bluuebunny/crossref_metadata_2025 huggingface dataset:
Short Rate Models
Authors: Björk Tomas
Published: February 2020

The simplest Markovian short rate model is analyzed using classical and martingale methods, and the term structure equation for the determination of zero coupon bond prices is derived.
Forward Rate Models
Authors: Björk Tomas
Published: February 2020

In this chapter we study the Heath–Jarrow–Morton framework for forward rate models. Building on results from the previous chapter, the HJM drift condition is derived, some examples are studied, and the general Gaussian HJM model is analyzed in detail. The Musiela parameterization of forward rates is introduced and discussed in the context of infinite dimensional SDEs.
Stochastic Optimal Control
Authors: Björk Tomas
Published: February 2020

We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.
Optimal Stopping Theory and American Options
Authors: Björk Tomas
Published: February 2020

In this chapter we present the dynamic programming approach to optimal stopping problems. We start by presenting the discrete time theory, deriving the relevant Bellman equation. We present the Snell envelope and prove the Snell Envelope Theorem. For Markovian models we explore the connection to alpha-excessive functions. The continuous time theory is presented by deriving the free boundary value problem connected to the stopping problem, and we also derive the associated system of variational inequalities. American options are discussed in some detail.
Incomplete Markets
Authors: Björk Tomas
Published: February 2020

This chapter is an introduction to a series of chapters on incomplete markets. We present the general setting in terms of a Markov factor and we discuss how incompleteness comes into play in this model.
Portfolio Optimization in Incomplete Markets
Authors: Björk Tomas
Published: February 2020

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.
Introduction
Authors: Cheyne Peter
Published: February 2020

After a preamble on Coleridge’s view of ‘Philosophy’ as ‘the doctrine and discipline of ideas’, the Introduction outlines the three main periods of Coleridge’s philosophical development. The author then pauses to explain his method in the book. After that, he provides initial definitions and descriptions of ‘reason’ and ‘the ideas’, the main terms of this book, in a discussion of these as Coleridge viewed them. That is followed by a section distinguishing ‘translucent’ from ‘transparent’ contemplation, with further reference to ‘opacity’ in perception. The Introduction then concludes with an outline of the remaining chapters of the book.
Contemplative Practice and the Ideas
Authors: Cheyne Peter
Published: February 2020

Chapter 2 turns to Coleridge’s increasing focus on ideas as diffused in and through different kinds of contemplative practice and everyday experience. Throughout his thinking about contemplative reason, or Platonic nóēsis, he retained a Plotinian sense of theoria in and through sense and imagination. Section 2.1 outlines what the author calls the con-templum, a mental space opened up by imagination for ideas, allowing them to receive aesthetic expression, bridging the gap to allow ideas to have a deeply felt meaning in human life. Section 2.2 introduces the argument that, like Plotinus, Coleridge elevated the role and status of imagination as an insightful and not just a merely imaging and often deceptive faculty, as Plato viewed it. Section 2.3 reconstructs Coleridge’s argument for that reason to be ‘higher than’ imagination and his related position that will is deeper than reason. Finally, Section 2.4 examines Coleridge’s claim that ideas of reason are confreres of the human soul.
Aesthetic Contemplation
Authors: Cheyne Peter
Published: February 2020

The ‘aesthetic’ referred to throughout Chapter 3 is not especially the aesthetics of art, but that of everyday experience, the shared world, and of nature. Section 3.1, following up some Coleridgean notes that relate ‘Ideas’ to ‘thoughts & enjoyments’, performs a Socratic elenchus on unreflective cognitive attitudes in aesthetic states to distinguish value in the experience from prejudice. Section 3.2 then explores Coleridge’s concern with the activity of ideas in everyday aesthetics and the aim of enlightening ‘our feelings’ so they ‘actualize our reason’ ‘with their vital warmth’, relating this to Schiller’s concept of aesthetic education. Section 3.3 introduces the author’s theory of inchoate contemplation that commences in aesthetically informed feelings, in local or national culture, as an initial and perhaps universal, non-intellectualist form of the intuition of ideas. This theory then helps to illuminate a Coleridgean ‘philosophy of life’ where everyday symbols and aesthetic practices reach ‘far higher and far inward’.
Adapting Böhme’s Bipolar Model
Authors: Cheyne Peter
Published: February 2020

Chapter 5 argues for the crucial importance for Coleridge’s philosophy of Böhme, whose works he annotated more than any other writer. Section 5.1 discusses Coleridge’s views of various mystics and of the poles of mysticism: one side valued for its sensuous connection, yet found prone to mistake inner idiosyncrasies for noetic insight; the other side, the transcendence-directed contemplation of mystics such as the Christian neo-Platonic Victorines. Section 5.2 argues that the chiasmic crux of Böhme’s thinking inspired three Coleridgean mainstays: the interpenetration of opposites, the intercirculation of energies, and the chiasmus between higher and lower levels. Section 5.3 further argues that an important form of Coleridge’s pentadic logical schemata, which includes his pentad of the ‘Powers of Nature’ and his ‘Order of the Mental Powers’, derives from his fusing Böhme’s transmutational, chiasmic schema of ‘The Seven Forms of Spirits’ with the Christian neo-Platonic, linear, hierarchical ascent from sensus to contemplatio.
Conclusion
Authors: Cheyne Peter
Published: February 2020

The Conclusion gives further remarks concerning Coleridge’s philosophy and the ‘sense’, ‘higher understanding’, and ‘reason’. Section 1 constellates Coleridge’s main philosophical influences and metaphysical positions. After a summary statement in Section 2 of Coleridge’s position regarding sense, feeling, and the empirical, Section 3 compares the higher understanding of elenctic discourse (Socrates, Plato, Coleridge) with what Paul Ricoeur calls the ‘School of Suspicion’ (Marx, Nietzsche, Freud), which has become the ‘hermeneutics of suspicion’. Both uncover negativities or aporia, but, the author argues, the former can inform the latter in virtue of its being guided by a greater positivity, a dimly intuited idea or value, in contrast to the ‘already known’ baser desires further uncovered by the more negative elenchus or hermeneutic. Section 4 discusses Coleridgean reason and contemplation as it actually occurs, as diffuse or reflected, through deep feelings stretching in a metaphysical direction.
The Formal and Informal Politics of British Rule In Post-Conquest Quebec, 1760-1837
Authors: Christie Nancy
Published: February 2020

Analyzing the vast judicial records of Quebec, A Northern Bastille uses a microhistorical approach to rethink the impact of the British Conquest upon the social, economic and political life of the colony. By expanding the concept of the political beyond the official script of government leaders to include the public sphere of print as well as the voices of ordinary litigants in the criminal and civil courts, this book seeks to understand both the assimilationist ‘project’ of British rule as well as the multiple ways in which individuals and groups contested an increasingly autocratic approach to imperial governance in an age of revolution. This book provides the first comprehensive analysis of the way in which the equation between Britishness and liberty was deployed both by government officials and out-of-doors political commentators to subvert French Canadian claims to political rights, thereby providing a novel explanation for the emergence of French Canadian nationalism between 1763 and 1837.
Introduction
Authors: Christie Nancy
Published: February 2020

This chapter canvasses the recent historiography on Quebec and discusses new developments within the history of the British Empire and the new legal history. It presents the principal theoretical framework of the book which has sought to expand conventional notions of the terrain of the political, to include not only the official transcript of government officials, but to examine the realm of opposition political commentary in the newspapers, as well as the terrain of the small politics of everyday life as articulated by ordinary people in the criminal and civil courts. It also demonstrates the importance of analyzing competing concepts of Britishness and the ways in which these sustained policies of British rule which sought to assimilate the French Canadian majority in Quebec, a perspective which presents a new portrait of post-Conquest Quebec which highlights ethnic conflict and the important role played by British nationalism in the development of French Canadian collective identities between 1763 and the Rebellion of 1837.
“In this Increasing Commercial Emporium”
Authors: Christie Nancy
Published: February 2020

From the perspective of governing elites on both sides of the Atlantic, the expanding world of goods was seen as a civilizing and assimilative process, but using an analysis of litigation this chapter shows that while enticing French Canadians into the marketplace did integrate them into global networks of trade and credit, they nevertheless sought to don British dress and purchase British manufactured goods to articulate and enhance their own identities. Not only does this chapter shift the historical gaze from production to consumption, but it greatly expands the term merchants beyond those large overseas merchants who have been well studied, to incorporate the vital world of licit and illicit trade by shopkeepers, artisans, women, and peasants, to draw attention to the importance to the internal circulation of goods. My exploration of the regulatory apparatus of government as well as the everyday understanding of goods, credit, and debt shows, however, that the eighteenth century was not a pivot to modernity; rather, conceptions of the marketplace remained tied to an older moral economy outlook.
“Qu’il étoit maître chez lui” (He is the master of his house)
Authors: Christie Nancy
Published: February 2020

Arguing against traditional liberal narratives of the linear development of unfree labor, this chapter explores the politics of the counterrevolution by examining the way in which the master and servant acts of 1802 enhanced patriarchal government and the authority of male household heads over their dependents in the wake of the American, French, and Haitian revolutions. It also shows how these new legal strategies to enforce subordination among marginal peoples took particular aim at French Canadians during a period of intense political ferment and rebellion in the colony. These amplified existing perceptions of French Canadians as seditious others. It explores the ramifications of these acts in terms of the practices of ordinary plebeian families, in which their broader meaning for reinstantiating hierarchy and subordination was challenged. The master and servant legislation aimed to circumscribe various freedoms, including the freedom to choose one’s sartorial presentation, an aspect of liberty that was consciously fostered as an element of political freedom.
Loving the Body, Loving the Soul
Authors: Borcherding Julia
Published: February 2020

This chapter examines Anne Conway’s ‘argument from love’ in her Principles of the Most Ancient and Modern Philosophy. This argument, supported by a further argument, the ‘argument from pain’, undermines the dualist dichotomy between mind and matter by appealing to a vitalist similarity principle. The goal is two-fold: first, to contribute to a close systematic reconstruction and analysis of Conway’s arguments, which so far is largely lacking in the literature; second, to establish that these arguments are richer and more compelling than commentators have thought. The chapter shows that Conway’s case against the dualist poses a considerable challenge to the dualisms of Henry More and Descartes.
Our Body Is the Measure
Authors: Chamberlain Colin
Published: February 2020

Malebranche holds that sensory experience represents the world from the body’s point of view. The chapter argues that Malebranche gives a systematic analysis of this bodily perspective in terms of the claim that the five external senses and bodily awareness represent nothing but relations to the body. The external senses represent relations between external objects and the perceiver’s body. Bodily awareness represents relations between parts of the perceiver’s body and her body as a whole, and the way she is related to her body. The senses thus represent the perceiver’s body as standing in two very different sets of relations. The external senses relate the body to a world of external objects, while bodily awareness relates this same body to the perceiver herself. The perceiver’s body, for Malebranche, is the center of the system of relations that make up her sensory world, bridging the gap between self and external objects.
Unperceived Existence and Hume’s Theory of Ideas
Authors: Cottrell Jonathan
Published: February 2020

Hume seems committed to an inconsistent triad: (i) we believe certain things to exist unperceived; (ii) if we believe a certain thing to exist unperceived, then we have (at our disposal) an idea that represents it as existing unperceived; and (iii) we do not have (at our disposal) an idea that represents anything as existing unperceived. This chapter aims to acquit him of this seeming inconsistency by arguing that, contrary to what others have claimed, Hume does not explicitly argue for (iii); his theory of mental representation does not implicitly commit him to (iii); and, moreover, this theory allows him to explain our having ideas that represent things as existing unperceived, contrary to (iii). To this end, the chapter offers Hume an account of negation modeled on his accounts of abstract ideas and ideas of substances and modes.
Sine Qua Non Causation
Authors: Sangiacomo Andrea
Published: February 2020

Kant’s New Elucidation (1755) is an important source for understanding how early modern debates managed to import and adapt the notion of sine qua non causation in the domain of natural philosophy. In order to clarify Kant’s position, the chapter focuses on two preliminary historical moments: the marginalization of sine qua non causation in Suárez’s account of efficient causation and the forceful revival of sine qua non causation in Malebranche’s occasionalism. In the New Elucidation Kant adopts an understanding of causation similar to that of Malebranche, while also clarifying the way in which God’s involvement in nature has to be understood. In so doing, Kant takes issue with some of the ambiguities of Malebranche’s own account that were hotly debated by his contemporaries.
Torts and Other Wrongs
Authors: Gardner John
Published: February 2020

This chapter focuses on the law of torts, not in the United States, but in other major common law jurisdictions (England and Wales, Canada, Australia, and New Zealand) in which tort cases are normally adjudicated by judges sitting without juries. It considers the so-called classical interpretation of the common law of torts by John Goldberg and Ben Zipursky, and how they tend to equivocate on an important point of law in a way that puts them at odds with some writers with whom they would do better to make common cause. It suggests that this equivocation is where the law of the United States parts company with the law in the rest of the common law world. The problem, an English lawyer might then teasingly say, is with American tort law rather than with the Goldberg and Zipursky rendition of it.
What is Tort Law For? The Place of Distributive Justice
Authors: Gardner John
Published: February 2020

This chapter defends the claim that certain questions of distributive justice are central to the law of torts, and cannot but be faced by those who administer and develop it, precisely because the law of torts is a site of corrective justice. Those with pigeonholing instincts may be tempted to label this a ‘mixed’ or ‘pluralistic’ explanation of tort law. The chapter endorses Peter Cane’s thesis that corrective justice provides the structure of tort law within which distributive justice operates. It presents a version of this thesis which shows that the place of corrective justice in tort law enjoys some kind of explanatory priority.
Obligations and Outcomes in the Law of Torts
Authors: Gardner John
Published: February 2020

This chapter argues that reasons to succeed are indeed intelligible apart from the law—i.e. morally intelligible in the relevant sense—and that reasons to try are not morally intelligible, in the relevant sense, without them. From here it is but a relatively short step to conclude that at least the first half of this conjunction still holds true when the reasons in question are obligatory. There is no special problem with mandatory categorical reasons to succeed. But instead of making that short step here, it is left in the hands of others, including those who remain attached to Kant’s curious argument, to try and block it. That is the best way to honour the spirit of Honoré’s ground-breaking contrarian contribution to the philosophical study of the law of torts, and indeed the philosophical study of the human condition.
Some Rule-of-Law Anxieties about Strict Liability in Private Law
Authors: Gardner John
Published: February 2020

Strict liability plays a significant role in many legal systems, in both criminal and private law. Its occasional use attracts a weary toleration from legal thinkers, but few stand up for it with enthusiasm, and few argue for its extension. Injustice challenges to strict liability take more than one form. This chapter focuses on those that see the injustice of strict liability as bound up with a failure, on the law’s part, to conform to the ideal of the rule of law. These challenges can be contrasted with those that complain of the injustice of attaching liability to morally blameless actions. Although strict liability is no-fault liability in a special lawyers’ sense of ‘fault’, it also extends in the process to many who are not at fault in the ordinary moral sense of ‘fault’, i.e. many whose actions are morally blameless.
The Many Faces of the Reasonable Person
Authors: Gardner John
Published: February 2020

The reasonable person is the longest-established of ‘the select group of personalities who inhabit our legal village and are available to be called upon when a problem arises that needs to be solved objectively’. These days, he has neighbours as diverse as the ordinary prudent man of business, the officious bystander, the reasonable juror properly directed, and the fair-minded and informed observer. In the minds of many, however, he is most closely associated with the law of torts, particularly the law of negligence. Because the reasonable person is used to set standards in so many corners of the law, it is natural to think that the standards he sets must be legal ones. This chapter seeks to convince the reader otherwise. It suggests that the services of the reasonable person are in such heavy demand in the law precisely because he sets extra-legal standards, and indeed extra-legal standards of a notably versatile kind.
Anti-Discrimination Law and Legal Culture in Germany
Authors: Wrase Michael
Published: February 2020

Drawing on the socio-legal concept of legal culture, this chapter tries to explain the initial objections by many traditionalist legal scholars, politicians, and legal practitioners alike against comprehensive anti-discrimination regulation in Germany. It contrasts the rather weak culture of non-discrimination with a broadly shared appreciation for civil rights fostered by a long-established and extensive adjudication of the Federal Constitutional Court (‘FCC’). It can be shown that the missing national support for the new regulation has led to a very restricted transposition of the EU anti-discrimination directives. The Allgemeines Gleichbehandlungsgesetz more or less confines itself to implementing the provisions stipulated in the directives, and even contains several shortcomings and potential breaches of EU law, especially with regard the provision of public goods and services. Consequently, mobilization of non-discrimination rights has been rather weak in practice so far. However, there is good reason to conclude that anti-discrimination law has been gaining ground in Germany in recent years, and that it will be even more relevant in future. The ECJ adjudication has exerted considerable influence on the case law of the German labour courts. This might in the longer run also impact on the adjudication of the FCC with regard to the clause on non-discrimination in Article 3 Basic Law.
Pares Inter Inequales? A First Glimpse of the Cases before Senate II of the Austrian Equal Treatment Commission
Authors: Risak Martin , Berger Christian , Rehm Miriam
Published: February 2020

This chapter undertakes a first explorative study of all the published decisions issued by Senate II of the Equal Treatment Commission between its establishment in 2004 and 2017, which deals with alleged discriminations on the grounds of age, ethnic origin, religion or belief, and sexual orientation. The aim of this contribution is to detect possible patterns in the practice of Senate II. It explores whether individual factors (such as gender or education), the workplace (e.g. job, sector), or aspects of the alleged discrimination (e.g. the moment of discrimination, that is harassment, or discrimination in the course of hiring or termination; grounds such as ethnicity, religion, or age; defendant as an individual or a corporation) influence the outcome of the procedure. By providing this analysis, the chapter challenges some widely held assumptions, such as that the Equal Treatment Commission is particularly applicant-friendly.
The Classical Ideal Gas: Energy Dependence of Entropy
Authors: Swendsen Robert H.
Published: February 2020

The energy-dependence of the entropy of the configurational contributions is derived by considering the exchange if energy is exchanged between two or more systems. The argument is analogous to that given in Chapter 5 for the configurational contributions to the entropy. The derivation requires evaluating the area and volume of an $n$-dimensional sphere, which is carried out explicitly. The entropy is calculated within the approximation that the width of the energy distribution is zero. The total entropy is just the sum of the configurational entropy and the energy-dependent terms, as discussed in Section 4.1. The significance of the non-zero width of the true energy distribution will be addressed in Chapter 21.
Classical Gases: Ideal and Otherwise
Authors: Swendsen Robert H.
Published: February 2020

As preparation for the derivation of the entropy for systems with interacting particles, the position and momentum variables are treated simultaneously, in this chapter, for the ideal gas. Releasing a constraint on the exchange of volume between two systems leads to an entropy maximum, just as the release of an energy- or particle-number constraint. This same principle is shown to be true for asymmetric pistons, which allow the total volume to change. The entropy of systems with interacting particles is then derived. The Second Law of Thermodynamics is established for general systems. Finally, the Zeroth Law of Thermodynamics is derived.
The Postulates and Laws of Thermodynamics
Authors: Swendsen Robert H.
Published: February 2020

The points of view about the behavior of macroscopic systems arising from thermodynamics and statistical mechanics are compared and contrasted. The concept of a state function is explained, and the postulates of thermodynamics, which describe fundamental properties of the entropy, are presented. Some are essential postulates, which are always valid, while others, called optional postulates, are very useful when they do apply. The Laws of Thermodynamics are derived from these postulates. With this chapter we begin the formal study of thermodynamics, which represents a detour from the development of the foundations of classical statistical mechanics that we began in Part I.
Thermodynamic Processes
Authors: Swendsen Robert H.
Published: February 2020

This chapter begins by defining terms critical to understanding thermodynamics: reversible, irreversible, and quasi-static. Because heat engines are central to thermodynamic principles, they are described in detail, along with their operation as refrigerators and heat pumps. Various expressions of efficiency for such engines lead to alternative expressions of the second law of thermodynamics. A Carnot cycle is discussed in detail as an example of an idealized heat engine with optimum efficiency. A special case, called negative temperatures, where temperatures actually exceed infinity, provides further insights. In this chapter we will discuss thermodynamic processes, which concern the consequences of thermodynamics for things that happen in the real world.
Thermodynamic Potentials
Authors: Swendsen Robert H.
Published: February 2020

Thermodynamics specifies the relation between an independent, predictor variable, and what is predicted. It is often the case that changing the variables regarded as independent can greatly simplify problem solving. The chapter shows how using an intensive variable (like temperature or pressure) as the predictor loses information that can be retained if it is expressed by a different function. It shows the importance of Legendre transforms, which contain the same information about the system as is available by using extensive variables. Legendre transforms exploiting the fundamental relation are shown to yield the Helmholtz free energy, the enthalpy, and the Gibbs free energy. Massieu functions are introduced as an alternative that is particularly important for models exhibiting negative temperatures.
The Consequences of Extensivity
Authors: Swendsen Robert H.
Published: February 2020

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the consequences of extensivity. The Euler equation can be derived from extensivity, and the Gibbs–Duhem equation can be derived from the Euler equation. The Gibbs–Duhem equation shows that changes in the chemical potential are not arbitrary, but are determined by changes in the temperature and pressure for. That in turn simplifies the reconstruction of the fundamental equation from the equations of state. The Euler equation also allows the various thermodynamic potentials to be rewritten in terms of other functions.
Thermodynamic Identities
Authors: Swendsen Robert H.
Published: February 2020

Many of the calculations in thermodynamics concern the effects of small changes. To carry out such calculations, we often need to evaluate first and second partial derivatives of some thermodynamic quantities with respect to other thermodynamic quantities. Although there are many such partial second derivatives, they are related by thermodynamic identities. This chapter explains the most straightforward way of deriving the needed thermodynamic identities. After explaining the derivation of Maxwell relations and how to find the right one for any given problem, Jacobian methods are introduced, with an accolade to their simplicity and utility. Several examples of the derivation of thermodynamic identities are given, along with a systematic guide for solving general problems.
Stability Conditions
Authors: Swendsen Robert H.
Published: February 2020

Stability exists when a thermodynamic phase remains homogenous instead of separating into phases of high and low density (clumping). Certain conditions on the second partial derivatives of extensive variables are necessary for stability, even when the first derivatives do not vanish. These conditions can be expressed in terms of the compressibility and specific heat. Inequalities involving second partial derivatives with respect to intensive variables are derived. We have been assuming that the density of a gas will remain uniform, rather than having most of the particles clump together in one part of the container, leaving the rest of the volume nearly empty.
The Nernst Postulate: The Third Law of Thermodynamics
Authors: Swendsen Robert H.
Published: February 2020

The Nernst postulate, or Third Law of Thermodynamics, is derived from quantum statistical mechanics. It states, ‘The entropy of a thermodynamic system goes to a constant as the temperature goes to zero.’ The main consequences are that specific heat and compressibility goes to zero as temperature goes to zero. Both are demonstrated. It is shown that, both with and without the Nernst postulate, zero temperature is not experimentally attainable. Gases are usually well behaved in this respect, but we all know from experience that molecules of H2O can clump together, form drops, and rain on us.
Irreversibility
Authors: Swendsen Robert H.
Published: February 2020

The phenomenon of irreversibility is explained on the basis of an analysis by H. L. Frisch. The history of the debate over irreversibility is briefly discussed, including Boltzmann’s H-theorem, Zermelo's Wiederkehreinwand, Poincaré recurrences, Loschmidt's Umkehreinwand and Liouville’s theorem. The derivation of irreversible behavior for the ideal gas position distribution is carried out explicitly. Using this derivation, the Wiederkehreinwand and the Umkehreinwand are revisited and explained. The first thing we must establish is the meaning of the term ‘irreversibility’. This is not quite as trivial as it might seem. The irreversible behavior I will try to explain is that which is observed. Every day we see that time runs in only one direction in the real world,.
Quantum Ensembles
Authors: Swendsen Robert H.
Published: February 2020

The study of quantum statistical mechanics begins with a review of the basic principles of quantum mechanics. Schrödinger’s equation is introduced and Eigenstates (or stationary states) are defined. Model probability for quantum statistics is assumed to have a uniform distribution in phases. Wave functions for many-body systems are defined. The density matrix is introduced. The Planck entropy and the microcanonical ensemble are defined. The differences between classical and quantum statistical mechanics are all based on the differing concepts of a microscopic ‘state’. While the classical microscopic state (specified by a point in phase space) determines the exact position and momentum of every particle, the quantum mechanical state determines neither; quantum states can only provide probability distributions for observable quantities.
Quantum Canonical Ensemble
Authors: Swendsen Robert H.
Published: February 2020

This chapter introduces the quantum mechanical canonical ensemble, which is used for the majority of problems in quantum statistical mechanics. The ensemble is derived and analogies with the classical ensemble are presented. A useful expression for the quantum entropy is derived. The origin of the Third Law is explained. The relationship between fluctuations and derivatives found in classical statistical mechanics is shown to have counterparts in quantum statistical mechanics. The factorization of the partition function is re-introduced as the best trick in quantum statistical mechanics. Due to their importance in later chapters, basic calculations of the properties of two-level systems and simple harmonic oscillators are derived.
Black-Body Radiation
Authors: Swendsen Robert H.
Published: February 2020

A black body is a perfect absorber of electromagnetic radiation. The energy spectrum was correctly calculated by Max Planck under the assumption that the energy of light waves only came in discrete multiples of a constant (called Planck’s constant) times the frequency. This was perhaps the first achievement of quantum mechanics. The derivation is presented here. The purpose of the current chapter is to calculate the spectrum of radiation emanating from a black body. The calculation was originally carried out by Max Planck in 1900 and published the following year. This was before quantum mechanics had been invented, or perhaps it could be regarded the first step in its invention.
Ideal Quantum Gases
Authors: Swendsen Robert H.
Published: February 2020

As a preliminary to discussing the properties of Bose–Einstein and Fermi–Dirac gases, this chapter presents the basic quantum equations that underlie both. The process of building N-body states from single-particle states is described, along with notation necessary to simplify the problem. The average number of particles in a given energy state and chemical potential is derived for fermions and bosons. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles.
Fermi–Dirac Statistics
Authors: Swendsen Robert H.
Published: February 2020

The main application of Fermi–Dirac Statistics is to calculate the properties of electrons. This chapter explains how the properties of fermions account for the behavior of metals. The Fermi energy is introduced and shown to correspond to a very high temperature, so that most properties can be obtained from low-temperature expansions. Both discrete and continuous densities of states are discussed. The Sommerfeld expansion is derived explicitly. The low-temperature specific heat and compressibility are derived. The most important fermions are electrons, and understanding the properties of electrons is central to understanding the properties of all materials. In this chapter we will study the ideal Fermi gas, which turns out to explain many of the properties of electrons in metals.
Introduction
Authors: Stewart Jon
Published: February 2020

The Introduction begins by trying to define the humanities disciplines in contrast to the natural and social sciences. It is explained that the present study distinguishes itself from similar works on Western civilization by its attempt to give a philosophical interpretation of this tradition. The Introduction further explains the nature and methodology of the work as a combination of philosophy of history and philosophical anthropology. The thesis of the investigation is that the development of inwardness and subjectivity is an important feature of Western culture. These are ideas and conceptions which, although largely absent among the ancients, are widely celebrated today in our modern world. An attempt is made to sketch the complex phenomena that we mean by the terms “subjectivity” and “inwardness.”
The Epic of Gilgamesh
Authors: Stewart Jon
Published: February 2020

Chapter 1 gives a reading of the Mesopotamian The Epic of Gilgamesh. At the outset an account is provided of the historical context of the work in antiquity and its discovery and translation in the nineteenth century. An interpretation is given of the creation of the wild man Enkidu. Parallels are pointed out between this story and that of the Fall in Genesis. The nature of the Mesopotamian gods is also explored in the context of an interpretation of the episode featuring the goddess Ishtar. Angered by Gilgamesh’s rejection of her advances, Ishtar sends the Bull of Heaven to destroy Uruk. Gilgamesh and Enkidu manage to kill it, but only after it has caused much death and destruction. Enkidu insults Ishtar, and she in turn causes his death. Gilgamesh is deeply distraught by the death of his friend and goes in search of a solution to the problem of human mortality. He has many adventures and ultimately finds Utnapishtim, the Mesopotamian Noah, who survives the Flood and is made immortal. An account is given to the parallels of this episode and that of the Flood in Genesis. Utnapishtim tells Gilgamesh about a magic plant that can restore youth. Gilgamesh manages to find it, but he loses it right away to a snake. The story is interpreted as a statement of the finitude and limitations of the human condition.
Homer’s Odyssey
Authors: Stewart Jon
Published: February 2020

Chapter 3 begins, by way of introduction, with an outline of the historical context of the Homeric poems. An account is given of the scholarly debates about their authorship and historicity. The chapter interprets key episodes of the Odyssey: Kalypso, the Lotus-Eaters, the Cyclops, the Underworld, and the Sirens. It discusses the Greek warrior ethic and tries to determine the nature of Odysseus as a model hero. It is shown that in the different stories it is possible to discern the Greek view of civilization in contrast to nature. For example, the Cyclops Polyphemus, who represents nature, has, for example, no agriculture or shipbuilding. Although physically much larger and stronger than Odysseus and his men, he is overcome by Odysseus’ knowledge that comes from civilized life in a community. Similarly, the satisfied yet bovine life of the Lotus-Eaters and the victims of the Sirens is rejected in favor of the life of struggle and hardship, which constitutes the true human lot and gives human existence its meaning.
Herodotus’ Histories
Authors: Stewart Jon
Published: February 2020

Chapter 4 begins with a general introduction to the life and work of the Greek historian Herodotus. This is followed by an analysis of the beginning of Herodotus’ Histories and a discussion of the nature of scholarly historiography in contrast to mythology. A series of individual episodes in Herodotus’ work are explored including the story of Gyges, Solon’s meeting with Croesus, and Polycrates’ inability to escape his fate. The key motif of Nemesis is explored as a levelling principle that cuts down what has grown beyond its allowed limit. Thus rich and powerful figures are consistently subject to a terrible fall in Herodotus’ account. The concept of Nemesis is compared with different accounts of justice that involve a balance between different competing elements. The chapter ends with a brief discussion of Xerxes’ plans to invade Greece and his lament about the finitude of human existence.
Sophocles’ OedipustheKing
Authors: Stewart Jon
Published: February 2020

After a brief introduction to the life and work of the Greek dramatist Sophocles, Chapter 5 interprets Oedipus the King as a critical story of the human search for knowledge. Oedipus is known for his intelligence as is exemplified by his ability to defeat the Sphinx by figuring out the answer to its riddle. The tragedy also portrays the idea of natural law as an extension of the world of nature. In the play natural law is portrayed in terms of the laws prohibiting patricide and incest, which are regarded not just as violations of the human world but rather of nature itself. This picture is set against the threat of relativism and subjectivism that was starting to arise in Greek culture. The story also illuminates the Greek concept of fate, to which Oedipus falls victim, although he at every step tries to avoid it. This raises difficult questions about human responsibility, culpability, and free will. Sophocles’ tragedy is read as a criticism of the Greek scientific revolution and the Socratic spirit which puts value on learning new things based on reason instead of relying on the ancient customs and religious traditions.
The Dialectic of the Ancient and Modern Principles: Homer and the Internet
Authors: Stewart Jon
Published: February 2020

Chapter 14 serves as a conclusion to the work. It attempts to show how the key theme of the development of inwardness and subjectivity has come to play an important role in our modern world. It is easy for us living in the twenty-first century to identify with this story of emerging freedom since we generally celebrate the value of individuality. We recognize that inwardness and subjectivity are constituent elements in the development of what it is to be fully human. However, in our modern world there has been a high price to pay for our hard-won individuality and subjectivity. As these modern principles develop, other traditional principles begin to recede. With the loss of community and tradition, the modern world is characterized by alienation, relativism, and the loss of self-identity. This is a dominant feature of modernity as people struggle desperately to establish some fixed sense of themselves in the absence of any external relations. An appreciation of the centrality of this for our modern life makes the study of the development of the idea of subjectivity and inwardness in the past more relevant than ever.
The Port Cities of the French Atlantic
Authors: Forrest Alan
Published: February 2020

This chapter discusses the fortunes of the principal ports of the French Atlantic in the eighteenth century, among them Bordeaux, La Rochelle, Nantes, Marseille, and Le Havre, but also smaller ports like Lorient, Saint-Malo, and Bayonne, which all at various moments enjoyed years of unprecedented prosperity. It shows how not all of them invested in the same forms of commerce or enjoyed the same peak years of prosperity. Some concentrated on direct commerce with the Caribbean islands, others on fishing off Newfoundland, but increasingly merchants were tempted by the rich profits to be made from slaving. The chapter looks at the investments made by the merchant community in the fabric of their cities, discusses their architecture and elegant town planning, and notes the impressions they made on foreign visitors who saw them in a comparative perspective.
Debating Slavery
Authors: Forrest Alan
Published: February 2020

The chapter examines the moral threat to slaving in the last years of the Ancien Régime with the rise of abolitionism, first in Britain, then more gradually, in France. Moral qualms about slavery had first been expressed by Enlightened authors like Raynal and Condorcet; but the writings of some English abolitionists, notably Thomas Clarkson, proved equally powerful. However, in merchant circles, especially the chambers of commerce, slaves continued to be seen as a commodity, and the slaving interest was violently defended as the Revolution approached. The chapter examines pamphlets produced by both sides in the debate, and discusses the role of masonic lodges, clubs, and learned societies in the port cities themselves.
The French Revolution in the Atlantic Ports
Authors: Forrest Alan
Published: February 2020

The chapter traces the course of the Revolution in the port cities and discusses the response of the merchant community to political change. The Revolution was initially widely welcomed, as it opened careers to talent, allowed freedom of religion, and abolished legal estates, which all appealed to the mercantile elites, who quickly took charge of municipal politics. But things quickly worsened with street violence in Paris, the federalist crisis in several of the ports, and the Vendean insurrection on Nantes’ doorstep. The Jacobin government and the Terror brought new threats for the merchant community, for whom surviving the revolutionary years took a degree of guile, as trade could easily be confused with speculation and an act of selfishness that rendered merchants instantly suspect.
Merchants, Planters, and Revolutionary Politics
Authors: Forrest Alan
Published: February 2020

The chapter deals with the interactions between the Atlantic ports in France and the colons in the Caribbean. At first the merchants were more concerned with their privileged access to the colonies than with the impact of the revolution on Saint-Domingue. But planter pressure was intense, and the Club Massiac championed their cause in France, blaming disorder and slave demands on the lobbying of the principal abolitionist faction, the Amis des Noirs. From 1791, Saint-Domingue and Guadeloupe were prey to increasing violence, first from free people of colour, then from slaves, and the slave trade with France collapsed. Many white colonists fled the Caribbean to the French ports, which mounted a major charity operation. Merchants and planters alike were left bewildered.
War and Revolution in the Caribbean
Authors: Forrest Alan
Published: February 2020

Whereas the previous chapter focused on the effects of events in Saint-Domingue on the French merchant community and on political sentiment in the French ports, this one examines events in the Caribbean and especially in Saint-Domingue. It discusses the complexities of the race question on the island, and especially the status of free people of colour, which dominated discussion during the early months of the Revolution. It also shows how, with the slave revolts and insurrections, opinions hardened after 1791, how the French administration became more dependent on the support of the mulattoes, and how the situation in Saint-Domingue was complicated by foreign war and invasion. The chapter ends by discussing the role of Toussaint Louverture and Leclerc’s fateful expedition
The Slave Trade in Collective Memory
Authors: Forrest Alan
Published: February 2020

This chapter discusses the memory of the slave trade in France’s Atlantic ports and the ways in which their slaving past is presented today in newspapers, school textbooks and museum exhibits. For many decades the trade was passed over in silence, a footnote to a golden age of mercantile prosperity, or was—as in Britain—viewed through the lens of an abolitionist movement that was to the credit of the nation. But from the mid-1980s the taboo has been broken. The chapter shows how major exhibitions have been staged to discuss and reflect on the slave trade, how city councils have built memorials to the victims of slavery, and how scholars and activists, often of African or French Caribbean descent, have played a major part in urging greater transparency and reflection.
Enclosure and its Critics
Authors: Marks Susan
Published: February 2020

The focus of this chapter is a series of texts by sixteenth-century English social critics: Edmund Dudley’s Tree of Commonwealth, Thomas More’s Utopia and Robert Crowley’s The Way to Wealth and other works. Inasmuch as these texts were composed at a moment of great change, the chapter highlights, in particular, concerns about enclosure. Alterations in land tenure and the extinguishment of rights of common were impoverishing ordinary people and depriving them of their capacity to live independently of wage-labour. The way to wealth for some was the way to poverty for others.
Rights in the English Revolution
Authors: Marks Susan
Published: February 2020

This chapter examines discussions of rights in the English Revolution of the mid-seventeenth century, focusing in particular on the Putney Debates and on the ideas put forward shortly afterwards by Gerrard Winstanley and his fellow Diggers. A key issue in the Putney Debates was the extension of the right to vote to men without property. That was also important for the Diggers, but in addition they argued for the right of all to direct access to the means of subsistence. The earth was a common treasury for all, wrote Winstanley, and could not justly be turned into a particular treasury for some.