Templates travel because they offer a tractable format that can be used for model-building in a variety of domains. It is often because of this quality that a particular template is chosen. But one cannot assume that there are always templates ready to model a new phenomenon, and moreover, templates have also been designed at some point. A critical aspect of this designing process is the choice of the mathematical objects with which one hopes to capture (...) this phenomenon. This means that one has to assess which of the properties of different kinds of mathematical objects and which combinations of them are most appropriate. The selection of these objects is based on whether their properties enable the model to perform its function. This selection of mathematical objects is similar to the selection of materials in mechanical design. (shrink)

Templates travel because they offer a tractable format that can be used for model-building in a variety of domains. It is often because of this quality that a particular template is chosen. But one cannot assume that there are always templates ready to model a new phenomenon, and moreover, templates have also been designed at some point. A critical aspect of this designing process is the choice of the mathematical objects with which one hopes to capture (...) this phenomenon. This means that one has to assess which of the properties of different kinds of mathematical objects and which combinations of them are most appropriate. The selection of these objects is based on whether their properties enable the model to perform its function. This selection of mathematical objects is similar to the selection of materials in mechanical design. (shrink)

The Build-Operate-Transfer (BOT) model is a financing model used especially in the financing of infrastructure projects in developing countries. It is one of the most common methods used by the countries to provide non-budgetary financing. The fact that becoming popular in the world as of the 20th Century, this model started to be implemented in the Islamic countries created the need for examining the model in terms of Islamic law. No substantive studies have been conducted on (...) this matter in Turkey. In the Arab world, the first significant development in this regard was the 23rd Term meeting of Al Baraka Group organized in Mecca in November 2002. Next, the Islamic Fiqh Community, which operates under the Organization of Islamic Cooperation, organized a meeting about the BOT model in 2009. At this meeting, ten experts from different countries presented papers on the BOT model, and a final declaration was announced at the end of the meeting. After this meeting, some independent studies were carried out on the BOT model. However, it was observed that these efforts did not reach a sufficient level, and generally remained within the framework of the papers presented at the meeting. The BOT model is a model that takes place in the form of the transfer of the facility to the relevant public institution or organization free of charge at the end of the period after the depreciation and profit of the invested capital are realized. All expenses are covered by the private enterprise. The public service or activity is operated for a certain period of time by the private enterprise. It was observed that the studies on the BOT model in Turkey mainly dated back to the last quarter of the Twentieth Century. In this context, the Law No. 3996 about the BOT model was enacted on 08 June 1994 in Turkey. Today, the BOT model is actively used in many areas, and the delivery of the service begins after the projects are completed. The BOT model has three main successive stages. In the first stage, the project is completed with the financing of OGS. In the second stage, the operating right of this project would be awarded to the investor in accordance with the contract. In the third stage, the ownership of the facility would be transferred to the relevant public institution. The BOT model was discussed in terms of Islamic law, firstly in general and then in terms of the interests and convictions. The BOT model contains many interests in terms of both the state and the society. In addition, it has certain disadvantages. There are many reasons and aims in selecting the BOT model. The most important of these reasons is the continuation of the projects and the required work without imposing a burden on the public budget. Islamic law has a structure that prioritizes public interest. In this context, the state must observe the public interest in its operations. In the BOT model, the existence of public interest is particularly notable with the projects implemented in the fields of hospitals, roads, bridges, airports and etc. Islamic jurists have different opinions regarding the contracts administered in the BOT model. Some of them consider this model as a new contract that does not exist in the tradition, while others compare it to a traditional contract. The analogies of the traditional contract have been compared to leasing, payment, foundation, fief, corporate (with partnership) and exception contracts. Others, on the other hand, considered the BOT model as an atramentous contract combining several different contracts. It seems difficult to argue that the BOT model is completely similar to any of the classical fiqh contracts. However, as a result of the BOT model, it is considered an agreement with a company to conclude a contract; therefore there is a more prominent similarity to an exception contract. Nonetheless, it is not possible to say that the BOT model fully complies with the traditional exception contract. As a matter of fact, while there is no time determination in the exception contract, the time is determined in the BOT model. In the exception contract, while the material must be completely covered by the private sector, in the BOT model, issues such as the right to land and building construction are covered by the employer. In addition, the classical exception contract does not contain many contracts as in the BOT model; and it is an agreement in which the fee is presented and terminated after the order is placed. Nonetheless, the BOT contract includes three basic contracts (construction-operation-transfer) as well as many contracts related to these contracts. Finally, considering that the BOT model was a contract, the issues in the context of the basic elements that should be included in a contract were discussed in this study. In addition, situations such as ignorance, gharar and interest in terms of affecting the validity of the contract were discussed and dealt with in terms of the BOT contract. (shrink)

Business cycle theory is a broad and disparate field. Different schools of thought offer alternative explanations for cycles, often using different mathematical methods. This book provides academics and graduate students of economics with a compact and accessible exposition of business cycle theory since Keynes. The author places the main theories -- Keynesian economics, monetarism, new classical economics, the real business cycles theory, and new Keynesian economics -- in an historical context by presenting them in (...) the chronological order of their appearance and highlighting their differences and commonalities. He minimizes the necessary mathematical prerequisites by using a unifying mathematical approach: stochastic second-order difference equations, which is explained in detail. Throughout the book, the international dimension of business cycles is acknowledged. The theoretical results obtained are set alongside empirical facts in separate boxes. Each chapter finishes with a set of problems designed to deepen the reader's understanding of the theories presented, and further reading sections which provide access to related material. (shrink)

Before being considered as independent fields, business cycles and productivity growth had long been regarded as closely interrelated dynamics. Growth and cycles theories and models developed independently. On one side, the growth analysis developed analyzing the existence and stability of a long-run deterministic growth path. On the other side, business cycles theory focused on the understanding of detrended data movements considering growth as an exogenous trend, independent of the cycle. This dichotomy is still present in the modern (...) literature. _Business Cycles and Growth Theory_ examines the role of monetary and financial factors in growth cycles dynamics interaction. It offers new perspectives for modelling growth cycles dynamics underlining the possibility of building an 'incomplete business cycles theory', as well as highlighting the existence of a convergence between the last theoretical developments of both growth and business cycles literatures. A significant read, this book demonstrates that such a convergence can provide benchmarks for a new paradigm of models in which endogenous growth mechanism, because it offers a strong propagation for shocks, can be the core of a new business cycles dynamics. (shrink)

The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which (...) can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear. (shrink)

The assessment of models in an experiment depends on their material nature and their function in the experiment. Models that are used to make the phenomenon under investigation visible - sensors - are assessed by calibration. However, calibration strategies assume material intervention. The experiment discssed in this paper is an experiment in economics to measure the influence of technology shocks on business cycles. It uses immaterial, mathematical instruments. It appears that calibration did not work for these kinds of (...) models, it did not provide reliable evidence for the facts of the business cycle. (shrink)

This unique compendium presents a comprehensive and self-contained theory of material development under imperfect information and its applications. The book describes new approaches to synthesis and selection of materials with desirable characteristics. Such approaches provide the ability of systematic and computationally effective analysis in order to predict composition, structure and related properties of new materials. The volume will be a useful advanced textbook for graduate students. It is also suitable for academicians and practitioners who wish to have fundamental (...) models in new material synthesis and selection. (shrink)

The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors (...) argue that the most important cause of cyclical crises stems from strong structural disproportions that develop during economic booms. These are not only disproportions between different economic sectors, but also disproportions between different societal subsystems; at present these are also disproportions within the World System as a whole. The proposed model of business cycle is based on its subdivision into four phases: – recovery phase (which could be subdivided into the start sub-phase and the acceleration sub-phase); – upswing/prosperity/expansion phase (which could be subdivided into the growth sub-phase and the boom/overheating sub-phase); – recession phase (within which one may single out the crash/bust/acute crisis subphase and the downswing sub-phase); – depression/stagnation phase (which we could subdivide into the stabilization subphase and the breakthrough sub-phase). The article provides a detailed qualitative description of macroeconomic dynamics at all the phases; it specifies driving forces of cyclical dynamics and the causes of transition from one phase to another (including psychological causes); a special attention is paid to the turning point from the peak of overheating to the acute crisis, as well as to the turning point from the downswing to recovery. The proposed mathematical model of Juglar cycle takes into account the following effects that are typical for the market economy: • positive feedbacks between various economic processes; • presence of a certain inertia, time lags in reactions of the economic subsystem to the change in conditions; • amplification by the financial subsystem of positive feedbacks and time lags in the economic subsystem; • excessive reaction to changing conditions during the acute crisis sub-phase. The authors suggest that the current crisis turns out to be rather similar to classical Juglar crises; however, there is also a significant difference, as the current crisis occurs at a truly global scale. Yet, due to this truly global scale of the current crisis, the possibilities of regulation with the national state's measures have turned out to be ineffective,whereas the suprastate regulation of financial processes hardly exists. It is shown that all these have led to the reproduction of the current crisis according to a classical Juglar scenario. (shrink)

Modelling became one of the primary tools of mathematical economic research in the twentieth century, but when we look at examples of how nonanalogical models were first built in economics, both the process of making representations and aspects of the representing relation remain opaque. Like early astronomers, economists have to imagine how the hidden parts of their world are arranged and to make images, that is, create models, to represent how they work. The case of the Edgeworth Box, a (...) model widely used for theoretical work in twentieth-century economics, provides a good example to explore the process of making mathematical representations of the economy. It shows how, in making these new representations, conceptual elements were developed which could not have been represented in the older verbal forms of economics. (shrink)

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely (...) homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

In several accounts of what models are and how they function a specific view dominates. This view contains the following characteristics. First, there is a clear-cut distinction between theories, models and data and secondly, empirical assessment takes place after the model is built. This view in which discovery and justification are disconnected is not in accordance with several practices of mathematical business-cycle model building. What these practices show is that models have to meet implicit criteria (...) of adequacy, such as satisfying theoretical, mathematical and statistical requirements, and be useful for policy. In order to be adequate, models have to integrate enough items to satisfy such criteria. These items include besides theoretical notions, policy views, mathematisations of the cycle and metaphors also empirical data and facts. So, the main thesis of this chapter is that the context of discovery is the successful integration of those items that satisfy the criteria of adequacy. Because certain items are empirical data and facts, justification can be built-in. (shrink)

This article solves the problem of ensuring database decision-making in conditions of growing uncertainty and risks based on the results of business diagnostics is solved in this article. The main purpose of the research is to further develop the methodology of forming an analytical database for making management decisions. The following methods formed the methodological basis of the research: abstract-logical – used to generalize theoretical approaches and confirm the practical significance of solving the problem of decision-making in conditions of (...) uncertainty and risk; system analysis – when building a model of decision-making while coordinating areas and methods of business diagnostics; generalization – when drawing conclusions based on research results. The results of solving the problem of decision-making by improving the methodological approach in selecting areas and methods of business diagnostics in the conditions of growing uncertainty and risks are given in the article. The results of the research have practical value for companies that seek to reduce uncertainty and risk in the decision-making process in business management. (shrink)

One striking feature of the contemporary modeling practice is its interdisciplinarity: the same function forms and equations, and mathematical and computational methods are being transferred across disciplinary boundaries. Within philosophy of science this interdisciplinary dimension of modeling has been addressed by both analogy and template-based approaches that have proceeded separately from each other. We argue that a more fully-blown account of model transfer needs both perspectives. We examine analogical reasoning and template application through a detailed case (...) study on the transfer of the Ising model from physics into neuroscience. Our account combines the analogy and template-based approaches through the notion of a model template that highlights the conceptual side of model transfer. (shrink)

One striking feature of the contemporary modelling practice is its interdisciplinary nature. The same equation forms, and mathematical and computational methods, are used across different disciplines, as well as within the same discipline. Are there, then, differences between intra- and interdisciplinary transfer, and can the comparison between the two provide more insight on the challenges of interdisciplinary theoretical work? We will study the development and various uses of the Ising model within physics, contrasting them to its applications to (...) socio-economic systems. While the renormalization group methods justify the transfer of the Ising model within physics – by ascribing them to the same universality class – its application to socio-economic phenomena has no such theoretical grounding. As a result, the insights gained by modelling socio-economic phenomena by the Ising model may remain limited. (shrink)

The omnipresence of the same basic equations, function forms, algorithms, and quantitative methods is one of the most spectacular characteristics of contemporary modeling practice. Recently, the emergence of the discussion of templates and template transfer has addressed this striking cross-disciplinary reach of certain mathematical forms and computational algorithms. In this paper, we develop a notion of a model template, consisting of its mathematical structure, ontology, prototypical properties and behaviors, focal conceptualizations, and the paradigmatic questions it (...) addresses. We apply this notion to three widely disseminated and powerful model templates: the Sherrington-Kirkpatrick model of spin glasses, scale-free networks, and the Kuramoto model of synchronization. We argue that what appears to be an interdisciplinary model transfer between different domains turns out, from a broader perspective, to be the application of transdisciplinary model templates across a multitude of domains. We also point out a further feature of template-based modeling that so far has not been discussed: template entanglement. Such entanglement enhances and makes manifest the conceptual side of model templates. (shrink)

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and (...) first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic. Treats traditional logic in a modern format. Presents relevance logic with applications. Provides an ideal text for a variety of one-semester upper-level undergraduate courses. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This paper focuses on the inferential configuration of arguments, generally referred to as argument scheme. After outlining our approach, denominated Argumentum Model of Topics (AMT, see Rigotti and Greco Morasso 2006, 2009; Rigotti 2006, 2008, 2009), we compare it to other modern and contemporary approaches, to eventually illustrate some advantages offered by it. In spite of the evident connection with the tradition of topics, emerging also from AMT’s denomination, its involvement in the contemporary dialogue on argument schemes should not (...) be overlooked. The model builds in particular on the theoretical and methodological perspective of pragma-dialectics in its extended version, reconciling dialectic and rhetoric; nevertheless, it also takes into account numerous other contributions to the study of argument schemes. Aiming at a representation of argument schemes able to monitor the inferential cohesion and completeness of arguments, AMT focuses on two components of argument scheme that could be distinguished, readapting pragma-dialectical terms, as procedural and material respectively. The procedural component is based on the semantic-ontological structure, which generates the inferential connection from which the logical form of the argument is derived. The material component integrates into the argument scheme the implicit and explicit premises bound to the contextual common ground (Rigotti 2006). In this paper, the comparison of the AMT to other approaches focuses on the inferential configuration of arguments and not on the typologies of argument schemes and on the principles they are based on, which the authors intend to tackle in a further paper. (shrink)

We develop a model of ideals-based accountability which we have witnessed at work in several long-thriving family businesses. The owners and managers of these firms eschew individualism and materiality in the pursuit of ethical ideals such as supporting democracy and bettering the human condition. Although accountability is to these ideals, not for outcomes such as profitability or even reputation, IBA has resulted in outstanding reputations for some firms. We characterize IBA according to its missions, leadership, culture, and stakeholder relationships. (...) We also contrast it with traditional forms of accountability and differentiate IBA from related stakeholder, stewardship, and CSR perspectives. Finally, we examine its manifestations within five long-lived family enterprises, in the process generating propositions to advance the concept. (shrink)

We develop an account of laboratory models, which have been central to the group selection controversy. We compare arguments for group selection in nature with Darwin's arguments for natural selection to argue that laboratory models provide important grounds for causal claims about selection. Biologists get information about causes and cause-effect relationships in the laboratory because of the special role their own causal agency plays there. They can also get information about patterns of effects and antecedent conditions in nature. But to (...) argue that some cause is actually responsible in nature, they require an inference from knowledge of causes in the laboratory context and of effects in the natural context. This process, cause detection, forms the core of an analogical argument for group selection. We discuss the differing roles of mathematical and laboratory models in constructing selective explanations at the group level and apply our discussion to the units of selection controversy to distinguish between the related problems of cause determination and evaluation of evidence. Because laboratory models are at the intersection of the two problems, their study is crucial for framing a coherent theory of explanation for evolutionary biology. (shrink)

Lacker (1981) and Lacker & Akin (1988) developed a mathematical model of follicular maturation and ovulation; this model of only four parameters accounts for a large number of results obtained over the past decade or more on the control of follicular growth and ovulation in mammals. It establishes a single law of maturation for each follicle which describes the interactions between growing follicles. The function put forward is sufficient to explain the constancy of the number of ovulations (...) or large follicles in a female as well as the variability of this number among strains or species and for either induced or spontaneous ovulators. According to the model, the number of ovulations or large follicles lies between two limits that are themselves simple functions of two parameters of the model. Moreover, Lacker's model exhibits interesting characteristics in agreement with results obtained by physiologists: in particular, it predicts that the number of ovulating or large follicles is independent of:1. the total number of maturing follicles, 2. the process of recruitment of newly maturing follicles towards the terminal maturation (Poisson or other), 3. the form of the LH or FSH secretion curves as functions of the systemic level of oestradiol. The model further predicts that 4. selection and dominance of follicles result from the feedback between the ovary and the hypophysis through the interactions between follicles; these interactions are expressed by the maturation function of the model. 5. recovery from atresia is possible for a follicle: from decreasing, the rate of secretion of oestradiol may increase. 6. the revised model suggests a renewal of follicles during the sexual cycle, as waves of follicular growth. Lacker's model is a model of strict dominance; it maintains a hierarchy of the follicles as soon as they start their final maturation to the ovulations as that is observed in bird or reptile ovary. Such a strict hierarchy is possible but it is probably not a general situation in all mammals. We therefore modified the maturing function of the follicle in order to make it compatible with the observations of physiologists: follicles always interact as in the initial model but they individually become old, the hierarchy of follicles can be modified with time and the largest follicles do not indefinitely grow as in the initial model. (shrink)

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to (...) the empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. 11 (...) EUCh. These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)

The starting premise of this paper is that business models can transform social reality—sometimes to an extreme. Then, building on the concept of “grand challenges,” we argue that such transformations can be either positive or negative in nature —even in the case of business models designed to improve value not only economically but environmentally and socially as well. To further our understanding of the negative aspects, we introduced two conceptual categories of business model: those for oppression (...) or depletion and exclusionary ones. We further argue that bringing the notion of grand challenges center-stage highlights four elements that can contribute to emerging research and inform practice on transformational business models. These elements are: participatory forms of architecture; multivocal inscriptions; scaffolding; and proximity. They are central components of what we name transformational business models. (shrink)

We show how to build prime models in classes of saturated models of abstract elementary classes (AECs) having a well‐behaved independence relation: Let be an almost fully good AEC that is categorical in and has the ‐existence property for domination triples. For any, the class of Galois saturated models of of size λ has prime models over every set of the form. This generalizes an argument of Shelah, who proved the result when λ is a successor cardinal.

This paper discusses the stability and Hopf bifurcation analysis of the diffusive Kaldor–Kalecki model with a delay included in both gross product and capital stock functions. The reaction-diffusion domain is considered, and the Galerkin analytical method is used to derive the system of ordinary differential equations. The methodology used to determine the Hopf bifurcation points is discussed in detail. Furthermore, full diagrams of the Hopf bifurcation regions considered in the stability analysis are shown, and some numerical simulations of the (...) limit cycle are used to confirm the theoretical outcomes. The delay investment parameter and diffusion coefficient can have great impacts on the Hopf bifurcations and stability of the business cycle model. The investment parameters for the gross product and capital stock as well as the adjustment coefficient of the production market are also studied. These parameters can cause instability in, and the stabilization of, the business cycle model. In addition, we point out that, as the delay investment parameter increases, the Hopf bifurcation points for the diffusion coefficient values decrease considerably. When the delay investment parameter has a very small value, the solution of the business cycle model tends to become steady. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

The papers included are divided into five sections: Psychology and Philosophy of Perception and Discovery, Integrations of Experimental Findings, Theoretical Developments, Experimental Results from Neurophysiology and Psychology Pertinent to Model Building, and Computer Simulations of Complex Models. The last of these sections will probably prove most interesting to the contemporary philosopher of mind. Peirce, Cassirer, and Wittgenstein are the philosophers who make the scene in the first section; inclusion of material from the last of these is no mean editorial (...) feat. The volume aims to be comprehensive rather than intensive and while this makes it ideal for the philosopher, the psychologist may find it thin in spots.—E. A. R. (shrink)

One of the most conspicuous features of contemporary modeling practices is the dissemination of mathematical and computational methods across disciplinary boundaries. We study this process through two applications of the Ising model: the Sherrington-Kirkpatrick model of spin glasses and the Hopfield model of associative memory. The Hopfield model successfully transferred some basic ideas and mathematical methods originally developed within the study of magnetic systems to the field of neuroscience. As an analytical resource we use (...) Paul Humphreys's discussion of computational and theoretical templates. We argue that model templates are crucial for the intra- and interdisciplinary theoretical transfer. A model template is an abstract conceptual idea associated with particular mathematical forms and computational methods. (shrink)

Student character survey in Indonesia in 2021, on average, produced lower index numbers compared to last year’s index results. This research aims to explore the policies and content of Character Building Training (CBT), and the impact of the programme on student character. This research was qualitative, involving informants: 60 students and 8 lecturers, who were selected using purposive and snowball techniques, so that if the data were saturated, collecting the data was considered sufficient. Data were collected through observation and in-depth (...) interviews carried out from June to September 2022. Data analysis was carried out manually using the Discovering Cultural Themes model by carrying out data reduction, data display, and drawing conclusions and verification. The research results show that CBT is implemented through a cycle of CBT campaign, capacity building, and institutionalisation with a nurturing, learning, mentoring, and consulting approach. The content includes attitudes and values, skills, knowledge and moderate integrative insight, as well as amplifying tolerant, open, critical, caring, and creative behaviour, respecting differences, and polite and commendable behaviour. The CBT programme has amplified some aspects: religious character, discipline, politeness, caring for the environment, and patriotism. The greatest and dominant strengthening was in religious character and love of the country. The implication and contribution of this research is the continuation of character education for young people as an instrument to substantiate religious moderation. Contribution: This research is important theoretically and practically to contribute to the formation of character building in young people in Islamic tertiary institutions. Currently, character education is the main vision of Islamic tertiary institutions in Indonesia, which is associated with religious moderation as one of the priorities in the national medium-term development plan. (shrink)

Frisch’s 1933 macroeconomic model for business cycles has been extensively studied. The present study is the first comprehensive mathematical analysis of Frisch’s model. It provides a detailed reconstruction of how the model was built. We demonstrate the workability of Frisch’s PPIP model without adding hypotheses or changing the value of Frisch’s parameters. We prove that (1) the propagation model oscillates; (2) the PPIP model is mathematically incomplete; (3) the latter could have been (...) calibrated by Frisch; (4) Frisch’s analysis and demonstration are based on Poincaré’s methodology. (shrink)

In this chapter, we discuss a specific kind of progress in economics, namely, progress that is pushed by the repeated use of mathematical models in most sub-branches of economics today. We adopt a functional account of progress to argue that progress in economics occurs via the use of what we call ‘common recipes’ and the use of model templates to define and solve problems of relevance for economists. We support our argument by discussing the case of twentieth-century (...) class='Hi'>business cycle research. By presenting this case study in detail, we show how model templates are not only re-applied to different phenomena. We also show how scientists come up with them in the first place and how – once they are considered less useful – they are replaced with new ones. Finally, our case also illustrates that it is not only the mathematical structure that is re-used but that such a re-use also requires a shared conceptual vision of core properties of the phenomenon. If that vision is not shared anymore among economists, a model template can become useless and has to be replaced – sometimes through overcoming resistance – with a different one. (shrink)

Metaphors and models involve correspondences between events in separate domains. They differ in the form and precision of how the correspondences are expressed. Examples include correspondences between phylogenic and ontogenic selection, and wave and particle metaphors of the mathematics of quantum physics. An implication is that the target article's metaphors of resistance to change may have heuristic advantages over those of momentum.

As organizations are benefiting from investments in big data analytics capabilities building and education, our study has analyzed the impact of big data analytics capabilities building and education on business model innovation. It has also assessed technological orientation and employee creativity as mediating and moderating variables. Questionnaire data from 499 managers at enterprises in Jiangsu, China have been analyzed using Structural Equation Modeling in SmartPLS. Big data analytics capabilities building and education strengthen technological orientation and increase business (...) model innovation. Technology orientation increases business model innovation and plays a mediating role. Employee creativity also boosts innovation. These findings show that business managers should adopt and promote a technological orientation. They should hire and train employees with big data education and training. Organizations can try to select and support employees who show creativity. (shrink)

In a context of growing environmental challenges, circular economy (CE) business models appear necessary for business to contribute positively to the ecological transition. While platform business models have been identified as a new and promising model in CE, we still lack a fine-grained understanding of the critical capabilities involved in developing and scaling them. To fill this gap, we build on a single case study of Phenix, a French-based fast-growing start-up in the food industry, tackling the (...) issue of food waste. We identify three core managerial capabilities involved in the successful scaling of Phenix's business model. In addition to ecosystem orchestration capabilities, we identify two types of ambidextrous capabilities – forms of ambidexterity operating both at the organizational and at the institutional level. Our analysis highlights the importance of considering these capabilities in a bundle as they collectively contribute to the performance and scaling potential of the business model. We also call for an increased consideration of the role of institutional factors in shaping opportunities to design and scale profitable business models. (shrink)

Fifty years ago, two Princeton professors established game theory as an important new branch of applied mathematics. Gametheory has become a celebrated discipline in its own right, and it now plays a prestigious role in many disciplines, including ethics,due in particular to the neo-Hobbesian thinking of David Gauthier and others. Now it is perched at the edge of business ethics. I believethat it is dangerous and demeaning. It makes us look the wrong way at business, reinforcing a destructive (...) obsession with measurableoutcomes and a false sense of competition. It falsely characterizes or insidiously advocates a style of human behavior that is utterlyunacceptable. To put the matter quite crudely, a person who actually practiced the form of "rationality" advocated by game theory wouldbe something of a monster. (shrink)

To evaluate Hume's thesis that causal claims are always empirical, I consider three kinds of causal statement: ?e1 caused e2 ?, ?e1 promoted e2 ?, and ?e1 would promote e2 ?. Restricting my attention to cases in which ?e1 occurred? and ?e2 occurred? are both empirical, I argue that Hume was right about the first two, but wrong about the third. Standard causal models of natural selection that have this third form are a priori mathematical truths. Some are obvious, (...) others less so. Empirical work on natural selection takes the form of defending causal claims of the first two types. I provide biological examples that illustrate differences among these three kinds of causal claim. (shrink)

continent. 1.2 (2011): 78-91. This article consists of three parts. First, I will review the major themes of Quentin Meillassoux’s After Finitude . Since some of my readers will have read this book and others not, I will try to strike a balance between clear summary and fresh critique. Second, I discuss an unpublished book by Meillassoux unfamiliar to all readers of this article, except those scant few that may have gone digging in the microfilm archives of the École normale (...) supérieure. The book in question is Meillassoux’s revised doctoral dissertation L’Inexistence divine (or The Divine Inexistence ), with its seemingly bizarre vision of a God who does not yet exist but might exist in the future. Without literally accepting this view, I will claim that it is philosophically interesting in ways that even a hardened sceptic might be able to appreciate. Third and finally, I will speculate on the possible future of Meillassoux’s speculative materialism itself. And here I mean its future development not by Meillassoux, but by those readers who might be inspired by his book. Plato could never have predicted the emergence of Aristotle’s philosophy, despite the obvious debt of the latter to the former. Nor could Descartes have predicted Spinoza and Leibniz, nor Kant the German Idealists, and neither could Husserl in 1901 have foreseen the later emergence of Heidegger. How are the works of interesting philosophers transformed by later thinkers of comparable importance? While it may seem that there are countless ways to do this, I think there are only two basic ways in which this happens: you can radicalize your predecessors, or you can reverse them. I will close this article with a few words about these two methods, and try to imagine how Meillassoux might be radicalized or reversed by some future admirer. My view is that the more important thinkers are, the easier they are to radicalize or reverse. This helps explain why the great philosophers of the West have so often appeared in clusters, succeeding one another at relatively brief intervals during periods of especial ferment. 1. After Finitude After Finitude is unusually short for such an influential book of philosophy: running to just 178 pages in the original French, and an even more compact 128 pages in the English version, despite the introduction of roughly eight pages of new material for the English edition. Rather than summarizing Meillassoux’s book in the order he intended, I will focus on six points that strike me as the pillars of his debut book. Along the way, I will offer a few criticisms as well. The first pillar of the book is Meillassoux’s own term “correlationism.”1 Although he introduces this term as the name for an enemy, it is striking that Meillassoux remains impressed by correlationism much more than his fellow speculative realists are. This continued appreciation for his great enemy influences the shape of his own ontology. Is there a world outside our thinking of it, or does the world consist entirely in being thought? Traditionally, this dispute between realism and idealism has been dismissed in continental philosophy as a “pseudo-problem,” in a strategy pioneered by Husserl and extended by Heidegger. We cannot be realists, since following Kant we have no direct access to things-in-themselves. But neither are we idealists, since the human being is always already outside itself, aiming at objects in intentional experience, deeply engaged with practical implements, or stationed in some particular world-disclosing mood. The centuries-old dispute between realism and idealism is dissolved by saying that we cannot think either real or ideal in isolation from the other. There is neither human without world nor world without human, but only a primordial correlation or rapport between the two. This is what “correlationism” means: philosophy trapped in a permanent meditation on the human-world correlate, trying to find the best model of the correlate: is it language, intentionality, embodiment, or some other form of correlation between human and world? Among other problems, this generates some friction between philosophy and the literal meaning of science. When cosmologists say that the universe originated 13.5 billion years ago, they do not mean “13.5 billion years ago for us ,” but literally 13.5 billion years ago, well before conscious life existed, and thus at a time when there was no such thing as a correlate. Meillassoux also coins the term “ancestrality” (10) for the reality that predated the correlate, and later expands this term to “dia-chronicity,” (112) to refer to events occurring after the extinction of human beings no less than to those occurring before we existed. Up to this point, Meillassoux’s focus on ancestral entities existing prior to consciousness might seem like a straightforward realist who wants to unmask correlationism as just another form of idealism. Yet Meillassoux also admires the correlationist maneuver, which can obviously be traced back to Kant. Unlike a thinker such as Whitehead, Meillassoux feels no nostalgia for the pre-critical realism that came before Kant: “we cannot but be heirs of Kantianism,” he says (29). What impresses Meillassoux about correlationism is something both simple and familiar. If we attempt to think a tree outside thought, this is itself a thought . Any form of realism which thinks it can simply and directly address the world the way it is fails to escape the correlational circle, since the attempt to think something outside of thought is itself nothing other than a thought, and thereby collapses back into the very human-world correlate that it pretends to escape. For Meillassoux this step, suggested by Kant but first refined by the ensuing figures of German Idealism, marks decisive forward progress in the history of philosophy that must not be abolished. Any attempt to break free from the correlate must first acknowledge its mighty intellectual power. Realist though he may seem, Meillassoux’s works are filled with praise of such figures as Fichte and Hegel, not of so-called “naïve realists.” It is also the case that for Meillassoux, not all correlationisms are the same. The second pillar of his book is a distinction between various positions that I have termed “Meillassoux’s Spectrum,” though of course he is never so immodest as to name it after himself. He distinguishes between at least six different possible positions, and perhaps we could add even subtler variations if we wished. But in its simplest form, Meillassoux’s Spectrum allows for just four basic outlooks on the question of realism vs. anti-realism. Three of these are easy to understand, since we have already been discussing them. At one extreme is so-called “naïve realism,” which holds that a world exists outside the mind, and that we can know this world. Meillassoux rejects this naïve realism as having been overthrown by Kant’s critical philosophy. At the other extreme is subjective idealism, in which nothing exists outside the mind. For to think a dog outside thought immediately turns it into a thought, and therefore there cannot be anything outside; the very notion is meaningless. In between these two is what we have called correlationism. And here comes a crucial moment for Meillassoux, since he distinguishes between the two forms of “weak” and “strong” correlationism, and chooses the strong form as the launching pad for his own philosophy. Weak correlationism is easy to explain, since we all know it from the philosophy of Kant. The things-in-themselves can be thought but not known. They certainly must exist, since there cannot be appearances without something that appears. And we can think about them, which idealism holds to be impossible. They are simply unknowable due to the finitude of human thought. Strong correlationism is the new position introduced by Meillassoux (though he sees it at work in numerous twentieth century thinkers), midway between weak correlationism and subjective idealism. The major difference between the three positions is as follows. Weak correlationism says: “The things-in-themselves exist, but we cannot know them.” The subjective idealist says: “This is a contradiction in terms, since when we think the things-in-themselves, we already turn them into thoughts.” But the strong correlationist says: “Just because ‘things-in-themselves’ is a meaningless notion does not mean that they cannot exist. No one has ever traveled to the world-in-itself and come back to make a report on it. Thus, the fact that we cannot think things-in-themselves without contradiction does not prove that they do not exist anyway. There may be things-in-themselves, we simply are not capable of thinking them without contradiction form within the correlational circle.” This step is crucial for Meillassoux, since strong correlationism is the position he attempts to radicalize into his own new standpoint: speculative materialism. As I see it, this step of the argument fails. Strong correlationism cannot avoid collapsing into subjective idealism, since the statements of the strong correlationist are rendered meaningless from within. All three of the other positions in the Spectrum make perfectly good sense even for those who disagree with them. The naïve realist says that things-in-themselves exist and we can know them; the meaning of this statement is clear. The weak correlationist can say that things-in-themselves exist but lie forever beyond our grasp; this too makes perfect sense, even though the German Idealists try to show a contradiction at work here. We can also understand the claim of the subjective idealist that to think anything outside thought turns it into a thought, and that for this reason we cannot think the unthought. The strong correlationist, alone among the four, speaks nonsense . This person says “I cannot think the unthought without turning it into a thought, and yet the unthought might exist anyway.” But notice that the final phrase “the unthought might exist anyway” is fruitless for this purpose. For we have already heard that to think any unthought turns it into a thought. But now the strong correlationist wants to do two incompatible things simultaneously with this unthought. On the one hand, he neutralizes the unthought by showing that it instantly changes into just another thought. But on the other hand, he wants to appeal to the unthought as a haunting residue that might exist outside thought, thereby undercutting the absolute status of the human-world correlate found in idealism. But this is impossible. If you accept the argument that thinking the unthought turns it into a thought, you cannot also add “but maybe there is something outside that prevents this conversion from being absolutely true,” because this “something outside” is immediately converted into nothing but a thought for us. In short, Meillassoux here seems to be offering a kind of Zen koan: his “strong correlationism” is reminiscent of the gateless gate, or the sound of one hand clapping, or the command to punch Hegel in the jaw when meeting him on the road. We cannot at the same time both destroy the realist challenge of the things-in-themselves in order to undercut realism and reintroduce that very realist sense in order to undercut idealism. In a world where everything is instantly converted into thought, we cannot claim that there might be something extra-mental anyway, because this “might be something” is itself converted into a thought by the same rules that condemned dogs, trees, and houses to the idealist prison. This brings us to the third pillar of Meillassoux’s argument, which is the key to all the rest: the necessity of contingency. His strategy is to transform our supposed ignorance of things-in-themselves into an absolute knowledge that they exist without reason, and that the laws of nature can change at any time for no reason at all. In this way the cautious agnosticism of Kantian philosophies is avoided, but so is the collapse of reality into thought as found in German Idealism. Meillassoux does try to prove the existence of things-in-themselves existing outside thought; he simply holds that they must be proven after passing through the rigors of the correlationist challenge, not just arbitrarily decreed to exist in the manner of naïve realism. As he puts it, “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws; and this not by virtue of some superior law whereby everything is destined to perish, but by virtue of the absence of any superior law capable of preserving anything, no matter what, from perishing” (53). If idealism thinks that the human-world correlate is absolute, for Meillassoux it is the facticity of the correlate that is absolute. He tries to show this with a nice brief dialogue between five separate characters (55-59) which is covered in detail in my forthcoming book,2 but which I will simplify here for reasons of time. In this simplified version, we first imagine a dogmatic realist arguing with a dogmatic idealist. The realist says that we can know the truth about the things-in-themselves; the idealist counters that we can only the truth about thought, since all statements about reality must be turned into statements concerning our thoughts about reality. Here the correlationist enters and proclaims that both of these positions are equally dogmatic. For although we have access to nothing but thoughts, we cannot be sure that these thoughts are all that exist; there could be a reality outside thought, there is simply no way to know for sure. And this latter position is the one that Meillassoux attempts to transform from an agnostic, skeptical point into an ontological claim about the contingency of everything. Consider it this way. How does the correlationist defeat the idealist? The idealist holds that the existence of anything outside thought is impossible. The correlationist, by contrast, holds that something might exist outside the human-world correlate. But this “something might” has to be an absolute possibility. It cannot mean that “something outside thought might exist for thought ,” because that is what the idealist already says. No, the correlationist must mean that something might exist outside thought quite independently of thought. In other words, the correlationist says that idealism might be wrong, and this means it is absolutely true that idealism might be wrong. Thus, correlationism is no longer just a skeptical position. It holds that all the possibilities of the world are absolute possibilities. We have absolute knowledge that any of the possibilities about the existence or non-existence of things-in-themselves might be true, and this means that correlationism flips into Meillassoux’s own position: speculative materialism. As Meillassoux sees it, there are only two options here. Option A is to absolutize the human-world correlate, which is what the idealist does: there absolutely cannot be anything outside thought. Option B, by contrast, is to absolutize the facticity of the correlate: its character of simply being given to us, without any inherent necessity. The correlationist cannot have it both ways by saying: “there absolutely might be something outside thought, yet maybe this is absolutely impossible.” In other words, once we escape dogmatism we can only be idealists or speculative materialists, not correlationists. The human-world correlate is merely a fact, not an absolute necessity. But this facticity itself cannot be merely factical: it must be absolute. Here Meillassoux coins the French neologism factualité , which has been suitably translated into the English neologism “factiality.” (7, 122-3) Factialty means that for everything that exists, it is absolutely possible that it might be otherwise, not just that we cannot know whether or not it might be otherwise. Just as Kant transformed philosophy into a meditation on the categories governing human finitude, Meillassoux wishes to turn philosophy into a meditation on the necessary conditions of factiality, which he calls “figures”—a new technical term for him. (80) One such figure is that the law of non-contradiction must be true, and for an unusual reason. Since everything is proven to be contingent, nothing that exists can be contradictory, for whatever is contradictory has no opposite into which it might be transformed, and thus contingency would be impossible.3 Another such figure is that there must be something rather than nothing: for since contingency exists, something must exist in order to be contingent. It is a daring high-wire act, one that sacrifices realism to the correlational circle in order to rebuild it from out of its own ashes. Some might conclude that the lack of reason in things is a byproduct of the ignorance of finite humans, Meillassoux is making precisely the opposite point. For in fact, the doctrine of finitude usually leads directly to belief in a hidden reason. The fact that it lies beyond human comprehension merely increases our belief in this arbitrarily chosen concealed ground. By defending anew the concept of absolute knowledge Meillassoux evacuates the world of everything hidden. The reason for things having no reason is not that the reason is hidden, but that no reason exists. Thus, even while insisting on the necessity of non-contradiction, he rejects the other Leibnizian principle: sufficient reason. Everything simply is what it is, in purely immanent form, without deeply hidden causes. Or as Meillassoux puts it: “There is nothing beneath or beyond the manifest gratuitousness of the given—nothing but the limitless and lawless power of its destruction, emergence, or persistence” (63).The world is a “hyper-chaos”(64). But this is not the same thing as flux. For the chaos of the world is such that stability might occur just as easily as constant, turbulent change. Let’s now digress a bit, and return to the question of ancestrality, which Meillassoux transforms later in the book into “dia-chronicity.” Correlationism holds that all talk of a world outside the correlate is immediately recuperated by the correlate. The phrase “13.5 billion years ago” becomes “13.5 billion years ago for us ,” and the phrase “the universe following the extinction of humans” becomes “the universe following the extinction of humans for humans .” But notice that whether we talk about the world before or after humans, in both cases it is time that is used to challenge the correlate. Meillassoux has no interest in challenges that might be posed by space. For example, what about a vase in a lonely country house that topples to the floor and smashes when no one is there to watch it? Isn’t this also a challenge to correlationism, no less than the Big Bang or the heat death of the universe long after humans have vanished? In an eight-page supplement to the English translation of After Finitude ,4 possibly in response to my own 2007 review of the French original,5 Meillassoux bluntly denies that space is of any relevance to the question. Spatial distance is a merely harmless challenge to the human-world correlate. After all, even though no one is there in the lonely country house to witness the shattering of the vase, we can say that had there been an observer , that observer would have witnessed the toppling and destruction of the vase. For this event still occurs in a world in which the human-world correlate already exists, whereas the diachronicity of events both before and after the existence of humans makes it impossible to say that had there been an observer they would have witnessed the Big Bang occurring in such and such a fashion. However, it seems to me that Meillassoux merely asserts that the temporal simultaneity of our existence with that of the vase in the lonely country house is enough to render it harmless. It is true that the house does not exist prior to the correlate, but nonetheless it exists outside the correlate, and that is enough to make the same challenge. It is difficult to see why the “had there been an observer” maneuver succeeds in the case of a vase in the countryside in April 2011 but fails in the case of the Big Bang. This is not just a matter of nitpicking Meillassoux’s argumentative style: the fact that he bases his argument on time has at least two important consequences for his position. For in the first place, even though Meillassoux insists that the laws of nature are absolutely contingent, this turns out to be true only in a temporal sense. That is to say, it is a paradoxical feature of Meillassoux’s philosophy that he does allow for the existence of laws of nature, and simply believes that they can change at any moment without reason. Within any given moment, laws of nature do exist. He never suggests that different parts of the universe can have different laws at the same time, nor does he have any interest in the laws of part/whole composition that take place within any given instant. Could it be the case that rather than being made of gold atoms, a small chunk of gold could be made of silver atoms, cotton, horses, or that this same small piece of gold could be made of gigantic vaults filled with even more gold? These are not topics that draw Meillassoux’s attention, since he is focused solely on how the laws of nature might change or endure from one moment to the next . Another implication for Meillassoux’s system is that his concept of things-in-themselves turns out to be to be inadequate. For when he proves that things-in-themselves can exist without humans, this turns out to be true only in a temporal sense as well. Namely, things-in-themselves existed ten billion years ago, and they will continue to exist after all humans have succeeded in exterminating themselves. However, being able to exist before our births and after our deaths is just one small part of what it means to be a thing-in-itself. The more important part is that even if a thing is sitting on a table right now, in front of me, even if I stroke it lovingly or press my face up against it directly, I am still dealing only with a phenomenal version of the thing; the thing-in-itself continues to withdraw from all access. Yet no such thing is acknowledged by Meillassoux. For him finitude is a disaster, and absolute knowledge is in fact possible. Meillassoux’s thing-in-itself exists in independence only of the human lifespan , not of human knowledge. The fifth pillar of Meillassoux’s argument is his use of Cantor’s transfinite mathematics to show that even if the laws of nature are contingent, they need not be unstable, and thus we cannot use the apparent stability of nature to disprove his metaphysics of absolute contingency. What Cantor showed is that there are different sizes of infinity, and that all these infinities cannot be totalized in a single infinite number of infinities. Meillassoux sees this as crucial, since it allows him to discredit any “probabilistic” argument against his theory. The probabilistic argument (as defended quite clearly by Jean-René Vernes)6 would say this: given that the laws of nature seem so stable, it it is extremely improbable that there is no hidden reason for their remaining so stable. As Meillassoux sees it, probability is of value only when we can index an accessible total of cases. These can even be infinite: for example, there are an infinite number of points where a rope can break when stretched tight, but this does not stop us from calculating probabilities for various sections of the rope to break. By contrast, there is no way to sum up the number of possible laws of nature. For here there is no way to totalize; we cannot stand outside of nature and calculate the possible number of laws so as to determine the probabilities that any one of them might change. Therefore, although we can speak of probability when dealing with intraworldly events such as elections, horse races, and coin-flips, we cannot use the words “probable” or “improbable” when describing alterations at the level of nature as a whole. Rather than commenting on the validity of this argument and its use of Cantor, let me simply note that it once again creates a dualistic ontology. We already saw that Meillassoux treats time differently from space. In analogous fashion, he now treats the level of world differently from that of intraworldly events. The emergence of worlds is purely contingent and virtual and governed by no probability at all, while events within the world necessarily follow laws (even if these laws can change at any moment without reason), and thus their probabilities can be calculated. It is a strategy deeply reminiscent of Badiou’s (2005) own dualism between the normal “state of the situation” and the rare and intermittent “event.” The sixth and final pillar of Meillassoux’s book can be dealt with briefly, since we have already touched on it elsewhere. It comes at the very beginning of the book, when Meillassoux says that we must revive the distinction between primary and secondary qualities, and that the primary qualities are the ones that can be mathematized. He admits that he has not yet published a proof of this idea, though in fact it is already known as one of his primary doctrines. And here we encounter the familiar problem with Meillassoux’s inadequate conception of things-in-themselves. “Primary qualities” refers to those qualities that a thing has independently of its relations with us or anything else. But if the primary qualities can be mathematized, this means that they are not entirely independent of us, since our knowledge can get right to the bottom of them. The mathematized qualities of things are independent of us only in Meillassoux’s sense that they will still have those qualities even when all humans are dead. But to repeat, autonomy from the human lifespan is not the same as autonomy from human access. Here once more Meillassoux is concerned only with independence from the human-world correlate across time, not in any given instant. 2. L’Inexistence divine In 1997, the same year in which he turned thirty years old, Meillassoux earned his doctorate at the École normale supériuere with a brazen dissertation entitled L’Inexistence divine ( The Divine Inexistence ). The work was substantially revised in 2003. But even then, with typical fastidiousness, Meillassoux decided that the work was not yet ready for press. It has now been scrapped in favor of some future, multi-volume work bearing the same title. While writing my book on Meillassoux for Edinburgh University Press, I was permitted to translate excerpts from this unpublished work for use as an appendix in my own book; in total, the appendix contains approximately twenty percent of Meillassoux’s 2003 manuscript, the first time any of it will be published in any language. Nonetheless, a portion of the argument was already tested in the article “Spectral Dilemma,” published in English in the journal Collapse (2008: 261-75). There the philosophical motives for the virtual God are already made clear. What troubles us most are early deaths, brutal deaths, deaths of especial injustice– the sorts of deaths in which the brutal twentieth century was so abundant. And here, neither the atheist nor the believer can help us. The atheist can offer nothing but a sad and cynical resignation when reflecting on the victims of these terrible crimes. The believer does little better, being unable to explain how God could have allowed such things to happen, due to the famous intractability of the problem of evil. The solution offered to this dilemma by Meillassoux is bold, and all the more so given that he emerges from such a deeply Leftist, materialist, and unreligious background. His solution is that God does not yet exist, and therefore is not blameworthy for these catastrophes. Given that everything is contingent in Meillassoux’s philosophy, this God and divine justice might never exist, but they can at least exist as an object of hope. Let’s begin by jumping to the end of L’Inexistence divine , where the alternatives are laid out so nicely. There are four basic attitudes that humans can have towards God, Meillassoux says. First, we can believe in God because he exists. This is the classical theist attitude, rejected for the simple reason that it would be amoral and blasphemous to believe in a God who allows children to be eaten by dogs, to use Dostoevsky’s example. Second, we can disbelieve in God because he does not exist: the classical atheist attitude. But this leads to sadness, cynicism, and a sneering contempt for the greatness of human capacity. The third option, rather more complex, is to disbelieve in God because he does exist: in other words, to exist in rebellion against God as the one who must be blamed for the evils of the earth. The examples here might range from Lucifer himself, to the more human figure of Captain Ahab in Melville’s Moby-Dick , to Werner Herzog’s even more recent catchphrase, “Every man for himself, and God against all.” That leaves only the fourth option: believing in God because he does not exist. Meillassoux closes his book by saying that the fourth option has now been tried (namely, in the course of his own book), and that now that all four have been specified, we must choose. The first reaction to this theory of the inexistent God will be laughter. Few readers will ever be literally convinced by it, and probably none will immediately be convinced by it. But if we ask ourselves why we laugh, the answer is because it sounds so improbable that an inexistent God might suddenly emerge and resurrect the dead. It obviously sounds more like a gullible theology than a rigorous piece of philosophical work. Yet two things need to be kept in mind. First, Meillassoux’s theories are hardly more unlikely than those of great philosophers of the past such as Plato, Plotinus, Avicenna, Malebranche, Spinoza, Leibniz, Nietzsche, or Whitehead. We read the great philosophers not because their systems are plausible in commonsense terms that can be measured by the laws of probability. Instead, we read them precisely because they shatter the existing framework of common sense and open up new window on the universe. Second, and even more importantly, Meillassoux has already rejected probability as a valid measuring stick in philosophy. Or rather, he accepts probability in the intra-worldly realm (where it is linked with potentiality), and rejects it at the level of the world itself (where potentiality is replaced with what he calls virtuality). The virtual God can appear at any moment for no reason at all, just as any other new configuration of laws of nature can appear: in a manner that the laws of probability cannot calculate. Responding to those who might ridicule the idea of a sudden emergence of God and a resurrection of the dead, Meillassoux cites Pascal, who asserts that the resurrection of the dead would be far less incredible than the fact that we were born in the first place. This shifts philosophy onto new ground. Rather than concerning ourselves with what is likely to happen in the world as we know it, we focus instead on the most important things that could happen. For this reason, the expected objection that a virtual God is no more likely to appear than a virtual unicorn or a virtual flying spaghetti monster misses the point. Unicorns and spaghetti monsters could also appear, just like any other non-contradictory thing. But these would just be novel bizarre entities among others, not the heralds of completely new worlds. For Meillassoux, the emergence of matter, life, and thought have been the three truly amazing advents of the world so far, each of them dependent on the advent(s) preceding them. As he sees it, there can be no greater intraworldly entity than the human beings who already exist, since nothing in the world is better than the absolute knowledge of which humans alone are capable. This means that the next great advent must be something that perfects human beings rather than superseding them. And this can only be the world of justice, in which the dead are resurrected and their horrible deaths partially cancelled (Meillassoux never considers the possibility of a God who would literally erase the pre-divine past so that it never happened at all). The only immortality worth having is an immortality of this life, not an existence in some ill-defined afterworld. Human existence, he holds, must always be governed by a “symbol” that gives us the “immanent and comprehensible inscription of values in a world.” And just as cosmic history made the three great contingent leaps of matter, life, and thought, with a leap to justice as the only one still to come, a similar structure occurs within human culture and its symbols, which consist so far of the cosmological, naturalistic, and historical symbols, with a “factial” symbol still to come. We can review each of these symbols briefly. The cosmological symbol refers to the ancient dualism between the terrestrial and celestial spheres. Here below everything is conflict, corruption, and decay; but in the heavens nothing is perishable, all movement is circular, and everything is arranged in mutual harmony. This symbol is ended by modern physics when Galileo discovers such blemishes as sunspots and craters on the moon, and when Newton integrates both celestial and terrestrial movement into a single gravitational law. Next comes the naturalistic or romantic symbol, in which perfection comes not from the sky but from nature itself. The world is filled with pretty flowers (Meillassoux claims that the ancients never discussed the beauty of flowers until Plotinus in the third century) and with living creatures naturally moved by pity, at least until society corrupts them. This symbol collapses in the face of reality as we know it, since pity is no more common than war, corruption, and violence. This brings us to the historical symbol, which only now is passing away. Bad things may happen, but history has an inner logic of its own, such that everything works out in the end. The ultimate form of the historical symbol is the economic symbol, whether in a Marxist or neo-liberal form. Just as the Marxist holds that the inner economic logic of the capitalists will inexorably lead them to self-destruction, the neo-liberal assumes that the sum total of individual selfish actions will lead, in the long run, to the greatest possible good. We worship the economy and let it guide history for us, just as the ancients worshipped celestial bodies and held them to be free from blemish. The final remaining symbol is the factial symbol, which Meillassoux hopes will now emerge. Factiality, we recall, is his term for the absolute contingency of everything that exists. Once we have grasped this absolute contingency, we are free to expect the dramatic advent of the coming fourth World: the world of justice, inaugurated by a virtual God and even mediated by a messianic human figure. There is the added feature, however, that this messiah must abandon all claims to special status once the messianic realm of justice is achieved. The messianic figure will then be no more special than any person on the street, since a reign of human equality will have arisen. Although this focus on human being might seem like a return to standard humanism, Meillassoux holds that human pre-eminence has never truly been maintained. Previously, humans have been treated as special only because they contemplate the Good, because they resemble their omnipotent creator, or because they happen to be the temporary victors in a cruel Darwinian death-match between millions of living species. For Meillassoux, by contrast, humans have value because they know the eternal. But it is not the eternal that is important, since this merely represents the blind, anonymous contingency of each thing. What is important is not knowledge of the eternal , but knowledge of the eternal. We should not admire Prometheus for stealing fire from the gods; Prometheus is simply as bad as all the gods, no matter how much he increased our power. Feuerbach and Marx were wrong to say that God is a projection of the human essence, since for Meillassoux the usual concept of God represents the degradation of the human essence. If the traditional God was allowed to inflict plagues and tsunamis on the human race, the Promethean human of the twentieth century simply assumes the right to inflict death camps and atomic fireballs instead. In this respect, we have simply begun to imitate the degradation of humanity that was formerly invested in an omnipotent and arbitrary God. In response to charges that absolute contingency might lead to political quietism, Meillassoux counters that the World of justice would mean nothing unless we had already hoped for it beforehand. A World of justice that came along at random would merely be an improved third World of thought: indeed, a perfect one. But it would have satisfied no craving, and would therefore have no redemptive power. For this reason, we must actively hope for the fourth World of justice for such a fourth World ever to arise. Not only justice, but beauty is dependent on such hope: for Meillassoux, who is here somewhat dependent on Kant, beauty means an accord between our human symbolization and the actual world, which could never be present in a World of the blessed any more than justice could. And just as a messianic figure is needed to incarnate our hope and then abandon power once the World of justice is realized, it is the figure of the child whose fragile contingency shows us a dignity and a demand for justice beyond all power. 3. Meillassoux Radicalized or Reversed Given the promising reception of Meillassoux’s first book, it would not be groundless to engage in early speculation about what it might take to earn him a place in the history of philosophy. Maybe this will never happen—who knows?—but quite possibly it will: his lucid argumentative methods and sheer philosophical imagination at least make him a good candidate to be read well into the future, especially following further elaboration in print of his mature system. Philosophy is often practiced as thought it were nothing more than the amassing of “knockdown arguments.” But this is no more insightful than saying that good architecture is the amassing of steal beams. It is true that poorly constructed building cannot stand for long, but sound construction is merely the first, indispensable step in building. In fact, I am inclined to say that what really makes a philosopher important is not being right, but being wrong . I mean this in a very specific sense. I once heard the interesting remark about twentieth century culture that “you have to remember that the sixties really happened in the seventies.” That is to say, it was in the 1970’s rather than the more honored 1960’s that civil rights, free love, long hair, and the rock and roll drug culture really took root. With respect to the history of philosophy, we might just as easily say: “you have to remember that Plato really happened in Aristotle,” that “Kant really happened in Hegel” or “Hume really happened in Kant,” or that “Husserl’s phenomenology first achieved its truth in Heidegger.” One becomes an important philosopher not by being right, but by attracting rebellious admirers who tell you that you are wrong , even as their own careers silently orbit around your own. To recruit faithful disciples may be comforting and flattering, but the greatest thinkers have generally had to experience refutation at the hands of their most talented heirs. For this reason, I would propose that we size up the magnitude of living thinkers not by deciding how many times they are right and wrong, but by asking instead: who would take the trouble to refute this author? For this reason I do not ask: “Is Meillassoux right?”, since I do not believe in the virtual God myself, nor am I convinced by any important aspect of Meillassoux’s philosophy. Instead, I ask if there are interesting ways to overturn him. Only by being overturned, by no longer remaining a contemporary, does one become a classic. Let’s begin with a simple model of refutation, which can be refined further at a later date once the basic point is established. One kind of refutation simply consists in saying: “This author is a complete idiot.” The refuter now walks away in celebration, and no link between the present and the future is built; all is reduced to rubble. But this sort of mediocre triumphalism is generally practiced by those who achieve little of their own, and is not especially interesting. Much more interesting is the sort of refutation that does not take its target to be a complete idiot. I would like to suggest that there are just two basic ways in which this can be done: radicalization and reversal . It has not escaped my notice that this is a fairly good match for the Deleuzian distinction between irony and humor. Whereas irony critiques and adopts the opposite principle of what it attacks, humor accepts what it confronts but pushes it into highly exaggerated form. The ironist is like the worker who sows chaos by rebeling and contradicting the boss, while the humorist is like the worker who follows orders to an absurdly literal degree, with equally chaotic results. Let’s start with a few examples. In Aristotle’s treatment of Plato, and Heidegger’s of Husserl, we find reversal. Plato’s eidei are transformed by Aristotle into mere secondary substances, and the individual worldly things despised by Plato become what is primary. For Husserl what is primary is whatever is present to consciousness, while for Heidegger this is precisely what is secondary, since the primary stuff of the world withdraws from any form of presence at all. As for radicalization, it is most easily found in the transformation of Kant by German Idealism: “Kant was right to wall off the things-in-themselves from human access, and simply should have realized that the thought of the Ding an sich is also a thought, and thereby the noumena are just special cases of the phenomena,” with much following from this discovery. It would also be easy to read Spinoza as a radicalizer of Descartes, and Berkeley and Hume as radicalized versions of Locke. Perhaps the distinction is now sufficiently clear. Admiring refutations are not those that say “Professor X is an idiot,” which is merely the flip side of the eager disciple’s fruitless “Professor X got everything right.” Instead, it will be some variant of one of the following two options: “Professor X is important, but got it backwards,” or “Professor X is important, but didn’t push things far enough.” In the history of philosophy these two latter cases have often been painful in purely human terms: Aristotle expresses sadness at refuting Plato, Kant is openly annoyed at Fichte, and Husserl feels betrayed and used by Heidegger. Rude handling from later figures almost seems to be the sine qua non of being a great philosopher. Now, it has already been claimed that Meillassoux is an emerging philosopher of the first importance, and by no less a figure than Alain Badiou: “It would be no exaggeration to say that Quentin Meillassoux has opened up a new path in the history of philosophy…” (Preface, vii). But rather than taking Badiou’s word for it, or rejecting his word, we might experiment by asking how Meillassoux could be radicalized or reversed. Are there interesting ways of doing this that might launch whole new schools of philosophy, unexpected or even condemned by Meillassoux himself? While no one can see the future, the present is poor when it is not riddled with virtual futures. The relation between philosophers and their predecessors and successors is always somewhat complicated, of course. But generally there is one central divergence at stake, which might be taken as the key to all the others. On this basis we could say that new thinkers primarily radicalize or primarily reverse the main ideas of their chief philosophical forerunner. There may be specific historical conditions and perhaps even personality traits connected with these two types, but this question can be left aside for now. More important for us is that radicalizers will generally be followed by reversers, and vice versa. Consider the textbook example of a reversal in the history of philosophy: Kant’s Copernican Revolution, which inverts the so-called dogmatic tradition that addresses the world itself, and makes the world revolve instead around the conditions by which it is known. While it is not completely impossible that Kant’s successors might have re-reversed this principle back into a new and stronger dogmatic realism, conditions were premature for such a move. Anyone doing this too early would likely have been an angry anti-Kantian reactionary rather than an original thinker in command of a genuinely new realist principle. The far more likely outcome is the one that actually happened: Kant’s reversal of his predecessors was viewed as incomplete, or as retaining lamentable bits of the traditional view, which despite his admirable breakthrough he was unable to shake off. This was the view of German Idealism, anyway. In similar fashion, Spinoza could also be viewed as a radicalizer of Descartes, who is equally accused of preserving various Scholastic dogmas in an otherwise radical project of philosophical reversal. The point is this: reversals in the history of thought tend to be followed soon thereafter by radicalizations of those reversals. The same may hold true in reverse: radicalizations might generally be followed by reversals, given that it is not always possible to be more radical than the radicals have already been. Consider the case of Husserl, who radicalizes Brentano’s early vagueness about what lies beyond immanent objectivity, and Twardowski’s assertion that there must be an external object lying outside the intentional content, by collapsing everything into the intentional sphere: there is no difference between the Berlin in my consciousness and the actual Berlin that is home to millions of people. It is difficult to see how one could be even more radical than Husserl’s idealist turn here. And thus the road is paved to Heidegger’s reversal of classical phenomenology, in which the key point is what lies deeper than any presence to consciousness: the Sein whose power and obscurity cannot be made exhaustively present, but only sends itself in historical epochs. In similar fashion we might also read Leibniz as a reverser of Spinoza’s radicalization, retrieving a strong sense of individual substance and a certain validity of what the Scholastics had said. Returning to Meillassoux, we might ask which kind of philosopher he is: a radicalizer or a reverser? At present, Meillassoux looks to me like a radicalizer (though for now his future remains shrouded in mist). He takes the correlationist tradition, which allows us to speak only of the relation between human and world, and tries to raise it into an even more extreme claim about the absolute contingency of everything. But whereas German Idealism did this by trying to collapse the distinction between thought and world entirely into the “thought” side, Meillassoux does it by trying to shift the non-absolute contingency of the thought-world correlate from epistemology to ontology. It is no longer a question of the inability of human knowledge to know what lies outside the correlate, but the inability of reality itself to be rooted in any definite laws. Furthermore, if we look at the various features of Meillassoux’s philosophy identified earlier tonight, all but one are already so radical that there is no obvious way to push them further. The one exception would be his claim that the world as a whole can change for no reason at any moment, coupled with the inconsistent claim that within a given world there are laws of nature that everything must follow. If gravitational attraction between all masses is a current law in our world, then for Meillassoux there can be no exceptions to this law for as long as it remains in force. A toppled vase will fall to the floor every time for sure,unless there is a cosmic change by which the laws of nature as a whole have altered. (This is reminiscent of the late medieval distinction between the absolute and ordained power of God, according to which God has the power to set or change the laws of nature, but not to contravene those laws locally once they are set.) On this point, to radicalize Meillassoux would simply be to say: there are no laws of nature even in the local sense. Everything that happens, even in the world here and now, is purely contingent and not governed by even a trace of law. And while this would be a more consistent development of Meillassoux’s thoughts on contingency, it is difficult to see how it could lead to a new philosophy. Instead, the admiring successors of Meillassoux are more likely to reverse one of his already sufficiently radical points. At least four candidates come to mind: *First, we have seen that Meillassoux thinks correlationism is challenged by a time before or after consciousness, but not by a space lying outside it. Perhaps this could be reversed into saying that spatial exteriority is the really crucial point. The arguments on this point are perhaps the least convincing in After Finitude (and do not even occur in the original French edition), and therefore it might be a candidate for the “blind spot” of which no philosopher is ever free. *Second, Meillassoux uses Cantor to claim that the contingency of laws of nature would not entail that they are unstable. A successor of Meillassoux might claim that it does make them unstable, and celebrate this fact. This person would then have to explain why common sense seems to encounter a relatively stable world despite its truly rampant instability. Whereas Meillassoux’s problem is to show how stability might exist despite contingency, this successor’s problem would be slightly different: to show why actual, full-blown instability might have the appearance of stability. *Third, Meillassoux claims that the primary qualities of things are those that can be mathematized. He might be reversed by a successor who says the opposite: the mathematizable qualities are the secondary ones, and the primary ones are those that elude symbolic formulation. While this is a perfectly valid possible objection to Meillassoux, it is one that is made in advance by some of his predecessors and is still made by some of his peers, making it less interesting for futurology than some of his other points. *Fourth and finally, whereas Meillassoux claims that God does not exist but might exist in the future, a successor might argue even more bizarrely that God has always existed but might vanish in the future. Let’s arbitrarily select the first of these possibilities, and imagine briefly where it might lead, if pursued in the future by admiring detractors. Meillassoux comes from the circle of Badiou, and some of Badiou’s most ardent admirers are found in Latin America. So, let’s imagine that towards mid-century some ingenious reversers of Meillassoux emerge in that portion of the Spanish-speaking world. Just for fun, let’s call them Castro and Chávez. And in order to avoid any confusion with the present-day politicians of those names, we will stipulate that Meillassoux’s great successors are both women. The philosopher Castro (we will suppose she comes from Peru) reverses Meillassoux’s argument that the ancestral or diachronic are what most threaten the human-world correlate. Instead, she claims that the diachronic does not threaten the correlate at all, and that we must instead look at space as what ruins the correlate and demands a strange new realism. What would such a philosophy look like? In order to determine this, we might ask what price Meillassoux pays for doing it the opposite way. As I see it, he pays in two separate ways. One is that laws of nature for him are contingent over time . The laws of nature apply to the universe as a whole at any given moment, and would be changed globally if they are ever changed at all. The second price he pays is that Meillassoux has no mereology , or theory of parts and wholes. Everything for him is on the level of the given, or immanent in experience, with the sole proviso that the laws governing this immanence might change without notice at any given moment. In reversing Meillassoux, Castro makes the following claims in the preface to her stunning debut book of 2045, The Cosmos and its Neighborhoods , rapidly translated from Spanish into all the languages of the world: Despite his brilliant analysis of the contingency of laws of nature over time, Meillassoux gets two important assumptions wrong. First, he allows for only one set of contingent laws to govern nature as a whole. Second, he allows laws to govern only the world that is immanent in experience, and thereby fails to explore the contingency among part-whole relations. In this book I will argue, first, that the laws of nature vary in any given instant between one region of the universe and the next; and second, that the world is made up of layers of parts and wholes that are also contingent with respect to one another. Those are the words of Castro. This may sound like a hopeless free-for-all of chaos, yet the book somehow succeeds in drawing some compelling deductions about how laws must vary from one place or level in the world to the next. Trapped in the limited horizon of 2011, and not yet inspired by the heavily balkanized political and technological situation of 2050 that somehow lends additional credence to Castro’s vision, we can only vaguely grasp what such a philosophy might look like. After this reversal of Meillassoux by Castro, the usual pattern leads us to expect a radicalization by Chávez, a young Argentine student of Castro. How could the already strange theories of Castro be radicalized? Perhaps as follows, in a disturbing new book entitled The Implosion of the Neighborhoods , which argues as follows: Castro was right to shift the Meillassouxian framework of contingency from time to space. However, in this respect she retained a surprisingly traditional opposition between the two. In this book I will show that time and space collapse into one another. This may sound too much like the discredited four-dimensional block universe of twentieth century physics and philosophy. However, the four-dimensional universe is a model biased in favor of space, merely adding an extra dimension to the commonsense spatial continuum while stipulating that the serial passage of time is an illusion. In this book I will argue instead for a one-dimensional space-time modeled after our experience of time, in which there is no simultaneous co-existence at all between different parts of the universe, or ‘neighborhoods’ as my esteemed teacher Castro has called them. Instead, the various portions of the universe link to one another by succession rather than by coexistence. Buenos Aires, New York, and Amsterdam do not exist simultaneously in the same landscape, but one after the other in the mind of some observer, and this observer can only be an observer much larger than any human. Against Meillassoux’s notion of a virtual God that does not exist now but might exist in the future, I will argue for an actual God that surveys the universe in sequence, thereby generating the illusion of spatial diversity and even the illusion of individual minds located within that diversity. Once this divine observer dies, the universe as a whole must perish. Again, these ideas are so bizarre that we of 2011 can barely comprehend them, just as Aristotle would have had a difficult time grasping the theories of Descartes. We could then perhaps imagine a further reversal of this theory, emanating from the intellectually resurgent Philippines of the twenty-second century. The Filipino School might argue that the universe is already dead, given the collapse of its spatial richness into the serial observations of a flimsy and mortal God. The virtual universe does not yet exist, but might exist in fully spatial form in the future, and this would require the death of God and the resulting liberation of God’s succession of images as independent, spatially situated realities. With a bit of sharpening, we might be able to make all of these imaginary thinkers more intuitively clear. Along with the history of philosophy, there might arise a new discipline generating imaginary futures for philosophy. The richness of Meillassoux’s system comes not from the fact that he is plausibly right about so many things, but because his philosophy offers such a treasury of bold statements ripe for being radicalized or reversed. He is a rich target for many still-unborn intellectual heirs, and this is what gives him the chance to be an important figure. NOTES 1. Quentin Meillassoux, After Finitude . Trans. R Brassier. (London: Continuum, 2008.) Page 5. The word “correlationism” does not appear in his doctoral thesis. As Meillassoux informed me in an email of February 8, 2011, he first coined this term in 2003 or 2004, while editing for publication a lecture he had given at the École normale supérieure on a day devoted to the theme of “Philosophy and Mathematics,” an event including Alain Badiou as one of the participants. 2. Graham Harman, Quentin Meillassoux: Philosophy in the Making . (Edinburgh: Edinburgh University Press, forthcoming 2011). 3. In an email of December 6, 2010, Meillassoux clarifies that in After Finitude he only deduces the impossibility of a “universal contradiction,” not of a determinate contradiction. In the same email he suggests that he can also prove the latter, though the proof is somewhat lengthier than the one found in After Finitude . 4. After Finitude (18-26), in the passage falling between the two sets of triple asterisks. These pages were sent by Meillassoux to translator Ray Brassier (in French) during the translation process, and do not appear in the original French version of the book. 5. Graham Harman, “Quentin Meillassoux: A New French Philosopher.” Philosophy Today 51.1 (2007): Pages 104-117. The passage where I raise the question of space can be found in the first column of page 107. 6. Vernes is first cited on p. 95 of After Finitude . See Jean-René Vernes, Critique de la raison aléatoire, ou Descartes contra Kant . (Paris: Aubier, 1982).  . (shrink)

Although the concept of value is central to sustainable business models (SBMs), the field has struggled to clarify what value is. SBM research accounts for multiple forms of value directed at multiple stakeholders. We argue that this diversity challenge should be addressed not by seeking a field-unifying definition of value but by developing methodological guidelines for a field-specific approach to defining value in SBM contexts. Based on Aristotelian logic and philosophical phenomenology of value, we develop an analytical framework that (...) can be used for generating good definitions of value. We use this framework to explore approaches to value in extant SBM literature, highlight problematic patterns in applications of this concept, and suggest ways to avoid these patterns. The result is a guide to assist SBM researchers in exploring and defining value, and in applying their definitions consistently in theory building efforts. (shrink)

Fifty years ago, two Princeton professors established game theory as an important new branch of applied mathematics. Game theory has become a celebrated discipline in its own right, and it npw plays a prestigues role in many disciplines, including ethics, due in particular to the neo-Hobbesian thinking of David Gauthier and others. Now it is perched at the edge of business ethics. I believe that it is dangerous and demeaning. It makes us look the wrong way at business, (...) reinforcing a destructive obsession with measurable outcomes and a false sense of competition. It falsely characterizes or insidiously advocates a style of human behavior that is utterly unacceptable. To put the matter quite crudely, a person who actually practiced the form of "rationality" advocated by game theory would be something of a monster. (shrink)

Context: This paper outlines how radical constructivist theory has led to a particular methodological technique, developing second-order models of student thinking, that has helped mathematics educators to be more effective teachers of their students. Problem: The paper addresses the problem of how radical constructivist theory has been used to explain and engender more viable adaptations to the complexities of teaching and learning. Method: The paper presents empirical data from teaching experiments that illustrate the process of second-order model building. Results: (...) The result of the paper is an illustration of how second-order models are developed and how this process, as it progresses, supports teachers to be more effective. Implications: This paper has the implication that radical constructivism has the potential to impact practice. Key Words: Second-order model, radical constructivism, teaching, mathematics education. (shrink)

This paper describes model building and manipulation in the solution of problems in mechanics. An automatic problem solver, MECHO, solving problems in several areas of mechanics, employs (1) a knowledge base representing the semantic content of the particular problem area, (2) a means-ends search strategy similar to GPS to produce sets of simultaneous equations and (3) a “focusing” technique, based on the data within the knowledge base, to guide the GSP-like search through possible equation instantiations. Sets of predicate logic (...) statements are employed to describe this model building activity. These clauses are used to give information content to the knowledge base and provide both basis and guidance for the goal driven search.It is hypothesized that humon subjects solving mechanics problems employ similar model building techniques. Protocols of several subjects are presented and comparisons are drawn with the traces of the automated problem solver. Adjustments are made to the program to provide a better fit of traces to protocols. Some implications are presented for using a rule based model for describing human problem solving performance in solving mechanics problems. (shrink)

Green design tools are emerging as a new response to the dilemmas that architects and designers face in preventing the toxic impacts of building construction. Environmental health advocates, scientists, and consulting firms are stepping in to provide designers with new tools—including science-based assessment methods, standards, databases, and software—intended to help structure and inform decision-making in sustainable design. We argue that green design tools play an important but largely uninvestigated role in giving designers new forms of influence while mediating how designers’ (...) values are translated into actual design choices. Tool makers embed their own values and politics into the construction of the tools, which function as “black boxes”—their internal operations are understood as less important than their outputs for informing sustainable design. Using the green building movement as a case study, we consider three tools for selecting environmentally benign materials: the GreenScreen for Safer Chemicals, Pharos, and the Health Product Declaration. Examining controversies about the scientific validity of green design tools, we suggest that they are rooted in value conflicts and tensions in the politics of chemical knowledge. Transparent engagement with values and politics among tool developers and users could strengthen the legitimacy and credibility of green design tools. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Complex Mimetic SystemsHans Weigand (bio)The goal of science is to make the wonderful and complex understandable and simple—but not less wonderful.—Herb Simon, The Sciences of the Artificial11. IntroductionComplex systems theory stands for an approach in the social as well as natural and computational sciences that studies how interactions between parts give rise to collective behaviors of a system, and how the system interacts and forms relationships with its environment. (...) A typical example is the market economy, in which the order is emergent: it is the result of human action, but not the execution of any human design.2 Complex systems theory is currently a popular vehicle for understanding the complexities of the Internet; other examples of its application are as diverse as the stock market, ant colonies, epidemics, and the spread of business innovations. The focus in this article is on modeling social systems rather than physical or biological phenomena. [End Page 63]The mimetic theory developed by René Girard fits well with a systems perspective, as it has specific ideas about the drivers of human action (at the micro level) and cultural processes (at the macro level). The relationship has been explored earlier in several books and articles;3 in particular, in the work of the Centre de Recherche en Epistémologie Appliquée (CREA) in Paris. The systems perspective received a new stimulus in the 1990s in the form of complex adaptive systems (CAS),4 not least because of the agent-based computer simulations adopted at that time. The objective of this article is to introduce a special version of CAS, called complex mimetic systems (CMS), which builds on mimetic theory. The purpose of this article is twofold. On the one hand, the phrasing of mimetic theory in terms of CMS poses an interesting challenge to the theory to formalize its concepts and explicate possible limitations. On the other hand, CMS might be a useful contribution to the CAS field, as it incorporates concepts such as “social influence” that are very basic to but typically not spelled out in current CAS work.The structure of this article is as follows. In section 2, I briefly review the CAS literature and introduce the idea of complex mimetic systems. Section 3 describes a straw-man agent architecture for CMS, whereas in section 4, I move to the macro level and formalize the culture reproduction cycle. To illustrate the applicability of the CMS framework, I discuss in section 5 Ingo Piepers’s recent CAS analysis of the European international system in the period 1490–1945, and comment on it from a CMS perspective.2. Complex Mimetic SystemsThe characteristic features of complex systems are as follows:• Nonlinear effects: a small perturbation may have a large effect.• Feedback loops: the effects of an element’s behavior are fed back to it in some way. The feedback can be positive (amplification, runaway) or negative (damping).• Openness: a typical complex system interacts with its environment.• Memory: the history of a complex system may be important. Prior states may have an influence on present states.• Nesting, hierarchy: a complex system may itself be an element of a larger complex system. For example, clans in a tribal society, nation-states in an international system, or divisions in a company. [End Page 64]• Topology: the interactions of the elements are enabled and constrained by the network, or grid, of relationships between them.Complex Adaptive SystemsComplex adaptive systems (CAS) are a modern variant of complex systems theory. The elements of a complex adaptive system are called agents, as CAS builds on computational research in the field of multiagent systems.5 Although there is not much difference in the overall objectives, the use of agent simulation opens up interesting research opportunities. Let me clarify this by means of an introductory example given by Miller and Page, the standing ovation problem.6Standing ovations, in which waves of audience members stand up to express their particular appreciation of a performance, usually arise and evolve spontaneously. Suppose that we want to model this phenomenon. A starting point could be a simple mathematical model in which we distinguish N people, each receiving a signal... (shrink)

Much of the scientific process involves “selective ignorance”: we include certain aspects of the systems we are considering and ignore others. This is inherent in the models that we utilize as proxies for biological systems. Our goal usually is to isolate components of these systems and consider them at only certain temporal and spatial scales. The scales and questions induce different metrics for what might be considered a “good” model. The study of mathematical and computational models is replete (...) with differing views of the terms verification, validation, corroboration, and so on. I have often argued that criteria for determination of model utility should be established prior to model construction, but this is rarely done in the application of models in biology. The question I address is whether it is feasible to develop a general approach to model evaluation, that includes all the forms of models typically applied in biology—animal and cell/tissue culture ones as well as mathematical and computational ones. (shrink)

In this chapter, we discuss a specific kind of progress that occurs in most branches of economics today: progress involving the repeated use of mathematical models. We adopt a functional account of progress to argue that progress in economics occurs through the use of what we call “common recipes” and model templates for defining and solving problems of relevance for economists. We support our argument by discussing the case of 20th century business cycle research. By presenting (...) this case study in detail, we show how model templates are not only reapplied to different phenomena. We also show how scientists first develop them and how, once they are considered less useful, they are replaced with new ones. Finally, our case also illustrates that it is not only the mathematical structure that is reused but that such reuse also requires a shared conceptual vision of the core properties of the phenomenon to be studied. If that vision is no longer shared among economists, a model template can become useless and has to be replaced, sometimes against resistance, with a different one. (shrink)

In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of differentiability assumptions and the application of (...) the methods of differential topology to the study of the equilibrium equation. Balasko's rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium's evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern" developments of the Arrow-Debreu model improve our understanding of modern market economies. (shrink)

The Erasmus + Play4Guidance project introduces an online business game, designed to help teach entrepreneurial, transversal and mathematical skills using a real-world business environment. This paper explains how the Business Model Canvas strategy tool facilitated student understanding of real life business development prior to playing the game. An initial mapping exercise was conducted to find out if the Business Model Canvas could transform the experience of playing the game by providing an overview (...) of real life business strategy, and explain the crucial role that markets and customers play in business growth. As a result of the mapping exercise a workshop session was developed to ensure that students could enact the real life business scenarios presented in the game. Three different types of videos were produced and integrated into the workshop to demonstrate key entrepreneurial competencies and graphically illustrate the nine key building blocks of the BMC. Survey responses from a student cohort evidenced that the workshop was central in helping them to understand real life business strategy prior to playing the game. (shrink)