This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set (...) theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas. (shrink)

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2 |A| = 2 |B| . This implies in particular that B has 2 |B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from [6]. The paper is intended to be accessible (...) as far as possible to a general audience, in particular we have confined the more technical material to a "black box" at the end. The proof involves a variation on Foreman and Woodin's model in which GCH fails everywhere. (shrink)

An attempt is made here to examine the analysis three political thinkers - Thomas Paine, William Godwin, and Jeremy Bentham have offered of the idea of equality. The inquiry underrtaken is philosophical and not historical in character, since no attempt is made either at tracing the influence ht the biographical-cum-intellectual level of one of them upon the other or at treating their ideas on equality as born out of their preoccupation with the same problem to which they give various answers (...) and which can therefore be considered within a single overall framework. Instead, each thinker is considered independently. And a study is undertaken of the way he understands equality, the way he justifies it, the sort of equality he considers most important and his reasons for this, the area of life he takes the idea of equality to illuminate, the manner in which he relates it to other ideas, etc.. In each case, a fairly coherent philosophy of equality is sought to be constructed out of their respective writings. These three thinkers are selected for two reasons. The idea of equality looms quite large in their thought; as such, it was felt that looking at their writings from the standpoint of equality may illuminate their certain features that may otherwise remain obscure or relatively underemphasized. Further, as they consider equality from different philosophical positions it was believed that a critical examination of their writings could, perhaps, point to the general merits and limitations of their respective positions in terms of equality. in chapter I, it is argued that there are distinct views of God discernible in Paine's writings, and that corresponding to them are three distinct views of equality, though only two of them are discussed by Paine at any length. in chapter II, it is argued that, though Godwin begins as a thoroughgoing rationalist, three are shifts in his general philosophical position, and that, with each shift, his ideas on truth, rationality and equality undergo important changes. Finally, in chapter III, it is argued that there are two distinct theories of equality in Bentham and that tension between them remains unresolved. (shrink)

Mastery imagery has been shown to be associated with more positive cognitive and emotional responses to stress, but research is yet to investigate the influence of mastery imagery ability on imagery’s effectiveness in regulating responses to acute stress, such as competition. Furthermore, little research has examined imagery’s effectiveness in response to actual competition. This study examined (a), whether mastery imagery ability was associated with stress response changes to a competitive stress task, a car racing computer game, following an imagery intervention, (...) and (b), the effects of different guided imagery content on pre-task cognitive and emotional responses. In Session 1, 78 participants (M age = 20.03 years, SD = 1.28) completed ratings of pre-task anxiety intensity and direction, confidence, and perceived control. Imagery ability was also assessed before completing the task. In Session 2, participants were randomly allocated to an imagery condition (positive mastery, negative mastery, relaxation) or control group (no imagery) before completing the task and outcome measures again. For the negative mastery group, greater positive mastery imagery ability was associated with greater perceived control and perceiving anxiety as more facilitative. Furthermore, mastery imagery ability moderated the relationship between anxiety intensity and direction. Altogether, results suggest that positive mastery imagery ability may act as a potential buffer against the effects of negative images. (shrink)

Existence, the middle volume of Neville’s Philosophical Theology, offers a theological anthropology, and so deals with “religious dimensions of human nature, its conditions, and processes”. As such it contrasts with the mainly metaphysical concerns of the volume that precedes it, Ultimates, and the social scientific interests of the volume that follows, Religion. After a preface and introduction, the volume is arranged in four parts, each of four chapters. The parts deal respectively with “ultimate boundary conditions” of human existence set by (...) the metaphysics of determinateness developed in volume 1; “predicaments and deliverances” of... (shrink)

The latest volume in the splendid critical edition of the Opera philosophica et theologica of William of Ockham in progress at the Franciscan Institute of St. Bonaventure University under the general editorship of Gedeon Gál, O.F.M. The project itself is something of a phenomenon in the area of critical editions of medieval Latin texts in terms of the rapidity at which quality volumes are produced at remarkably reasonable costs. Since 1967 five quarto volumes, totaling some three thousand four hundred pages, (...) have appeared. Three of these contain the first portion of Ockham’s most important theological work, the Ordinatio of his "commentary" on book 1 of the Sentences. The final portion is scheduled to appear early in 1979 as volume 4 of the Opera theologica. Volume 1 of the philosophical opera contains the monumental Summa Logicae, and volume 3 will also appear this year, thus completing with the present volume the edition of the most important of Ockham’s logical works. Editors are also assigned and are already at work on the other major non-political writings, notably the Quodlibet and commentaries on Aristotle’s Physics. Since the Opera politica Guillelmi de Ockham were published in three octavo volumes by the University of Manchester Press, we may expect to have very shortly substantially all the works of the Venerable Inceptor, thanks to the exceptional industry of a team of highly qualified researchers as well as substantial grants by the National Endowment for the Humanities and the De Rance Corporation. Two of the editors of individual works in the present volume are deceased. Father Philotheus Boehner, O.F.M., who came to the Franciscan Institute from Germany before the outbreak of World War II, first conceived of and began work on the critical edition. His text of the Tractatus de praedestinatione was first published in 1945 in Franciscan Institute Publications, Text Series No. 2 and was subsequently translated into English by M. M. Adams and N. Kretzmann in 1969. It differs little in Brown’s revision, which adds variants from the Bruges MS, unavailable to Boehner because of the war. The other posthumous edition is that of E. A. Moody. This too appeared in the aforesaid Text Series as No. 14. The present text is identical with the earlier version, but observations and suggested alternate readings by the general editor are added in footnotes. The thirty-two pages of introduction contains a wealth of information. To mention but two items: One concerns the probable reason why Ockham only incepted in theology but never served as regent master. This apparently had little or nothing to do with Lutterall’s opposition, as Chancellor of the University, to Ockham’s views and his summons later to the papal court at Avignon. It stemmed rather from the Franciscan custom of promoting those bachelors who had completed their magisterial studies to regent master on the basis of seniority. At his time a junior like Ockham could expect a wait of eight to ten years. It was during this period, beginning probably in 1321 that he began his lectures on logic, probably at the Franciscan house of studies in London where he later composed the Summa Logicae and his exposition of Aristotle’s Physics, before the summer of 1324 when he went to Avignon. Another item is the effective refutation of the authenticity views of Prantl and Anneliese Maier of the Expositiones and their relationship to the spurious and derivative Notabilia. As a final comment, we note that this second volume of the Opera philosophica contains all the works of Ockham edited by Marcus de Benevento under the title Expositio aurea et admodum utilis super artem veterem edita per Ven. Inceptorem Guilielmum de Occham, [[sic]] cum quaestionibus Alberti Parvi de Saxonia.—A.B.W. (shrink)

The famous eastern tour of inspection undertaken by Scipio Aemilianus, L. Metellus Calvus and Sp. Mummius is now generally dated 140/39 b.c., where Diodorus seems to put it. The accepted view, however, involves discounting an explicit statement by Cicero. It also presents historical difficulties. In 140 b.c. there was no need for such a high-powered Roman initiative, and scholars can discover only very minor political results. Sherwin-White indeed criticised the envoys severely, especially Scipio; they were culpably blind to the new (...) menace of Parthia, which was steadily dismembering the Seleucid Empire east of the Euphrates. This is fair criticism only on the 140/39 b.c. dating. Did Scipio and his colleagues fail to see what is patent to us today? It is time to reexamine rigorously the underlying assumption. In Acad. prior. 2.5 Cicero defends a Roman noble's love of Greek learning in the following terms: ego autem cum Graecas litteras M. Catonem in senectute didicisse acceperim, P. autem Africani historiae loquantur in legatione illa nobili, quam ante censuram obiit, Panaetium unum omnino comitem fuisse, nec litterarum Graecarum nee philosophiae iam ullum auctorem requiro. The date of the embassy must be 144/3 b.c., if we follow the logic of this passage. Scipio was censor with L. Mummius in 142/1 b.c. and their public quarrel was hardly less notable than the embassy, in which L. Mummius' brother shared. Another Ciceronian passage – written some six years earlier – seems to contradict the dating offered in 45 b.c. In de republica 6.11 the elder Africanus prophesies his grandson's future greatness in the famous dream. (shrink)

The famous eastern tour of inspection undertaken by Scipio Aemilianus, L. Metellus Calvus and Sp. Mummius is now generally dated 140/39 b.c., where Diodorus seems to put it. The accepted view, however, involves discounting an explicit statement by Cicero. It also presents historical difficulties. In 140 b.c. there was no need for such a high-powered Roman initiative, and scholars can discover only very minor political results. Sherwin-White indeed criticised the envoys severely, especially Scipio; they were culpably blind to the new (...) menace of Parthia, which was steadily dismembering the Seleucid Empire east of the Euphrates. This is fair criticism only on the 140/39 b.c. dating. Did Scipio and his colleagues fail to see what is patent to us today? It is time to reexamine rigorously the underlying assumption. In Acad. prior. 2.5 Cicero defends a Roman noble's love of Greek learning in the following terms: ego autem cum Graecas litteras M. Catonem in senectute didicisse acceperim, P. autem Africani historiae loquantur in legatione illa nobili, quam ante censuram obiit, Panaetium unum omnino comitem fuisse, nec litterarum Graecarum nee philosophiae iam ullum auctorem requiro. The date of the embassy must be 144/3 b.c., if we follow the logic of this passage. Scipio was censor with L. Mummius in 142/1 b.c. and their public quarrel was hardly less notable than the embassy, in which L. Mummius' brother shared. Another Ciceronian passage – written some six years earlier – seems to contradict the dating offered in 45 b.c. In de republica 6.11 the elder Africanus prophesies his grandson's future greatness in the famous dream. (shrink)

In his book on Plutarch's Maxime cum principibus philosopho esse disserendum from 2009, Geert Roskam takes up the question of the genre of the work. Few scholars have approached this question and they have had little to say. Hence, Roskam's treatment of the question is much appreciated. Among the suggestions previously put forth is the suggestion by F.H. Sandbach, who argued that the work should be regarded as a treatise, while H.N. Fowler stated in the ‘Introduction’ to the Loeb Classical (...) Library translation that the work is an essay. Other suggestions regarding the genre of Maxime cum principibus include the notion that it is a diatribe and a parva disputatio e magisterio orta. Of course, although all four suggestions have something to say for themselves, they are rather imprecise and not actual genres in a specific sense. The diatribe often surfaces as a convenient label for ancient philosophical discourses, but it is a misleading label, since what it picks out was not recognized as a distinctive form or stylistic level in antiquity. In addition, the technical and literary uses of the Greek word διατριβή were entirely different. (shrink)

Some propositional attitude verbs require that the complement contain some “subjective predicate”. In terms of the theory proposed by Lasersohn, these verbs would seem to identify the “judge” of the embedded proposition with the matrix subject, and there have been suggestions in this direction. I show that it is possible to analyze these verbs as setting the judge and doing nothing more; then according to whether a judge index or a judge argument is assumed, unless the complement contains a subjective (...) predicate, the whole matrix is redundant or there is a type conflict. I further show that certain clear facts argue for assuming a judge argument which can be filled by a contextually salient entity–or by the subject of a subjective attitude verb. (shrink)

Treatises of this length and care are rarely written today and in the course of Cumming's explorations there is an enormous richness of insight, commentary, and analysis of the history of liberal thought. But at the same time, it is difficult to keep the main themes of this study in clear focus. One gets the impression that Cumming originally set out to understand liberal thought as expressed by John Stuart Mill and found himself digging into origins. Dig he does, taking (...) into account in his intellectual journey through Western Civilization: Polybius, Cicero, Augustine, Petrarch, Machiavelli, Hobbes, Locke, Hume, Bentham, James Mill and many others along the way. One can learn a great deal about this western political tradition by following Cumming's patient explications and critiques. In the foreground is always John Stuart Mill and at times Cumming fosters the misimpression that Mill culminates this entire tradition. Yet Cumming's attitude toward Mill is strangely ambivalent and toward the end of this study, Cumming seems to be more fascinated with the stages of Mill's development and his mental crisis rather than with the integrity and coherence of his political philosophy. Liberal political thought has recently come in for a severe polemical thrashing and Cumming's study might have been a detailed, eloquent defense of this tradition. But the study is deficient in attempting to show how liberal thought can directly meet the numerous criticisms that have been raised from many sides. In the preface, Cumming reports that the manuscript was on the way to the typesetters during the upheaval at Columbia when police arrived on campus. This episode symbolizes the strange feeling one has that the book is dated by the time it appeared. Despite its weaknesses as an apology for liberal thought, it excels in making us sensitive to its long and vital history.--R. J. B. (shrink)

The merit of Plato’s Laws remains largely untapped by those seeking genuinely collaborative models of the doctor–patient tie as alternatives to paternalism and autonomy. A persistent difficulty confronting proposed alternatives has been surpassing the notion of pronounced intellectual and values asymmetry favoring the doctor. Having discussed two prominent proposals, both of which evince marked paternalism, I argue that reflection on Plato yields four criteria that a genuinely collaborative model must meet and suggest how the Laws addresses them. In the process, (...) the Laws’ doctor–patient tie is shown to be far more nuanced than interpreters have previously observed. Although Plato’s account will not solve our own quandaries, it illustrates how one might retain asymmetry of a kind without capitulating to familiar oppositional modalities. Through this account, I hope to show that the Laws merits fuller inclusion in contemporary discussions than it has heretofore received. (shrink)

Logicians and theoretical physicists will also benefit from this book.

Two main methods for analysing de re readings of definite descriptions in intensional contexts coexist: that of evaluating the description in the actual world, whether by means of scope, actuality operators, or non-local world binding, and that of substituting another description, usually one expressing a salient or ‘vivid’ acquaintance relation to an attitude holder, prior to evaluation. Recent work on so-called descriptive indexicals suggests that contrary to common assumptions, both methods are needed, for different ends. This paper aims to show (...) that there is indeed a division of labour between the two methods of analysis and to identify criteria for choosing among alternative ways to model the second, substitutional method. (shrink)

One of the most interesting phenomena of our religious-political life is the considerable difference in attitude toward religion between the popular masses and the political elite. In our survey of public opinion, the respondents had to express their attitude to two alternative statements: "There are national, traditional religions in our country. They should have more rights than representatives of religions that are new to our country "; and "All religions should have absolutely equal rights." Only 9 percent agreed with the (...) first statement, while the vast majority agreed with the second. Even among the Orthodox, adherents of the Moscow patriarchy, only 13 percent were supporters of special patronage by the state for the traditional religions, while those who advocated an equality of religion made up 69 percent. Thus, the idea of a state church is alien to the contemporary popular consciousness. The evolution of mass consciousness is toward an even greater amorphousness and indefiniteness with regard to religion and further away from the idea of a national, state church. The data confirming this have already been presented. Let me just recall that the percentage of persons who approved of the church's participation in political life decreased from 74 percent to 48 percent from 1990 to 1991. (shrink)