Purdue University and Syracuse University.

Since the appearance of Bertrand Russell’s A Critical Exposition of the Philosophy of Leibniz, Leibniz’s theory of relations has been a topic of considerable discussion and controversy. Russell himself argued that Leibniz cannot consistently assert both the primary motivation for his denial of relations—that all propositions are of subject-predicate form—and also that relations are to be understood as somehow mental, their foundations being guaranteed by the divine mind. For on the one hand, God must know all relational truths about numbers, (...) aggregates, and relations among monads; but on the other hand, any judgment lacking a subject and predicate will be meaningless. (shrink)

This book offers a sustained re-evaluation of the most central and perplexing themes of Leibniz's metaphysics. In contrast to traditional assessments that view the metaphysics in terms of its place among post-Cartesian theories of the world, Jan Cover and John O'Leary-Hawthorne examine the question of how the scholastic themes which were Leibniz's inheritance figure - and are refigured - in his mature account of substance and individuation. From this emerges a fresh and sometimes surprising assessment of Leibniz's views on (...) modality, the Identity of Indiscernibles, form as an internal law, and the complete-concept doctrine. As a rigorous philosophical treatment of a still-influential mediary between scholastic and modern metaphysics, their study will be of interest to historians of philosophy and contemporary metaphysicians alike. (shrink)

By now widely read, Catherine Wilson’s book on Leibniz’s metaphysics needs no introduction to Leibniz scholars. This volume, like its companions in the ‘Studies in Intellectual History and the History of Philosophy’ series, succeeds in meeting high standards of historical and textual scholarship; of special note are Wilson’s remarkable grasp of the contribution that relatively minor figures made to Leibniz’s thought, and her familiarity with the European secondary literature. The book is, as a consequence, broader and historically richer than other (...) books on Leibniz in English. Contributing to this historical flavor is also a more strategic feature of Wilson’s project—namely its exploration of Leibniz’s metaphysics “[not] as a collection of theses and principles, but developmentally and thematically”. The distinction seems to imply that while one could view Leibniz’s metaphysics as a collection of principles and theses, exactly “which principles and theses?” threatens to get wrongly answered: the “governing assumption” of a developmental approach is that “what the words of a [long-dead philosopher] mean cannot be determined by an internal inspection of the texts”. Or anyway, not precisely determined, with a high confidence of Leibniz’s intentions, and for some projects this may well matter. Surely it may well matter for someone inclined—as Wilson is not—to see the largest part of Leibniz’s metaphysics as a relatively unified system of theses and principles: the governing assumption, which beckons us to read Leibniz against the backdrop of his ancient, medieval, and modern heritage, is consistent with exploring the internal coherence of the theses and principles making up his metaphysical system. If much of the older secondary literature was mistaken in doing almost to the exclusion of, Wilson’s book can scarcely be charged with the same mistake. Were I asked to complain about Wilson’s approach, I would only suggest that her eagerness and ability to do has sometimes obscured the extent to which an internal inspection of the texts is needed in fairly doing. (shrink)

Precipitated largely by publication of the Theodicy in 1706, requests for a systematic exposition of Leibniz’s philosophy led to his self-described Éclaircissement sur les monades, begun in the summer of 1714 at the request of Remond. Unlike the treatise on philosophical theology, Leibniz’s Monadology is at once broadly systematic but sketchy and compressed: so it is useful, but then not so useful, as an introduction to his philosophy. Leibniz later decompressed it somewhat by adding references to the Theodicy, where certain (...) issues received fuller treatment. Rescher’s new book goes several steps further, still reckoning Leibniz as his own best commentator: in addition to those passages from the Theodicy, other passages from the Leibniz corpus are brought alongside each section of the Monadology, letting them pretty much speak for themselves about the ideas of that section, with a miminum of added commentary. This is a swell idea, and I think Rescher succeeds in executing it. The result is a useful work for students, who in a single edition get Leibniz’s original effort at carving his system at its joints—the principles of philosophy, he called them—and enough additional text to flesh out a full-bodied picture of his mature philosophy. (shrink)

Temporal analyses of causal directionality fail if causes needn't precede their effects. Certain well-known difficulties with alternative (non-temporal) analyses have, in recent accounts, been avoided by attending more carefully to the formal features of relations typically figuring in philosophical discussions of causation. I discuss here a representative of such accounts, offered by David Sanford, according to which a correct analysis of causal priority must issue from viewing the condition relation as nonsymmetrical. The theory is shown first to be an implicitly (...) counterfactual treatment at its base: this provides for an explicit reformulation of several key notions in the theory. An argument is then presented, independent of these modal considerations, for the conclusion that causal priority is possible only given certain implausible assumptions about the asymmetric character of causal laws which, I claim, are not met. The best objection to this argument is shown to fail on several counts, partly in light of the counterfactual results offered earlier. It is concluded that, if laws are symmetric, analyses of the sort discussed must look elsewhere for the source of causal priority; but if laws are not symmetric, resting causal priority so heavily on nomological asymmetry is no analysis at all. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Leibniz & Clarke: A Study of Their Correspondence by Ezio VailatiJan A. CoverEzio Vailati. Leibniz & Clarke: A Study of Their Correspondence. New York and Oxford: Oxford University Press, 1997. Pp. xii + 250. Cloth, $45.00.When Leibniz received the 1710 issue of the Royal Society’s Philosophical Transactions in early 1711, he read John Keill’s public charge that he had stolen the calculus from Newton. Leibniz twice sought amends (...) from the Society in the form of a retraction, in response to which a committee was formed to investigate and issue a report. The resulting Commercium epistolicum, written by the good Isaac Newton himself and condemning Leibniz, was published in early 1713. In Vienna at the time, Leibniz learned of its contents in a June letter from Johann Bernoulli, who complained about this “scarcely civilized way” of holding what was in effect a tribunal from which the chief witness was absent. By year’s end Leibniz had enlisted Wolff to see into print Leibniz’s anonymous statement—overstatement, in fact—of his case, and nine months later Keill replied with an equally overstated rejoinder. Late autumn of 1714 found Leibniz back in Hannover, suffering from gout and the tiresome pressure to advance his work on the history of the house of Brunswick-Lüneburg. If only he felt better and had more free time, he could collect his mathematical papers and set an end to the dispute by writing his own Commercium epistolicum: as it was (Leibniz told Wolff in the spring of 1715), he had no intention of giving Newton’s cronies the luxury of his time.The Leibniz-Clarke exchange began in the shadows of this dispute, contributing to Leibniz’s already established distaste for parts of British philosophy. Already in 1690 he was describing (to Huygens and others) Newton’s gravitational attraction as “inexplicable.” Soon after Leibniz was surprised to discover that Locke had accepted Newtonian attraction in the second edition of the Essay—surprised, at least, until he came to see it as part and parcel of the dangerous idea that God could attach any old property whatever to matter if He chose, including thought. Materialism and frequent miracles [End Page 533] were just around the corner, and from there it was a short distance to the mortality of the soul, and a mean view of God’s power; the decay of natural theology itself could only follow. Leibniz’s misgivings didn’t see the light of day in the early 1700s, when he penned them in the Preface to the Nouveaux Essais; but he went out of his way to work an explicit complaint about Mr. Newton and Mr. Locke into the Théodicée of 1710 (§19 of the Preliminary Discourse). The calculus dispute followed. By the time Leibniz got round to writing Princess Caroline about the dispute in a letter of May 1715, he was insisting that the Newtonians deserved public censure, and that the Britons deserved Leibniz as historiographer of England. For her own part, Caroline now wondered if Samuel Clarke, who had translated Newton’s Opticks into Latin, would in the end be unbiased enough to translate Leibniz’s Théodicée into English. Moreover Caroline doubted that Clarke’s notion of the soul was theologically innocent. Replying in November, Leibniz summarized his view that natural religion was in great decline in England, and the famous exchange began.Despite there being no monograph devoted to it until now, the Correspondence ıs (and was) famous. If a book-length study is overdue, so perhaps are three reminders—that a significant portion of the Correspondence is devoted to issues other than space and time and gravitation, that the depth to which its issues are pursued was compromised by impatience on the side of both parties, and that Clarke’s philosophical views aren’t so well-understood as Leibniz’s own. Nowhere does Vailati set out to make these points explicitly, but they emerge over the course of his book, and together with exegetical soundness are its chief contributions. While this volume makes no historical or philosophical waves, it indirectly (perhaps unwittingly) explains why none are readily forthcoming in a book... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Causation Debate in Modern Philosophy: 1637–1739J. A. CoverKenneth Clatterbaugh. The Causation Debate in Modern Philosophy: 1637–1739. New York and London: Routledge, 1999. Pp. xi + 239. Cloth, $75.00. Paper, $21.00.Over the scholastics and earliest moderns, Hume had an advantage of hindsight in declaring that "There is no question, which on account of its importance, as well as difficulty, has caus'd more disputes both among ancients and modern (...) philosophers, than this concerning the efficacy of causes, or that quality which made them be followed by their effects" (Treatise I.iii.14). Between the scholastics and Hume fell (i) Descartes, (ii) classical mechanists such as Hobbes and Gassendi, (iii) the Cartesians Le Grand and Malebranche, (iv) the explanatory rationalists Spinoza and Leibniz, (v) later experimental mechanists such as Boyle, Rohault and Newton, and (vi) the so-called empiricists Locke and Berkeley. This book presents an accessible and admirably broad overview of the modern debate about causation, without sacrificing serious attention to textual details. With two chapters on (i) and one apiece on (ii) - (vi), Clatterbaugh earns for himself and his reader a helpfully synoptic picture of philosophical shifts in the causation debate in the hundred years separating Descartes' Discourse and Hume's Treatise. By the end of the (modern) day, (1) the four-fold causes of Aristotelian-Scholasticism have given way to efficient causation alone; (2) no pre-existing forms in efficient causes are to be found, nor indeed any substantial active powers whatever; (3) there is no deep sense in which causes communicate reality to effects; (4) necessary connection has gone by the board; (5) divine causation has no place in a natural philosophy of causation. No surprises there, but Clatterbaugh's effort reminds us afresh of the varied and torturous routes to such shifts, helping advanced students better (or newly) appreciate them in the comfortable space of 200 pages.Of those pages, a third are devoted to Descartes and the Cartesians. That's not inappropriate, given the importance and difficulty of Descartes's response to Aristotelian-Scholastic accounts of causation, and its influence on occasionalist sentiments on the Continent. The tenor and value of this book may be illustrated by reflecting on the first of these—a rich and frustrating business, both in Descartes's texts and in Clatterbaugh's book. Suppose we grant Descartes the back of his hand to substantial forms and active formal causes as at best "unexplanatory" (counseling Regius): his "at-least-as-much-reality-in-the-cause-as-in-the-effect" principle might be treated as the basis of "an alternative" metaphysical account of causation (19-32). Well, it might be so-treated: but three versions of the principle later, the reader will be excused for judging it little more than a necessary condition for some event-pair x,y counting as a cause-effect pair. If the scholastic appeal to active forms is unexplanatory, then Descartes's [End Page 600] principle—which isn't Descartes's principle at all but a scholastic commonplace—can scarcely fill the explanatory gap. Glossed as a predictable consequence of some strong form of influxus physicus, it is embarrassed by Foucher's objection (that mind bears no likeness to body) and by the weight of texts urging that accidents are individual to their bearers. Having offered us no deep metaphysical story about what in the world answers to 'vis,' Descartes is at best a bungling "interactionist" (here appropriating Clatterbaugh's word for someone whose apparent talk of secondary causes we are asked to respect as expressing a strict and considered philosophical commitment). One can only side with Voetius in reckoning Descartes's replacement of forms by purely quantitative, mechanical principles of motion as expressing a mere "disposition of the movable to move... not an activity of an efficient cause, but merely a necessary condition and a causa sine qua non" (my emphasis: Selectarum Disputationum I [1648-59], 873). Descartes has no deep theory about the nature of causation.Is that too harsh? Had this book a different target, one could fairly complain that the author too infrequently steps away from the texts and commentators to offer and defend a... (shrink)

Leibniz war gewillt, die Idee der kontingenten Wahrheiten über nur mögliche individuelle Substanzen ernst zu nehmen -unabhängig davon, ob diese Substanzen existieren oder nicht. Einer der Wege, diese Idee zu erklären, ist die berühmte Lehre von der unendlichen Analyse. Eine wichtige und verwirrende Schwierigkeit für diese Lehre ist das von Robert M. Adams erörterte Problem des Beweises mit Glück. Auch wenn der vollständige individuelle Begriff einer möglichen Substanz S sich durch Analyse in unendlich viele einfache Begriffe zerlegen läßt, ist es (...) schwerlich erforderlich, daß der Beweis für das Enthaltensein eines Prädikats F im vollständigen Begriff von 5 unendlicher Analyse bedarf: Beweise gehen schrittweise vor; es ist offensichtlich möglich, daß einige Prädikate früher und schneller hergeleitet werden als andere. In diesem Aufsatz zeigen und entwickeln wir zwei leibnizische Wege, die das Problem des mit Glück kurzen Beweises beantworten. (shrink)

There is something undeniably puzzling, difficult, about relations. Socrates is a fine individual substance, and his paleness a fine accident; but what of his being taller than Simmias? If to our eyes Aristotle is working no harder in chapter seven of the Categories than in chapter eight, to medieval eyes things were messier there—or at any rate sufficiently unsettled to yield an extended and hotly disputed controversy than which only the question of universals is knottier. Leibniz evidently managed no better (...) than Aristotle, which scarcely counts against him: there were of course more medieval thinkers offering their glosses on Aristotle on relations than there are Leibniz scholars, but those of the latter who’ve thought they had something helpful to say about Leibniz on relations would agree that things are unsettled, and maybe even hotly disputed. Readers can gain some sense of this from Dennis Plaisted’s excellent but sadly under-reviewed contribution to the debate in Leibniz on Purely Extrinsic Denominations, which represents the most extended and detailed attack on broadly “reductionist” readings of Leibniz on relations to date. For reasons owing more to divine intervention than creaturely freedom, the present review is delinquent in a way that discussion of Plaisted’s work should not be. (shrink)

Inherited primarily from Aristotle and his scholastic commentators, the concept of substance plays a central role in early modern metaphysics. Roger Woolhouse's book is the first monograph-length introduction devoted to this important philosophical concept. Aimed primarily at the advanced undergraduate and beginning graduate, this wide-ranging and clearly-written book offers a judiciously compendious but rich account of the doctrine of substance in the hands of Descartes, Spinoza, and Leibniz.

Contents Preface General Introduction 1 | Science and Pseudoscience Introduction Karl Popper, Science: Conjectures and Refutations Thomas S. Kuhn, Logic of Discovery or Psychology of Research? Imre Lakatos, Science and Pseudoscience Paul R. Thagard, Why Astrology Is a Pseudoscience Michael Ruse, Creation-Science Is Not Science Larry Laudan, Commentary: Science at the Bar---Causes for Concern Commentary 2 | Rationality, Objectivity, and Values in Science Introduction Thomas S. Kuhn, The Nature and Necessity of Scientific Revolutions Thomas S. Kuhn, Objectivity, Value Judgment, and (...) Theory Choice Ernan McMullin, Rationality and Paradigm Change in Science Larry Laudan, Kuhn’s Critique of Methodology Helen E. Longino, Values and Objectivity Kathleen Okruhlik, Gender and the Biological Sciences Commentary 3 | The Duhem-Quine Thesis and Underdetermination Introduction Pierre Duhem, Physical Theory and Experiment W. V. Quine, Two Dogmas of Empiricism Donald Gillies, The Duhem Thesis and the Quine Thesis Larry Laudan, Demystifying Underdetermination *Colin Howson and Peter Urbach, The Duhem Problem Commentary 4 | Induction, Prediction, and Evidence Introduction Peter Lipton, Induction Karl Popper, The Problem of Induction Wesley C. Salmon, Rational Prediction Carl G. Hempel, Criteria of Confirmation and Acceptability Peter Achinstein, Explanation v. Prediction: Which Carries More Weight? *Nelson Goodman, The New Riddle of Induction Commentary 5 | Confirmation and Relevance: Bayesian Approaches Introduction Wesley C. Salmon, Rationality and Objectivity in Science *Deborah G. Mayo, A Critique of Salmon’s Bayesian Way *Alan Chalmers, The Bayesian Approach Paul Horwich, Therapeutic Bayesianism Commentary 6 | Models of Explanation Introduction Rudolf Carnap, The Value of Laws: Explanation and Prediction Carl G. Hempel, Two Basic Types of Scientific Explanation Carl G. Hempel, The Thesis of Structural Identity Carl G. Hempel, Inductive-Statistical Explanation Peter Railton, A Deductive-Nomological Model of Probabilistic Explanation *Philip Kitcher, Explanatory Unification *James Woodward, The Manipulability Conception of Causal Explanation Commentary 7 | Laws of Nature Introduction A. J. Ayer, What Is a Law of Nature? Fred I. Dretske, Laws of Nature D. H. Mellor, Necessities and Universals in Natural Laws Nancy Cartwright, Do the Laws of Physics State the Facts? Commentary 8 | Intertheoretic Reduction Introduction Ernest Nagel, Issues in the Logic of Reductive Explanations Paul K. Feyerabend, How to Be a Good Empiricist *Jerry A. Fodor, Special Sciences Philip Kitcher, 1953 and All That: A Tale of Two Sciences Commentary 9 | Empiricism and Scientific Realism Introduction Grover Maxwell, The Ontological Status of Theoretical Entities Bas C. van Fraassen, Arguments Concerning Scientific Realism Alan Musgrave, Realism versus Constructive Empiricism Larry Laudan, A Confutation of Convergent Realism *Juha T. Saatsi, On the Pessimistic Induction and Two Fallacies Ian Hacking, Experimentation and Scientific Realism David B. Resnik, Hacking’s Experimental Realism *Martin Carrier, What Is Right with the Miracle Argument Arthur Fine, The Natural Ontological Attitude Alan Musgrave, NOA’s Ark---Fine for Realism Commentary Glossary Bibliography Name Index Subject Index. (shrink)

Adherents of traditional western Theism have espoused CONJUNCTION: God is essentially perfectly good and God is thankworthy for the good acts he performs. But suppose that (i) God’s essential perfect goodness prevents his good acts from being free, and that (ii) God is not thankworthy for an act that wasn’t freely performed. Together these entail the denial of CONJUNCTION. The most natural strategy for defenders of CONJUNCTION is to deny (i). We develop an argument for (i), and then identify two (...) ways for the defender of CONJUNCTION to respond. Next we turn to a considerably different, rather less obvious route toward defending CONJUNCTION that is compatible with (i)—one which instead denies (ii). Here too we identify two ways for the defender of CONJUNCTION to proceed, yielding a total of four ways for the theist to respond. Because the last of these represents an important and underappreciated alternative for the theist, we devote the second half of the paper to developing and defending it. We argue that divine responsibility is sufficient for divine thankworthiness and consistent with the absence of divine freedom. We do this while insisting on the view that both freedom and responsibility are incompatible with causal determinism. (shrink)

The revival of Leibniz studies in the past twenty-five years has cast important new light on both the context and content of Leibniz's philosophical thought. Where earlier English-language scholarship understood Leibniz's philosophy as issuing from his preoccupations with logic and language, recent work has recommended an account on which theological, ethical, and metaphysical themes figure centrally in Leibniz's thought throughout his career. The significance of these themes to the development of Leibniz's philosophy is the subject of increasing attention by philosophers (...) and historians. This collection of new essays by a distinguished group of scholars offers an up-to-date overview of the current state of Leibniz research. In focusing on nature and freedom, the volume revisits two key topics in Leibniz's thought, on which he engaged both contemporary and historical arguments. Important contributions to Leibniz scholarship in their own right, these articles collectively provide readers a framework in which to better situate Leibniz's distinctive philosophy of nature and the congenial home for a morally significant freedom that he took it to provide. (shrink)

Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥ΘL(ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is (...) the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ. (shrink)

"Central Themes in Early Modern Philosophy is a selection of some of the best work being done in early modern philosophy by Anglo-American philosophers today.... The essays in this collection are historically informed and philosophically challenging. The book is a fitting tribute to Jonathan Bennett." -- Daniel Garber, University of Chicago.

A partire dal commento ad una sentenza sul problema della discriminazione razziale in una scuola privata, Cover presenta una teoria del pluralismo normativo fondata sulla distinzione fra autorità e significato. A tale dicotomia è dovuta la “proliferazione” dei mondi normativi e delle interpretazioni costituzionali. L’autore descrive i processi di formazione dei significati giuridici – la cosiddetta “giusgenesi” – ed offre una teoria della giurisdizione adatta ad un universo giuridico connotato da un radicale pluralismo. Così facendo, Cover intende mettere (...) in luce il potenziale trasformativo del diritto e in particolare del costituzionalismo. (shrink)

Working in ZF+AD alone, we prove that every set of ordinals with cardinality at least Θ can be covered by a set of ordinals in HOD of K (ℝ) of the same cardinality, when there is no inner model with an ℝ-complete measurable cardinal. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.

In the treatise On the Change of Names (part of his magnum opus, the Allegorical Commentary), Philo of Alexandria brings his figurative exegesis of the Abraham cycle to its fruition. Taking a cue from Platonist interpreters of Homer's Odyssey, Philo reads Moses's story of Abraham as an account of the soul's progress and perfection. Responding to contemporary critics, who mocked Genesis 17 as uninspired, Philo finds instead a hidden philosophical reflection on the ineffability of the transcendent God, the transformation of (...) souls which recognize their mortal nothingness, the possibility of human faith enabled by peerless faithfulness of God, and the fruit of moral perfection: joy divine, prefigured in the birth of Isaac. (shrink)

The experience of digital platforms in the 2020s is often marked by a lack of ethical care: increasing rates of online abuse, trolling and adversarial speech in many cases lead to harmful outcomes including suicidality. Underlying the ineffectiveness of extant regulation and platform policy has been a significant focus on users as individuals rather than as participants in a digital ecology with ethical responsibilities for the care of the other. Addressing these harms calls for cultural change in how we perceive (...) interactive communication, digital use, bodies and subjectivity. This paper asks what a feminist approach might contribute to the framing of improved online communication and the detoxification of the digital ecology. Drawing on recent work on non-violence by Judith Butler and approaches to ecologies and infrastructure by Lauren Berlant, the paper proposes an ethics of mutual care in communication, recognising communication and interactivity and online sociality as an a priori factor of liveable human lives. (shrink)

The Dodd–Jensen Covering Lemma states that “if there is no inner model with a measurable cardinal, then for any uncountable set of ordinals X, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|”. Assuming ZF+AD alone, we establish the following analog: If there is no inner model with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb (...) {R}}$$\end{document} –complete measurable cardinal, then the real core model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} is a “very good approximation” to the universe of sets V; that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} and V have exactly the same sets of reals and for any set of ordinals X with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${|{X}|\ge\Theta}$$\end{document}, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K(\mathbb {R})}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|. Here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document} is the set of reals and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}. (shrink)

A poetic study of a singular form of urban industrial art and its place in American culture. They lie underfoot, embellished and gleaming. They seal off and provide entry to an underground world of conduits, water mains, power lines, and sewers. They appear by the thousands in our cities, but very few people ever look at them or think about them as art. At once completely ordinary and totally unexpected, manhole covers present an infinite variety of design in the commonplace (...) as well as a record of defunct utility companies, forgotten business firms, and obsolete foundries. Manhole Covers documents this singular form of urban industrial art and its place in American culture. Mimi and Robert Melnick first revealed their obsession with street hardware twenty years ago in a remarkable little book called Manhole Covers of Los Angeles. Printed in a small format and a limited edition, it quickly went out of print and is now a scarce collector's item. But that was just an introduction to their larger project, which has come to fruition in this book of 200 photographs and an extended narrative documenting manhole covers throughout the United States and discussing the history of their use, manufacture, and function. A subject that at first seems straightforward and commonplace becomes redolent and poetic in the Melnicks' hands, for their hieroglyphic reading of manhole covers reveals a chapter of urban history that can only be recovered from the logos and markings of these early disks. There are square lids, convex lids, perforated lids. And the older ones wear an astonishingly diverse range of anything-but-blank faces expressed in raised crosses, waffle grids, cut-out diamonds, radial stars, floral patterns, and honeycomb treads. The diversity of design corresponds to an equally diverse typology of form and function, as indicated by their evocative labels: handholes, vents, coalholes, grates, lampholes, storm drains, steam covers, meter lids, traffic buttons. (shrink)

We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal \. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that \<\mathrm {cov}<\mathrm {cof}\), which is the first consistency result where more than two cardinal invariants (...) associated with \ are pairwise different. Another consequence is that \ in ZFC where \ denotes Marczewski’s ideal. (shrink)

In the treatise On the Change of Names (part of his magnum opus, the Allegorical Commentary), Philo of Alexandria brings his figurative exegesis of the Abraham cycle to its fruition. Taking a cue from Platonist interpreters of Homer's Odyssey, Philo reads Moses's story of Abraham as an account of the soul's progress and perfection. Responding to contemporary critics, who mocked Genesis 17 as uninspired, Philo finds instead a hidden philosophical reflection on the ineffability of the transcendent God, the transformation of (...) souls which recognize their mortal nothingness, the possibility of human faith enabled by peerless faithfulness of God, and the fruit of moral perfection: joy divine, prefigured in the birth of Isaac. (shrink)

DISCOURSE; EXPRESSION (i) 'Discourse' is a word with a variety of meanings. One of the more useful is as an omnibus word covering both thought and talk. ...