In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding (...) a middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

Recently in the philosophical literature there has been some effort made to understand the proper application of the theory of utilitarianism to worlds in which there are infinitely many bearers of utility. Here, we point out that one of the best, most inclusive principles proposed to date contradicts fundamental utilitarian ideas, such as the idea that adding more utility makes a better world.

ABSTRACT This essay shows how certain limit-points of Lacan's psychoanalytic discourse in his 1955–56 seminar on The Psychoses tangentially brush up against Maurice Blanchot's writing on the neuter, as presented in The Space of Literature from 1955. The effort is to strike up a conversation between Lacan's “clinical discourse” and Blanchot's “critical writing” on the topics of language, writing, authority, and madness. In this regard, the essay approaches an infinite point of approximation between the procedure of psychosis and the (...) procedure of literary writing by questioning whether, at some point in these different ways of proceeding, they may share a certain experience of language. Namely, this is an experience of a language that, as stated by both Jacques Lacan and Maurice Blanchot, “speaks all by itself” and does so incessantly and with a certain furious neutrality. (shrink)

Drawing upon the practice of caregiving and the insights of feminist care ethics, I offer a phenomenology of caregiving through the work of Eva Feder Kittay and Emmanuel Lévinas. I argue that caregiving is a material dialectic of embodied response involving moments of leveling, attention, and interruption. In this light, the Levinasian opposition between responding to another's singularity and leveling it via parity-based principles is belied in the experience of care. Contra much of response ethics’ and care ethics’ respective literatures, (...) this dialectic suggests that they are complementary in ways that productively illuminate themes of each. I conclude by suggesting that when response and care ethics are thought together through the experience of caregiving, such labors produce finite responsibility with infinite hope. (shrink)

Infinite idealizations appear in our best scientific explanations of phase transitions. This is thought by some to be paradoxical. In this paper I connect the existing literature on the phase transition paradox to work on the concept of indispensability, which arises in discussions of realism and anti-realism within the philosophy of science and the philosophy of mathematics. I formulate a version of the phase transition paradox based on the idea that infinite idealizations are explanatorily indispensable to our best (...) science, and so ought to attract a realist attitude. I go on to offer a solution to the paradox by drawing a distinction between two types of indispensability: constructive and substantive indispensability. I argue that infinite idealizations are constructively indispensable to explanations of phase transitions, but not substantively indispensable. This helps to resolve the paradox, I maintain, since realist commitment tracks substantive, and not constructive, indispensability. (shrink)

According to one of Leibniz's theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof , namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but (...) related problem that we dub the Problem of Guaranteed Proof . We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)

This paper analyses Giordano Bruno's dialogue De l’infinito universo e mondi (The Infinite Universe and Worlds), written during his stay in England (1583–85), in the context of his philosophical works and, particularly, within the context of scientific and imaginative writings such as Cyrano de Bergerac's Other Worlds (published posthumously in 1662) and Francis Godwin's The Man in the Moone (1638). The article also discusses the contemporary speculations of Galileo and Kepler regarding the existence of a plurality of worlds and (...) the presence of creatures on the moon and their rapport with humans. Besides the imaginative, fantastic and pseudoscientific elements, attention is also given to religious implications and attitudes, especially in the case of Godwin, who, like his countryman John Wilkins—author of The Discovery of the Worlde in the Moone (1638)–was a bishop and therefore wanted to avoid any controversy with the church. (shrink)

This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the (...) question is: what exactly is an infinite regress argument, and when is such an argument a good one? (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov–Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

According to current scholarly consensus, the pre- and post-exilic strata of Biblical Hebrew differ sufficiently to allow for the relative dating of biblical texts on linguistic grounds. Challengers to this view have objected that the received orthography of the Hebrew Bible, which is fuller than that of any pre-exilic epigraphic source, shows that no pre-exilic biblical text escaped post-exilic spelling revision. Moreover, so it is claimed, susceptibility to scribal modification on the level of orthography implies susceptibility to scribal modification on (...) the higher linguistic levels as well, which would effectively obscure a text’s original linguistic profile. In the present article it is argued that the degree of scribal modification involved in the process of orthographical revision was not so great as to distort irremediably the picture of linguistic development seen in biblical literature, so that distinctively late linguistic features can still be distinguished from their classical counterparts. Significantly, as has been argued elsewhere, diachronic development is still discernible even in the domain of orthography, a fact demonstrated on the basis of several examples, including the spelling of the qṭol-pattern qal infinitive construct. (shrink)

How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that worlds are made better if we increase the value in every region of space and time, or that they are made (...) better if we increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most. (shrink)

In this article we analyze the claim that a probabilistic interpretation of the infinite epistemic regress problem leads to a unique solution, the so called “completion” of the regress. This claim is implicitly based on the assumption that the standard Kolmogorov axioms of probability theory are suitable for describing epistemic probability. This assumption, however, has been challenged in the literature, by various authors. One of the alternatives that have been suggested to replace the Kolmogorov axioms in case of an (...) epistemic interpretation of probability, are belief functions, introduced by Shafer in 1976. We show that when one uses belief functions to describe the infinite epistemic regress problem, it is no longer the case that the solution is unique. We also argue that this complies with common sense. (shrink)

Dance is intimately connected to both Kierkegaard’s personal life and his life in writing, as exemplified in his famous nightly attendance at the dance-filled theater, and his invitation to the readers of “A First and Last Explanation” to “dance with” his pseudonyms. The present article’s acceptance of that dance invitation proceeds as follows: the first section surveys the limited secondary literature on dance in Kierkegaard, focusing on the work of M. Ferreira and Edward Mooney. The second section explores the hidden (...) dancing dimensions of Kierkegaard’s “leap” and “shadow-dance”. And the third section reinterprets the pseudonymous works richest in dance, Repetition and Postscript, concluding that the religious for him is the lighthearted dance of a comic actor through the everyday theater of the world. (shrink)

This article gives insight into the world of 3rd century BCE Alexandrian Judaism by analysing one aspect of the Greek translation of Exodus and provides a detailed evaluation of the way the translator managed to express the essence of the Hebrew text of Exodus while reflecting to some degree the form of the Hebrew text. No previous study only analyses this translator’s treatment of Hebrew paronymous infinitive absolute constructions in Greek Exodus. This research contributes to the preparation of a commentary (...) on Greek Exodus in the Society of Biblical Literature Septuagint Commentary Series. Using the Göttingen text of Greek Exodus prepared by John William Wevers, it evaluates how this translator rendered each occurrence of a paronymous infinitive absolute construction in Hebrew Exodus, defining the primary modes employed and also seeking to explain variations from these norms. The primary method incorporates a close exegetical reading of both the Hebrew and Greek texts and comparing their texts, in order to discern how the translator treated this Hebrew idiom and illustrating his translation approach.Contribution: The results contribute to our understanding of how the translator of Greek Exodus approached his task. He was more concerned to express the sense of the Hebrew text, than producing a literal translation. He generally follows the Hebrew text’s word order, but is creative in his choice of Greek equivalents, often showing sensitivity to context and Greek idiom. This translation approach differentiates this translator’s approach somewhat from those responsible for other portions of the Pentateuch. (shrink)

The concept of an infinite game played on a finite graph is perhaps novel in the context of an rather extensive recent literature in which infinite games are generally played on an infinite game tree. We claim two advantages for our model, which is admittedly more restrictive. First, our games have a more apparent resemblance to ordinary parlor games in spite of their infinite duration. Second, by distinguishing those nodes of the graph that determine the winning (...) and losing of the game , we are able to offer a complexity analysis that is useful in computer science applications. (shrink)

A prominent Thomistic cosmological argument maintains that an infinite regress of causes, which exhibits a certain pattern of ontological dependence among its members, would be vicious and so must terminate in a first member. Interestingly, Jonathan Schaffer offers a similar argument in the contemporary grounding literature for the view called metaphysical foundationalism. I consider the striking similarities between both arguments and conclude that both are unsuccessful for the same reason. I argue this negative result gives us indirect reason to (...) consider metaphysical infinitism as a genuine possibility, the view that chains of ontological dependence or ground can descend indefinitely. (shrink)

We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time (...) generalization of the countable Borel equivalence relations, a key subclass of the Borel equivalence relations, and again show that several key properties carry over to the larger class. Lastly, we collect together several results from the literature regarding Borel reducibility which apply also to absolutely $\Delta^1_2$ reductions, and hence to the infinite time computable reductions. (shrink)

The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. (...) We propose and defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition (...) in the arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (shrink)

Many cosmological arguments for the existence of a first cause or a necessary being rely on a premise which denies the possibility of an infinite regress ofsome particular sort. Adequate and satisfying support for this premise, however, is not always provided. In this paper I attempt to address this gap in the literature. After discussing the notion of a causal explanation (section I), I formulate three principles which govern any successful causal explanation (section II). I then introduce the notions (...) of a caused being, a causal network, and a causal chain, and argue that (roughly) an infinite causal chain cannot be explained merely by reference to the causal activities of the members of that chain (section III). In a sequel to the present paper, I employ this result to construct two closely related arguments for the existence of a necessary being. (shrink)

One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions (...) with a truth predicate and argue that they fail to support the necessity of transparency for that purpose. Second, we show that, with the aid of some regimentation, many expressive functions of the truth predicate can actually be performed using truth principles that are consistent in classical logic. Finally, we suggest a reconceptualisation of deflationism, according to which the principles that govern the use of the truth predicate in natural language are largely irrelevant for the question of what formal theory of truth we should adopt. Many philosophers think that the paradoxes pose a special problem for deflationists; we will argue, on the contrary, that deflationists are in a much better position to deal with the paradoxes than their opponents. (shrink)

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully (...) adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)

The examples of dynamic supertasks analyzed to date in the philosophical literature, in which both determinism and the classical laws of conservation of energy and momentum are violated, all share the important limitation of requiring material systems of infinite mass. This paper demonstrates that this limitation is not necessary. This has important consequences for the scope and meaning of such violations.

The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. (...) We propose and defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

The rationale clause infinitive is a modifier of the verb which expresses an agent's intention in acting as they do. The rationale clause is related to the matrix in two important ways: the null subject of the infinitive (PRO) is usually coreferential with a phrase in the matrix (control), and the intention it expresses is usually assigned to a phrase in the matrix (predication). Given that the controller and argument of the rationale clause are usually clausemates of the infinitive itself, (...) the strongest hypothesis is that both control and predication are strictly local. However, there has been much debate in the literature concerning the viability of such a locality constraint. In this article, I argue in favour of a locality-based account of control and predication in the rationale clause, comparing it with a discourse-semantic constraint approach and a logophoricity constraint approach. Data from two related modifier infinitives (the purpose clause and the telic clause) will be used to sharpen the discussion. (shrink)

This essay is an attempt to plumb the conventions which exist at a specific historical moment in both the aesthetic and scientific spheres. I will assume the existence of a web of conventions within the world of the aesthetic—conventions which have elsewhere been admirably illustrated—but will depart from the norm by examining the synchronic existence of another series of conventions, those of medicine. I do not mean in any way to accord special status to medical conventions. Indeed, the world is (...) full of overlapping and intertwined systems of conventions, of which the medical and the aesthetic are but two. Medicine offers an especially interesting source of conventions since we do tend to give medical conventions special “scientific” status as opposed to the “subjective” status of the aesthetic conventions. But medical icons are no more “real” than “aesthetic” ones. Like aesthetic icons, medical icons may iconographic in that they represent these realities in a manner determined by the historical position of the observers, their relationship to their own time, and to the history of the conventions which they employ. Medicine uses its categories to structure an image of the diversity of mankind; it is as much at the mercy of the needs of any age to comprehend this infinite diversity as any other system which organizes our perception of the world. The power of medicine, at least in the nineteenth century, lies in the rise of the status of science. He conventions of medicine infiltrate other seemingly closed iconographic systems precisely because of this status. In examining the conventions of medicine employed in other areas, we must not forget this power.One excellent example of the conventions of human diversity captured in the iconography of the nineteenth century is the linkage of two seemingly unrelated female images—the icon of the Hottentot female and the icon of the prostitute. In the course of the nineteenth century, the female Hottentot comes to represent the black female in nuce, and the prostitute to represent the sexualized woman. Both of these categories represent the creation of classes which correspondingly represent very specific qualities. While the number of terms describing the various categories of the prostitute expanded substantially during the nineteenth century, all were used to label the sexualized woman. Likewise, while many groups of African blacks were known to Europeans in the nineteenth century, the Hottentot remained representative of the essence of the black, especially the black female. Both concepts fulfilled an iconographic function in the perception and the representation of the world. How these two concepts were associated provides a case study for the investigation of patterns of conventions, without any limitation on the “value” of one pattern over another. Sander L. Gilman is professor of Humane Studies in the Department of German Literature and Near Eastern Studies and professor of Psychiatry in the Cornell Medical College, Cornell University. He is the author or editor of numerous studies of European cultural history with a focus on the history of stereotypes. In addition, he has coedited Degeneration with J. E. Chamberlin. His study Jewish Self-Hatred is forthcoming. (shrink)

Abstract:What is the relationship between philosophical understandings of the infinite and their narrative expressions? This article explores the infinite in two aesthetic paradigms: the horror of the infinite in classical Greece, and Romanticism's glorification of the unlimited. It argues that these two approaches paved the way for a third, a "relational infinite" that emerged in the second half of the twentieth century. To illustrate this third paradigm, I draw on the works of Argentine author Jorge Luis (...) Borges and on other fictions of the fantastic genre that make the boundless and endless a key element of the plot. (shrink)

Catherine Malabou, Antonio Negri, John D. Caputo, Bruno Bosteels, Mark C. Taylor, and Slavoj Zizek join seven others--including William Desmond, Katrin Pahl, Adrian Johnston, Edith Wyschogrod, and Thomas A. Lewis--to apply Hegel's thought to twenty-first-century philosophy, politics, and religion. Doing away with claims that the evolution of thought and history is at an end, these thinkers safeguard Hegel's innovations against irrelevance and, importantly, reset the distinction of secular and sacred. These original contributions focus on Hegelian analysis and the transformative value (...) of the philosopher's thought in relation to our current "turn to religion." Malabou develops Hegel's motif of confession in relation to forgiveness; Negri writes of Hegel's philosophy of right; Caputo reaffirms the radical theology made possible by Hegel; and Bosteels critiques fashionable readings of the philosopher and argues against the reducibility of his dialectic. Taylor reclaims Hegel's absolute as a process of infinite restlessness, and Zizek revisits the religious implications of Hegel's concept of letting go. Mirroring the philosopher's own trajectory, these essays progress dialectically through politics, theology, art, literature, philosophy, and science, traversing cutting-edge theoretical discourse and illuminating the ways in which Hegel inhabits them. (shrink)

A simultaneous collision that produces paradoxical indeterminism (involving N0 hypothetical particles in a classical three-dimensional Euclidean space) is described in Section 2. By showing that a similar paradox occurs with long-range forces between hypothetical particles, in Section 3, the underlying cause is seen to be that collections of such objects are assumed to have no intrinsic ordering. The resolution of allowing only finite numbers of particles is defended (as being the least ad hoc) by looking at both -sequences (in the (...) context of a very basic supertask, in Section 4) and *-sequences (reversed -sequences, in the form of paradoxical results from the recent literature). Introduction The simultaneous collision The paradox in other contexts The basic problem is N0 things The recent literature Generating N0 things. (shrink)

When it comes to specifying the moral duties we bear towards future generations, most political philosophers position themselves on what could be regarded as a safe ground. A variant of the Lockean proviso is commonplace in the literature on intergenerational justice, taking the form of an obligation to bestow upon future people a minimum of goods necessary for reaching a certain threshold of well-being (Meyer, 2017). Furthermore, even this minimum is often frowned upon, given the non-identity problem and the challenges (...) this presents to the topic of justice between generations. Additional issues are raised at the level of non-ideal theory, the most significant being the problem of non-compliance (Gosseries and Meyer, 2009).In this paper I intend to probe the limits of “practical political possibility” (Rawls 1999), by inquiring whether embracing the sufficiency view (Frankfurt, 1987; Crisp, 2003; Benbaji, 2005) as a distributive pattern and capabilities as a metric can lead to more burdensome obligations for present generations. More specifically, I try to show that we have a duty to invest in research that aims at prolonging the lifespan of humans (the idea can already be found in the sufficientarian literature, for instance in Farrelly, 2007). Moreover, given the Earth’s limited resources, we ought to encourage the terraforming of other planets in order to make them inhabitable for (future) people.I argue that these two seemingly far-fetched projects are in fact worthwhile goals to pursue on the one hand, and moral obligations on the other hand. Nonetheless, they are not the only ones we ought to take on; for instance, we must simultaneously pursue them and try to improve the prospects of those who fall under a sufficiency threshold here and now. That is, specifying these (prima facie) duties towards future generations is connected with stronger obligations towards the current generation.Towards the end of the paper I engage in a discussion regarding the role of the feasibility constraint in a theory of justice, as rationales pertaining to feasibility are perhaps going to be the most recurrent criticisms raised against my proposal. To that end, I defend limitarian policies, which aim at setting an upper limit to how much money individuals are allowed to possess (Robeyns, 2017; Volacu and Dumitru, 2019). (shrink)

It has been argued in the conservation literature that giving conservation absolute priority over competing interests would best protect the environment. Attributing infinite value to the environment or claiming it is ‘priceless’ are two ways of ensuring this priority (e.g. Hargrove 1989; Bulte and van Kooten 2000; Ackerman and Heinzerling 2002; McCauley 2006; Halsing and Moore 2008). But such proposals would paralyse conservation efforts. We describe the serious problems with these proposals and what they mean for practical applications, and (...) we diagnose and resolve some conceptual confusions permeating the literature on this topic. (shrink)

The interpretation of propositions in Lukasiewicz's infinite-valued calculus as answers in Ulam's game with lies--the Boolean case corresponding to the traditional Twenty Questions game--gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.

“Wuqiong,” namely the concept of infinite regress has been identified with the hallmark of the Huayan scholasticism, which is dubbed as “chongchong wujin” (repetitive containment ad infinitum). Such an inconceivable perspective is drawn from the Huayan thinkers’ presupposition that a part contains the whole, which is again composed of such parts. But many philosophical traditions, in general, try to avoid the infinite regress as one of the logical fallacies. This paper examines the Buddhist literature that alludes to “wuqiong” (...) as infinite regress, and highlights that the Huayan thinkers also had a critical attitude toward this issue when they discussed the ontological status of the dissociated factors. But they also used the term in a positive sense of inexhaustiveness. This twofold usage of the term seems to show that the Huayan thinkers critically incorporated the elements of previous scholarship even when they created their own unique metaphysical theories. ‘무궁’, 곧 무한소급은 ‘중중무진’으로 표현되는 화엄교학과 동일시되어 왔다. 그것은 부분이 전체를 포함한다는 화엄사상가들의 이론적 전제로부터 각각의 부분들에 전체가 끊임없이 내포된다는 불가사의한 세계관이 도출되기 때문이다. 그러나 불교철학은 물론, 서양철학에서도 무한소급은 논리적 오류로서 회피해야 하는 것으로 간주되어 왔다. 이와 관련하여 본 논문에서는 화엄사상 성립 이전의 몇몇 불교 문헌들에서 특히 유위 4상(相), 득(得)과 같은 불상응행법을 설정할 경우 ‘무궁과’라는 논리적 오류가 발생함을 지적한 사례들을 살펴보았는데, 그러한 비판이 화엄의 문헌들에도 거의 그대로 수용되고 있음을 확인할 수 있다. 그러나 화엄의 문헌에는 ‘무궁’이라는 용어가 ‘무궁진’, ‘무진’, ‘무변’과 동의어로서 긍정적인 맥락에서 사용하고 있는 경우도 자주 발견된다. 이처럼 화엄의 문헌에 이중적인 의미로 사용된 ‘무궁’이라는 개념은 화엄사상가들이 자신들의 독특한 형이상학을 제시하면서도 그들 이전의 여러 교학체계들을 비판적으로 수용했음을 보여주는 증거라고 할 수 있을 것이다. (shrink)

This paper offers a defense of Charles Parsons’ appeal to mathematical intuition as a fundamental factor in solving Benacerraf’s problem for a non-eliminative structuralist version of Platonism. The literature is replete with challenges to his well-known argument that mathematical intuition justifies our knowledge of the infinitude of the natural numbers, in particular his demonstration that any member of a Hilbertian stroke string ω-sequence has a successor. On Parsons’ Kantian approach, this amounts to demonstrating that for an “arbitrary” or “vaguely represented” (...) string of strokes, we can always “add” one more stroke. Critics have contested the cogency of a notion of an arbitrary object, our capacity to vaguely represent a definite object, and the role of spatial and temporal representation in the demonstration that we can “add” one more. The bulk of this paper is devoted to demonstrating how to meet all extant criticisms of his key argument. Critics have also suggested that Parsons’ whole approach is misbegotten because the appeal to mathematical intuition inevitably falls short of providing a complete solution to Benacerraf’s problem. Since the natural numbers are essentially and exclusively characterized by their structural properties, they cannot be identified with any particular model of arithmetic, and thus a notion of intuition will fail to capture the universality of arithmetic, its applicability to all entities. This paper also explains why we should not reject appeal to mathematical intuition even though it is not itself sufficient to fully “close the gap” on Benacerraf’s challenge. (shrink)

Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols.Monadic second order logic over infinite words can alternatively be described as a first-order logic interpreted in${\cal P}\left$, the power set Boolean algebra of the natural numbers, equipped with modal operators for ‘initial’, ‘next’, and ‘future’ states. We prove that the (...) first-order theory of this structure is the model companion of a class of algebras corresponding to a version of linear temporal logic without until.The proof makes crucial use of two classical, nontrivial results from the literature, namely the completeness of LTL with respect to the natural numbers, and the correspondence between S1S-formulas and Büchi automata. (shrink)

In this article, we will describe two theistic modes of “paradoxical detachment” from the Presence of the Infinite, implying the coexistence of attachment and detachment. We will analyze two forms of Christianity-based paradoxical detachment: being dependent on the Ground of soul, while being detached from the representations of the Infinite ; being absolutely dependent on the Infinite, while being detached from any religious morality. The nontheistic mode of detachment from the Presence of the Infinite requires an (...) absolute detachment. We will examine two forms of absolute detachment towards the Presence of the Infinite: on one hand, the all-encompassing emptiness in the Kagyü and Gelug lineages of Tibetan Buddhism; on the other hand, the Heideggerian notion of “groundless abyss.” In the Kagyü and Gelug lineages of Tibetan Buddhism, being absolutely detached is searching for the Enlightenment, while being detached from all concepts. Heideggerian notions of “groundless abyss” and “de-hominization” allow us to reach absolute detachment, while remaining in a non-theistic way of thinking. (shrink)

The article proposes looking at children's literature, particularly the form of the picture book, as an educational resource for producing body awareness in school. Eight reading steps for as many bodily actions aimed at naming the body, activating it, getting to know it and moving it in space, on and off the pages; between grounding, listening, breathing, playing and moving, the rediscovery of gestures and anatomical truths invites to deepen self-knowledge as a preliminary act to the encounter and relationship with (...) the other and with the environment. The picture books by their specificities of short form and cross-over, offer, even in non-fiction production, the possibility of bringing attention back to the body dimension within the school and educational debate, where it lives today in a state of malaise and oblivion. Meaningful conversations, explorations and relationships flow from the pages of the albums: research on language as a tool that gives dignity and value to each person, and encounters with the artistic representation of the world as an infinite mirror of its multiplicity and variety, constitute valuable opportunities for an education that is aware of the wholeness of learners and teachers and the integrated, erotic and embodied dimension of their relationship. (shrink)

Open peer commentary on the target article “From Objects to Processes: A Proposal to Rewrite Radical Constructivism” by Siegfried J. Schmidt. Upshot: This commentary asks if Schmidt’s latest process-orientated philosophy is based on a vicious infinite regress argument. The commentator uses recent literature on the distinction of vicious and benign infinite regresses (from Claude Gratton and Nicholas Rescher) and tries to show that – taken verbatim – there is a serious logical problem in Schmidt’s argumentation.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.2 (2002) 405-414 [Access article in PDF] Nihilism in Seamus Heaney Irene Gilsenan Nordin I WISH TO BEGIN WITH THE WORDS of Nietzsche's madman as he makes his famous appearance, running into the crowded marketplace in the bright morning with his lit lantern in his hand, crying out his proclamation of the death of God: "'Where has God gone?' he [cries]. 'I shall tell you. We (...) have killed him—you and I. We are all his murderers.'" He calls out in despair to the bemused and indifferent crowd his rhetorical questions: How were we able to drink up the sea? Who gave us the sponge to wipe away the entire horizon? What were we doing when we unchained the earth from its sun? Whither is it moving now? Away from all suns? Are we not plunging continually? Backward, sideward, forward, in all directions? Is there still any up or down? Are we not straying as through an infinite nothing? 1These words of the madman express the abyss of despair experienced on the realization that God is dead, the state of desolation which articulates what Nietzsche himself understood to be the consequences of the triumph of the Enlightenment. But these words of despair sum up more than that; they sum up the underlying problems of Nietzsche's age, and indeed our age: the basic mistrust of all previously held systems of value; the collapse of all ordering principle; and the erosion of the authority of tradition. In other words, reason has revealed the inadequacy of tradition, and has itself lost the ability to provide us with [End Page 405] any reliable means of evaluation—since any such evaluation must be based on the very principles which are themselves under attack.This stark realization of the absence of all sense of meaning in values previously held to be true leads to the condition that Nietzsche calls "nihilism," (Latin nihil, "nothing"), the condition that he considered to be the central problem of Modernity. This condition, Nietzsche believed, is brought about by the realization of three factors: first, the loss of faith in what he calls a "'meaning' in all events," a loss which contributes to an experience of aimlessness; second, the realization that there is no inherent pattern to the world or to history that can lend universal coherence; and third, the loss of faith in the existence of a stable world of being which can be evaluated according to steadfast, enduring principles. The rejection of these three categories, which Nietzsche terms "aim," "unity," and "being," leads to an experience of a world that appears "valueless," in other words, the experience of nihilism. 2Nietzsche, whose thought was considered by Heidegger to be the "final thought of Western metaphysics," 3 is seen as a heralding voice of postmodernism. 4 In this respect, Nietzsche's "death of God" can be seen to be about the death of modernist philosophical presuppositions, the death of the logocentric metaphysics of presence. But, parallel with the notion of crisis that Nietzsche's announcement of the death of God expresses and the ensuing critique of "metanarratives" which his thought has helped to give rise to, 5 Nietzsche's declaration of crisis can also be seen as a statement of faith. His interpretation of the problems of our age, while on the one hand "negatively" proclaiming the death of God and denying the possibility of shared meaning—or in Lyotard's terms "the consensus of a taste which would make it possible to share collectively the nostalgia for the unattainable" (p. 81), can, on the other hand, be viewed in a more "positive" light. The term "nihilism" itself, as Nietzsche has shown us, is ambiguous, comprising both the concepts of what he termed "active nihilism" and "passive nihilism," which involves a complex interplay between the dual forces of affirmation and negation (WP, p. 22).As the Italian philosopher, Gianni Vattimo, points out, the most general distinction between these forces can be seen in terms of "strength of spirit," where nihilism is considered as both "a sign (Zeichen) of the strengthened power... (shrink)

In the beginning was the triangle, the apostles of semiology say. In arguing for a semiological approach to literature, this paper highlights first that theconsecrated semiotic triangle seen in perspective proves to be a pyramid, with its faces consisting of minimal semiotic triads; it then suggests that the pyramidalsemiotic constructs within a given context project the figure of infinite semiosis; finally, it proposes an illustration of the literary process of signification using thealchemical image of the clepsydra.

The object of research in this article is the motif of caryatids in the decoration of the Forum of Augustus. Along with other elements, it is repeated in the ensembles of the cities of Roman Spain and region of Campania. It is believed that the August Forum in its decorative program broadcasts the most important ideological markers of the Early Empire era. In particular, the caryatids decorating the attic of the portico are reduced replicas of the famous figures of the (...) Erechtheion. Such a reference is connected with the glorification of Rome's power over Greece in the reproduction of its figurative system. The subject of the study was the process of transformation that occurs with the motif of caryatids in non-classical ensembles. Following the iconographic, stylistic and semantic changes in the caryatid motif in the ensembles of the cities of August Emerita, Tarracon and Puteola, the author suggests possible causes and options for the transformation of these decorative elements. The article focuses on the possible causes of such a transformation, and also attempts to clarify the concept of the "Forum Augusti model", which is found in the research literature in various meanings and variants, through the analysis of a single element. The lack of a single definition of this phenomenon makes it possible to infinitely expand the range of monuments that could be created in imitation of the metropolitan prototype. The author of the article does not support this position, focusing on a few ensembles in which not only the same iconographic schemes occur, but also the logic of the decorative system is preserved. As a result of the research, it was possible to clarify the concept of the Forum Augusti model, which implies not so much the reproduction of the iconography and stylistics of the original. (shrink)

Gargani's work aims at discovering the link connecting the multifarious aspects of contemporary Austrian culture in the connection between ethics and aesthetics. In Gargani's view this connection is responsible for the strong criticism of contemporary society, based on mechanization and automatic processes, as it is instanced by such authors as F. Kafka, L. Wittgenstein, R. Musil, I. Bachmann and above all Thomas Bernhard. According to Gargani's essay, starting from the rejection of the notion of a correspondence relation of language to (...) the world, T. Bernhard puts forward a sort of literature conceived no more as being a description of reality, but rather as being a critical analysis and a deconstruction of human existence. In substance, the core of Bernhard's literary work consists in revealing the truth content of the lie (der Wahrheitsgehalt der Lüge). If human existence on the whole is doomed to failure on the one hand, Bernhard acknowledges literature itself as the only possibility of safety for man on the other hand. On clarifying the peculiar structure of Bernhard's writing, Gargani shows how the indirect narration of events and thoughts carried out by Bernhard aims at an indirect truth, which is the only available one and which is preciselythe mediated truth of literature. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.1 (2000) 59-74 [Access article in PDF] Francesco Patrizi in the "Time-Sack": History and Rhetorical Philosophy * Paul Richard Blum Contemporary theory of history is much concerned with the narrative structure of history, its nature, and its epistemic status. 1 The problem is not only that sources present events mostly wrapped in narrative language but also that temporality is an inherent feature both (...) of the events told and of storytelling. 2 Narrativity and temporality touch upon basic metaphysical and anthropological questions, as Paul Ricoeur has pointed out, if narration is to be understood as self-explanation of a human being in whom "time" occurs as "being-in-time." 3 The following paper cannot claim to contribute to the current debate but presents Francesco Patrizi (1529-97) 4 as a Renaissance philosopher who addressed several of these problems. In discussing his conceptions of history and time, however, it is the aim of this paper only to locate these within his own philosophy. [End Page 59]One of the unresolved problems in the writings of Francesco Patrizi is the difference between his earlier contributions to the humanistic canon and his late philosophical main treatise, Nova de universis Philosophia. The earlier writings conform to the usual humanist literary topics: the political program of a città felice, the treatises on honor, the poetic fury, Petrarch (1553), and then his two dialogues on history (1560) and rhetoric (1562). The two works which followed, the Discussiones peripateticae (1571) and the Poetics (1586), show a characteristic development of humanist thinking, namely, the differentiation of purely philological from essentially philosophical literature.Patrizi's Discussiones peripateticae 5 is a polemic against Aristotle, written from a Platonic viewpoint, but his own philosophy is concealed under a mass of philological material. In an attempt that seeks to be virtually definitive, he cites passages from Aristotle and the Peripatetic tradition in order to point out mistakes and contradictions. It was on this account that Giordano Bruno heaped ridicule on him, calling him "sterco di pedanti." Simply put, he tells us, Patrizi demonstrates "how like he is to an ox or an ass." One cannot say that he has understood Aristotle either well or ill, but merely that he has read him and reread him, cut him up and stitched him together, compared him with a thousand other Greek writers, friends and foes alike, and altogether gone to an immense deal of trouble, not only to no purpose whatsoever but also to our infinite disappointment. Anyone who wishes to see into just what folly and self-regarding vanity pedantic drudgery can plunge and sink should read this book. 6This was one contemporary reaction to Patrizi's attempt to explore all the possibilities of a humanistic style of literary criticism, via the comparison between Plato and Aristotle. 7The Poetics 8 is essentially divided into two quite distinct halves: Della poetica la deca istoriale and Della poetica la deca disputata. The first is a lexicon of [End Page 60] the ancient authors, categories, styles, etc., and the second a series of dissertations on the theory of poetry but these, too, with abundant reference to both ancient and contemporary literature.Finally, and entirely different in style, there is his principal work, the Nova de universis Philosophia (1591). 9 Here the philosopher systematically departs from his accustomed field, ranging from a theory of light (Panaugia), via a discussion on theological principles (Panarchia) and a theory of the soul (Pampsychia) to the Pancosmia, a treatise on cosmology and physics. Even to this work he appends a number of documentary excerpts, and there is no lack of excursions into literary history, but the main part of the work is entirely axiomatic--"methodical"--in approach and argumentative in style.These works of Patrizi represent the development of philosophical humanism in the sixteenth century, a development away from a unified presentation of the problems of the human sciences by the explicit use of the tools of literary rhetoric, and towards the research of philological sources on the one hand and... (shrink)

In working his way through his complex conception of the relation of fiction and reality, [Henry] James thus found the unconscious moral dimension inextricably embedded within "realism" itself. In following the threads of realism back to consciousness itself, James invariably found there intertwined with its roots those aspects and elements that other theorists kept carefully separate. By exploring experience to its source, he found imagination. By following objective life from "out there" to conception, he found individual vision. By following the (...) seeming oneness of the passing show back to perception, he found infinite variation and multiplicity. By following the uncolored flux and flow of events to their embodiment in the fictional medium, he found coloration of personality. And by following the "felt life" back to the artist's "prime sensibility", James found there the "moral sense" and the "enveloping air of the artist's humanity"—that which gives "the last touch to the worth of a work." James E. Miller, Jr., professor of English at the University of Chicago, is the author of A Critical Guide to Leaves of Grass; Walt Whitman; F. Scott Fitzgerald: His Art and His Technique; J.D. Salinger; Theory of Fiction: Henry James; and numerous articles on American literature and education. He contributed "Catcher In and Out of History" to Critical Inquiry, Spring 1977. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 27.2 (2003) 304-317 [Access article in PDF] Sovereign Love and Atomism in Racine's Bérénice Ellen Mcclure ALTHOUGH CRITICS HAVE NOTED links between the new science of the seventeenth century and the works of La Fontaine and Molière, 1 a similar influence of Epicureanism or even Cartesianism upon French classical tragedy is harder to trace. No two areas of seventeenth-century cultural life would seem farther apart than (...) the emerging science, with its rejection of Aristotelian categories as inadequate to experienced reality, and classical French tragedy, with its antimaterialism and claims to universal truth often bolstered by references to none other than Aristotle himself. Yet René Pintard reminds us that the 1660s and 1670s—the period when many of the tragedies we regard as "classical" were written—saw a strong renewal of interest in the philosophies articulated in the first half of the century. 2 So widespread was this interest that Pierre Gassendi's friend and follower Bernier was able to publish an edition and translation of the philosopher's works in 1674-1675 which proved to be a resounding success. It is hard to believe that the much-discussed new science somehow missed writers of tragedies, especially given the extensive contacts between Molière, La Fontaine and Racine.In this article, I demonstrate this influence by positing that Racine's play Bérénice, ostensibly a reworking of a well-known love story that Corneille was also producing on the Paris stage at the same time, is in part a reflection on the pressing question of what holds the universe together. Through his exploration of the possibility of satisfactory love between two independent sovereigns, Racine explores issues that the revival of Epicureanism had brought into the philosophical foreground. This reading of the play brings into focus the incredibly [End Page 304] important, yet too-often neglected, 3 role of Antiochus, the character whom Racine invented for his version of the play. I will show that his tragic in-betweenness offers a necessary alternative to Titus' and Bérénice's valorization of self-contained sovereignty. I Before embarking on a close reading of the play itself, however, I would like to offer a brief survey of the debate to which I believe Racine refers. Both Michel Foucault and Timothy Reiss have identified the seventeenth century as a transitional period between the age of correspondences exemplified in Aristotelian philosophy and the age of representation and quantification that characterized eighteenth-century thought. 4 This transition, however, was far from smooth, as philosophers sought to articulate a universe whose separate and radically de-hierarchized elements remained somehow joined together.For most seventeenth-century philosophers, the sacrifice of Aristotelian categories and scholasticism in no way lessened the imperative for a sense of divine order and causation. Gassendi's often self-contradictory efforts to reconcile Epicurus and Christianity provide perhaps the most striking example of this transitional struggle. The atomism posited by Epicurus through Lucretius posed particular difficulties for a Christian worldview. A world governed by the chance interactions of atoms eliminates any sense that things happen for a purpose; God cannot be the benevolent author and overseer of the universe. Gassendi's equal respect for atomism and for Christianity should be read as evidence of the profound struggle between separateness and interconnection (or, as Gassendi would call it, harmony) taking place during this period. 5 For, as Bloch points out, although Gassendi partially reconciled the demands of the two systems by situating atoms in an uncreated, infinite, and contiguous space and time, he continued to hold to the profoundly troubling existence of the void in the universe. Once again, the chief objection to the void implicit in atomism was religious, since if God is everywhere, the void cannot exist, and likewise, God cannot create nothing. The revival of stoicism supplied instead a vision of the universe ultimately comprised and held together by an ethereal pneuma that some neo-Stoics did not hesitate to identify as a sort of divine presence. 6 Descartes himself made heroic attempts, in his Principes... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE ANALOGIES OF BEING IN ST. THOMAS AQUINAS RICHARD LEE New School for Social Research New York, New York IN HIS Commentary on the Sentences of Peter Lombard, Aquinas offers three modes of analogy.1 The three modes offered there are referred to, though not by the names given them, throughout his works. It remains a curious fact, however, that Aquinas varies his opinion as to whether analogy of attribution (...) or analogy of proportionality (sometimes referred to as analogy of proper proportionality as attribution is referred to in the literature as analogy of proportion) is the proper mode of analogical predication. In fact, as we shall see, Aquinas himself imports elements of the analogy of attribution into the analogy of proportionality. What needs to be investigated, then, is what characterizes these two modes of analogy; what makes them both analogy; why do they differ. Before understanding the specific nature of each form of analogy, however, one should understand why Aquinas appealed to analogy in the first place. Finally, one should attempt to grasp what the implications of each form of analogy are for Aquinas's metaphysical system and why he seems to favor the analogy of attribution over that of proportionality at crucial points in his thought. Why analogy? In general, one can say that Aquinas uses the concept of analogy (and that of proportionality) to solve two problems. On the one hand, the concept of analogy is used to argue that God does, 1 In I sent., 19. 5. 2, ad 1. 471 472 RICHARD LEE in fact, have knowledge of his creatures. The issue here is that the intellect knows in proportion to the thing known. However, God is infinite and if he knows anything finite he would know that thing in proportion to the created, finite thing. Since there is no proportion between finite and infinite, God cannot have any knowledge of his creatures.2 The element of knowledge, however, is not merely a preface to the discussion of the types of analogy. Aquinas argues that we can name a thing insofar as it is known.3 Since we have no concept of God (in his essence), we cannot name God, at least in the same way we name other things. On the other hand, Aquinas uses analogy to fill a metaphysical gap in his system. For he agrees with Pseudo-Dionysius and Maimonides that we cannot know God in his essence. Therefore, any names that we apply to God are not names which tell us anything about God. Aquinas is well aware that the God of revelation is not a God about whom one ought to speak. To say anything at all about God is already to say too much; it is already doomed to failure because of God one should not speak. However, this situation leaves Aquinas in a peculiar position. For he takes seriously the Aristotelian dictum that a thing is known only when its principles are known.4 If God is the principle, something must be known of him if anything is to be known at all. There must be some way to speak of God. Aquinas sees in analogy a middle ground between these two positions. For what he seeks is a mode of predication that lies between univocity and equivocity. In other words, he seeks a mode of predication that predicates the same thing in a different way of two (or more) things. In univocal predication the same term is applied according to the same ratio.5 Thus, the community 2 This is the issue, for example, in De Veritate, q. 8, a. 1, ad 6; De Veritate, q. 2, a.3, ad 4. 3 Cf. Summa Theologiae I, 13, 1, c. 4 For example, cf. Physics I, 1. 5 One is tempted to render ratio as " definition." However, it is not clear that definition is enough. Clearly, in univocal predication the definition must be the same (e.g., predicating animal of man and ox). But is it enough that only the definition is the same? Is there not some metaphysical element lack- THE ANALOGIF'.$ OF BEING 473 that applies to univocal predication is one of identity. The concept of animal... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:When an Arab Laughs in Toledo: Cervantes’s Interpellation of Early Modern Spanish OrientalismE. C. Graf (bio)My purpose has been to place in the plaza of our republic a game table which everyone can approach to entertain themselves without fear of being harmed by the rods; by which I mean without harm to spirit or body, because honest and agreeable exercises are always more likely to do good than harm.—Miguel (...) de Cervantes Saavedra, Prologue to Novelas ejemplares [my translation]We are engaged in a technical enterprise at the species scale.—Jacques Lacan, “L’agressivité en psychanalyse” [my translation]While I was all intent on watching him, he looked at me, and with his hands he spread his chest and said: “See how I split myself!”!—Dante Alighieri, Inferno 28.28–30 Click for larger view View full resolutionFigure 1.Sandro Botticelli, The Virgin and Child (c. 1490). Courtesy of the Fogg Art Museum, Harvard University; ©1999 President and Fellows of Harvard College. Click for larger view View full resolutionFigure 2.Salvador Dalí, Dream Caused by the Flight of a Bee around a Pomegranate One Second Before Awakening (1941). Courtesy of Museo Thyssen-Bornemisza, Madrid; ©1999 Artists' Rights Society (ARS), New York.For much of this century, Hispanists have labored in an effort to elevate Miguel de Cervantes Saavedra’s El ingenioso hidalgo don Quijote de la Mancha (1605, 1615) to the coveted status of the “first modern novel.” Today this kind of criticism may strike our postmodern sensibilities as a rather traditional enterprise, the kind more interested in establishing an elite hierarchy of literary tastes than in saying anything new about an author or text. For many, the study of literature is still an aesthetic beauty pageant in which “great books” like Laurence Sterne’s Tristram Shandy (1767) or Marie de la Vergne de La Fayette’s La princesse de Clèves (1678) are paraded across the stage in a contest to seduce the Western intelligentsia. 1 The postmodern student of literature may not have much concern for this age-old territorial contest, but she might be interested to learn that the fallout from Hispanism’s quest for the “first modern novel” has involved so much attention to, indeed complication of, Don Quixote, that the book now resembles more a postmodern text than an early modern one. At the turn of the century, we have been left with what Jorge Luis Borges would recognize as an “aleph”: an infinite ideological labyrinth that reflects and/or cannibalizes all forms, thereby escaping all attempts [End Page 68] to describe it. 2 Whatever we currently mean by “Cervantes” (an author, a collection of texts, an ideological construction, and so forth) carries with it an impressive range of critical responses. Cervantes has been labeled converso (Castro, Canavaggio), Christian humanist (Castro, Bataillon, Forcione, Herrero, Vilanova), disillusioned secularist (Lukács, Cascardi), precapitalist (Johnson), anti-essentialist (Wilson), anti-Eusebian (Presberg), Menippean (Bakhtin), feminist (El Saffar, Rabin, Cruz), sadist (Nabokov), ethnocentric imperialist (Mariscal), medieval (Gorfkle), homophobic (Martín), non-organicist Aristotelian (Read), and either discursively or actually homosexual (Combet, Rossi, Smith, Arrabal). This list is nowhere near complete, but the reader will grasp the robust effects of the plurality of perspectives on Cervantes.Each of these interpretations is valid to varying degrees within various contexts, but at present I am interested in reading Cervantes as the author of a multicultural manifesto on behalf of the Moriscos of Southern Spain. 3 Within the contexts of French Marxist philosopher Louis Althusser and Palestinian postcolonial literary critic Edward Said, materialist, postcolonial, and multicultural critiques of various forms of power and their ideologies can be seen as the fundamental propositions of Cervantes’s Don Quixote. 4 Cervantes’s ultimate orientation may perhaps be inescapably Eurocentric, but his responses to the European experience of the rise and expansion of an ethnocentric militaristic nation state are relatively centrifugal when compared to the attitudes of many of his contemporaries.In surveying some of the antihegemonic details of Cervantes’s novel, I am also interested in dispelling the popular myth of Don Quixote. Especially in the English-speaking world, and particularly in the United States, Don Quixote remains captive to a... (shrink)

Space and time are the most fundamental features of our experience of the world, and yet they are also the most perplexing. Does time really flow, or is that simply an illusion? Did time have a beginning? What does it mean to say that time has a direction? Does space have boundaries, or is it infinite? Is change really possible? Could space and time exist in the absence of any objects or events? What, in the end, are space and (...) time? Do they really exist, or are they simply the constructions of our minds? Robin Le Poidevin provides a clear, witty, and stimulating introduction to these deep questions and many other mind-boggling puzzles and paradoxes. He gives a vivid sense of the difficulties raised by our ordinary ideas about space and time, but he also gives us the basis to think about these problems independently, avoiding large amounts of jargon and technicality. His book is an invitation to think philosophically rather than a sustained argument for particular conclusions, but Le Poidevin does advance and defend a number of controversial views. He argues, for example, that time does not actually flow, that it is possible for space and time to be both finite and yet be without boundaries, and that causation is the key to an understanding of one of the deepest mysteries of time: its direction. Drawing on a variety of vivid examples from science, history, and literature, Travels in Four Dimensions brings to life some of the most profound questions imaginable. (shrink)