bluuebunny/crossref_metadata_2025 huggingface dataset:
Modal Realism, Modal Rationalism, Modal Naturalism
Authors: Stalnaker Robert
Published: November 2017

This chapter summarizes the accounts of modal realism, modal rationalism, and modal naturalism. It details the author's attempt to develop a framework that is compatible with the denial of actualist accounts of modality. It also alludes to some ways that the contrast between modal naturalism and modal rationalism connects with many of the issues that have been the focus of attention in recent philosophical discussions about reference, intentionality, and knowledge: Frege puzzles about singular reference, the phenomenon of a posteriori necessities, the interpretation and application of two-dimensional modal semantics, contextualism about knowledge. This book has not been about those problems, but the development of the framework of modal semantics is motivated in large part by its relevance to them.
Order, Symmetry, and the Organization of Matter
Authors: Stein Daniel L. , Newman Charles M.
Published: November 2017

This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and several thermodynamic terms. It also presents the necessary concepts from thermodynamics and statistical mechanics that will be needed later. It boils down the latter to its most elemental and essential ingredient: that of temperature as controlling the relative probabilities of configurations of different energies. For much of statistical mechanics, all else is commentary. This is sufficient to present an intuitive understanding of why and how matter organizes itself into different phases as temperature varies, and leads to the all-important concept of a phase transition.
A Quick Introduction to Benfordʼs Law
Authors: Miller Steven J.
Published: November 2017

This chapter provides a brief overview of Benford's law. It states Benford's law of digit bias and describes its history. The chapter then discusses the origins of Benford's law and gives numerous examples of data sets that follow this law, as well as some that do not. From these examples this chapter extracts several explanations as to the prevalence of Benford's law. Finally, the chapter closes with a quick summary of many of the diverse situations in which Benford's law holds, and why an observation that began in looking at the wear and tear in tables of logarithms has become a major tool in subjects as diverse as detecting tax fraud and building efficient computers.
Measuring the Quality of European Statistics
Authors: Rauch Bernhard , Göttsche Max , Brähler Gernot , Engel Stefan
Published: November 2017

This chapter analyzes Greek statistics which are not relevant to government deficit spending and compare the findings with the results of prior research, which had shown a significant deviation from Benford's law of the first digits distribution of Greek financial statistics. The hypothesis here is that the social data set should conform better with Benford's law than the financial data set, as the incentive for manipulation is lower. However, the results in this chapter show that, in contrast to their financial data, the Greek social statistics data have a good fit with Benford's law. The chapter interprets this outcome as a sign for the effectiveness of the Benford test.
Managing Risk in Numbers Games
Authors: Chou Mabel C. , Kong Qingxia , Teo Chung-Piaw , Zheng Huan
Published: November 2017

This chapter applies Benford's law to study how players choose numbers in fixed-odds number lottery games. Empirical data suggests that not all players choose numbers with equal probability in lottery games. Some of them tend to bet on (smaller) numbers that are closely related to events around them (e.g., birthdays, anniversaries, addresses, etc.). In a fixed-odds lottery game, this small-number phenomenon imposes a serious risk on the game operator of a big payout if a very popular number is chosen as the winning number. The chapter quantifies this phenomenon and develops a choice model incorporating a modified Benford's law for lottery players to capture the magnitude of the small-number phenomenon observed in the empirical data.
PV Modeling of Medical Imaging Systems
Authors: Chiverton John , Wells Kevin
Published: November 2017

This chapter applies a Bayesian formulation of the Partial Volume (PV) effect, based on the Benford distribution, to the statistical classification of nuclear medicine imaging data: specifically Positron Emission Tomography (PET) acquired as part of a PET-CT phantom imaging procedure. The Benford distribution is a discrete probability distribution of great interest for medical imaging, because it describes the probabilities of occurrence of single digits in many sources of data. The chapter thus describes the PET-CT imaging and post-processing process to derive a gold standard. Moreover, this chapter uses it as a ground truth for the assessment of a Benford classifier formulation. The use of this gold standard shows that the classification of both the simulated and real phantom imaging data is well described by the Benford distribution.
Averting Two Dystopias
Authors: Brettschneider Corey
Published: November 2017

This introductory chapter provides an overview of value democracy. According to value democracy, all viewpoints should be protected by rights of free speech from coercive bans or punishment. However, the state also has an obligation in value democracy that extends beyond protecting freedom of speech. It should engage in democratic persuasion, actively defending the democratic values of freedom and equality for all citizens when it “speaks.” The notion of state speech is common in First Amendment jurisprudence. It often refers to the various non-coercive functions of the state, ranging from pure expression, such as speeches, to issues of funding. By using democratic persuasion to articulate the reasons for rights, value democracy aims to answer the critics who contend that liberalism cannot defend its most basic values or counter the threat to equality that might come from hate groups in civil society.
Publicly Justifiable Privacy and Reflective Revision by Citizens
Authors: Brettschneider Corey
Published: November 2017

This chapter discusses the conception of “publicly justifiable privacy,” which clarifies the implications of the principle of public relevance for thinking about the divide between public and private. This conception of publicly justifiable privacy challenges the traditional liberal approach of separating public values from the internal dynamics of the family and civil society. According to publicly justifiable privacy, family and civil society practices that conflict with free and equal citizenship should be protected by rights, but ideally should be amended to be compatible with public values. The chapter then argues that people should engage in reflective revision to change those personal beliefs and practices.
Democratic Persuasion and State Subsidy
Authors: Brettschneider Corey
Published: November 2017

This chapter examines the notion that, while persuasion should not be backed by coercive force, it should be backed by the state's subsidy power. It defines subsidy power as the ability of the state to spend money and, as crucially, to refuse to spend money on certain organizations. The state's subsidy power includes the ability to grant or withdraw tax-exempt, tax-deductible non-profit status. Its use is compatible with the right of free expression. Indeed, the chapter argues that the reasons justifying free expression require the state to withdraw subsidies from groups that oppose the core values of free and equal citizenship.
Religious Freedom and the Reasons for Rights
Authors: Brettschneider Corey
Published: November 2017

This chapter focuses on the freedom of religion. On some accounts of religious freedom, religious beliefs deserve a presumptive protection from state influence. The chapter argues against such “static” views of religious freedom, and claims that rights should not entail the absence of public justification. Not only are some religious beliefs publicly relevant, but the state should seek to transform them through its persuasive capacity. In making this argument, the chapter appeals to the ideal of religious freedom itself. Some religious conceptions are at odds with the ideal of religious freedom—suggesting that religious freedom itself requires an account of the public relevance of hateful religious beliefs and a role for state transformation in the realm of religion.
Data and Hypothesis Tests
Authors: Temin Peter
Published: November 2017

The Romans talked and wrote constantly about prices. It seems obvious that they must have been using these prices in their daily lives to leave us so many price quotes. Yet there has been doubt over the years whether the Roman economy was dominated by markets. I reviewed a small corner of this debate in ...
Variations on a Theme
Authors: Nadeem Shehzad
Published: November 2017

This chapter considers how place-bound practices, policies, and identities are being reconfigured by cross-border processes. Globalization has been accused of decreasing the significance of place. Through the diffusion of communication technologies, our experiences of place are transformed and the turnover time of capital is truncated. The chapter first explains how place is being altered by global capitalism before discussing the basic characteristics of global outsourcing and the historical and institutional context in which it takes place. It then examines the production of space in India, focusing in particular on how the country became the “world's back office.” It also looks at the emergence of consumer-oriented mimicry as an integral component of class and personal identity. The chapter argues that globalization does not substitute the dynamism of modernity for the complacent solidity of tradition nor the Occident for Orient. Its genius and mystery lay in the balancing of diametric modes.
Cyber-Coolies and Techno-Populists
Authors: Nadeem Shehzad
Published: November 2017

This chapter examines the normative visions that animate globalization: namely, the cosmopolitan ideologies of global capitalism and labor's internationalist challenges to them. Using the idea of an economy of utopia, it demonstrates how these universalizing ideals are transformed through their application in particular contexts. More specifically, it considers how capital and labor are adjusted to accommodate distinct political and economic realities. The chapter begins with a discussion of what it calls business cosmopolitanism and how the realities of uneven development, poor infrastructure, and a labor shortage in India lead executives and their political allies to espouse a vision of techno-populism that is more politically viable. It then explores the ideal of worker internationalism, along with the assertion that workers' individualism and indifference to unions are a species of false consciousness. Finally, it describes work sites as branded electronic sweatshops and workers as cybercoolies.
Rites of Passage and the Grand Tour: Discovering, Imagining and Inventing European Civilization in the Age of Enlightenment
Authors: Wokler Robert , Brooke Christopher
Published: November 2017

This chapter discusses the significance of the Grand Tour in the eighteenth century. The itinerary of the Grand Tour offered a program of postgraduate studies which aimed to lift the veil of ignorance of an undergraduate curriculum that embraced classical languages but not the civilizations that had produced them. Tourists of one denomination or another had been in great abundance in European history before the eighteenth century, and many of the motives that had inspired travelers in medieval and early modern Europe—diplomacy, commerce, adventure and, especially outside Europe, missionary zeal and anthropological curiosity—remained widely prevalent. But perhaps the most striking differences between grand tourism in the eighteenth century and journeys undertaken by earlier travelers revolve around the conceptions of civilization which inspired eighteenth-century voyagers to retrace Europe's origins and partake of its most glorious antiquity.
Rouseau on Rameau and Revolution
Authors: Wokler Robert , Brooke Christopher
Published: November 2017

This chapter re-examines the controversy over the nature and extent of Rousseau's influence on the French Revolution of 1789. It does so against the background of the Lettre sur la musique françoise and the uprising which he claimed this work had averted, rather than in the more customary context of the Contrat social and the chain of political events that text may have heralded or initiated. It argues that in effect, if not by design, the Lettre constitutes a critique of the musical philosophy of Rameau—a critique which Rameau himself attempted to refute in his own replies to Rousseau's text. Moreover, it was in the course of Rousseau's formulations of his rejoinders to the counterattacks of Rameau that he came to develop the ideas of the Lettre as a part of his more general social theory—and, indeed, as that part which was to prove the most politically radical in tone and the most revolutionary in its implications.
The Enlightenment Hostilities of Voltaire and Rouseau
Authors: Wokler Robert , Brooke Christopher
Published: November 2017

This chapter details the relationship between Voltaire and Rousseau, highlighting their personal and doctrinal differences. The two men could not be friends, nor hold to the same principles of Enlightenment. However, they were at least both critics of the Enlightenment's enemies, and from different perspectives they attacked similar targets—obscurantism and superstition in theology, metaphysics and dogmatism in philosophy, and despotic systems of tyranny and privilege in politics and economics. Both figures were also generally critical of the great speculative systems of European philosophy that prevailed in the seventeenth and early eighteenth centuries: Voltaire challenging mainly the metaphysics of Descartes and the theodicy of Leibniz, Rousseau objecting more to the natural law philosophies of Grotius, Hobbes, Pufendorf and even Locke.
Rousseau’s Pufendorf: Natural Law and the Foundations of Commercial Society
Authors: Wokler Robert , Brooke Christopher
Published: November 2017

This chapter analyzes Rousseau's conception of the political dimension of liberty in the light of a particular debate which has formed the most important contribution to the study of Rousseau's political thought in the twentieth century. This debate has to do with the place of natural law in Rousseau's philosophy, and with the extent to which, in his idea of the foundations of the state, he upheld or rejected principles of jurisprudence espoused by earlier thinkers. It considers such principles in three rather different forms, which are termed superior, anterior, and generative natural law. It also comments on Rousseau's idea of representation in the light of arguments drawn from a number of jurisprudential thinkers before him. In the course of the discussion, the chapter aims to offer a new interpretation of Rousseau's assessment of Pufendorf, whom Rousseau came to confront in his writings as much as, if not more than, any other political thinker.
Rouseau and Marx
Authors: Wokler Robert , Brooke Christopher
Published: November 2017

The political theories of Rousseau and Marx arouse stronger feelings than do most doctrines, and they have exercised a greater influence on the course of social revolutions than have the ideas of any other modern writers. But while each continues to attract widespread interest, they are seldom compared with one another. This chapter contrasts the doctrines of Rousseau and Marx. It argues that elements of Rousseau's philosophy of culture, together with his conception of property embrace a wider spectrum of human activities than Marx allowed to be of central significance. It stresses the greater scope of Rousseau's vision of our civilization's decline as compared with Marx's account of the factors which shape our historical epochs. The discussion then turns to the place of moral values in their doctrines.
Educating Citizen-Soldiers in World War II
Authors: Loss Christopher P.
Published: November 2017

This chapter moves the story from the New Deal to the U.S. Army. As the state's main wartime hub for psychological research, the Army Research Branch, headed by University of Chicago sociologist Samuel A. Stouffer, presented evidence to military commanders that better-educated soldiers were more efficient, exhibited higher morale, and were less likely to desert or suffer a psychoneurotic breakdown than their educationally deprived peers. Military and educational policymakers were galvanized by this finding and joined forces to create the Army Information and Education Division—the education clearinghouse for the common soldier. With the steady support of General George C. Marshall, the chief of staff of the army, who believed wholeheartedly in the transformative power of education, millions of G.I.s made use of the educational services provided to them.
A Brief Overview of Recent Climate Change and Its Ecological Context
Authors: Post Eric
Published: November 2017

This introductory chapter summarizes the most prominent abiotic components of recent climate change to establish the environmental context from which the discussion in the rest of the book proceeds. From an ecological perspective, climate change is most meaningfully considered as the suite of abiotic changes occurring across Earth coincident with the onset of the Industrial Revolution and progressing over the past 150 years. These abiotic changes include rising temperatures, temperature variability, changes in precipitation and snow cover, and diminishing sea and land ice. All these changes can be linked to ecological dynamics, though it is probably fair to state that most research to date on the ecological consequences of climate change has focused on temperature changes.
Entrepreneurship and Innovation
Authors: Acs Zoltan J.
Published: November 2017

This chapter examines entrepreneurship and innovation as fundamental elements of American-style capitalism. It first provides a historical background on how America got to an era of cowboy capitalism before discussing how the American economy evolved after the settlement of the western frontier. The major changes moved in the direction of large industrial processes and an attitude that, among firms, bigger is better; this period is known as the managerial economy, which lasted through the 1970s. The chapter also considers why the information technology revolution happened in America and concludes with an assessment of whether the past three decades really is a new era of cowboy capitalism—a shift from the managerial economy that dominated for most of the twentieth century to a renewed entrepreneurial economy.
The Emergence of Corporate Merchant-Banks in Dugento Tuscany
Authors: Padgett John F.
Published: November 2017

This chapter illustrates that the Tuscan merchant-banks organizationally sat at the intersection of the otherwise distinct relational-flow domains of international trade, state finance, and noble kinship. Instead of mobile merchants from many nations traveling with their wares to and from central markets in France, a network of Italian (mostly Tuscan) merchant-banks developed in the mid-1200s effecting international movements of both goods and currency through themselves. Such banks were constructed out of sedentary merchants arranged in geographically distributed filiali or branches, sending letters to each other. Their multifunctional network position, the chapter argues, is why organizational innovations cascaded from one domain to another.
Organizational and Institutional Genesis
Authors: Powell Walter W. , Packalen Kelley , Whittington Kjersten
Published: November 2017

This chapter examines eleven regions in the United States in the 1980s and 1990s that were all rich in resources—ideas, money, and skills—which might have led to the formation of life sciences clusters. Yet only three of the regions—the San Francisco Bay Area, Boston, and San Diego—developed into robust industrial districts for biotechnology. Most research on the emergence of high-tech cluster samples on successful cases and traces backward to find a developmental pattern. In contrast, rather than read in reverse from a positive outcome, the chapter builds networks forward from their early origins, revealing three crucial factors: organizational diversity, anchor tenant organizations that protect the norms of a community and provide relational glue across multiple affiliations, and a sequence of network formation that starts with local connections and subsequently expands to global linkages.
Valuing Persons
Authors: Jollimore Troy
Published: November 2017

This chapter argues that the perceived tension between loving persons and valuing the qualities and other properties that attach to persons is largely ungrounded. In particular, we need not worry that valuing those properties must necessarily imply that the person herself is not being valued, or that in valuing a person for assessable contingent properties we are, in any objectionable or worrisome sense, objectifying her. Rather than regarding themselves as alienated from their (attractive) “accidental” properties, persons who have them typically identify with them and want to be perceived by others as possessing them. Individuals conceive of themselves as entities in possession of certain features that are observable by others and assessable in terms of value and attractiveness, and almost all of them strongly desire that at least some of these features be judged by others to be attractive and desirable. It is not as if our observable qualities appear only in the way in which others conceive of us but do not infect our own self-understandings. Rather, they figure prominently in both contexts.
Between the Universal and the Particular
Authors: Jollimore Troy
Published: November 2017

This chapter argues that love lies somewhere between reason and unreason, just as it lies somewhere between the particular and the universal. It places a particular individual at the center of my field of vision, and in doing so makes my experience of my life very different from what it would otherwise have been, and very different from other people's experiences of their lives. It even makes my experience of life different from that of my beloved. It is sometimes suggested that the most unified lovers are not those who gaze lovingly into each other's eyes but those who are perceiving some third thing, who share some object of attention and thus share an experience. However, we can surely say that even if the particular details of the experience are different, there is undoubtedly a kind of experience—seeing one's beloved—that is shared by lovers who are looking at each other.
Love Stories
Authors: Inhorn Marcia C.
Published: November 2017

This chapter discusses how husbands' loving commitments toward their wives are a major part of Middle Eastern conjugality and an important feature of emergent masculinities in the region. Even seemingly traditional men such as Hatem—a farmer from a “closed” rural Syrian community—defy masculine stereotypes. Although conventional wisdom suggests that Middle Eastern men routinely divorce their infertile wives, Hatem's case provides evidence to the contrary. His story suggests that enduring conjugal commitments are a key feature of emergent masculinities in the Middle East, even in the face of intractable infertility. According to studies, this is as true among lower-class Middle Eastern couples, both urban and rural, as it is among cosmopolitan elites.
Plato and His Predecessors
Authors: Cohen G. A.
Published: November 2017

This chapter explores how the nature/convention distinction is taken up by Plato and many of his Sophistic predecessors. It argues that the philosophically most fundamental motivation of Plato's Republic is to reply to a staple proposition of fifth-century Greek thought, a proposition propounded by many of Plato's Sophistic predecessors: that there is a distinction between nature and convention, phusis and nomos, and that nomos, convention, human law, cannot be derived from nature and even contradicts nature. The chapter first considers the historical importance of Sophism as well as Sophistic universalism before discussing Socrates' response to the Sophists, particularly Glaucon, and Plato's arguments against a contractarian account of justice. It also examines the concepts of authoritarianism, totalitarianism, and the lower class, along with Aristotle's rejection of the Sophist opposition between nature and convention.
Hegel: Minds, Masters, and Slaves
Authors: Cohen G. A.
Published: November 2017

This chapter examines G. W. F. Hegel's dialectic of the master and the slave which he articulated in his book Phenomenology of Spirit and how it is related to his general philosophy. Hegel thought that everything the mind, any mind, experiences is in some sense a product of mind itself. One way of explaining how he arrived at this strange idea is by describing how he responded to the thought of Immanuel Kant. Kantian philosophy features a set of dualities or oppositions, such as those between freedom and necessity, between the sensibility and the understanding, between the analytic and the synthetic, and between the infinite and the finite. Whereas Kant loved dichotomies, Hegel abhorred ultimate dichotomies in the scheme of things. The chapter considers some tenets of Absolute Idealism in order to elucidate some of the more general philosophical questions with which Hegel was concerned in the course of his master/slave discussion.
Bourgeois and Proletarians
Authors: Cohen G. A.
Published: November 2017

This chapter explores the question of the nature of the alienation of the bourgeoisie under capitalism. In particular, it considers the distinction made by Karl Marx in The Holy Family between the alienation endured by the worker and the alienation endured by the capitalist in bourgeois society. According to Marx: “The possessing classes and the class of the proletariat present pictures of the same human self-estrangement. But the former class feels at home in and confirmed by this self-estrangement.” The chapter analyzes the meaning of this passage by focusing on a characterization of the human essence in The German Ideology and on the doctrine of alienation articulated in the Paris Manuscripts. It also discusses the worker's alienation in his relation to the machine, and the capitalist's alienation in his relation to money, as well as the latter's relation to his capital. Finally, it restates the contrast between bourgeois and proletarian.
The Workers and the Word: Why Marx Had the Right to Think He Was Right
Authors: Cohen G. A.
Published: November 2017

This chapter defends Karl Marx against the criticism that he lacks the right to regard his theory as true, insisting that he had the right to think that he was right. To this end, it advances four arguments intended to show that if Marx's theory serves and represents the working class, then it is reasonable to think that it is correct. The first argument relates to Marx's thinking that every class which makes a revolution does so in order to advance its own material interests; the second deals with the suffering of the proletariat in capitalist society; the third concerns the workers' revolutionary struggle, a socialist revolution; and the fourth argument is based on the premise that when a class is secure in its position it needs no illusions. The chapter also considers Reinhold Niebuhr's views on how the proletariat can effect its revolution.
Reply to Elster on “Marxism, Functionalism, and Game Theory”
Authors: Cohen G. A.
Published: November 2017

In this chapter, the author responds to Jon Elster's criticism of his use of functional explanation in his account of historical materialism. Elster rejects the association between Marxism and functional explanation, arguing that there is no scope for functional explanation in social science. He therefore concludes that the Marxist theory of society and history should abandon functional explanation and that it should, instead, draw for its explanations on the resources of game theory. The author offers an explanation of historical materialist theory that he attributes, on a textual basis, to Karl Marx, and that he articulates and defends in his book Karl Marx's Theory of History. He asserts that game theory cannot replace functional explanation within Marxist social analysis and that it has no place at the heart of historical materialism, alongside functional explanation.
Structure of Crystal, Bucket of Dust
Authors: Galison Peter
Published: November 2017

This chapter advances the idea that every mathematical argument tells a story by focusing on the biographies of two pioneers: American physicist John Archibald Wheeler and the Bourbaki collective of young French mathematicians. Wheeler viewed mathematical arguments essentially as compound machines; his is a world where instructions pull dimensionality itself out of a Borel sets that he referred to as a “bucket of dust.” Whereas Wheeler's story is a set of linked machine-stories, a hybrid of discovery accounts, speculative machine-like functions and mechanisms, Bourbaki's account is a crystal of symbols. The chapter contrasts Wheeler's way of relating the narrative of mathematics with that of Bourbaki. In particular, it considers Wheeler's machine metaphor and its rejection by Bourbaki; his mathematical physics, and especially his views on gravitational collapse; and Bourbaki's “abstract package.”
Deductive Narrative and the Epistemological Function of Belief in Mathematics
Authors: Nave Federica La
Published: November 2017

This chapter explores the epistemological function of belief in mathematical thinking by considering Rafael Bombelli's contribution to the creation of imaginary numbers. The discussion focuses on Bombelli's L'Algebra, which he wrote in 1550 in five books, three of them published in 1572. Over that period, Bombelli completely changed his mind about the solvability of the so-called irreducible case of cubic equations—that is, the case in which the solution of the cubic equation contains square roots of negative numbers—and about the nature of the numbers involved in such a solution. The chapter explains the evolution in Bombelli's thinking in those years: he initially believed that the irreducible case was insolvable and that the roots of negative numbers were unacceptable, but eventually made a complete turnaround. Bombelli's pursuit reflected his concept of algebra as a discipline that was no less speculative than geometry.
Do Androids Prove Theorems in Their Sleep?
Authors: Harris Michael
Published: November 2017

This chapter examines the role of dreams in mathematics by focusing on Robert Thomason's decision to add as co-author of an important paper his deceased friend Tom Trobaugh, a non-mathematician. The reason Thomason gave was that Trobaugh, who had committed suicide a few months earlier, appeared to him in a dream and helped him complete a particularly difficult proof. The chapter first considers what the dream tells us about the narrative structure of a mathematical proof before discussing the use of automated theorem provers in creating new proofs. It also explores how K-ness can be defined and whether it can be calculated in the context of the Thomason–Trobaugh article. Finally, it describes the division in the mathematical literature between ghost and ghostwriter, citing as an example the work done regarding Grigori Perelman's proof of the Poincaré conjecture.
Visions, Dreams, and Mathematics
Authors: Mazur Barry
Published: November 2017

This chapter considers the role of visions and dreams in mathematics by focusing on Leopold Kronecker's desire—or dream—to find solutions to a large and interesting collection of polynomial equations. It begins with a discussion of three kinds of storytelling in mathematics: origin stories, purpose stories, and raisins in the pudding. It then examines Kronecker's so-called liebster Jugendtraum, the “beloved dream of (his) youth,” arguing that the seed of this dream lay in Carl Friedrich Gauss's expression for square roots of integers as trigonometric sums. It also describes three truths about explanation as opposed to proof, along with basic concepts in the epistemology of mathematics, such as the difference between explicit and implicit statements. Finally, it speculates on how Girolamo Cardano, Gauss, Isaac Newton, and Kronecker might solve cubic equations.
Vividness in Mathematics and Narrative
Authors: Gowers Timothy
Published: November 2017

This chapter examines vividness in mathematics and narrative. It first gives two presentations of the mathematical notion of a group before explaining how to calculate highest common factors. It then considers the role of figures of speech, such as metaphor and irony, in mathematics and proceeds by citing a few passages from literature that highlight the use of concrete details to convey abstract thoughts; these include passages from Charles Dickens's Bleak House, Alan Hollinghurst's The Folding Star, and George Eliot's Middlemarch. The chapter argues that when working through a totally analogous process, exactly the same response can be created in certain mathematical texts.
Mathematics and Narrative: An Aristotelian Perspective
Authors: Lloyd G. E. R.
Published: November 2017

This chapter explores the relationship between mathematics and narrative from an Aristotelian perspective. Aristotle's philosophy of mathematics is radically different from that of Plato. For example, Aristotle did not postulate separate intelligible mathematical objects. For Aristotle, mathematics studied the mathematical properties of physical objects, in abstraction from the physical properties those objects possessed. Another divergence between Aristotle and Plato relates to comments that the former made in the Metaphysics about the activity of mathematicians and the actualization of certain potentialities in their work. In particular, three terms mentioned by Aristotle are problematic: orthe, diagramma, and energeia. The chapter argues that Aristotle challenged the conception of mathematics as atemporal, soon after Plato defended it, by insisting that mathematical proofs are produced by energeia.
Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative
Authors: Plotnitsky Arkady
Published: November 2017

This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the question of the potentially uncircumventable limits of thought and knowledge; and second, to the question of a certain heterogeneous and yet interactive multiplicity of concepts and of different fields such as algebra and geometry. The chapter starts with the Pythagoreans' discovery of the concept of “incommensurability,” or the irrationality of certain numbers, specifically the side and the diagonal of the square, and the narrative associated with this discovery. It then examines the transition from non-Euclidean physics to non-Euclidean mathematics by focusing on quantum mechanics and its relation to non-Euclidean epistemology. It also discusses the algebraic aspects of non-Euclidean geometry and concludes with the suggestion that non-Euclidean thinking retains the essential, shaping role of the movement of thought.
The Growth of Algebraic Thought in Sixteenth-Century Europe
Authors: Katz Victor J. , Parshall Karen Hunger
Published: November 2017

This chapter traces the growth of algebraic thought in Europe during the sixteenth century. Equations of the third and fourth degrees sparked quite a few algebraic fireworks in the first half of the century. Their solutions marked the first major European advances beyond the algebra contained in Fibonacci's thirteenth-century Liber abbaci. By the end of the century, algebraic thought—through work on the solutions of the cubics and quartics but, more especially, through work aimed at better contextualizing and at unifying those earlier sixteenth-century advances—had grown significantly beyond the body of knowledge codified in Luca Pacioli's fifteenth-century compendium, the Summa de arithmetica, geometria, proportioni, e proportionalita. Algebra during this period was evolving in interesting ways.
Democratic Legitimacy
Authors: Rosanvallon Pierre
Published: November 2017

It's a commonplace occurrence that citizens in Western democracies are disaffected with their political leaders and traditional democratic institutions. But this book argues that this crisis of confidence is partly a crisis of understanding. The book makes the case that the sources of democratic legitimacy have shifted and multiplied over the past thirty years and that we need to comprehend and make better use of these new sources of legitimacy in order to strengthen our political self-belief and commitment to democracy. Drawing on examples from France and the United States, the book notes that there has been a major expansion of independent commissions, NGOs, regulatory authorities, and watchdogs in recent decades. At the same time, constitutional courts have become more willing and able to challenge legislatures. These institutional developments, which serve the democratic values of impartiality and reflexivity, have been accompanied by a new attentiveness to what the book calls the value of proximity, as governing structures have sought to find new spaces for minorities, the particular, and the local. To improve our democracies, we need to use these new sources of legitimacy more effectively and we need to incorporate them into our accounts of democratic government. This book is an original contribution to the vigorous international debate about democratic authority and legitimacy.
The Great Transformation
Authors: Rosanvallon Pierre
Published: November 2017

This chapter describes the dawn of a new “age of particularity” which has changed what citizens expect from politics and fostered the emergence of new democratic institutions. More specifically, the chapter looks at the 1980 collapse of dual legitimacy, upon which democratic institutions had depended up until that point, as well as the social, political, and economic changes that emerged from and also helped to facilitate the aforementioned collapse. In a society of particularity, the whole idea of administration—management on the basis of fixed rules—loses its central role. Its emergence has coincided with a perception that hierarchical, centralized bureaucracies have had to evolve in important ways.
Independent Authorities: History and Problems
Authors: Rosanvallon Pierre
Published: November 2017

This chapter considers the rise of independent authorities within democratic countries. In most of these countries, the pace of creation of independent bodies charged with regulatory and oversight functions that had previously been entrusted to “ordinary” bureaucratic departments increased in the last two decades of the twentieth century. Although quite diverse in character, all of these organizations share a certain hybrid quality: they have an executive dimension even though they also exercise normative and judicial functions. The traditional concept of separation of powers has had to be stretched to accommodate them. The scope of the change has furthermore been considerable. In many countries vast areas of government intervention have increasingly been entrusted to these new organizations, clearly reducing the scope of administrative-executive power.
Is Impartiality Politics?
Authors: Rosanvallon Pierre
Published: November 2017

This chapter examines conceptions of impartiality and looks at how impartiality itself is approached in a political context. In doing so the chapter asks if the shift from positive to negative generality reflects a decline in the democratic–republican ideal and a greater role for law. From here, the chapter turns to the idea of a democratic impartiality—an active impartiality whose intervention helps to build a political community. Impartiality has established itself in the political order as the vector of aspirations to construct a more deliberative and transparent public space. It is also a key to understanding new ways of thinking about the social.
Morocco
Authors: Jamal Amaney A.
Published: November 2017

This chapter focuses on Morocco, highlighting how citizens across the North African monarchy rationalize authoritarianism through the prism of strategic utility to U.S. (and EU) ties. Morocco includes one of the most progressive Islamic movements in the region, and citizens, while applauding the movement's moderation, remain wary of its foreign intentions. Enhancing ties with the United States and maintaining ties to Europe were often cited as key reasons why the status quo was preferable to increasing levels of democracy. It became apparent that although the Islamic Party for Justice and Development is considered moderate in terms of its internal Islamic agenda, many in the kingdom worried about the party's stance toward the United States.
Causal Models
Authors: Goertz Gary , Mahoney James
Published: November 2017

This chapter compares two causal models used in qualitative and quantitative research: an additive-linear model and a set-theoretic model. The additive-linear causal model is common in the statistical culture, whereas the set-theoretic model is often used (implicitly) in the qualitative culture. After providing an overview of the two causal models, the chapter considers the main differences between them. It then gives an example to illustrate how a set-theoretic causal model is implicitly used in the within-case analysis of a specific outcome. It also explains how the form of causal complexity varies across the quantitative and qualitative paradigms. Finally, it examines another difference between the causal models used in quantitative and qualitative research, one that revolves around the concept of “equifinality” or “multiple causation.” The chapter suggests that while the two causal models are quite different, neither is a priori correct.
Causal Mechanisms and Process Tracing
Authors: Goertz Gary , Mahoney James
Published: November 2017

This chapter examines how the qualitative and quantitative research traditions empirically assess theories about mechanisms when making causal inferences. In the qualitative paradigm, researchers carry out this assessment by attempting to observe causal mechanisms through process tracing and through the analysis of causal-process observations. In the qualitative paradigm, the within-case analysis of specific cases is combined with the effort to observe mechanisms. By contrast, statistical methods are not designed to observe mechanisms within particular cases. The chapter considers the importance of mechanisms in causal inference as well as the use of process tracing in multimethod vs. qualitative research. It shows that multimethod research, which integrates regression and case study analysis, is increasingly regarded as a best practice.
Counterfactuals
Authors: Goertz Gary , Mahoney James
Published: November 2017

This chapter examines the use of counterfactual analysis in making causal inferences in the qualitative and quantitative research paradigms. To assess a counterfactual claim about a particular case, the typical approach is to conduct a within-case analysis of that case. Qualitative researchers formulate counterfactuals that are “conceivable,” in the sense that imagining that a cause had not occurred (or occurred differently) does not require fundamentally rewriting history. By contrast, quantitative scholars use counterfactuals mainly to illustrate a general causal model. The chapter first considers the Fundamental Problem of Causal Inference, which is the problem of a counterfactual, before discussing the statistical approach to counterfactuals. In particular, it describes the “minimum rewrite” rule. It suggests that counterfactual analyses are an important mode of causal inference within the qualitative tradition, but not commonly used within the quantitative tradition.
Semantics, Statistics, and Data Transformations
Authors: Goertz Gary , Mahoney James
Published: November 2017

This chapter examines the qualitative view of variable transformation using the Fundamental Principle of Variable Transformation. According to the Fundamental Principle of Variable Transformation, all transformations of variables must be meaning preserving or increasing. Within the qualitative research tradition, transformations that do not conform to this principle are viewed as suspect. In the quantitative culture, variable transformations respond to the imperatives of statistics, whereas qualitative scholars work under a different set of norms and values that emphasize the importance of semantics and the meaning embodied in concepts. The chapter first considers standardization versus meaning retention as well as logging versus fuzzy-set transformations in qualitative and quantitative research paradigms before concluding with a discussion of rationales behind data transformations.
Case Selection and Hypothesis Testing
Authors: Goertz Gary , Mahoney James
Published: November 2017

This chapter discusses quantitative and qualitative practices of case-study selection when the goal of the analysis is to evaluate causal hypotheses. More specifically, it considers how the different causal models used in the qualitative and quantitative research cultures shape the kind of cases that provide the most leverage for hypothesis testing. The chapter examines whether one should select cases based on their value on the dependent variable. It also evaluates the kinds of cases that provide the most leverage for causal inference when conducting case-study research. It shows that differences in research goals between quantitative and qualitative scholars yield distinct ideas about best strategies of case selection. Qualitative research places emphasis on explaining particular cases; quantitative research does not.
Conclusion
Authors: Goertz Gary , Mahoney James
Published: November 2017

This book concludes by reemphasizing important differences in the nature of qualitative and quantitative research—differences that extend across research design, data analysis, and causal inference. While their differences are considerable, the book argues that both research cultures can complement one another in terms of explaining the social and political world. However, a fruitful collaboration between quantitative and qualitative research—one built around mutual respect and appreciation—is possible only if scholars of both traditions understand and acknowledge their differences. These differences, summarized in tables, come in the areas of individual cases, causality and causal models, populations and data, concepts and measurement, and asymmetry. The book also contends that mixing the qualitative and quantitative cultures will contribute to methodological pluralism in the social sciences.