A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the origin and evolution of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who have no prior knowledge of the universe and people who are interested in learning.

The concept of black holes or completely collapsed gravitational objects as they were originally called has fascinated the scientific community and writers of science fiction for centuries. The mathematical proof of the existence of black holes came from the collation of multiple lines of evidence, some of which were highly debated and was derived from both indirect and direct sources. The measurement of gravitational waves and the observation of a black hole represent one of the (...) most astounding achievements in astrophysics which will open up new areas of investigation for the role that black holes play in the formation, maintenance and evolution of galactic structure. (shrink)

What, if anything, is wrong with conspiracy theories? A conspiracy refers to a group of people acting in secret to achieve some nefarious goal. But given that the pages of history are full of such plots, why are CTs regarded with suspicion? Just like with the traditional demarcation problem, philosophers disagree about where to draw the line between legitimate hypotheses about conspiracies and unfounded ‘conspiracy theories’. Some believe that there is no such demarcation line to be drawn, that each (...) CT should be evaluated on its own merits, and that the bad reputation of CTs is wholly undeserved. In this paper, I intend to rescue the intuition that there is indeed something prima facie suspicious about CTs. First, I demarcate legitimate theorizing about real-life conspiracies from “mere conspiracy theories”. Along the way, my analysis will clarify some epistemological issues surrounding falsifiability, asymmetries between causes and effects, and hypotheses involving intentional agents. Because of their extreme resilience to external criticism and counterevidence, I argue, CTs are the epistemological equivalent of a ‘black hole’, in which unwary truth-seekers are drawn, never to escape again. But this strong attraction of CTs comes at a steep price: their theoretical parameters are essentially arbitrary, making them vulnerable to internal disruption. In essence, because it is so easy to construct a novel CT, it is equally easy to construct many ones about the same historical event. And that is what justifies our suspicion of CTs. (shrink)

This paper presents a philosophical analysis of the structure of black holes, focusing on the event horizon and its fundamental status. While black holes have been at the centre of countless paradoxes arising from the attempt to merge quantum mechanics and general relativity, recent experimental discoveries have emphasised their importance as objects for the development of Quantum Gravity. In particular, the statistical mechanical underpinning of black hole thermodynamics has been a central research topic. The Quantum (...) Membrane Paradigm, proposed by Wallace (Stud Hist Philos Sci Part B 66:103-117, 2019), posits a real membrane made of black hole microstates at the black hole horizon to provide a statistical mechanical understanding of black hole thermodynamics from an exterior observer’s point of view. However, we argue that the Quantum Membrane Paradigm is limited to low-energy Quantum Gravity and needs to be modified to avoid reference to geometric notions, such as the event horizon, which presumably do not make sense in the non-spatiotemporal context of full Quantum Gravity. Our proposal relies on the central dogma of black hole physics. It considers recent developments, such as replica wormholes and entanglement wedge reconstruction, to provide a new framework for understanding the nature of black hole horizons in full Quantum Gravity. (shrink)

Black holes entered scientific literature as early as at the end of eighteenth century. They had been known at that time as dark stars, but their concept did not find its way to physics or astronomy, and had been abandoned for more than one hundred years. I shall sketch historical developments and discuss present mathematical and observational status of black holes.

The Continuous Parameter Estimation Model is applied to develop individual genomic-level heritabilities for the latent hierarchical structure and developmental dynamics of Life History (LH) strategy LH strategies relate to the allocations of bioenergetic resources into different domains of fitness. LH has moderate to high population-level heritability in humans, both at the level of the high-order Super-K Factor and the lower-order factors, the K-Factor, Covitality Factor, and General Factor of Personality (GFP). Several important questions remain unexplored. We developed measures of (...) genome-level heritabilities employing an American sample of 316 monozygotic (MZ) and 274 dizygotic (DZ) twin dyads and a Swedish sample of 863 MZ and 475 DZ twin dyads. This novel heritability index measures individual genetic transmissibility, therefore opening new avenues for analyzing complex interactions among heritable traits inaccessible to standard structural equations methods. For these samples: (1) moderate to high heritability of factor loadings of Super-K on its lower-order factors is demonstrated, evidencing biological preparedness, genetic accommodation, and the gene-culture coevolution of biased epigenetic rules of development; (2) moderate to high heritability of the magnitudes of the effect of the higher-order factors upon their loadings on their constituent factors, evidencing genetic constraints upon phenotypic plasticity; and (3) that heritability of the LH factors, of factor loadings, and of the magnitudes of the correlations among factors are weaker among those with slower LH speeds, demonstrating that inter-individual variation in transmissibility is a function of individual socioecological selection pressures. (shrink)

I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; the central role of (...) Hawking radiation in permitting black holes to be in thermal contact with one another; the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics. (shrink)

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. I focus on three lines of argument: zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal (...) black holes; recovery of the qualitative and quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used at a introductory level: the paper is aimed at students and non-specialists and does not presume advanced knowledge of quantum gravity.. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity. (shrink)

Stephen Hawking is well known for his research on general relativity and black holes. The present work is his attempt to explain his research in a form intelligible to the nonspecialist.

We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein–Langevin equation. Once (...) the thermal Green's function in a Schwarzschild background becomes available to the required accuracy, the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories. (shrink)

The relevance of gravitational boundary degrees of freedom and their dynamics in gravity quantization and black hole information has been explored in a series of recent works. In this work we further progress by focusing keenly on the genuine gravitational boundary degrees of freedom as the origin of black hole entropy. Wald’s entropy formula is scrutinized, and the reason that Wald’s formula correctly captures the entropy of a black hole examined. Afterwards, limitations of Wald’s method are discussed; (...) a coherent view of entropy based on boundary dynamics is presented. The discrepancy observed in the literature between holographic and Wald’s entropies is addressed. We generalize the entropy definition so as to handle a time-dependent black hole. Large gauge symmetry plays a pivotal role. Non-Dirichlet boundary conditions and gravitational analogues of Coleman-De Luccia bounce solutions are central in identifying the microstates and differentiating the origins of entropies associated with different classes of solutions. The result in the present work leads to a view that black hole entropy is entanglement entropy in a thermodynamic setup. (shrink)

Almost all of the entropy in the universe is in the form of Bekenstein–Hawking (BH) entropy of super-massive black holes. This entropy, if it satisfies Boltzmann’s equation S=logN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=\log \mathcal{N}$$\end{document}, hence represents almost all the accessible phase space of the Universe, somehow associated to objects which themselves fill out a very small fraction of ordinary three-dimensional space. Although time scales are very long, it is believed that black holes (...) will eventually evaporate by emitting Hawking radiation, which is thermal when counted mode by mode. A pure quantum state collapsing to a black hole will hence eventually re-emerge as a state with strictly positive entropy, which constitutes the famous black hole information paradox. Expanding on a remark by Hawking we posit that BH entropy is a thermodynamic entropy, which must be distinguished from information-theoretic entropy. The paradox can then be explained by information return in Hawking radiation. The novel perspective advanced here is that if BH entropy counts the number of accessible physical states in a quantum black hole, then the paradox can be seen as an instance of the fundamental problem of statistical mechanics. We suggest a specific analogy to the increase of the entropy in a solvation process. We further show that the huge phase volume (N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{N}$$\end{document}), which must be made available to the universe in a gravitational collapse, cannot originate from the entanglement between ordinary matter and/or radiation inside and outside the black hole. We argue that, instead, the quantum degrees of freedom of the gravitational field must get activated near the singularity, resulting in a final state of the ‘entangled entanglement’ form involving both matter and gravity. (shrink)

Some belief systems postulate intelligent agents that are deliberately evading detection and thus sabotaging any possible investigation into their existence. These belief systems have the remarkable feature that they predict an absence of evidence in their favor, and even the discovery of counterevidence. Such ‘epistemic black holes’, as I call them, crop up in different guises and in different domains: history, psychology, religion. Because of their radical underdetermination by evidence and their extreme resilience to counterevidence, they develop (...) and evolve in certain predictable ways. Shedding light on how epistemic black holes function can protect us against their allure. (shrink)

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space–time does not match the generally accepted definition of a black hole (derived from his concept of null (...) infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the pde literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the definition of a black hole. (shrink)

The ArgumentThe question of the possible existence of black holes is closely related to the question of the action of gravitation on the propagation of light. It has been raised recurrently from the when that Newton referred to a possible bending of light in hisOpticks. And it relies on apparently simple questions: Is light subject to gravitation? What is the effect of a gravitational field on the propagation of light? Could a particle of light emitted by a star (...) be retained by its gravitational field?From the end of the 1960s, the black hole idea has had a very important place in the relativistic literature, not to speak of the popularization of the theory. It turned out to be not only an important concept but also a tool that permitted us to understand general relativity better, indeed a tool that contributed greatly to changing the interpretation of Einstein's theory of gravitation. Here too I want to use this concept of the black hole to assist our understanding of the history of general relativity: the black hole is a fundamental milestone in the evolution of general relativity. (shrink)

Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt (Etesi in Found Sci 25:327–340, 2020), the aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness present in the set of real numbers, a set-theoretic entropy is assigned to it using the Kullback–Leibler relative entropy of a pair of Riemannian (...) manifolds. Then exploiting the non-negativity of this relative entropy an abstract Hawking-like area theorem is derived. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the set of real numbers in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too. (shrink)

A complete history of Islamic political thought from early Islam to the present Now in its 2nd edition, this textbook describes and interprets all schools of Islamic political thought, their origins, inter-connections and meaning. It examines the Qur'an, the early Caliphate, classical Islamic philosophy and the political culture of the Ottoman and other empires. It covers major thinkers such as Averroes and Ibn Taymiyya as well as a number of lesser authors, and Ibn Khaldun is presented as one of (...) the most original political theorists ever. It draws on a wide range of sources including writings on religion, law, philosophy and statecraft expressed in treatises, handbooks and political rhetoric. The new edition analyses the connections between religion and politics, covering the most recent developments in Islamic political thought and the most recent historical scholarship. It ends with a critical survey of reformism and Islamism from the late-19th century up to the present day. (shrink)

This paper discusses some philosophical aspects related to the recent publication of the experimental results of the 2017 black hole experiment, namely the first image of the supermassive black hole at the center of galaxy M87. In this paper I present a philosophical analysis of the 2017 Event Horizon Telescope (EHT) black hole experiment. I first present Hacking’s philosophy of experimentation. Hacking gives his taxonomy of elements of laboratory science and distinguishes a list of elements. I show (...) that the EHT experiment conforms to major elements from Hacking’s list. I then describe with the help of Galison’s Philosophy of the Shadow how the EHT Collaboration created the famous black hole image. Galison outlines three stages for the reconstruction of the black hole image: Socio-Epistemology, Mechanical Objectivity, after which there is an additional SocioEpistemology stage. I subsequently present my own interpretation of the reconstruction of the black hole image and I discuss model fitting to data. I suggest that the main method used by the EHT Collaboration to assure trust in the results of the EHT experiment is what philosophers call the Argument from Coincidence. I show that using this method for the above purpose is problematic. I present two versions of the Argument from Coincidence: Hacking’s Coincidence and Cartwright’s Reproducibility by which I analyse the EHT experiment. The same estimation of the mass of the black hole is reproduced in four different procedures. The EHT Collaboration concludes: the value we have converged upon is robust. I analyse the mass measurements of the black hole with the help of Cartwright’s notion of robustness. I show that the EHT Collaboration construe Coincidence/Reproducibility as Technological Agnosticism and I contrast this interpretation with van Fraassen’s scientific agnosticism. (shrink)

Book Review of The Future of Spacetime, by Stephen Hawking et al.

Early communities and states -- Egypt -- Mesoptamia, Assyria, Babylon -- Iran -- Israel -- India -- China -- The Greeks -- Rome -- Graeco-Roman humanism -- The Kingdom of Heaven and the Church of Christ -- Themes : similarities and differences between cultures -- General conclusion.

Covid-19 presents itself as a strange catastrophe. It has neither destroyed the planet nor has it erased humanity… but it has, in many ways, served to upend and alter what was previously considered ‘normal.’ As a result, what is perhaps the most notable characteristic of the Covid catastrophe is the very way it endures. Beyond any notion of catastrophic shock, the Covid catastrophe continues, indeed, it lingers in daily news cycles, changes to working environments and restrictions on travel. It is (...) an enduring presence, from which any determination of its ‘end’ is either nullified by an unending stream of Covid reports, or worse, ignored altogether. On this basis alone, is it even possible to discern an ‘end’ to Covid? (shrink)

This revised and expanded edition of A World History of Ancient Political Thought examines the political thought of ancient Egypt, Mesopotamia, Israel, Iran, India, China, Greece, Rome and early Christianity, from prehistory to c.300 CE. The book explores the earliest texts of literate societies, beginning with the first written records of political thought in Egypt and Mesopotamia and ending with the collapse of the Han dynasty and the Western Roman Empire.

Kin relations have a strong theoretical and empirical basis for explaining cooperative behavior. Nevertheless, there is growing recognition that context—the cooperative environment of an individual—also shapes the willingness of individuals to cooperate. For nomadic pastoralists in Norway, cooperation among both kin and non-kin is an essential predictor for success. The northern parts of the country are characterized by a history of herder-herder competition exacerbating between-herder conflict, lack of trust, and subsequent coordination problems. In contrast, because of a history (...) of herder-farmer competition, southern Norway is characterized by high levels of between-herder coordination and trust. This comparative study investigates the relative importance of “cooperative context” and kinship in structuring cooperative behavior using an experimental gift game. The main findings from this study were that in the South, a high level of cooperation around an individual pushes gifts to be distributed evenly among other herders. Nevertheless, kinship matters, since close kin give and receive larger gifts. In contrast, kinship seems to be the main factor affecting gift distribution in the North. Herders in the North are also concerned with distributing gifts equally, albeit limiting them to close kin: the level of intragroup cooperation drives gifts to be distributed evenly among other closely related herders. The observed regional contrasts in cooperative decisions fit with the different historical levels of conflict and trust in the two regions: whereas herders in the South are affected by both cooperative context and kinship, kinship seems to be the main determinant of cooperation in the North. (shrink)

Through examining the BBC television series, Black and British: A Forgotten History, written and presented by the historian David Olusoga, and in extending Paul Gilroy’s assertion that the everyday banality of living with difference is now an ordinary part of British life, this article considers how Olusoga’s historicization of the Black British experience reflects a convivial rendering of UK multiculture. In particular, when used alongside Žižek’s notion of parallax, it is argued that understandings of convivial culture can (...) be supported by a historical importance that deliberately ‘shocks’, and subsequently dislodges, popular interpretations of the UK’s ‘white past’. Notably, it is parallax which puts antagonism, strangeness and ambivalence at the heart of contemporary depictions of convivial Britain, with the UK’s cultural differences located in the ‘gaps’ and tensions which characterize both its past and present. These differences should not be feared but, as a characteristic part of our convivial culture, should be supplemented with historical analyses that highlight but, also, undermine, the significance of cultural differences in the present. Consequently, it is suggested that if the spontaneity of conviviality is to encourage openness, then understandings of multiculturalism need to go beyond reification in order to challenge our understandings of the past. Here, examples of ‘alterity’ are neither ‘new’ nor ‘contemporary’, but instead, constitute a fundamental part of the nation’s history: of the ‘gap’ made visible in transiting past and present. (shrink)

Dialogue is a recurring and significant component of Indian religious and philosophical literature. Whether it be as a narrative account of a conversation between characters within a text, as an implied response or provocation towards an interlocutor outside the text, or as a hermeneutical lens through which commentators and modern audiences can engage with an ancient text, dialogue features prominently in many of the most foundational sources from classical India. Despite its ubiquity, there are very few studies that explore this (...) important facet of Indian texts. This book redresses this imbalance by undertaking a close textual analysis of a range of religious and philosophical literature to highlight the many uses and functions of dialogue in the sources themselves and in subsequent interpretations. Using the themes of encounter, transformation and interpretation - all of which emerged from face-to-face discussions between the contributors of this volume - each chapter explores dialogue in its own context, thereby demonstrating the variety and pervasiveness of dialogue in different genres of the textual tradition. This is a rich and detailed study that offers a fresh and timely perspective on many of the most well-known and influential sources from classical India. As such, it will be of great use to scholars of religious studies, Asian studies, comparative literature and literary theory. (shrink)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

The recent publication of the translation of Jacques Derrida’s Athens, Still Remains, a small volume of photographs and commentary, affords an opportunity to probe Derrida’s reflections on death and therefore on life as well. Looking at photographs and objects of everyday life, Derrida emphasizes the deferred yet certain nature of death and the way in which this deferral opens the opportunity to devote ourselves to life. His grounding of his philosophical and deconstructionist argument in contemplation of material fragments invites a (...) comparison with the writing of sociologist Georg Simmel on ruins, time and death. Both writers attempt to discover practices of survival, the techne of affirming life in the face of death. For both of them these practices are sociological as well as philosophical, individual as well as collective, and aesthetic as well as intellectual. While their reflections thematically converge, their strategies for the affirmation of life are not identical, and we contrast Derrida’s approach, rooted in a concept of being in the world and a connection to others, to Simmel’s analysis which is focused on the role of culture and the force of the human spirit. Reconstructing a conversation between Derrida and Simmel and examining their intellectual rapprochement deepen our thinking about temporality and death as we confront the question ‘How are we to live?’. (shrink)

It has long been a truism of the history of philosophy that intentionality is an invention of the medieval period, and within this standard narrative, the central place of Arabic philosophy has always been acknowledged. Yet there are many misconceptions surrounding the theories of intentionality advanced by the two main Arabic thinkers whose works were available to the West, Avicenna and Averroes. In the first part of this paper I offer an overview of the general accounts of intentionality and (...) intentional being found in the linguistic, psychological, and metaphysical writings of Avicenna and Averroes, and I trace the terminology of “intentions” to a neglected passage from Avicenna’s logic. In the second part of the paper I examine the way that Avicenna and Averroes apply their general theories of intentionality to the realm of sense perception. I offer an explanation of why Avicenna might have chosen to denominate the objects of the internal sense faculty of estimation as “intentions”, and I explore the implications of Averroes’s decision to attribute intentionality to the external senses and the media of perception. (shrink)

Cover -- Half Title -- Title Page -- Copyright Page -- Original Copyright Page -- Dedication -- Table of Contents -- INTRODUCTION -- VOLTAIRE -- HUME -- ROBERTSON -- GIBBON -- INDEX.

To travel round the world is to be reminded of the very public presence of history, of the past as issue and identity. Yet this is widely underrated. Using History is the first book to tackle public, non-academic history for the student and general reader. Furthermore, it does so from a truly global perspective as opposed to focusing on the traditional Western-dominated model.

Many think that the aim of Hume’s Dialogues is simply to discredit the design argument for the existence of an intelligent designer. We think instead that the Dialogues provides a model of true religion. We argue that, for Hume, the truly religious person: believes that an intelligent designer created and imposed order on the universe; grounds this belief in an irregular argument rooted in a certain kind of experience, for example, in the experience of anatomizing complex natural systems such as (...) the eye; and retains this belief, on the basis of these reasons, even after careful scrutiny. We argue that two of the Dialogues’s characters, Philo and Cleanthes, exhibit true religion. A third character, Demea, exhibits false religion and a persistent impiety. Taken as a whole, we see the Dialogues as an educational performance for the benefit of Pamphilus, Cleanthes’s ward, as well as for the benefit of readers of the Dialogues. Specifically, we think, given that its lessons concern theology and the principles of religion, the dynamics of the Dialogues’s discussion and the interplay between its characters can be seen as a demonstration of a method for becoming truly religious. (shrink)

Western Political Thought in Dialogue with Asia is a unique collection of essays that examines the exchange of political ideas between Western Europe and Asia from the Middle Ages to the early twentieth century. The contributors to the volume call for globalizing the scope of research and teaching in the history of political thought.

Malebranche's Theodicy ANDREW G. BLACK LEIBNIZ'S SOLUTION tO the problem of evil, his theodicy, might be regarded as a paradigm of philosophical theology. Its pattern, as with so much of Leibniz's philosophy, is reconciliation of deep metaphysical truth with recalcitrant ap- pearance. Thus, a theodicy is not just any solution to the problem; strictly speaking it is a vindication of divine providence in the face of the challenge posed by apparent imperfections of all kinds in creation.' The preeminence of (...) Leibniz's theodicy as a modern solution to the problem of evil has helped to obscure distinguished contributions from among his contemporaries. Not least among these is that made by Nicolas Malebranche, a philosopher having much in common with Leibniz . ~ Malebranche shows a deep concern for the problem of evil throughout his philosophical writings, though nowhere more so than in his Treatise on Nature and Grace, a a book written in response to the Jansenist4 challenge to orthodox In addition to an entire and substantial book, the Theodicy , a number of Leibniz's essays contain versions of his theodicy. See, for example, articles 1- 7 of the Discourse on Metaphysics; also "A Vindication of God's Justice Reconciled with his.. (shrink)