{ , and if κ is weakly compact $\dbinom{\kappa^+}{\kappa} \rightarrow \dbinom{\kappa}{\kappa}_{.

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and causal (...) powers. (shrink)

Over the past two decades, the renowned political theorist William E. Connolly has developed a powerful theory of pluralism as the basis of a territorial politics. In this concise volume, Connolly launches a new defense of pluralism, contending that it has a renewed relevance in light of pressing global and national concerns, including the war in Iraq, the movement for a Palestinian state, and the fight for gay and lesbian rights. Connolly contends that deep, multidimensional pluralism is the best way (...) to promote justice and inclusion without violence. He advocates a deep pluralism—in contrast to shallow, secular pluralism—that helps to create space for different groups to bring their religious faiths into the public realm. This form of deep pluralism extends far beyond faith, encompassing multiple dimensions of social and personal lives, including household organization and sexuality. Connolly looks at pluralism not only in light of faith but also in relation to evil, ethics, relativism, globalization, and sovereignty. In the process, he engages many writers and theorists—among them, Spinoza, William James, Henri Bergson, Marcel Proust, Gilles Deleuze, Giorgio Agamben, Talal Asad, Michael Hardt, and Antonio Negri. _Pluralism_ is the first book in which Connolly explains the relationship between pluralism and the experience of time, and he offers readings of several films that address how time is understood, including _Time Code_, _Far from Heaven_, _Waking Life_, and _The Maltese Falcon_. In this necessary book Connolly brings a compelling, accessible philosophical critique together with his personal commitment to an inclusive political agenda to suggest how we might—and why we must—cultivate pluralism within both society and ourselves. (shrink)

It is shown that if ZF is consistent, then so is ZFC + GCH + "There is a graph with cardinality ℵ 2 and chromatic number ℵ 2 such that every subgraph of cardinality ≤ ℵ 1 has chromatic number ≤ ℵ 0 ". This partially answers a question of Erdos and Hajnal.

The conventional interpretation of Adam Smith is that he is a prophet of commercialism. The liberal capitalist reading of Smith is consistent with the view that history culminates in commercial society. The first part of the article develops this optimistic interpretation of Smith's view of history. Smith implies that commercial society is the end of history because (1) it supplies the ends of nature that he identifies; (2) it is inevitable; and (3) it is permanent. The second part of the (...) article shows that Smith has some dark moments in his writings where he seems to reject completely such teleological notions. In this more civic humanist mood he confesses that commercial society does not supply the ends of nature, nor is it inevitable, nor is it permanent. Both views exist in Smith and the commentator is forced to choose between passages in Smith's work in order to support a particular interpretation of the former's view of history. (shrink)

The essays range from Hegel and Modernism to Marcel Duchamp and the Avant-Garde, postmodern poetics, boredom and Proust, the romance of Arendt and Heidegger, ...

Primary, or basic, colors have been discussed for centuries. Over time, three criteria have emerged on their behalf: (a) their physical mixture yielding all other spectral colors, (b) the physiological attunement of receptors or pathways to particular wavelengths, and (c) the etymological history of the color term. These criteria can be applied usefully to taste to clarify issues.

The concepts of invariants and cues are useful, as are those of dorsal and ventral streams, but Norman overgeneralizes when interweaving them. Cues are not confined to identification tasks, invariants not to action, and both can be learned.