Critical discussion of J.M.E. Moravcsik's paper on Plato's method of division.

In the second half of Book One of the Prior Analytics, Aristotle reflects on the application of the formalized logic has developed in the first half, focusing particularly on the non-modal or assertoric syllogistic developed in the first seven chapters. These reflections lead Alexander of Aphrodisias, who was a great exponent of Aristotelianism in the late second century, to explain and sometimes argue against subsequent developments of Aristotle's logic and alternatives and objections to it, ideas associated mainly with his colleague (...) Theophrastus and with the Stoics. The other main topic of this part of the Prior Analytics is the specification of a method for discovering true premises needed to prove a given proposition. Aristotle's presentation is sometimes difficult to follow, and Alexander's discussion is extremely helpful to the uninitiated reader. In his commentary on the final chapter translated in this volume, Alexander provides an insightful account of Aristotle's criticism of Plato's method of division. (shrink)

As Aristotle himself says, A.Po. 2.13 is an attempt to provide some rules to hunt out the items predicated in what something is, namely to discover definitions. Since most of this chapter is devoted to the discussion of some rules of division , it may be inferred that somehow division plays a central role in the discovery of definitions. However, in the following pages I shall not discuss what this role is. Nor shall I discuss what place (...) class='Hi'>division has in the wider discussion of definition and explanation as it emerges from A.Po. 2. 1 shall rather focus on the argument that Aristotle reports and discusses in A.Po. 2.13.97a6–22, and which our extant sources ascribe to Speusippus. As will become clear later on, this argument undermines the possibility of giving any definition, and Aristotle deals with it here because he can block it by exploiting some properties of the method of division. (shrink)

As Aristotle himself says, A.Po. 2.13 is an attempt to provide some rules to hunt out the items predicated in what something is, namely to discover definitions. Since most of this chapter is devoted to the discussion of some rules of division, it may be inferred that somehow division plays a central role in the discovery of definitions. However, in the following pages I shall not discuss what this role is. Nor shall I discuss what place division (...) has in the wider discussion of definition and explanation as it emerges from A.Po. 2. 1 shall rather focus on the argument that Aristotle reports and discusses in A.Po. 2.13.97a6–22, and which our extant sources ascribe to Speusippus. As will become clear later on, this argument undermines the possibility of giving any definition, and Aristotle deals with it here because he can block it by exploiting some properties of the method of division. (shrink)

In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis, parallel division, and chiasmus. I attempt to explain the relationship among the three kinds of division, namely, how they transform from one to another. Starting with Plato’s division of constitution in the Statesman, I illuminate that from ostensible diairesis emerges a parallel division, and the parallel division causes a cross-division (...) to occur. Thus, the sixfold division of constitution is not a diairesis but rather is a 3 x 2 cross-division. Inheriting the three kinds of division from Plato, Aristotle advances the form by providing a theoretical explanation to the transformation of the three kinds of division. In Topics Z6, Aristotle prescribes two conditions under which a parallel division can originate from or construct ostensible diairesis and how the parallel division further causes a cross-division to occur. (shrink)

Aristotle’s influence on D’Arcy Thompson was praised by Thompson himself and has been recognized by others in various respects, including the aesthetic and normative dimensions of biology, and the multicausal explanation of living forms. This article focuses on the relatedness of organic forms, one of the core problems addressed by both Aristotle’s History of Animals (HA), and the renowned chapter of Thompson’s On Growth and Form (G&F), “On the Theory of Transformations, or the Comparison of Related Forms.” We contend that, (...) far from being an incidental inspiration stemming from Thompson’s classicist background, his translation of HA played a pivotal role in developing his theory of transformations. Furthermore, we argue that Thompson’s interpretation of the Aristotelian method of comparison challenges the prevailing view of Aristotle as the founder of “typological essentialism,” and is a key episode in the revision of this narrative. Thompson understood that the method Aristotle used in HA to compare animal forms is better comprehended as a “method of transformations,” leading to a morphological arrangement of animal diversity, as opposed to a taxonomical classification. Finally, we examine how this approach to the relatedness of forms lay the foundation for a causal understanding of parts and their interconnections. Although Aristotle and Thompson emphasized distinct types of causes, we contend that they both differ in a fundamental sense from the one introduced by Darwin’s theory of natural selection, which was formulated as a solution to the species problem rather than the form problem. We conclude that Thompson’s interpretation of Aristotle’s approach to form comparison has not only impacted contemporary scholarship on Aristotle’s biology, but revitalized a perspective that has regained significance due to the resurgence of the problem of form in evo-devo. (shrink)

The strange and challenging stretch of dialectic with which Plato’s Sophist begins and ends has confused and frustrated readers for generations, and despite receiving a fair amount of attention, there is no consensus regarding even basic issues concerning this method. Here I offer a new account of bifurcatory division as neither joke nor naïve method, but instead a valuable, propaedeutic method that Plato offers to us readers as a means of embarking upon the kind of mental (...) gymnastics that will stretch us properly in preparation for further, more challenging dialectical work. Considering several interpretive issues, I argue that bifurcatory division is a process of collective inquiry into the common through which an account, both definitional and taxonomical, is discovered. Depending on the level of understanding exhibited by the inquirers, this account may or may not allow for noetic understanding of the object in the deepest sense. (shrink)

When dealing with the metaphysical and epistemological implications of the Phaedrus, scholars have had the tendency to focus either on recollection or on discerning the methodological articulations of dialectical rhetoric. The present paper explores the relation between recollection and the dialectical method, and argues that recollection and the method of collection and division are complementary aspects of dialectical investigation, the method providing a strategy of reasoning, while the theory of recollection provides the metaphysical horizon within which (...) collection and division can lead to successful results. (shrink)

When dealing with the metaphysical and epistemological implications of the Phaedrus, scholars have had the tendency to focus either on recollection or on discerning the methodological articulations of dialectical rhetoric. The present paper explores the relation between recollection and the dialectical method, and argues that recollection and the method of collection and division are complementary aspects of dialectical investigation, the method providing a strategy of reasoning, while the theory of recollection provides the metaphysical horizon within which (...) collection and division can lead to successful results. (shrink)

All scientific knowledge is in some way unified; the scheme of the speculative sciences is not just a method of arrangement that is casual and artificial. There is a true hierarchy of the sciences. In popular thought to-day the empirical sciences have gained the ascendancy; there are those who are confident that science will not only unlock the mysteries of nature but will solve eventually all our problems. There is no mistake about its success, for its practical benefit to (...) mankind is immense. The modern mind is so impressed by utility that it refuses to be concerned with anything else. (shrink)

This dissertation concerns the methodology Kant employs in the first two sections of the Groundwork of the Metaphysics of Morals (Groundwork I-II) with particular attention to how the execution of the method of analysis in these sections contributes to the establishment of moral metaphysics as a science. My thesis is that Kant had a detailed strategy for the Groundwork, that this strategy and Kant’s reasons for adopting it can be ascertained from the Critique of Pure Reason (first Critique) and (...) his lectures on logic, and that understanding this strategy gains us interpretive insight into Kant’s moral metaphysics. At the most general level of methodology, Kant says there are four steps for the establishment of any science: 1) make distinct the idea of the natural unity of its material 2) determine the special content of the science 3) articulate the systematic unity of the science 4) critique the science to determine its boundaries The first two of these steps are accomplished by the genetically scholastic method of analysis, paradigmatically the method whereby confused and obscure ideas are made clear and distinct, thereby logically perfecting them and transforming them into possible grounds of cognitive insight that are potentially complete and adequate to philosophical purposes. The analysis of Groundwork I is a paradigmatic analysis that makes distinct what is contained in common understanding, i.e. its Inhalt or intension, making distinct the higher partial concepts that together define the concept of morality. The analysis of Groundwork II is an employment more specifically of the method of logical division, which makes distinct what is contained under the concept, i.e. its Umfang, by which the extension or object of morality is determined. Part I introduces Kant’s conception of moral metaphysical science and why he took it to be in need of establishment, explains the general method for establishing science and the scholastic method of analysis by which its first two steps are to be accomplished, then provides an interpretation of Groundwork I as an execution of this method. Part II details Kant’s determination of the special content of moral science in Groundwork II in relation to the central problem for moral metaphysics – how synthetic a priori practical cognition is possible. (shrink)

Free Trade Reimagined begins with a sustained criticism of the heart of the emerging world economy, the theory and practice of free trade. Roberto Mangabeira Unger does not, however, defend protectionism against free trade. Instead, he attacks and revises the terms on which the traditional debate between free traders and protectionists has been joined. Unger's intervention in this major contemporary debate serves as a point of departure for a proposal to rethink the basic ideas with which we explain economic activity. (...) He suggests, by example as well as by theory, a way of understanding contemporary economies that is both more realistic and more revealing of hidden possibilities for transformation than are the established forms of economics. One message of the book is that we need not choose between accepting and rejecting globalization; we can have a different globalization. Traditional free trade doctrine rests on shaky empirical and theoretical ground. Unger takes a new approach to show when international trade is likely to be useful or harmful to the socially inclusive economic growth that every nation wants. Another message is that the movement of people and ideas is more important than the movement of things and money, and that freedom to change the institutions defining a market economy is just as important as freedom to exchange goods on the basis of those institutions. Free Trade Reimagined ranges broadly within and outside economics. Presenting technical issues in plain language, it appeals to the general reader. It puts a disciplined imagination in the service of rebellion against the dictatorship of no alternatives that characterizes life and thought today. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kant on the Method of MathematicsEmily Carson1. INTRODUCTIONThis paper will touch on three very general but closely related questions about Kant’s philosophy. First, on the role of mathematics as a paradigm of knowledge in the development of Kant’s Critical philosophy; second, on the nature of Kant’s opposition to his Leibnizean predecessors and its role in the development of the Critical philosophy; and finally, on the specific role of (...) intuition in Kant’s philosophy of mathematics. One of the points that I want to make is that recognizing the importance of these first two issues is essential to giving an adequate account of the third. That is, only by appreciating how Kant uses the example of mathematical knowledge, and in particular the objections he had to previous accounts of such knowledge, can we understand the philosophical role that he ascribes to intuition in his own account of mathematics.I don’t propose to explain the details of Kant’s philosophy of mathematics, but rather to compare his views on mathematics in the pre-Critical Prize Essay of 1764 to those of the Critique of Pure Reason, with the aim of showing how Kant’s doctrine of construction in pure intuition arises out of a combination of two factors: first, his attempt to ground the distinction between the respective methods of mathematics and philosophy, and second, his concern to defend the reality of mathematical knowledge against the views of those he called ‘the metaphysicians.’ The first factor demands an account of the certainty of mathematics, the second requires an account of its content. I shall argue that there is a possible conflict between Kant’s accounts of these features in the Prize Essay, a possibility which is finally ruled out only by means of the Critical doctrine of pure intuition. So I hope to show that there is a significant philosophical role for intuition in Kant’s account of mathematical knowledge (over and above the more logical role attributed to it on readings [End Page 629] such as those of Friedman, Beth, and Hintikka1) in reconciling the content of mathematics and its certainty.2. THE MATHEMATICIANS VS. THE METAPHYSICIANSThroughout his early writings, Kant appealed to the evidence and certainty of mathematics; his attitude towards metaphysics, however, underwent a dramatic shift. In the Physical Monadology of 1756, Kant asked how metaphysics and geometry can be united,[f] or the former peremptorily denies that space is infinitely divisible, while the latter, with its usual certainty, asserts that it is infinitely divisible. Geometry contends that empty space is necessary for free motion, while metaphysics hisses the idea off the stage. Geometry holds universal attraction or gravitation to be hardly explicable by mechanical causes but shows that it derives from the forces which are inherent in bodies at rest and which act at a distance, whereas metaphysics dismisses the notion as an empty delusion of the imagination [1:475–6].2He attempted in this work to reconcile the respective positions of metaphysics and geometry regarding infinite divisibility, thereby demonstrating that “it is neither the case that the geometer is mistaken nor that the opinion to be found among metaphysicians deviates from the truth” [1:480]. But in a series of works from 1762–3, Kant reveals a markedly different attitude towards metaphysics. For example, in “The only possible argument in support of a demonstration of the existence of God,” Kant says:the mania for method and the imitation of the mathematician, who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps on the slippery ground of metaphysics. These mishaps are constantly before one’s eyes, but there is little hope that people will be warned by them, or that they will learn to be more circumspect as a result [2:71].In contrast, Kant describes the geometer as uncovering “with the greatest certainty” the most secret properties of that which is extended [2:70]. But the less conciliatory attitude to metaphysics comes out most clearly in Kant’s actual procedure in “The only possible argument.” In the Seventh Reflection, he presents an attempt to explain the origin of... (shrink)

This book is a good idea, well-executed. The setup of the book mirrors one way of dividing up normative ethics. We divide theorists into Kantians, consequentialists and virtue theorists on the assumption that these are distinct and incompatible approaches to ethics. Each position is represented by one of the co-authors with Baron representing Kantians, Pettit consequentialists and Slote virtue theorists. What emerges is that each approach has virtues, but also that the division is neither neat nor exhaustive. As Pettit (...) notes, the issue that divides consequentialists from non-consequentialists is whether it is always right to promote agent-neutral value. While Kantians answer no where the consequentialists answer yes, a consequentialist can agree with Kantians about many other issues. And while Kantians are often portrayed as being exclusively interested in the rightness of actions, their actual emphasis on motivation and reasons for action make it difficult to distinguish their views from virtue theories that focus on the way an agent’s character and practical wisdom is reflected in her choices. The complexity of the positions defended by the authors highlight these difficulties for the standard division of the terrain. (shrink)

The debate on the possibility of attaining metaphysical knowledge by the method of reasoning began with the ancient Greek philosophers and continues to this day. This article aims to examine how Râzî argues for the possibility of attaining metaphysical knowledge through the method of reasoning. He first argues that existence has two parts, the sensed and the thought, in order to demonstrate that metaphysical knowledge can be obtained through the method of reasoning. Then he tries to prove (...) that existence is not limited to the material. After presenting evidence for the existence of things other than the sensible in existence that can be perceived with the intellect, he tries to discuss our devices to relate to this sphere of existence in a comparative manner. In this comparison, two possible devices for attaining metaphysical knowledge emerge: the theoretical intellect and the purified soul. After revealing the positive and negative aspects of both in this comparison, he argues that the most reliable device is the theoretical intellect and the technique is the method of reasoning Râzî gives various answers to those who object to the possibility of obtaining metaphysical knowledge through the method of reasoning. Râzî tries to put forward the grounds on which the groups who object to the method of reasoning are based. He then evaluates their justifications in terms of accuracy and consistency. Thus, he tests both the relevance of each group's objection to the subject and its consistency with the group's other beliefs. He then presents the justifications for his own opinion on the method of reasoning and the consistency of this method with his other beliefs. Following this method, Râzî first divides those who object to the method of reasoning into two categories according to whether or not they accept a metaphysical sphere of existence. According to this division, those who object to the method because they do not accept a metaphysical sphere of existence are the Sophists, Sumeniyya, Mujasimah, Dhahriyya, and Hashawiyya. Although this group does not accept a metaphysical sphere of existence, they are divided into two classes: those who believe in God and those who do not. According to Râzî, the group that accepts the metaphysical sphere of existence but objects to the method of reasoning is the Talimiyya. They claim that metaphysical knowledge can only be attained through the teaching of an innocent instructor, not by the method of reasoning. The different approaches of these groups are the reason why Râzî sometimes emphasizes accuracy, sometimes consistency, and sometimes proving the metaphysical domain of existence in his answers to those who object to the method of reasoning. (shrink)

플라톤 대화편에서는 엘렌코스, 가정의 방법, 그리고 나눔과 모음의 방법 등 다양한 철학적 탐구 방법이 사용된다. 기존 연구는 각각의 방법들이 서로가 서로를 대치한다고 보는 해석과, 각 방법들은 서로 긴밀하게 연결되어 발전한다는 해석으로 나뉜다. 이 논문에서는 플라톤의 철학적 탐구 방법이 하나로 통일되어 사용되면서 대상에 대한 위계적인 지식 뿐 아니라 네트워크적인 지식까지도 얻을 수 있게 하는 탐구 방법이라는 사실을 보인다. 이를 위해 『필레보스』 후반에서 지식의 종류를 나누는 과정을 분석하여 지식의 종류를 구분하여, 산술과 같이 다양한 영역에 걸쳐있는 지식의 성격을 드러낼 수 있는 나눔과 모음의 (...) 방법의 특징을 검토한다. 결론적으로 대상에 대한 지식을 갖지 않은 대화자들 사이에서도 지식을 획득할 수 있게 해주는 이상적인 탐구 방법으로서의 나눔과 모음의 방법이????필레보스????에서 사용되었다고 주장한다. (shrink)

Excerpt from The Fields and Methods of Sociology His volume is intended to serve as a textbook for advanced T courses in sociology in which the purpose is to survey the various divisions of sociology as this science has developed in the United States in particular, and in all other countries where the subject is taught or studied. It emphasizes especially the sources of materials for investigation, the methods of research, and the processes of generalization in the various fields of (...) sociological science. Present day sociologists are more interested in research than in classification. It is recognized, however, that intelligent research cannot be undertaken to the best advantage without an adequate understanding of the various divisions into which the general science of sociology falls. Consequently, the first part of the volume is devoted to an analysis of the fields and problems of sociology and the second part to sources and methods. While the volume is organized in textbook form, it is expected that it will appeal very largely to the general reader who is searching for a well organized and clear presentation of the subject of sociology in all its aspects. It is believed that the present volume offers the most complete and thoroughgoing analysis and synthesis of sociological content and methodology now available. I wish to emphasize especially the inductive approach of the present treatise. Every chapter is the result of a careful study of the data it treats. Speculative and a priori approaches have been avoided. Consequently each field of sociology has been analyzed realistically as to subject matter, sources and methods and the results are set forth as clearly and as simply and directly as pos sible. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In an effort to ease the task of developing new ideas, whether in research, development or some other endeavor, it is generally accepted to resort to a method of problem solving. Although the use of such a method may, in many cases, be done without the realization of the individual, it does not detract from the fact that such methods play a part in our mental processes and research techniques. It is the purpose of this paper to discuss (...) the methods and to arbitrarily classify them so that they can be consciously applied. Inasmuch as all methods must to some extent ultimately define the problem, the division presented here is obviously arbitrary, based on the degree of specificity with which the problem must be defined. (shrink)

There are many passages in Plato which look as if they alluded to well-worn practices, discussions, or lessons in the Academy. As is natural with allusions, they are often marked by a puzzling brevity or oddity of expression. One need not assume that they are always conscious allusions; for every writer has moments of obscurity which are due not so much to his conclusions as to his reaching them along lines that have long been familiar to Mm. To appreciate his (...) whole meaning the reader has then to infer as best he can the writer's train of thought. I wish to suggest that the language in which Dialectic is described in the later Dialogues presupposes a particular and probably familiar method of illustrating it. This was a geometrical illustration of the rules of Division by means of a divided line. By failing to notice it readers have not been led into any important misunderstanding of the Academy's rules. But I hope it will appear that the recognition of it makes Plato's manner of describing Division intelligible to an extent that is otherwise difficult. It is only a tentative suggestion, and would perhaps not have been worth making but for the possibility that some points of interest might at the same time emerge for those who were unconvinced by it. (shrink)

There are many passages in Plato which look as if they alluded to well-worn practices, discussions, or lessons in the Academy. As is natural with allusions, they are often marked by a puzzling brevity or oddity of expression. One need not assume that they are always conscious allusions; for every writer has moments of obscurity which are due not so much to his conclusions as to his reaching them along lines that have long been familiar to Mm. To appreciate his (...) whole meaning the reader has then to infer as best he can the writer's train of thought. I wish to suggest that the language in which Dialectic is described in the later Dialogues presupposes a particular and probably familiar method of illustrating it. This was a geometrical illustration of the rules of Division by means of a divided line. By failing to notice it readers have not been led into any important misunderstanding of the Academy's rules. But I hope it will appear that the recognition of it makes Plato's manner of describing Division intelligible to an extent that is otherwise difficult. It is only a tentative suggestion, and would perhaps not have been worth making but for the possibility that some points of interest might at the same time emerge for those who were unconvinced by it. (shrink)

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means of (...) subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

The purpose of the study is to present the author's method of digitalization of transactions of solved business tasks to reduce transaction costs of a manufacturing enterprise. The scientific novelty of the research lies in the fact that the elements of digitalization are proposed in the work to reduce the transaction costs of searching for information, negotiating, measuring, and concluding a contract. The introduction of digital technologies into specific business tasks contributes to the optimization of transaction costs in the (...) modern institutional environment. As a result, the information relationship of the structural divisions of the production company was established during the performance of their functions at all stages of the production cycle from procurement to sales, the functional filling subsystems of the organizational structure were determined. Transaction costs, in accordance with their classification, are structured according to these subsystems, they represent the elements of digitalization recommended for use in the business processes of a manufacturing company to reduce its transaction costs. The introduction of digitalization processes of business tasks into the management structure helps to increase the level of validity and speed of decisions in the subsystems of the organizational structure of the company. (shrink)

In order to realize the sustainable development of urban overall space, aiming at the increasingly serious environmental problems in the process of contemporary rapid urbanization, based on the relationship between urban and rural space and environmental capacity, a suitability evaluation method of urban and rural spatial planning based on artificial intelligence is proposed. This paper constructs the theoretical system of sustainable development evaluation of urban and rural spatial resources and uses artificial intelligence technology to reasonably select evaluation factors and (...) standardize the evaluation indicators so as to achieve the research goal of accurately evaluating the suitability of urban and rural spatial planning. It analyzes the influencing factors of urban–rural spatial standard regional division, develops the design of the spatial planning suitability analysis system, and establishes the urban-rural spatial suitability evaluation. The scope of sustainability evaluation was extended to the level of urban and rural spatial planning and design, and the preliminary work was done to solve the problems of urban spatial structure and decision-making. The experimental results show that the planning method has high environmental adaptability and rationality. (shrink)

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of (...) class='Hi'>division as it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic. (shrink)

Despite Aristotle’s claim in Topics I that all dialectical argument is either syllogism or epagōgē, modern scholars have largely neglected to assess the role of epagōgē in Platonic dialectic. Though epagōgē has no technical use in Plato, I argue that the method of collection (which, along with division (diairēsis), is central to many of the dialogues’ accounts of dialectic) functions as the Platonic predecessor to Aristotelian epagōgē. An analysis of passages from the Sophist and Statesman suggests that collection (...) is a purificatory practice. I argue that collection is not only Plato’s account of generalization from a sensible many to an intelligible many, as suggested by the Phaedrus, but also functions as a method of diacritical selection that allows inquiry to move from the intelligible many produced by division to the intelligible unity of a definition. This reading contributes a deeper understanding of the mutual relationship of division and collection within Platonic dialectic as well as a way of unifying the accounts of dialectic in the Sophist and Statesman with the otherwise idiosyncratic account of dialectic in the Republic. Finally, this analysis of Platonic epagōgē sheds light on the connection between inquiry and argument present in Aristotle’s use of epagōgē. (shrink)

Albert the Great was one of the earliest Western scholars to apply the methodology of Aristotle's Posterior Analytics to diverse fields of natural philosophy. Some medievalists, however, question Albert's commitment to Aristotelianism, interpreting his paraphrastic commentaries as an exposition of views he did not hold himself. Further, some modern Aristotle scholars argue that the methodology of the Posterior Analytics has little to do with Aristotle's actual practice in his scientific treatises. Albert, however, argued that this methodology is essential for achieving (...) a true scientia of nature and that Aristotle employed this methodology in his zoological books. In his commentary on the first book of the Parts of Animals , Albert shows how the method of demonstration applies to the study of animals. He elaborates an account of demonstration ex suppositione finis as the sort of reasoning proper to a science of contingent things. He also argues that scientific explanation must be a two-part procedure. Preceding the final step of causal demonstration the data to be explained must be organized in such a way that the causally significant connections between them are discovered. This is achieved through a restricted application of Platonic division. Albert makes a careful study of the conditions for non-accidental division and shows how they result in quia demonstrations which in turn yield propter quid demonstrations of the cause. ;This two-step methodology is evident, Albert argues, in the arrangement of Aristotle's zoological treatises. The books of the Historia animalium are placed first because they contain the preliminary organization of animal differentiae through division. These are followed by books on the parts, generation and motion of animals which make use of the material so organized to demonstrate their causes. Thus, Albert agrees with recent scholars who argue that the Historia animalium is not a treatise on systematics, but a pre-causal study of animal morphology. ;Albert's careful interpretation of Aristotle's zoology in light of the methodological requirements of the Posterior Analytics taken together with his own research on animal differentiae demonstrates his commitment to Aristotelian principles of natural philosophy. (shrink)

Contested Pile methods are two-phase procedures for the fair allocation of indivisible items to two players. In the Generation Phase, items over which the players’ preferences differ widely enough are allocated. “Contested” items are placed in the Contested Pile, which is then allocated in the Splitting Phase. Each phase can be carried out using several different techniques; we perform a comprehensive analysis of the resulting design variants using a computational model. The properties of fairness and efficiency, generally achieved in the (...) Generation Phase, must be traded off against robustness to manipulation. We find that the recently developed Undercut procedure for the Splitting Phase outperforms alternative methods in both fairness and efficiency. In general, procedures that keep the Contested Pile relatively small and incorporate the Undercut procedure score well in both fairness and efficiency, but are prone to manipulation. (shrink)

Despite Aristotle’s claim in Topics I that all dialectical argument is either syllogism or epagoge, modern scholars have largely neglected to assess the role of epagoge in Platonic dialectic. Though epagoge has no technical use in Plato, I argue that the method of collection functions as the Platonic predecessor to Aristotelian epagoge. An analysis of passages from the Sophist and Statesman suggests that collection is a purificatory practice. I argue that collection is not only Plato’s account of generalization from (...) a sensible many to an intelligible many, as suggested by the Phaedrus, but also functions as a method of diacritical selection that allows inquiry to move from the intelligible many produced by division to the intelligible unity of a definition. This reading contributes a deeper understanding of the mutual relationship of division and collection within Platonic dialectic as well as a way of unifying the accounts of dialectic in the Sophist and Statesman with the otherwise idiosyncratic account of dialectic in the Republic. Finally, this analysis of Platonic epagoge sheds light on the connection between inquiry and argument present in Aristotle’s use of epagoge. (shrink)