Whether we're in the boardroom or the classroom, we spend far too much time and energy looking for the right answer. But the truth is that questions are just as important as answers, often more so. If you ask the wrong question, for instance, you're guaranteed to get the wrong answer. A good question, on the other hand, inspires a good answer and, in the process, invites deeper understanding and more meaningful connections between people. Asking a good question requires us (...) to move beyond what we think we know about an issue or a person to explore the difficult and the unknown, the awkward, and even the unpleasant. Expanding on his 2016 commencement address, Jim Ryan, dean of Harvard University's Graduate School of Education, celebrates the art of asking -- and answering -- good questions. Five questions in particular: Wait, what?; I wonder...? Couldn't we at least...?; How can I help?; and What truly matters? Using examples from politics, history, popular culture, and social movements, as well as his own personal life, Ryan demonstrates how these essential inquiries generate understanding, spark curiosity, initiate progress, fortify relationships, and draw our attention to the important things in life -- from the Supreme Court to Fenway Park. By regularly asking these five essential questions, Ryan promises, we will be better able to answer life's most important question: "And did you get what you wanted out of life, even so? (shrink)

Although Justice Scalia purported to be driven by originalism and precedent, his opinions in three education cases—Grutter v. Bollinger, Parents Involved v. Seattle School District, and United States v. Virginia —tell a different tale. In these cases, his arguments are difficult to defend on originalist grounds and, surprisingly, Justice Scalia himself makes no attempt to do so. Similarly, his views are difficult to square with precedent. It is hard to escape the conclusion that, in some of his most noteworthy cases (...) related to education, Justice Scalia was as results-oriented as the justices and judges he loved to criticize. (shrink)

The Metaphysical Club, a gathering of intellectuals in the 1870s associated with Harvard, is widely recognized as the crucible where pragmatism, America's distinctively original philosophy, was refined and proclaimed. Louis Menand's bestseller about the group was a dramatic publishing success. However, only three actual members - Oliver Wendell Holmes Jr., Charles S. Peirce, and William James - appear in this book, alongside other thinkers such as John Dewey who were never in the Club. The Real Metaphysical Club tells the (...) full story of how this influential group shifted the course of philosophy in America. In addition to pioneering pragmatism, the group explored radical empiricism and idealism, and formulated personalism and process philosophy, equally important developments. This volume contains thirty-seven important writings dating from 1870 to 1885 by the real members of the Metaphysical Club. The first section centers on pragmatism and science; the second part collects writings of the lawyers; and the third part covers idealist and personalist philosophers. Many of these writings have never been reprinted before, and nothing like this impressive collection has ever been attempted. A general introduction provides a narrative history, and the editors' three introductions to the volume's sections vividly bring to life the intense meetings, sustained debates, and pioneering thought from the Metaphysical Club. (shrink)

Features of gait are determined at multiple levels, from the selection of the gait itself (e.g. walk or run) through the specific parameters utilized (stride length, frequency, etc.) to the pattern of muscular excitation. The ultimate choices are neurally determined, but what is involved with that decision process? Human locomotion appears stereotyped not so much because the pattern is predetermined, but because these movement patterns are good solutions for providing movement utilizing the machinery available to the individual (the legs and (...) their requisite components). Under different circumstances the appropriate solution may differ broadly (different gait) or subtly (different parameters). Interpretation of the neural decision making process would benefit from understanding the influences that determine the selection of the appropriate solution in any set of circumstances, including that of normal conditions. In this review we survey an array of studies that point to energetic cost as a key input to the gait coordination system, and not just an outcome of the gait pattern implemented. We then use that information to rigorously define the construct proposed by Sparrow and Newell (1998) where the effects of environment, organism and task act as constraints determining the solution set available, and the coordination pattern is then implemented under a pressure for energetic economy. Environment is defined in terms of affordances based on the ecological psychology definition of the concept and organism is defined as classic morphology and physiology based capabilities. We rely on a novel conceptualization of task that recognizes that the task goal needs to be separated from the mechanisms that achieve the goal if the motivation behind the selection of the mechanism strategy is to be exposed and understood. This reformulation of the Sparrow and Newell construct is then linked to the proposed pressure for economy by considering it as an optimization problem, where the most readily selected gait strategy will be that which achieves the task goal at (or near) the energetic minimum. (shrink)

Throughout the biological and biomedical sciences there is a growing need for, prescriptive ‘minimum information’ (MI) checklists specifying the key information to include when reporting experimental results are beginning to find favor with experimentalists, analysts, publishers and funders alike. Such checklists aim to ensure that methods, data, analyses and results are described to a level sufficient to support the unambiguous interpretation, sophisticated search, reanalysis and experimental corroboration and reuse of data sets, facilitating the extraction of maximum value from data sets (...) them. However, such ‘minimum information’ MI checklists are usually developed independently by groups working within representatives of particular biologically- or technologically-delineated domains. Consequently, an overview of the full range of checklists can be difficult to establish without intensive searching, and even tracking thetheir individual evolution of single checklists may be a non-trivial exercise. Checklists are also inevitably partially redundant when measured one against another, and where they overlap is far from straightforward. Furthermore, conflicts in scope and arbitrary decisions on wording and sub-structuring make integration difficult. This presents inhibit their use in combination. Overall, these issues present significant difficulties for the users of checklists, especially those in areas such as systems biology, who routinely combine information from multiple biological domains and technology platforms. To address all of the above, we present MIBBI (Minimum Information for Biological and Biomedical Investigations); a web-based communal resource for such checklists, designed to act as a ‘one-stop shop’ for those exploring the range of extant checklist projects, and to foster collaborative, integrative development and ultimately promote gradual integration of checklists. (shrink)

After briefly arguing that neither (Kantian or utilitarian) rule-based ethics nor virtue ethics offers promise as a moral theory, I state that argument by analogy (i.e., deliberation within coherence constraints) is a satisfactory form of moral deliberation. I show that what is right must be whatever corresponds to the largest and most coherent set of a society’s moral values. Since we would not know how to interpret the claim that what is right might be repugnant to all our shared moral (...) values, I argue that a definitional naturalist position passes Moore’s open question test. “X is right” just means “performing X satisfies the largest and most coherent set of our altruistic and self-interested desires.” On this view, moral properties are real relational properties. I raise and respond to several objections. (shrink)

After briefly arguing that neither (Kantian or utilitarian) rule-based ethics nor virtue ethics offers promise as a moral theory, I state that argument by analogy (i.e., deliberation within coherence constraints) is a satisfactory form of moral deliberation. I show that what is right must be whatever corresponds to the largest and most coherent set of a society’s moral values. Since we would not know how to interpret the claim that what is right might be repugnant to all our shared moral (...) values, I argue that a definitional naturalist position passes Moore’s open question test. “X is right” just means “performing X satisfies the largest and most coherent set of our altruistic and self-interested desires.” On this view, moral properties are real relational properties. I raise and respond to several objections. (shrink)

Michael Ruses Darwinian metaethics has come under just criticism from Peter Woolcock (1993). But with modification it remains defensible. Ruse (1986) holds that people ordinarily have a false belief that there are objective moral obligations. He argues that the evolutionary story should be taken as an error theory, i.e., as a theory which explains the belief that there are obligations as arising from non-rational causes, rather than from inference or evidential reasons. Woolcock quite rightly objects that this position entails moral (...) nihilism. However, I argue here that people generally have justified true beliefs about which acts promote their most coherent set of moral values, and hence, by definition, about which acts are right. What the evolutionary story explains is the existence of these values, but it is not an error theory for moral beliefs. Ordinary beliefs correspond to real moral properties, though these are not objective or absolute properties independent of anyones subjective states. On its best footing, therefore, a Darwinian metaethics of the type Ruse offers is not an error theory and does not entail moral nihilism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.4 (2001) 602-603 [Access article in PDF] Paul B. Thompson and Thomas C. Hilde, editors. The Agrarian Roots of Pragmatism. The Vanderbilt Library of American Philosophy. Nashville: Vanderbilt University Press, 2000. Pp. ix + 342. Cloth, $39.95. If "racial memory" is a viable concept, then the enduring paradigm of human productivity is agriculture, whose seventy-century dominion Western industry and urbanization have eclipsed only (...) within the last two hundred years. The fifteen essays collected here explore America's distinctive form of agrarianism: where individualism, democracy, and a seemingly endless frontier transcended European quarrels over "commons" versus "containment." These values also helped forge our indigenous philosophy—pragmatism—and it is the confluence of these two distinctive American forms that intrigues each of these authors.The essays fall roughly into three groups: 1) historical queries whose connection to pragmatism is marginal, 2) expositions of the agrarian roots of pragmatism, and 3) estimates of the influence of classical pragmatism on the recent rise of neoagrarianism. The first category offers sparkling essays by Charles Taliaferro, James Campbell, Paul B. Thompson, Robert S. Corrington, and Douglas R. Anderson. Together these scholars sketch a history from colonial times to the mid-twentieth century—from Jefferson's "noble agrarian" to the agony of reconstruction, which hastened the split between Northern transcendentalists and Southern romantics. There are some surprises: Franklin outshines even Jefferson with his balanced vision of self-improvement and community weal, and Jefferson's correspondent Crèvecoueur emerges as a visionary who foresaw farming as a wholesome and integrated way of life a century before Emerson and Thoreau. Thomas C. Hilde finds an engagingly pragmatic notion of community in Josiah Royce, and Richard E. Hart discovers Dewey's sense of concrete experience in the novels of John Steinbeck. The contributions of neglected figures such as Francois Quesnay, Liberty Hyde Bailey, John Brewster, and A Whitney Griswold are also recovered.Turning to the second group, though obviously an irresistible title the notion that classical pragmatism is robustly "rooted" in agrarianism is slightly disingenuous. Peirce and James have no direct ties to agrarianism. And though Dewey's themes of innovation, social intelligence, community, and a conception of experience broadly inclusive of organisms and environments reflect obvious affinities, they do not show that pragmatism grew directly from or is a variant of agrarianism. Happily, the pieces on Dewey contributed by Larry A. Hickman and Armen Marsoobian harbor no such illusions, [End Page 602] and Dewey is specifically disassociated from the claim that agriculture is a privileged form of experience.The third, and perhaps most significant, aim of the volume is to bring pragmatic insights into the recent groundswell toward neoagrarianism. Where traditional agrarianism was polarized between the domination of nature and its romantic beatification, the movement pioneered by Wendell Berry in the 1970s portrays the farmer as a nurturer whose goal is to seek an optimal harmony in the health of the land, the family, the community, and the country. In this James A. Montmarquet finds a Deweyan respect for an encompassing "situation," a unity of fact and value in stark opposition to the "corporate" mentality of specialization and success measured in economic gain alone. For Jeffrey Burkhardt, land grant universities must renew their original commitment to the family farm by distancing themselves from the forces of positivism and scientism—the technocrats and bio-chemical engineers who have imperiled both the land and the communities who depend upon it. Neither Montmarquette nor Burkhardt are looking for handouts, or for a return to the "idyllic" life of the one-horse plow. They emphasize moral training and a combination of practices designed to support the sustainability of the smaller farm in a competitive marketplace.One author compares the mention of agrarianism in philosophical discourse to committing a rude act in public. Clearly, however, mere "respectability" is not enough. If the contributors to this volume are correct, agrarianism is a lantern that may illuminate our ongoing search for wholeness and integrity. Frank X. Ryan Kent State University... (shrink)

Este é um conto sobre visão, pensamento e contradição, bem como sobre o papel que desempenham na primeira metade da Ciência da Lógica de Hegel. A Lógica começa com uma descida, nesse caso, uma queda do Ser ao Nada. Posteriormente, aproximadamente na metade de cada texto, há um certo paradoxo em que tudo está em jogo, a categoria da contradição. Nesse exato momento, o pensamento ao mesmo tempo falha e é renovado em um viés especulativo. Nessa seção, nos debruçamos sobre (...) algumas das interpretações influentes do uso hegeliano da contradição. Para isso, voltamo-nos a uma curiosa obra de arte, Pleiades, de James Turrell, como um exemplo estético dessa primeira queda. Progrediremos, então, através do texto com pensamento e visão como nosso duplo norteador em um passo relativamente rápido, sem desacelerar até encontrarmos a história de Hegel da contradição, onde mostro a natureza explosiva da contradição. Isso nos permitirá ver como Hegel invoca o poder da contradição para gerar a segunda metade da história da Ciência da Lógica. Eu começo com a descida do Ser ao Nada, o momento em que a escuridão emerge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.2 (2001) 312-314 [Access article in PDF] Shook, John R. Dewey's Empirical Theory of Knowledge and Reality.The Vanderbilt Library of American Philosophy. Nashville: Vanderbilt University Press, 2000. Pp. ix + 316. Cloth, $46.00; Paper, $22.95. The current renaissance of American pragmatism, and John Dewey's philosophy in particular, began two decades ago with Richard Rorty's refashioning of Dewey as a postmodernist who renounces the (...) "professional philosophy" of metaphysics and epistemology for the fluidity of conversation in the life and growth of a community. This depiction, though praised for rekindling Dewey's star, has been widely challenged by subsequent commentators. Ralph Sleeper's 1986 The Necessity of Pragmatism persuasively argues that Dewey reconfigures, rather than renounces, the logical and metaphysical grounds of knowledge. Despite an archaic Hegelian vocabulary that misleadingly suggests idealism and antirealism, Sleeper finds Dewey advancing a genuine metaphysics of existence, not merely a conversation about experience: a naturalistic realism of independent existences that enter into and are transformed by human interactions with them.This perspective is shared by most Dewey scholars, including Sandra Rosenthal, Raymond Boisvert, and J. E. Tiles. At least until now. In a profound and provocative exploration of his early philosophy, John R. Shook, presents a compelling case that Dewey's reconstruction of metaphysics and epistemology is deeper than even Sleeper imagined. Dewey did not merely abandon idealism under the influence of William James, as most assume; he transformed it in a original way that, while wholly naturalistic, [End Page 312] is a fusion of idealism and realism that overcomes both the former's "mind-stuff" and the latter's "in-itself reality."Dewey began his philosophical odyssey with the searing desire to eradicate the dualisms of mind versus world, phenomenal versus noumenal, perceptual versus conceptual. Post-Hegelian idealists agreed that this division is ultimately reconciled in the "absolute," though they disagreed about whether the absolute is psychological or cosmological, social or supernatural, knowable or unknowable. From the very beginning, Shook argues, Dewey accepted the psychological path as sketched by James Ward, and also Edward Caird's claim that the absolute must be knowable in some sense. Intriguingly, the missing link between perception and conceptual awareness is Wilhelm Wundt's notion of volition: percepts are neither mechanically attached to concepts nor are they overlaid by Kantian "faculties of mind." Instead, a disruption of perceptual or noncognitive experience generates a desire for reconciliation that calls forth ideas that diagnose the problem and suggest ways to resolve it. Achieved solutions, in turn, forge a background of habitual dispositions that shape interpretations within the noncognitive realm.While still an idealist, then, Shook finds the essential elements of the "method of inquiry" that later anchored Dewey's instrumentalism and pragmatism. Prior to 1890, however, he still construed this as individual "mental activity," and the problem of its relation to God's Absolute Mind remained. Upon relinquishing the supernatural for the social, however, this final obstacle was eliminated. The dispositional background extends beyond the individual to the customs, traditions, and values of a culture—indeed, even the barest notions of "self" and "reality" are inconceivable without reference to such a background. This is Dewey's broad conception of "experience"—a humanistic naturalism with no trace of mind-stuff or subjectivism. In this sense Dewey is a realist, though his affirmation of things-themselves (including things we have not or may never actually discover) avoids the things-in-themselves that is the bane of metaphysical realism. To claim that things exist without an experiential background of how we may find them to exist is at best empty verbiage, and at worst hypnosis by the dervishes of dualism.Scrupulous in research, penetrating in detail, Shook's presentation is so faithful to Dewey that it will undoubtedly draw many of the same criticisms once hurled at the master. Though careful readers will be able to identify "experience" in its broadly social and functional sense, others will be confused by applications as diverse as "mental activity," "soul," "reality," "the history of the... (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, ...

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Search for Unity in Diversity: The "Permanent Hegelian Deposit" in the Philosophy of John DeweyFrank X. RyanJames A. Good A Search for Unity in Diversity: The "Permanent Hegelian Deposit" in the Philosophy of John Dewey Lanham, MD: Lexington Books, 2006. xxx + 288 pp.Among the revelations of Dewey's rare moments of autobiographical reflection, none has generated more curiosity and investigative zeal than his 1930 claim to have (...) "drifted" from Hegel in the decade following his move from Michigan to Chicago in 1894. Beginning with Morton White's Origin of Dewey's Instrumentalism (1943), biographers have divided on the question of whether Dewey's later philosophy was more strongly influenced by William James's experimental psychology or F. J. E. Woodbridge's Aristotelian naturalism. Despite their differences, both approaches are essentially empirical and realistic, and thus the majority of sympathetic commentators have agreed that Dewey was a realist, albeit of a decidedly unorthodox stripe. For them the notion that Dewey retained any significant commitment to idealism, given its virtual eradication at the beginning of the twentieth century, would damage his influence and legacy.It has been something of a puzzle, accordingly, that in the same autobiographical essay Dewey alludes to a "permanent Hegelian deposit." For years Richard Rorty has claimed this differentiates a "good" Dewey committed to "social flourishing" from a "bad" Dewey prone to metaphysical dalliance. But the first systematic inquiry into Dewey's enduring Hegelianism is John R. Shook's Dewey's Empirical Theory of Knowledge and Reality (2000). Shook argues convincingly that Dewey never abandoned idealism, but rather transformed it into an experimental naturalism by doing away with both "mind-stuff" and equally noxious "things-in-themselves." In many ways James Good's A Search for Unity in Diversity is a bookend to Shook's project, though Good further differentiates Anglo-American Neo-Hegelianism from Hegel himself. According to Good, Dewey endorsed a Humanistic/Historicist interpretation of Hegel rooted in the reciprocal engagement of individuals and societies, rather than the supernatural and architectonic absolute championed by Neo-Hegelians such as T. H. Green, and F. H. Bradley. With [End Page 216] top-notch scholarship and scrupulous attention to detail, A Search for Unity in Diversity is both an excellent intellectual biography and a penetrating plea for a radical reinterpretation of Dewey's contribution to philosophy. I'll briefly sketch the historical account before addressing the more controversial claims about the "permanent Hegelian deposit."Even readers familiar with the half-dozen book-length treatments of Dewey's development will find this account refreshing and informative. Good's professional credentials as a historian shine as he recreates the rough and bustling Burlington of Dewey's youth. In the 1870s, German idealism was considered the epitome of political liberalism and progressive education, and Dewey's journey toward the "inclusive philosophical idea" of the social began in an environment swirling with the crosscurrents of Kant, Hegel, and Schelling. At the White Street Congregational Church, Lewis Barstow preached a liberal orthodoxy that was essentially "man-building" (102), and Good presents a convincing case for the likelihood that even in boyhood Dewey never viewed God as an aloof law-giver or cosmic architect, but as a process unifying the individual and the social within a natural world of unlimited potential. At the University of Vermont Dewey encountered a struggling rural college transformed into the first bastion of American transcendentalism by James Marsh, who inspired a "Burlington philosophy" that rejected atomistic empiricism for a holistic integrity of knowing and doing, facts and values, and pure and practical reasons (57–59).In noting the influence of the "St. Louis Hegelians" upon Dewey, most biographers have focused on W. T. Harris, the prominent founder of The Journal of Speculative Philosophy who published Dewey's earliest submissions and offered encouragement that led to his pursuit of graduate work at Johns Hopkins. Good augments this familiar tale with fascinating depictions of equally influential yet lesser-known Hegelians such as H. C. Brokmeyer, Denton Snider, and Thomas Davidson. At a time when European Hegelianism was polarized between, on the one hand, reactionary apologists for traditional Christianity and Prussian militarism and, on the other, radical... (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.

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)