Reverse Mathematics (RM) is a program in the foundations of mathematics where the aim is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. Generally, the minimal axioms are equivalent to the theorem at hand, assuming a weak logical system called the base theory. Moreover, many theorems are either provable in the base theory or equivalent to one of four logical systems, together called the Big Five. For instance, the Weierstrass approximation theorem, i.e., that (...) a continuous function can be approximated uniformly by a sequence of polynomials, has been classified in RM as being equivalent to weak König’s lemma, the second Big Five system. In this paper, we study approximation theorems for discontinuous functions via Bernstein polynomials from the literature. We obtain many equivalences between the latter and weak König’s lemma. We also show that slight variations of these approximation theorems fall far outside of the Big Five but fit in the recently developed RM of new ‘big’ systems, namely the uncountability of ${\mathbb R}$, the enumeration principle for countable sets, the pigeon-hole principle for measure, and the Baire category theorem. (shrink)

SummaryDate from the Census Fertility Reports are used to investigate social and regional variations in family size in the Republic of Ireland. Although Ireland is noted for its high level of fertility, average family size declined by approximately 10% between 1946 and 1971. There are distinct socioeconomic variations in family size in that Roman Catholic family size is greater than that of non-Catholics and the middle classes have the smallest families within each of the religious groups. There are also marked (...) regional differences in family size. In 1946, there was a clear division between the west coast counties with the largest families and the east coast conties with the smaller families. By 1961 and 1971 this pattern had become less clearly demarcated and areas with relatively large families were found in most parts of the country. It is suggested that regional variations in family size can be influenced by a variety of factors, such as differences in religious affiliation, occupation, infant mortality and the degree of selection through emigration. Of these factors, it is found that in both 1946 and 1971 variations in occupation were most strongly related to family size and it appears that economic and occupation changes within Ireland have brought about the changing regional pattern of family size. (shrink)

Resumen: En este trabajo, se observa la variación fonética del fonema oclusivo bilabial sonoro en el español no estándar en una muestra de hablantes chilenos de ocho ciudades, cuyas ubicaciones geográficas permiten cubrir los principales sectores urbanos del país. En los resultados se evidencia un marcado uso del alófono aproximante labiodental sonoro en este tipo de habla y un comportamiento relativamente homogéneo en todo el país respecto de las principales variantes del fonema oclusivo bilabial sonoro. La comparación del fonema oclusivo (...) bilabial sonoro entre el español no estándar y el estándar muestra marcadas diferencias, datos que sugieren un cambio lingüístico en proceso desde el alófono aproximante bilabial sonoro al alófono aproximante labiodental sonoro.: In this study, we observed the phonetic variation of voiced bilabial occlusive phoneme in non-standard Spanish in a sample of Chilean speakers from cities whose geographical locations allow to cover the main urban sectors of the country. The results that show a marked use of voiced labiodental approximant allophone in this type of speech an a relatively homogenous behaviour in the whole country of the main variants of the voiced bilabial occlusive phoneme are presented. The comparison of voiced bilabial occlusive phoneme between non-standard and standard Spanish shows clear differences, data that suggest a linguistic change in process from voiced bilabial approximant allophone to voiced labiodental approximant allophone. (shrink)

We study some variations of the so-called Hardy hierarchy of quickly growing functions, known from the literature, and obtain analogues of Ratajczyk's approximation lemma for them.

In this analysis, we develop a new approach to investigate the semianalytical solution of the delay differential equations. Mohand transform coupled with the homotopy perturbation method is called Mohand homotopy perturbation transform method and performs the solution results in the form of series. The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as (...) in the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. Some illustrated examples are interpreted to confirm the accuracy of the newly developed scheme. (shrink)

Traditionally, epistemologists have held that only truth-related factors matter in the question of whether a subject can be said to know a proposition. Various philosophers have recently departed from this doctrine by claiming that the answer to this question also depends on practical concerns. They take this move to be warranted by the fact that people’s knowledge attributions appear sensitive to contextual variation, in particular variation due to differing stakes. This paper proposes an alternative explanation of the aforementioned fact, one (...) that allows us to stick to the orthodoxy. The alternative applies the conceptual spaces approach to the concept of knowledge. With knowledge conceived of spatially, the variability in knowledge attributions follows from recent work on identity, according to which our standards for judging things (including concepts) to be identical are context-dependent. On the proposal to be made, it depends on what is at stake in a context whether it is worth distinguishing between knowing and being at least close to knowing. (shrink)

The Spanish approximators como and como que serve multiple pragmatic functions. They can be employed in similar contexts to express vagueness when speakers experience uncertainty or to hedge and avoid being straightforward. Furthermore, these forms can alternate according to context since they represent two ways of saying the same thing. This study investigated the use of como and como que in two speech events: narratives of personal experience and therapeutic interviews, which were generated by Spanish speakers of several varieties, educational (...) levels, and lengths of residence in the United States. The study was informed by the theoretical frameworks of sociolinguistic and pragmatic variation, and the data were analyzed using quantitative and qualitative approaches. The findings revealed that while como was the preferred form among the speakers of the study they employed como que more often in the therapeutic interviews. Thus, both discourse and the pragmatic functions conditioned the use of these approximators. (shrink)

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to (...) the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

We start with a nearly arbitrary standard classical first order "language" $C\sb{o},$ which is expanded to $C\sb{M,T}$ = "$C\sb{o}+M+T$", where for any variable x, M and T are unary formulas. We start also with a model ${\cal T}\sb{o},$ which together with $C\sb{o}$ represents a fixed non-problematic interpreted first order language. For each $\mu,\tau\subseteq U\sb{o},$ the universe of discourse for ${\cal T}\sb{o},$ the model ${\cal T}\sb{\mu,\tau}$ over $C\sb{M,T}$ is given so that its reduct to $C\sb{o}$ is just ${\cal T}\sb{o},$ and so (...) that for any $C\sb{M,T}$-variable x, the set-extensions of M and T are $\mu$ and $\tau$ respectively. For each $C\sb{M,T}$-expression e, $\vec e$ is its distinctly chosen representative in $U\sb{o},$ and $\lbrack\!\lbrack e\rbrack\!\rbrack$ is a constant $C\sb{o}$-term which names $\vec e.$ ;The goal is to find $\mu\sb*$ and $\tau\sb*,$ such that $\mu\sb*$ and $\tau\sb*$ plausibly and "self-referentially" approximate meaningfulness and truth respectively for any interpreted language represented by ${\cal T}\sb{\mu\sb*,\tau\sb*},$ by satisfying at least the following conditions. ; $\tau\sb*\subseteq\mu\sb*,$ and for each $C\sb{M,T}$-sentence $\sigma$ such that ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack\sigma\rbrack\!\rbrack,$ $$\eqalign{&\ {\cal T}\sb{\mu\sb*,\tau\sb*} \models\sigma\Longleftrightarrow{\cal T}\sb{\mu\sb*,\tau\sb*}\models T\lbrack\!\lbrack\sigma\rbrack\!\rbrack,\ {\rm and}\cr&\ {\cal T}\sb{\mu\sb*,\tau\sb*}\models T\lbrack\!\lbrack\sigma\\leftrightarrow T\lbrack\!\lbrack\sigma\rbrack\!\rbrack\rbrack\!\rbrack.\cr}$$ ; There is a class of expression representatives $\mu\sp{D}\subseteq\mu\sb*$ containing every $C\sb{o}$-expression representative, such that the set $\tau\sp{D}=\mu\sp{D}\ \cap\ \tau\sb*$ itself satisfies the following properties. ;First, for each $\vec\sigma$ such that $\sigma$ is a $C\sb{M,T}$-sentence, if for all $\mu,\tau\subseteq U\sb{o}$ satisfying $\mu\supseteq\mu\sb*$ and $\tau\supseteq\tau\sp{D},$ it is the case that ${\cal T}\sb{\mu,\tau}\models\sigma,$ then $\vec\sigma\in\tau\sp{D}.$ ;Second, whenever $\vec\sigma\in\tau\sp{D},$ then also $\sp{\vec{\enspace}}\ \in\tau\sp{D}.$ ;Third, $\tau\sp{D}$ is "upwardly closed" with respect to the strong-Kleene rules for the truth-value evaluation of Boolean combinations of formulas. For example, for $C\sb{M,T}$-sentences $e\sb1$ and $e\sb2$: $$\eqalign{&\ \vec e\sb1\in\tau\sp{D}\Longleftrightarrow)\sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr&\ {\rm If}\ \vec e\sb1\in\tau\sp{D}\ {\rm or}\ \vec e\sb2\in\tau\sp{D},\ {\rm then\ so\ is}\ \sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr&\ {\rm If}\ \sp{\vec{\enspace}}\ \in\tau\sp{D}\ {\rm and}\ \sp{\vec{\enspace}}\ \in\tau\sp{D},\ {\rm then}\ )\sp{\vec{\enspace}}\ \in\tau\sp{D}.\cr}$$ ; For each $C\sb{M,T}$-expression e not involving T, ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack e\rbrack\!\rbrack$; in particular, for any $C\sb{M,T}$-expression e whatsoever, ${\cal T}\sb{\mu\sb*,\tau\sb*}\models M\lbrack\!\lbrack\\neg M\lbrack\!\lbrack e\rbrack\!\rbrack\rbrack\!\rbrack.$ ; ;In this dissertation, it is shown for the first time that there are in fact $\mu\sb*$ and $\tau\sb*$ which simultaneously satisfy all three conditions , , and , even when the consequent of the Godel fixed point theorem must hold. (shrink)

The evolution of the history of physics shows how natural phenomena can be grouped into discrete regimes, between which there are precise relationships and specific connecting elements but which, with an excellent approximation, can be considered independent of each other. Here it is clarified, in the light of developments in contemporary physics, in what sense theory of everything means "theory that aims to explain a specific and limited level of energy", highlighting the link between the world we experience daily (...) and the background of the theories of everything. Keywords: theories of everything; quantum gravity; principle of collective organization Sunto L’evoluzione della storia della fisica mostra come i fenomeni naturali possono essere raggruppati in regimi discreti, tra cui esistono precise relazioni e specifici elementi di raccordo ma che, con un’ottima approssimazione, si possono considerare indipendenti l’uno dall’altro. Qui si chiarisce, alla luce degli sviluppi della fisica contemporanea, in che senso teoria del tutto significa “teoria che si propone di spiegare un livello di energia specifico e limitato”, evidenziando il legame tra il mondo che sperimentiamo quotidianamente e il background delle teorie del tutto. Parole Chiave: teorie del tutto; gravità quantistica; principio di organizzazione collettiva. (shrink)

Hidden Markov models (HMMs) have been successful for modelling the dynamics of carefully dictated speech, but their performance degrades severely when used to model conversational speech. Since speech is produced by a system of loosely coupled articulators, stochastic models explicitly representing this parallelism may have advantages for automatic speech recognition (ASR), particularly when trying to model the phonological effects inherent in casual spontaneous speech. This paper presents a preliminary feasibility study of one such model class: loosely coupled HMMs. Exact model (...) estimation and decoding is potentially expensive, so possible approximate algorithms are also discussed. Comparison of one particular loosely coupled model on an isolated word task suggests loosely coupled HMMs merit further investigation. An approximate algorithm giving performance which is almost always statistically indistinguishable from the exact algorithm is also identified, making more extensive research computationally feasible. (shrink)

The present article intends at shedding some light on how Voltaire's Candide enacts its criticism of the Leibnizian system. In order to do that, we shall follow different paths. Firstly, we will consider a brief history of the problem of evil, especially the Bayle and Leibniz debate on it. Secondly, we shall briefly refer to Voltaire's metaphysics of evil. The almost forty years he dedicated to the question are not monotonous, they are constituted of variations, approximations and criticisms on both (...) Alexander Pope and Leibniz. Thirdly, we shall consider some examples of caricatures of Leibniz's philosophy in Candide in order to show that they bear real criticism on the philosophical optimism. (shrink)

Compound Gauss-Markov random field model is one of Markov random field models for natural image restorations. An optimization algorithm was constructed by means of mean-field approximation, which is a familiar techniques for analyzing massive probabilistic models approximately in the statistical mechanics. Cluster variation method was proposed as an extended version of the mean-field approximation in the statistical mechanics. Though the mean-field approximation treat only the marginal probability distribution for every single pixel, the cluster variation method can take (...) acount into the correlation between pixels by treating the marginal probability distribution for every nearest neighbor pair of pixels. In this paper, we propose a newstatistical-mechanical iterative algorithm by means of the cluster variation method for natural image restorations in the compound Gauss-Markov random field model. In some numerical experiments, it is investigate howthe proposed algorithm improves the quality of restored images by comparing it with the algorithm constructed from the mean-field approximation. (shrink)

Teleological variations of non-deterministic processes are defined. The immediate past of a system defines the state from which the ordinary (non-teleological) dynamical law governing the system derives different possible present states. For every possible present state, again a number of possible states for the next time step can be defined, and so on. After k time steps, a selection criterion is applied. The present state leading to the selected state after k time steps is taken to be the effective present (...) state. Hence, the present state of a system is defined by its past in the sense that the past determines the possible states that are to be considered, and by its future in the sense that the selection of a possible future state determines the effective present state. A system that obeys this type of teleological dynamics may have significantly better performance than its non-teleological counterpart. The basic reason is that evolutions that are less optimal for the present time step, but which lead to a higher optimality after k time steps, may be preferred. This abstract concept of teleology is implemented for two concrete systems. First, it is applied to a general method for function approximation and classification problems. The method at issue treats all problems handled by conventional connectionism, and is suited for information with inner structure also. Second, it is applied to a dynamics in which forms of maximal homogeneity have to be produced. The relevance of the latter dynamics for generative art is illustrated. The teleology is `deep' in the sense that it is situated at the cellular level, in contradistinction with the teleology that is usually met in cognitive contexts, and which refers to macroscopic processes such as making plans. It is conjectured that deep level teleology is useful for machines, even though the issue if natural systems use this teleology is left open. (shrink)

We present a neuro-geometrical model for generating the shape of Kanizsa's modal subjective contours which is based on the functional architecture of the primary areas of the visual cortex. We focus on V1 and its pinwheel structure and model it as a discrete approximation of a continuous fibration π: R × P → P with base space the space of the retina R and fiber the projective line P of the orientations of the plane. The horizontal cortico-cortical connections of (...) V1 implement what the geometers call the contact structure of the fibration π, and defines therefore an integrability condition which can be shown to correspond to Field's, Hayes', and Hess' psychophysical concept of association field. We present then a variational model of curved modal illusory contours based on the idea that virtual contours are “geodetic” integral curves of the contact structure. (shrink)

Variations in life history define key comparative and evolutionary biological questions, important for understanding the mechanisms of mammalian evolutionary divergence, developmental adaptability and plasticity. In this regard, the differences among predominantly altricial and precocial species represent a particularly significant, if still poorly understood and contested case. Here, it will be shown how the classical analysis of such ontogenetic variations, going back to the semantic biology of A. Portmann, can be expanded and synthesized with comparative physiological approaches, based on the negentropic (...) theory of ontogeny by I. A. Arshavsky and his school. In this little received but pioneering tradition, extensive comparative and experimental investigations were carried out on the role of musculoskeletal systems and stressors in driving life history variations, particularly in the altricial-precocial spectrum. As shown by Arshavsky and co-workers, by focusing on general allometric regularities, the approximations based on the classical energy rules of surface and mass offer valuable benchmarks, but also predictions that are frequently violated by the variability of physiological and metabolic scaling relationships among altricials and precocials, and thus, a complex and historical approach is needed to describe their local physiological mechanisms and systemic regularities. This paper shows how Arshavsky’s findings and framework can play an integrative role in this context, potentially helping to bridge the mainly descriptive approach of semantic morphology, as developed by Portmann’s school, with the more functional explanations predominating current ecology and life history theory. These problems can be important for biosemiotics by highlighting the contingent, activity-dependent, and surplus anabolic stress mechanisms underlying diversification in eutherian developmental systems and possibly, the epigenetic evolution of pace-of-life syndromes. (shrink)

Here, in our approximation of polaron theory, we examine the importance of introducing theT product, which turn out to be a very convenient theoretical approach for the calculation of thermodynamical averages.We focus attention on the investigation of the so-called linear polaron Hamiltonian and present in detail the calculation of the correlation function, spectral function, and Green function for such a linear system.It is shown that the linear polaron Hamiltonian provides an exactly solvable model of our system, and the result (...) obtained with this approach holds true for an arbitrary coupling constant which describes the strength of interaction between the electron and the lattice vibrations. Then, with the help of a variational technique, we show the possibility of reducing the real polaron Hamiltonian to a socalled trial or approximate linear model Hamiltonian.We also consider the exact calculation of free energy with a special technique that reduces calculations with the help of the T product, which, in our opinion, works much better and is easier than other analogous considerations, for example, the path-integral or Feynman-integral method.(1,2)Here we furthermore recall our own work,(4) where it was shown that the results of Refs. 7 and 8 concerning the impedance calculation in the polaron model may be obtained directly without the use of the path-integral method.The study of the polaron system's thermodynamics is carried out by us in the framework of the functional method. A calculation of the free energy and the momentum distribution function is proposed.Note also that the polaron systems with strong coupling(9) proved to be useful in different quantum field models in connection with the construction of dynamical models of composite particles. A rigorous solution of the special strong-coupling polaron problem, describing the interaction of a nonrelativistic particle with a quantum field, was given by Bogolubov.(3) The works of Tavkhelidze, Fedyanin, Khrustalev, and others(10–13) are dedicated to the further development and generalization of the Bogolubov method.Notice, too, that the electron-photon interaction effects play an important part in many problems of modern solid state theory (see, e.g., Refs. 7 and 14–19).The present paper summarizes a set of lectures delivered as a special course in the physics department of Moscow State University. (shrink)

In the first section, I consider what several logicians say informally about the notion of logical consequence. There is significant variation among these accounts, they are sometimes poorly explained, and some of them are clearly at odds with the usual technical definition. In the second section, I first argue that a certain kind of informal account—one that includes elements of necessity, generality, and apriority—is approximately correct. Next I refine this account and consider several important questions about it, including the appropriate (...) characterization of necessity, the criterion for selecting logical constants, and the exact role of apriority. I argue, among other things, that there is no need to recognize a special logical sense of necessity and that the selection of terms to serve as logical constants is ultimately a pragmatic matter. In the third section, I consider whether the informal account I have presented and defended is adequately represented by the usual technical definition. I show that it is, and provably so, for certain limited ways of selecting logical constants. In the general case, however, there seems to be no way to be sure that the technical and informal accounts coincide. (shrink)

The basic idea of his Origin of Species is that in nature there is a process similar to what goes on in the breeding of domestic plants and animals. If a breeder wants to produce a variety with certain characteristics, he/she keeps an eye out for individuals that have some approximation to those characteristics and breeds from them and not from individuals that do not have something like the desired characteristics. The other individuals may be destroyed, or they may (...) just be segregated; at any rate they are not allowed to breed with the selected stock. The breeder follows this policy also with the second generation of the offspring of the selected individuals of the first generation; those that after all do not have the desired characteristics are rejected, those that do are selected to produce the third generation, and so on. The whole process presupposes some degree of variability within the plant or animal being bred from. There have to be spontaneously produced individuals with something like the desired characteristics for the breeder to select. What can be accomplished by selection breeding depends of the range of variation that occurs spontaneously. (Hence the topic of Darwin's book of 1868, Variation of Plants and Animals under Domestication.) See in the Readings book the picture of the different breeds of pigeons from the Illustrated London News, 1864; Darwin was a pigeon fancier. (shrink)

Deterministic models in population dynamics often are really approximations to stochastic models, justified by an appeal to the law of large numbers. It is proposed to call such models pseudodeterministic. Four questions are discussed in this article: (1) What errors may be made by equating deterministically predicted values to expectations? (2) When, and in what sense, may numbers be assumed to be large? (3) How large are the variances, coefficients of variations, etc., as assigned to the variables in the stochastic (...) versions of the models? (4) What role may pseudodeterministic models play in empirical research, where problems of statistical reliability arise?As an example, a modified Nicholson-Bailey model of the interaction between insect parasitoids and their hosts is discussed; the modification consists of assigning a random (density-independent) mortality to the parasitoid population. A stochastic version of this model is discussed. The expectation of the final host density is compared with the value computed from the deterministic model. The latter value is systematically lower than the former. The magnitude of the difference depends on parameter values. The variability to be expected with the stochastic model is characterized by the coefficient of variation of the final host density; its dependence on parameter values and initial conditions is discussed. It is concluded that it is worthwhile in practical applications to estimate parasitoid mortality, and that the coefficient of variation in real situations may be far from negligible. (shrink)

Both biologists and philosophers often make use of simple verbal formulations of necessary and sufficient conditions for evolution by natural selection (ENS). Such summaries go back to Darwin's Origin of Species (especially the "Recapitulation"), but recent ones are more compact.1 Perhaps the most commonly cited formulation is due to Lewontin.2 These summaries tend to have three or four conditions, where the core requirement is a combination of variation, heredity, and fitness differences. The summaries are employed in several ways. First, they (...) are often used in pedagogical contexts, and in showing the coherence of evolutionary theory in response to attacks from outside biology. Second, they are important in discussions of extensions of evolutionary principles to new domains, such as cultural change. The summaries also have intrinsic scientific and philosophical interest as attempts to capture some core principles of evolutionary theory in a highly concise way. Despite their prominence, both the proper formulation and status of these summaries are unclear. Standard formulations are subject to counterexamples, and their relations to formal models of evolutionary change are not straightforward. Here I look closely at these verbal summaries, and at how they relate to formal models. Are the summaries merely rough approximations that have no theoretical role of their own? Perhaps they could operate as theoretical statements in Darwin's time, but have now been superseded by more exact treatments. (shrink)

Weaver birds create intricate nests; sculptors and other artists and artisans also create intricate, ingenious constructions out of similar materials. The products may look similar, and outwardly the creative processes that create those processes may look similar, but there are surely large and important differences between them. What are they, and how important are they? The weaverbird nestmaking is ‘instinctual,’ and ‘controlled by the genes’ some would say, but we know that this is a crude approximation of a more (...) interesting truth, involving an intricate interplay between genetic variation, long-term developmental and environmental interaction and short-term environmental variation–in opportunities and materials accessible at the time of nest building. And on the side of the human creator, a similarly complex story must be told. Genes play some role surely (think of the likelihood of heritable differences in musical aptitude, for instance), but so do both long-term and short-term environmental interactions. The myth of the artist “blessed†by a spark of ‘divine genius’ is even cruder and more distorted than the myth of the birdnest as a simple product of a gene–as if it were a protein.                Our thinking about human creativity is pulled out of shape somewhat by a famous contrast introduced to the world by Darwin. One of his earliest–and most outraged–critics summed it up vividly:   In the theory with which we have to deal, Absolute Ignorance is the artificer; so that we may enunciate as the fundamental principle of the whole system, that, IN ORDER TO MAKE A PERFECT AND BEAUTIFUL MACHINE, IT IS NOT REQUISITE TO KNOW HOW TO MAKE IT. This proposition will be found, on careful examination, to express, in condensed form, the essential purport of the Theory, and to express in a few words all Mr. Darwin's meaning; who, by a strange inversion of reasoning, seems to think Absolute Ignorance fully qualified to take the place of Absolute Wisdom in all the achievements of creative skill.. (shrink)

The transitions between turns at talk in conversation tend to occur quickly, with only a slight gap of approximately 100 to 300 ms between them. This estimate of central tendency, however, hides a wealth of complex variation, as a number of factors, such as the type of turns involved, have been shown to influence the timing of turn transitions. This article considers one specific type of turn that does not conform to the statistical trend, namely turns that deal with troubles (...) of speaking, hearing, and understanding, known as other-initiations of repair. The results of a quantitative analysis of 169 other-initiations of repair in face-to-face conversation reveal that the most frequent cases occur after gaps of approximately 700 ms. Furthermore, other-initiations of repair that locate a source of trouble in a prior turn specifically tend to occur after shorter gaps than those that do not, and those that correct errors in a prior turn, while rare, tend to occur without delay. An analysis of the transitions before other-initiations of repair, using methods of conversation analysis, suggests that speakers use the extra time (i) to search for a late recognition of the problematic turn, (ii) to provide an opportunity for the speaker of the problematic turn to resolve the trouble independently, (iii) and to produce visual signals, such as facial gestures. In light of these results, it is argued that other-initiations of repair take priority over other turns at talk in conversation and therefore are not subject to the same rules and constraints that motivate fast turn transitions in general. (shrink)

In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski :559–582, 2016) and Gładziejewski and Miłkowski, to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing that it (...) is consistent with approaches implicit in theories of unsupervised learning in neural networks. In the course of this discussion, we argue that the structural representation proposal, properly understood, has more in common with functional-role than with causal/informational or teleosemantic theories. In the remainder of the paper, we describe the PEM framework for approximate Bayesian inference in some detail, and discuss how structural representations might arise within the proposed Bayesian hierarchies. After explicating the notion of variational inference, we define a subjectively accessible measure of misrepresentation for hierarchical Bayesian networks by appeal to the Kullbach–Leibler divergence between posterior generative and approximate recognition densities, and discuss a related measure of objective misrepresentation in terms of correspondence with the facts. (shrink)

Background: Ascertaining the relationship between ethical ideology, moral judgment, and ethical decision among academic nurse educators at work appears to be a challenge particularly in situations when they are faced with a need to solve an ethical problem and make a moral decision. Purpose: This study aims to investigate the relationship between ethical ideology, moral judgment, and ethical decision as perceived by academic nurse educators. Methods: A descriptive correlational research design was conducted at Faculty of Nursing, Alexandria University. All academic (...) nurse educators were included in the study (N = 220). Ethical Position Questionnaire and Questionnaire of Moral Judgment and Ethical Decisions were proved reliable to measure study variables. Ethical considerations: Approval was obtained from Ethics Committee at Faculty of Nursing, Alexandria University. Privacy and confidentiality of data were maintained and assured by obtaining subjects’ informed consent. Findings: This study reveals a significant positive moderate correlation between idealism construct of ethical ideology and moral judgment in terms of recognition of the behavior as an ethical issue and the magnitude of emotional consequences of the ethical situation (p < 0.001; p = 0.031) respectively. Also, there is a positive significant moderate correlation between relativism construct of ethical ideology and overall moral judgment (p = 0.010). Approximately 3.5% of the explained variance of overall moral judgment is predicted by idealism together with relativism. Discussion: The findings suggest that variations in ethical position and ideology are associated with moral judgment and ethical decision. Conclusion: Organizations of academic nursing education should provide a supportive work environment to help their academic staff to develop their self-awareness and knowledge of their ethical position and promoting their ethical ideologies and, in turn, enhance their moral judgment as well as develop ethical reasoning and decision-making capability of nursing students. More emphasis in nursing curricula is needed on ethical concepts for developing nursing competencies. (shrink)

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

According to a classical work on experimental design internal validity “refers to the approximate validity with which we infer that a relationship between two variables is causal or that the absence of a relationship implies the absence of cause”. External validity “refers to the approximate validity with which we can infer that the presumed causal relationship can be generalized to and across alternate measures of the cause and effect and across different types of persons, settings, and times”. Since then, these (...) have been the accepted definitions, with slight variations, of both concepts. However, there have been deep differences in interpreting the scope and limits of validity concepts in economics. From theory-driven experimental designs that defend the priority of the internal over the external validity to those researches that are demanding the importance of external validity in economics, we can find the most diverse points of view. What can experimental ethics learn, then, from recent debates on external and internal validity in experimental economics? If we want to elicit moral intuitions into the lab, are we testing moral theories that way? Could intuitions be generalized “across different types of persons, settings, and times”? Is that really possible? (shrink)

Models of planetary motion as observed from Earth must account for two principal anomalies: the nonuniform speed of the planet as it circles the zodiac, and the correlation of the planet’s position with the position of the Sun. In the context of the geometrical models used by the Greeks, the practical difficulty is to somehow isolate the motion of the epicycle center on the deferent from the motion of the planet on its epicycle. One way to isolate the motion of (...) the epicycle center is to determine the longitude and time of oppositions of the planet with the mean Sun. A Greek astronomer might have realized that the predictions of mean oppositions by Babylonian models could serve as useful proxies for real empirical observations. It is shown that a Greek astronomer with a reasonable understanding of Babylonian System A models for the outer planets and the Sun–Moon could have used those models to estimate approximate values for the eccentricity e and longitude of apogee A required for geometrical models. The same method would work for the inner planets if conjunctions were observable, but they are not, and the variation of the observable synodic events—first and last morning and evening visibilities—is dominated more by the motion of the planet in latitude than the nonuniform motion of the epicycle center. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:IntroductionF. S. [email protected] and Richard [email protected] state that there are no sound bites or video clips from classical antiquity is to repeat the obvious. But it is a surprise perhaps to realize how seldom we can recall our field’s most influential scholars even of the very recent past through such now commonplace media. Moreover, the chance to view and hear personal reflections articulated by any such figures about their (...) career, influences, and impact is rare indeed. It was precious opportunities of this type that Pat Thane, Alastair Reid, and Michael Thompson had the foresight to capture from the mid-1980s by developing a video Interviews with Historians series between 1985 and 1996.1 The series was produced by the Publications Department of the Institute of Historical Research at the University of London. In each instance (eventually a total of twenty-eight), a leading historian is interviewed—usually in a studio—by a younger colleague in the same field; three cameras are used, one long shot and one close-up of each participant.2The interview with Sir Moses Finley was one of the first two made (in October 1985) and, as it turned out fortuitously, only months before his sudden death in June 1986 at age 74. The interviewer is Keith Hopkins (a youthful 51), Finley’s one-time graduate student, who had himself just become Cambridge’s professor of ancient history, the position that Finley occupied from 1970 to 1979. They talked in the studio for approximately one hour, and Alastair Reid then edited the master tape with notable skill [End Page 167] to shorten the interview to thirty-five minutes; once both participants had given their approval, the interview was released.3 Meantime, the hour-long U-Matic master tape was archived, but otherwise forgotten. Fortunately, however, in response to inquiries made by Richard Talbert during summer 2013, the Institute proved able to retrieve the tape and—despite its fragility and long outmoded format—to arrange for a successful transfer of the interview to DVD by Soho Broadcast, London.4Our original intention was to offer a transcript of the edited thirty-five-minute version,5 but once the hour-long tape surfaced, we decided instead to offer the interview in its entirety. Our transcript (below, p. 179) inevitably has its limitations and can make no claim to substitute for the video itself.6 It cannot reproduce the unfailingly good-humored atmosphere throughout the interview, nor the range of tones and emphases, nor Finley’s New York accent, nor the marked variations in the pace at which he makes his points, nor of course his constant, characteristic gestures. The variations in pace have influenced how we resolved to punctuate some passages, an unavoidably subjective exercise. Above all, however, we have resisted the recurrent temptation to “clean up” the conversation, so that repetitious, inconsequential, and incomplete remarks are eliminated, and readers are left with a text that more readily approximates to standard written prose.7 Au contraire, our transcript consciously aims to preserve the untidiness and immediacy of the interview; in consequence, very little in the way of repetitive and inconsequential remarks has been omitted.The transcript must be approached, therefore, as the opportunity to listen in on a cordial conversation. One might fairly wonder how far Hopkins had settled in advance with Finley the directions that it might take. No more than minimally, we may suspect, beyond their mutual acknowledgment of the general scope and purpose outlined by the series organizers—hence Hopkins’ unfailing deference towards Finley and his [End Page 168] successive cues to advance the conversation instructively. But recalling the stage where Hopkins asks, “How did you come to cross the Atlantic?” and Finley blithely declines to offer more than the briefest response, we can only speculate whether this was a prearranged rejection of a question which it was reasonable for Hopkins to pose but which Finley preferred not to pursue; or whether Hopkins failed to anticipate quite such a rapid, firm rebuff, and so had to introduce a fresh line of questioning sooner than expected. After all, if Finley had opted to take up the... (shrink)

Background: People in both Taiwan and China originally descended from the Han Chinese, but the societies have been separated for approximately 38 years. Due to different political systems, variations exist in healthcare and nursing education systems in Taiwan and China. Objective: The purpose of this study was to examine the professional values of nursing students in Taiwan and China. Design: A cross-sectional design was applied in this study. The Nursing Professional Value Scale–Revised was used to measure the professional values of (...) the students. The questionnaire was distributed to eligible undergraduate students in a classroom setting. Ethical considerations: This study was approved by the Institutional Review Board at the first investigator’s university. Participants were informed that completion and return of the questionnaire was voluntary, and confidentiality was ensured by keeping the responses anonymous. Participants: A convenience sample included 292 Taiwanese students and 654 Chinese students. Findings: A total of 11 individual Nursing Professional Value Scale–Revised items showed significant differences between the two groups. These results reflect the differences in the perceived importance of these items between the groups. There was no significant difference between the two groups in the mean overall scores for the Nursing Professional Value Scale–Revised (p =.766) and three subscales (all p >.05). Conclusion: There are some differences in professional values between nursing students in Taiwan and China. Given the increasingly frequent and close interactions between Taiwan and China and the globalization of nursing, understanding these differences may help nursing educators identify students’ perceptions of their professional values and support the development of strategies to improve weaknesses in professional values. (shrink)

Natural languages vary in their quantity expressions, but the variation seems to be constrained by general properties, so-calleduniversals. Their explanations have been sought among constraints of human cognition, communication, complexity, and pragmatics. In this article, we apply a state-of-the-art language coordination model to the semantic domain of quantities to examine whether two quantity universals—monotonicity and convexity—arise as a result of coordination. Assuming precise number perception by the agents, we evolve communicatively usable quantity terminologies in two separate conditions: a numeric-based condition (...) in which agents communicate about a number of objects and a quotient-based condition in which agents communicate about the proportions. We find out that both universals take off in all conditions but only convexity almost entirely dominates the emergent languages. Additionally, we examine whether the perceptual constraints of the agents can contribute to the further development of universals. We compare the degrees of convexity and monotonicity of languages evolving in populations of agents with precise and approximate number sense. The results suggest that approximate number sense significantly reinforces monotonicity and leads to further enhancement of convexity. Last but not least, we show that the properties of the evolved quantifiers match certain invariance properties from generalized quantifier theory. (shrink)

Music performance anxiety is a commonly present topic among musicians. Most studies on MPA investigated effects of a more general occurrence of MPA on performances. Less is known about individual variations of MPA within a performance, more specifically at the times before, during, and after the performance. This study used a questionnaire to investigate these performance times in order to find out if there occur different types in the variation of the perceived MPA across the performance. The study was performed (...) with 532 musicians; 27% of them being professional orchestra musicians, 45% non-professional orchestra musicians, and 28% non-professional choir singers. The musicians were asked to fill in the Performance-specific Questionnaire for Musicians immediately after a performance. The questionnaire contains three scales regarding symptoms of MPA, functional coping with MPA and performance-related self-efficacy. A cluster analysis was performed on the PQM scales to identify systematic variations. Findings indicate that there are three different types of MPA in the sample studied. Type 1 describes musicians who have few symptoms of MPA throughout the performance, show functional coping with MPA, and have a stable and well-developed self-efficacy. Type 2 describes musicians who begin their performance with rather high symptoms of MPA but can positively reduce these by the end of the performance and show high values in self-efficacy and in functional coping. Type 3 contains musicians who begin their performance with some symptoms of MPA, which increase to the end of the performance. The values of self-efficacy and functional coping in this type are rather low. Of the total sample, half of the musicians were assigned to Type 1 and approximately a quarter each to Type 2 and Type 3. In accordance with the literature, the results confirm the importance of self-efficacy and functional coping for a positive performance experience. (shrink)

The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, (...) e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect, and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra. (shrink)

How do people gather samples of evidence to learn about the world? Adults often prefer to sample evidence from diverse sources—for example, choosing to test a robin and a turkey to find out if something is true of birds in general. Children below age 9, however, often do not consider sample diversity, instead treating non‐diverse samples (e.g., two robins) and diverse samples as equivalently informative. The current study (N = 247) found that this discontinuity stems from developmental changes in standards (...) for evaluating evidence—younger children chose to learn from samples that best approximate idealized views of what category members are supposed to be like (e.g., the fastest cheetahs), with a gradual shift across age toward samples that cover more within‐category variation (e.g., cheetahs of varying speeds). These findings have implications for the relation between conceptual structure and inductive reasoning, and for the mechanisms underlying inductive reasoning more generally. (shrink)

This paper investigates relationships between men’s testosterone and family life in a sample of approximately 350 Jamaican fathers of children 18–24 months of age. The study recognizes the role of testosterone as a proximate mechanism coordinating and reflecting male life history allocations within specific family and cultural contexts. A sample of Jamaican fathers and/or father figures reported to an assessment center for an interview based on a standardized questionnaire and provided a saliva sample for measuring testosterone level. Outcomes measured include (...) subject demographics such as age and relationship status as well as partnership quality and sexuality and paternal attitudes and behavior. The variation in these fathers’ relationship status (e.g., married co-residential fathers, fathers in new non-residential relationships) was not associated with men’s testosterone. Too few stepfathers participated to enable a direct test of the prediction that stepfathers would have higher testosterone than biological fathers, although fathers who reported living with partners’ (but not his own) children did not have higher testosterone than fathers not reporting residing with a non-biological child. Fathers’ relationship quality was negatively related to their testosterone. Measures of paternal attitudes and behavior were not related to fathers’ testosterone. Consistent with previous ethnography, this sample of Jamaican fathers exhibited variable life history profiles, including residential status. We discuss why fathers’ relationship quality was found to be negatively related to their testosterone level, but other predictions were not upheld. (shrink)

BackgroundProfessional guidelines have addressed ethical dilemmas posed by a few types of nontraditional procreative arrangements, but many questions arise regarding how providers view and make decisions about these and other such arrangements.MethodsThirty-seven ART providers and 10 patients were interviewed in-depth for approximately 1 h each. Interviews were systematically analyzed.ResultsProviders faced a range of challenges and ethical dilemmas concerning both the content and the process of decisions about requests for unconventional interfamilial and other reproductive combinations. Providers vary in how they respond (...) — what they decide, who exactly decides, and how — often undergoing complex decision-making processes. These combinations can involve creating or raising the child, and can shift over time — from initial ART treatment through to the child’s birth. Patients’ requests can vary from fully established to mere possibilities. Arrangements may also be unstable, fluid, or unexpected, posing challenges. Difficulties emerge concerning not only familial but social, combinations. These arrangements can involve blurry and confusing roles, questions about the welfare of the unborn child, and unanticipated and unfamiliar questions about how to weigh competing moral and scientific concerns — e.g., the autonomy of the individuals involved, and the potential risks and benefits. Clinicians may feel that these requests do not “smell right”; and at first respond with feelings of “yuck,” and only later, carefully and explicitly consider the ethical principles involved. Proposed arrangements may, for instance, initially be felt to involve consanguineous individuals, but not in fact do so. Obtaining and verifying full and appropriate informed consent can be difficult, given implicit familial and/or cultural expectations and senses of duty. Social attitudes are changing, yet patients’ views of these issues may also vary, based on their cultural backgrounds.ConclusionsThese data, the first to examine how clinicians make decisions about unconventional reproductive arrangements, highlight several critical ethical questions and ambiguities, and variations in clinicians’ responses. While several professional guidelines exist, the current data highlight additional challenges, and have vital implications for improving future guidelines, practice, education and research.Trial registrationNot applicable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Queer Defamiliarisation: Writing, Mattering, Making Strange by Helen PalmerTrevor Norris (bio)Helen Palmer, Queer Defamiliarisation: Writing, Mattering, Making Strange Edinburgh: Edinburgh University Press, 2020, 214 pp. ISBN 978-1-4744-3414-0Helen palmer is senior lecturer in English literature and creative writing at Kingston University in London and the author of Deleuze and Futurism: A Manifesto for Nonsense (2014). Her research examines queer theory, performance, literary modernism, gender, aesthetics, and feminist and Afrofuturist (...) fiction. Queer Defamiliarisation explores these ideas and also includes part of Palmer’s literary creative response to James Joyce. The project here is an inquiry into reading, thinking, writing, and pleasure and considers how language can change us when we experience the relationship between naming and the performance of identity as a material boundary: the places where our bodies, behavior, and language are subject to violence in gendered, sexualized, and racialized forms. Palmer also suggests how our own and others’ experiences of violence might be bound up with an aesthetics of linguistic and formal complexity, and she reimagines the difficulty of naming for violently excluded identities by reviewing a range of complex experimental and avant-garde literary works in which new identities can emerge. Showing us how we might understand the materiality of bodies, sense making, and desire in emancipa-tory ways, Palmer attunes us to a phenomenology of reading in which we [End Page 217] recognize how argument undergoes metamorphosis by always being a hybrid of theory, criticism, cultural history, appropriation, memoir, and experimental form. Palmer’s wide-ranging arguments speak about the porosity and mutual embeddedness of our selves, our language, our bodies and environments, and the queer processes of world creation that act on and emerge from these things. Placing her work with other texts that rethink gender, personhood and ecology through new materialisms is productive, therefore, and readers might find value in looking at Queer Defamiliarisation alongside Donna Haraway’s (2016) Staying with the Trouble, Timothy Morton’s (2019)Humankind, and Rebecca Tamás’s (2020) Strangers inasmuch as they think through the ethics and emergence of relatedness and examine what it means to play, be alongside, care for, and nurture other beings and their worlds. Palmer’s project stays with the kind of “serious and... lively” trouble that allows “unexpected collaborations and combinations, in hot compost piles” (Haraway 2016, 4).The fertile landscape is mapped out in three introductions whose themes are explored in four chapters. Palmer transforms the early-twentieth-century Russian formalist concept of defamiliarization as literary and aesthetic device, the “paradoxical process that... restores sensations to things through a [linguistic] distancing that is also a re-proximation, an approximation, a touching” (9), by reading early- to mid-twentieth-century literary and cultural theorists such as Shklovsky, Brecht, and Jakobson through the ideas of contemporary queer, feminist, and decolonial scholars such as Sara Ahmed, Rosi Braidotti, and Vicki Kirby. She questions how the estrangement of naming operates for those whose bodies are not normatively gendered, racialized, and sexualized in relation to dominant forms of representation and power and explores concerns with and for queer, trans, decolonial, and feminist aesthetics. Throughout, she encourages us to think of the strangeness of language in relation to an ethics and an erotics of radical sympathy with the stranger because it is in the “continuous movement and continual transformation” (13) of naming, and categories of naming, that an emancipatory ethics can be found. This is a timely intervention by Palmer given current anxieties around naming gender and sex, and her argument seeks to move beyond “unhelpful binaries” to acknowledge the “infinite variations and permutations of existence and experience” (14).Palmer productively combines Sara Ahmed’s concept of disorientation from Queer Phenomenology (2006) with the psycholinguistic registers of Jakobson’s “contiguity and displacement” to suggest that queer defamiliarization is a performance of language and naming that “cleaves through and between sameness and difference,” “knocking signifiers loose and ungrounding bodies,” leading to “perceptual shifts and corporeal responses” that can “materially en-gender newness” (Palmer 17). From the start of the section “Spectaxa” (152), Palmer foregrounds the materiality of her text in increasingly modernistic excess to illustrate what we have been reading and... (shrink)

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of (...) polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness. (shrink)

The broad arc of islands north of Australia that extends from Indonesia east towards the central Pacific is home to a set of human populations whose concentration of diversity is unequaled elsewhere. Approximately 20% of the worlds languages are spoken here, and the biological and genetic heterogeneity among the groups is extraordinary. Anthropologist W.W. Howells once declared diversity in the region so Protean as to defy analysis. However, this book can now claim considerable success in describing and understanding the origins (...) of the genetic and linguistic variation there. In order to cut through this biological knot, the authors have applied a comprehensive battery of genetic analyses to an intensively sampled set of populations, and have subjected these and complementary linguistic data to a variety of phylogenetic analyses. This has revealed a number of heretofore unknown ancient Pleistocene genetic variants that are only found in these island populations, and has also identified the genetic footprints of more recent migrants from Southeast Asia who were the ancestors of the Polynesians. The book lays out the very complex structure of the variation within and among the islands in this relatively small region, and a number of explanatory models are tested to see which best account for the observed pattern of genetic variation here. The results suggest that a number of commonly used models of evolutionary divergence are overly simple in their assumptions, and that often human diversity has accumulated in very complex ways. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating level-k, (...) QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

Vague predicates, those that exhibit borderline cases, pose a persistent problem for philosophers and logicians. Although they are ubiquitous in natural language, when used in a logical context, vague predicates lead to contradiction. This paper will address a question that is intimately related to this problem. Given their inherent imprecision, why do vague predicates arise in the first place? I discuss a variation of the signaling game where the state space is treated as contiguous, i.e., endowed with a metric that (...) captures a similarity relation over states. This added structure is manifested in payoffs that reward approximate coordination between sender and receiver as well as perfect coordination. I evolve these games using a variation of Herrnstein reinforcement learning that better reflects the generalizing learning strategies real-world actors use in situations where states of the world are similar. In these simulations, signaling can develop very quickly, and the signals are vague in much the way ordinary language predicates are vague—they each exclusively apply to certain items, but for some transition period both signals apply to varying degrees. Moreover, I show that under certain parameter values, in particular when state spaces are large and time is limited, learning generalization of this sort yields strategies with higher payoffs than standard Herrnstein reinforcement learning. These models may then help explain why the phenomenon of vagueness arises in natural language: the learning strategies that allow actors to quickly and effectively develop signaling conventions in contiguous state spaces make it unavoidable. (shrink)

The following is excerpted from Sean Gurd’s translation of Euripides’ Hippolytus published with Uitgeverij this year. Though he was judged “most tragic” in the generation after his death, though more copies and fragments of his plays have survived than of any other tragedian, and though his Orestes became the most widely performed tragedy in Greco-Roman Antiquity, during his lifetime his success was only moderate, and to him his career may have felt more like a failure. He was regularly selected to (...) have his plays performed in the annual festival of Dionysus at Athens. But the plays were performed in a competition, and in the competitions he lost and lost, winning first place only five times in a career that spanned more than forty years. His corpus reads like the remains of a life spent trying to get a few things right and never being quite satisfied: scenes and schematized combinations of elements recur again and again, each time slightly changed. Hippolytus itself is an example: it contains two scenes in which a sick or dying character lies on a couch or a stretcher and is surrounded by silence and grief; he had experimented with such scenes in Alcestis, and would work with them again in Herakles and Orestes. Nor, judging from appearances, was he immune to the desire to score a hit, or to satisfy the audiences and the judges at the competition. Hippolytus is a rewrite of another Hippolytus, performed several years earlier, which scandalized the audience and certainly did not take first place. In that earlier Hippolytus (called by later writers Hippolytus Veiled), Euripides fashioned a Phaedra who was neither ashamed of loving her stepson nor incapable of taking steps to satisfy her desire. The forwardness of her approach to Hippolytus so outraged him that he covered his head with a robe (hence the play’s later title). Euripides liked to write energetic and self-confident women like this. He staged his Medea in 431, just three years before he revised Hippolytus, and in it the jilted title character murders her children in revenge for Jason’s new marriage to a more politically advantageous wife. Another flop: the play came in third of three. Evidently the judges did not like their women showing agency, especially when the consequences were transgressive. “The ornament of women,” wrote another great Athenian a little earlier, “is silence.”i Euripides’ Medea and his first Phaedra had other decorations. So three years after Medea crashed and burned and some time after the first Hippolytus suffered the same fate, he produced another Hippolytus play with a different setting and story. How could this one not have been a reaction to the failure of the first? “Second thoughts are always better,” he has one of his characters say, as though he were offering an apology for his first thoughts on the same story. In this new version, Phaedra is suicidally ashamed of her love, choosing to die rather than have it discovered, and willing to bring down her beloved Hippolytus in the service of the same end. Now it is Phaedra herself who covers her head in shock and horror at her desire. Only an intermediary, a slave of the house and an old crone with her fingers in all sorts of illicit pots, communicates Phaedra’s secret – against orders – and in consequence brings about the demise of two resolutely moral figures. It worked. For his tale of two well-born nobles with an unswerving commitment to moral action, destroyed by the meddling of a slave (and by the hostility of some particularly uncaring divinities), the judges crowned Euripides winner. It was the first time he had won, after almost thirty years of work. *** What Hippolytus wants more than anything else, as he protests with outrage just before leaving Trozen for the last time, is the benefit of due process – oaths, witnesses, an investigation that would reveal who really lusted after whom. Ironic, given that in the first Hippolytus, as far as we can make out, he did get a trial – but too late, and Theseus’ successful processing of Hippolytus failed to prevent his death. I cannot help hearing in the second Hippolytus’ complaints the anger of his authorial semblable who lost year after year by a process of judging that might have seemed brutal to him. Judges took no cognizance of how he worked, how long or hard or why; they just voted, and Euripides lost. But then I hear, in the fate of the first Hippolytus, an even grimmer commentary. Processed or not, we lose. We run aground. At the very least, this might cast a darker shadow on the business of watching or reading a play: in that twilight, things move too fast to make a fair assessment and, in any case, the reasonably high definition of what you see and hear belies the truth of indistinction, the multiplicities just below the surface. Watching is a constrained activity, a form of captivity, but reading is plastic. This translation was begun to supply the script for an audio version of the play, recorded in the spring of 2012, and here and there it sacrifices literalness for sayability and the voices and passions of the actors on that occasion. But it was finished to be read, and engineered to create a reading caught between the poles of specificity and non-specificity that the play itself conjures and relies on at its generative core. Thus two texts: the one clear, perhaps overprecise, respectably modern in its presentation, and the other ancient, a reasonable approximation of the classical reading process, and indistinct in vital ways. Like early modern dramatic texts, the exact provenance and original function of the scripts that have made it down to us are unknown. We do know that the ultimate survival of Hippolytus was thanks to its wide-spread use as a school text. But its relation to the first performance in 428 BCE is a matter only of speculation. Euripides presumably had a fair copy before production began; it was probably modified during rehearsals. The actors may have had copies, too (probably the young men who served in the chorus did not). The chor?gos, a wealthy Athenian who paid for the production, might have been presented with or just made sure to get his hands on a high-quality text, to commemorate the play’s success. Fans might have been able to buy copies. Any one of these sources might have provided the ultimate progenitor of our text. Several of them might have, in fact, if later editors compared and conflated traditions. The plays toured extensively in the Greek-speaking world, and were restaged as repertoire for centuries afterwards. In the process they were subjected to enough modifications by producers and actors that in the later fourth century the Athenian statesman Lycurgus had a law passed prohibiting performances at Athens from deviating from the official “city” text of the tragedies (which he had commissioned). It is unlikely that the city text was the last word; but it marks an important moment in Athens’ role in their dissemination, since after this the major sites of textual curatorship moved overseas, to Alexandria, Pergamum, Rome, Antioch, Constantinople. Any single text of any single play is thus no more than a moment of clarity and stability, crossed and subtended by multiple vectors of change, including that of textual flux (from Euripides’ first drafts to the latest printed text) and that of Euripides’ life work as a writer, in the light of which the Hippolytus is just one attempt to produce something exactly right, to win the prize or finally satisfy himself or prove to himself that all this longing for perfection was a waste of time. I am intrigued by the possibility that a single text might somehow serve as a lens onto this wider zone of indistinction, representing a small region clearly but nonetheless containing a blurred image of the whole, like a Leibnizian monad. After all, no text is a witness: it is, rather, a perception and a performance, and what every Hippolytus must perform is the awkward overlay of singular and plural, social practise and subliminal drive, that structures the tragedy. Modern critical editions can do this by juxtaposing a (relatively) clean and simple text with a textual apparatus reporting variants and theorizing the relationship between textual instantiations. A translation lacks the resolution to catch the fine variations which feed into the construction of an apparatus. But there are other means to hand. Guessing at the exact words of the original text is always just that – guessing – though Hippolytus is less problematic than plays like Iphigenia at Aulis. But we can make a pretty secure guess at what such a text looked like. Texts read by fifth-century readers were fundamentally different from what is presented in the best medieval MSS and printed in modern publications. The texts of Euripides’ time and for many centuries afterwards did not indicate word division with spaces (or by any other means) and were extremely sparing in punctuation, often avoiding it altogether. There was only one “case” of letters – what we call “capitals.” Musical sections were inscribed as though they were prose, without line endings to reflect their rhythm or their rhetorical structure. There was no indication of the speakers within a dramatic text, either. The earliest surviving dramatic texts, which come from over a century after Euripides’ death and a time which was much more elaborate and precise in its textual culture, indicated speaker-change with a little line or paragraphos below the line and a double-point [:] at its end. This convention almost certainly does not date back to Euripides’ own time; it may not even date to Lycurgus. In any case, such indications were understood to be readers’ marks: they did not have the same authority as the text and they were subject to readers’ revisions. At least ideationally, if not in concrete and distinguishable fact, a dramatic text was understood as containing no indication of speaker-change (and certainly none of who was saying what). The reader had to figure that out for him-/herself. The clear, legible, easy texts we are accustomed to reading are the fabrications of medieval and modern reading cultures. The first text, then, presents the translation as the text would have been in the mid-fourth century, perhaps decades after Euripides’ death. The second text processes Hippolytus, makes sense of it and makes it “readable.” That is: too distinct, dangerously so. It gets in your way, conjures fantoms, tries to make you see. Fragments of the Hippolytus Veiled, otherwise almost entirely lost, are juxtaposed with similar passages in the text – not to suggest a reconstruction, but a dialogue and a complex set of reassessments. I have not tried to represent the full variety of textual variants, but I have signalled where, for one reason or another, the text is soft and different editions propose excisions or changes. The two texts must be read together: you, reader, form the bridge between the distinctly seen and the indistinct invisible. You, in the end, will be its mask. *** illsandhateddiseaseswhatcanidoforyouwhatshouldinotdohereisthelightandthebrightairyoursickbedisnowout s idethehouseyoureverywordwastocomeherebutyouwillrushbacktoyourbedroomagainyoufadequicklyyoudelig htinnothingyoudislikewhatyouhaveyoulovewhatyoudontitsbettertobesickthantendthesickthefirstissimpleto the secondattachesheartspainandhandsworkeveryhumanlifeispainfulthereisnoendtotoildarknesshidesbehindclo udswhateverisdearerthanlifeweproveunhappyloversofwhatshineshereforlackofknowledgeofanotherlifethere isnoproofforthingsbeneaththeearthonlystoriessustainus liftmybodystraightenmyheadthebondsofmylimbsareloosenedtakemyhandsandmypalearmsthishatistooheavy formyheadtoweartakeitoffspreadmyhairovermyshoulders couragechilddonttossandturnsoviolentlyyouwillbearyoursicknessmoreeasilywithpeaceandanoblemindallmort alssuffer aiaiiwanttodrinkpurewaterfromadewyspringiwanttoliebackandrestunderthetreesinsomegrassymeadowchildw hycrydontsaythesethingsnearthecrowdhurlingwordsmountedonmadness sendmetothemountainiwillgototheforestwherebeastkillingdogspressthespotteddeergodsilongtoshouttothedo gstoshootthethessalianjavelinpastmyblondhairtoholdthebarbeddartinmyhandwhythisanxietychildwhatdoyouc areabouthuntingwhydoyoulustforflowingspringstheresahillwithwaterjustnexttothetowerwecangetyouadrinkt h ereartemismistressofthesaltlakeandthecoursethunderingwithhorseshoovesiwishiwereonyourplainsbreakings t uds whythrowthesefrenziedwordsaboutjustnowyouweresettingoutforthemountaintohuntandnowyoulongforhorses onthewavelesssand thesethingsneedanoracletotellwhichgodreinsyouinanddrivesyoufromyoursenseschild whathaveidonehowfarhaveibeendrivenfromgoodthoughtsiwascrazyiwascursedbysomepowerpheupheualasn ursecovermyheadagainimashamedofwhativesaidcovermeatearmovesdownfrommyeyeanditembarrassesm eithurtstostraightenourmindanditisterribletobeinsanebesttodiebeforeyoubecomelucidagain illcoveryoubutwhenwilldeathcovermeimoldivelearnedalotmortalsshoulddrinkoffriendshipmoderatelynotfrom th edeepestmarrowofthesoulamindslovecharmsshouldbeeasytoundoorthrustawayortiemoretightlyitisaverydiffic ultweightforonesoultolaborovertwopeopleasiamwrackedbypainforhertoomuchdisciplinecausesmoreharmthan pleasureandwarswithhealthipraisetoomuchlessthannothinginexcessandthewiseagreewithme *** Scene 1 Enter Phaedra and the Nurse; the former is recumbent on a couch while the latter bustles about her with gestures that might be those of a caregiver or a guard. NURSE Ills and hated diseases! What can I do for you? What should I not do? Here is the light, and the bright air; your sick bed is now outside the house. Your every word was to come here, but you will rush back to your bedroom again. You fade quickly. You delight in nothing. You dislike what you have. You love what you don’t. It’s better to be sick than tend the sick – the first is simple. To the second attaches heart’s pain and hand’s work. Every human life is painful. There is no end to toil. Darkness hides behind clouds whatever is dearer than life. We prove unhappy lovers of what shines here for lack of knowledge of another life. There is no proof for things beneath the earth. Only stories sustain us. PHAEDRA Lift my body, straighten my head: the bonds of my limbs are loosened. Take my hands and my pale arms. This hat is too heavy for my head to wear. Take it off, spread my hair over my shoulders. NURSE Courage, child; don’t toss and turn so violently. You will bear your sickness more easily with peace and a noble mind. All mortals suffer. PHAEDRA Aiai. I want to drink pure water from a dewy spring. I want to lie back and rest under the trees in some grassy meadow. NURSE Child, why cry? Don’t say these things near the crowd, hurling words mounted on madness. PHAEDRA Send me to the mountain. I will go to the forest where beast-killing dogs press the spotted deer. Gods! I long to shout to the dogs, to shoot the Thessalian javelin past my blond hair, to hold the barbed dart in my hand. NURSE Why this anxiety, child? What do you care about hunting? Why do you lust for flowing springs? There’s a hill with water just next to the tower; we can get you a drink there. PHAEDRA Artemis, mistress of the salt lake and the course thundering with horse’s hooves: I wish I were on your plains breaking studs! NURSE Why throw these frenzied words about? Just now you were setting out for the mountain to hunt – and now you long for horses on the waveless sand. These things need an oracle to tell which god reins you in and drives you from your senses, child. PHAEDRA What have I done? How far have I been driven from good thoughts? I was crazy, I was cursed by some power. Pheu pheu. Alas. Nurse, cover my head again. I’m ashamed of what I’ve said. Cover me – a tear moves down from my eye and it embarrasses me. It hurts to straighten your mind and it is terrible to be insane. Best to die before you become lucid again. NURSE I’ll cover you. But when will death cover me? I’m old; I’ve learned a lot. Mortals should drink of friendship moderately, not from the deepest marrow of the soul. A mind’s love-charms should be easy to undo, or thrust away, or tie more tightly. It is a very difficult weight for one soul to labor over two people, as I am wracked by pain for her. Too much discipline causes more harm than pleasure and wars with health. I praise “too much” less than “nothing in excess,” and the wise agree with me. ***. (shrink)

It has been argued within some philosophy of quantum gravity circles that endorsing Lewisian modal metaphysics is incompatible with endorsing the fundamental physical ontology of any quantum gravity theory. Speaking concisely, the unsolvable tension would be between Lewis' metaphysical commitment to the fundamentality of space and time, and the physical lesson of quantum gravity about the disappearance of space and time from the fundamental structure of the world. In this essay I argue against the idea that the tension is unsolvable. (...) The analysis does not apply to quantum gravity in general, but only to the specific perspective delivered by quantum string theory. In the first two sections I describe what I think is the general formal payoff of Lewisian possible worlds semantics, and more importantly the general metaphysical payoff generated by some Lewisian metaphysical applications of that formal framework. Lewisian possible worlds semantics is not among the topics of this essay, still a concise presentation of its basic features is required for a more accurate description of the type of modal metaphysics Lewis delivers by applying that formal machinery. The moral of the story in the first two sections is that an attempt of preserving crucial features of Lewisian modal metaphysics, although endorsing the quantum string theory lesson on spacetime non fundamentality, would be not only possible, but also philosophically worthy in a general sense. Then, section three is divided in three parts. In the first part I summarize some formal tools of the methodology used elsewhere - (Vistarini, Routledge, 2019, chapter 6)- to argue for string theory background independence. More precisely, I briefly re-describe some crucial features of a topological-vector bundle structure there defined on a "space" associated to the theory. Such structure is there shown to carry physical and dynamical information about quantum strings systems supporting the thesis of background independence of quantum strings laws (string theory background independence is not a topic of this essay, and the construction of the full formal structure as well as the full argumentative line can be found in the work cited above). The rationale behind the choice of including these formal tools is explained in the second and third parts of section three: that very same topological-fiber bundle structure associated to string theory, if read differently, is shown to also carry structural properties of the Lewisian metaphysical scheme. More precisely, in the second part of section three I attempt to show that such topological-fiber bundle structure owns a topology which qualifies as a plausible accessibility structure extending the Lewisian similarity accessibility. To avoid confusion, I will denote the extended similarity order with S*, or S*-similarity. The latter has some interesting properties. It is quantitatively describable, and even more interestingly its spectrum of variation is a countable one. Then, insofar Lewisian similarity order can be regained from the S*-similarity, one might say that the latter is a metaphysical accessibility relation underlying the former because "more fundamental". As we will see, the explanation of what "more fundamental" means in this metaphysical context mainly involves the idea that the formal nature of S*-similarity, in particular its property of having a countable spectrum of variation, calibrates a metaphysical similarity that reflects the discreteness of the fundamental quantum nature of reality. The extended modal metaphysics with accessibility structure S*-similarity is informed by quantum string physics. Within the extended scheme, the Lewisian claim "things could have been different in countless ways" (Lewis 1973) is an approximate one because only permitted by ordinary language. As soon as one refines the accessibility structure by using the formal language of quantum string theory, it appears things could have been different in countable ways. But the Lewisian variety of alternative states of affairs can be regained from the underlying countable variety via a specific interpretation of the Humean supervenience thesis, one that changes the metaphysical status of the thesis' content and restricts the thesis' domain of application. Finally, in the third part of section three I attempt to show that the same topological-fiber bundle structure used to extend Lewisian similarity has a bundle component producing the formal scheme for a tentative extension of Lewisian nomological accessibility through the lens of string dualities. This will prove to be a non trivial task, and the Lewisian accessibility structure will be regained from the extended one only partially. Finally, the essay contains two short appendices summarizing two argumentative lines outside the main topic of the essay. They briefly describe different ways in which the non fundamentality of spatiotemporal structures can be found in quantum string theory. These sections can be skipped. Nevertheless, they might contribute to understand more robustly the general view endorsed by this essay, i.e. that there isn't any unsolvable tension between Lewis' commitment to the fundamentality of spatiotemporal relations and quantum gravity's lesson about their non fundamentality. -/- . (shrink)

The large scale, time varying, and diversification of physically coupled networked infrastructures such as power grid and transportation system lead to the complexity of their controller design, implementation, and expansion. For tackling these challenges, we suggest an online distributed reinforcement learning control algorithm with the one-layer neural network for each subsystem or called agents to adapt the variation of the networked infrastructures. Each controller includes a critic network and action network for approximating strategy utility function and desired control law, respectively. (...) For avoiding a large number of trials and improving the stability, the training of action network introduces supervised learning mechanisms into reduction of long-term cost. The stability of the control system with learning algorithm is analyzed; the upper bound of the tracking error and neural network weights are also estimated. The effectiveness of our proposed controller is illustrated in the simulation; the results indicate the stability under communication delay and disturbances as well. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.1 (2002) 173-187 [Access article in PDF] Symposium: On Ken Burns's "Jazz" Jazz After Jazz: Ken Burns and the Construction of Jazz History Theodore Gracyk As all action is by its nature to be figured as extended in breadth and in depth, as well as in length; and so spreads abroad on all hands... so all narrative is, by its nature, of only one dimension; only (...) travels forward towards one, or towards successive points; narrative is linear, action is solid. Alas for our "chains" or chainlets, of "causes and effects." —Thomas Carlyle, "On History," 1830 Jazz and freedom are synonyms. —Mezz Mezzrow I JAZZ, A FILM BY KEN BURNS is a fascinating and monumental achievement. In this essay, I identify and critique some of the project's core assumptions. My principal target is the assumption that a specific essence of jazz underlies most (but not all) of the music that is regularly identified as jazz and that the historical unfolding of this essence is the true subject of a historical investigation of jazz. This assumption accounts for the project's otherwise puzzling suggestion that jazz history ended approximately thirty-five years ago.The most visible element of the historical project is the ten-part, nineteen-hour documentary, Jazz: A Film by Ken Burns. However, the historical project has three other public elements. The first is a book, Jazz: A History of America's Music. 1 Credited to both Geoffrey C. Ward and Ken Burns, the bulk of the book is the film's spoken text, which includes both a unifying narrative and numerous quotations. The book makes it clear that this text is primarily Ward's work. Second, there is a website that makes available extensive transcripts of many of the [End Page 173] seventy-five interviews conducted for use in the film. Third, there is a set of twenty-two compact discs, each giving an overview of an important jazz musician (e.g., one devoted to Count Basie, one devoted to Dizzy Gillespie). Highlights of these discs have, in turn, been assembled into a five-disc box set called Ken Burns Jazz. My aim is to reveal and examine the conceptual scaffolding that supports and organizes this vast, multifaceted project.What is the principal assumption of this historical project? The project consistently emphasizes the music's capacity to give audible embodiment to the idea of American democracy. At the same time, the project is less than forthcoming about the aesthetic assumptions embraced by Ward and Burns. Familiar and predictable arguments are introduced to justify the appellation of "art" and to address the issue of the purported death of jazz in the 1970s. However, these two strands of the larger argument may be at cross-purposes with the principal assumption and the ideology that jointly justify the project's status as jazz history.Let me begin by describing the principal assumption in some detail. While there is no reason to suppose that its source is Ken Burns or his chief collaborator, historian Geoffrey Ward, the following blurb was used to advertise the project: Jazz has been called the purest expression of American democracy; a music built on individualism and compromise, independence and cooperation. Join us for an exploration of jazz, America's greatest cultural achievement. In keeping with this theme, the narration and principal interviewees of the film are positioned to emphasize that jazz is an audible embodiment of the idea of American democracy. Let us call this idea the democracy thesis. It is placed as a frame around the whole film: Wynton Marsalis announces it in the opening minutes of the first episode, and then he reiterates it in fresh words at the end of the last episode. Although it is repeated with numerous variations, the democracy thesis proposes that jazz involves an ideal of democratic America, not the fact of life in America: jazz, Wynton Marsalis assures us, is "a glimpse of what America is going to be when it becomes itself. And this music tells you that it will become itself." 2 Jazz... (shrink)

In this paper, we connected Zeno’s paradoxes and motions with the viscous friction force \. For the progressive version of the dichotomy paradox, if the body speed is constant, the sequences of positions and instants are infinite, but the series of distances and time variations converge to finite values. However, when the body moves with force \, the series of time variations becomes infinite. In this case, the body crosses infinite points, approximating to a final position forever, as the progressive (...) version of the dichotomy paradox describes. The same procedures with constant speed and motion with force \ result in different spatial sequences and the same series for the regressive version of the dichotomy paradox. Nonetheless, the regressive version of the dichotomy paradox does not describe a body that approximates a final position forever. Finally, for the Achilles paradox, we find the positional and temporal sequences of the man and the tortoise at constant speeds. Analogously to the progressive version of the dichotomy paradox, the positional and temporal sequences are infinite, but the spatial and temporal series converge to finite values. If Achilles and the tortoise are identical points that move with force \, and the turtle’s position in function of time presents a temporal advantage, the man and the animal will cross successive infinite places forever, and the quick hero will never overtake the slow reptile, as the paradox described. We conclude that the progressive version of the dichotomy and Achilles paradoxes can describe motions when the force is \. (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)

This study examines linguistic co-occurrence patterns in the discourse of individuals with communication impairments who use augmentative and alternative communication devices in the workplace by comparing them to those of non-AAC users in similar job settings. A typical workweek per focal participant was recorded and transcribed to create a specialized corpus of workplace discourse of approximately 464,000 words at the time of this analysis. A multidimensional analysis of co-occurrence patterns along functional linguistic dimensions, following Biber [Variation across Speech and Writing. (...) Cambridge: Cambridge University Press; Dimensions of Register Variation: A Cross-Linguistic Perspective. Cambridge: Cambridge University Press], reveals differences in the macro discourse characteristics of AAC vis-a-vis non-AAC texts. Results indicate that AAC texts make use of more informational, non-narrative, and explicit textual features of discourse than their non-AAC counterparts. Implications to improve the capabilities of AAC devices to produce speech that matches baseline expectations of co-workers in the workplace are discussed. (shrink)

Each year in the UK there are approximately 250,000 miscarriages, 3,000 stillbirths and 3,000 terminations following a diagnosis of fetal-abnormality. This paper draws from original empirical research into the experience of pregnancy loss and the accompanying decisionmaking processes. A key finding is that there is considerable variation across England in the range of options that are offered for disposal of pregnancy remains and the ways in which information around disposal are communicated. This analysis seeks to outline the key features of (...) what constitutes effective communication in this context, where effective communication is taken to mean that patients are provided with the key information necessary, in an appropriate manner, so that they are fully able to make a decision. A primary source of evidence includes interviews with the bereaved and pregnancy-loss support workers, in order to understand how the options available, and associated necessary procedures, are communicated. In addition, patient information leaflets are also analyzed as they offer an important tool for information delivery at a difficult and emotionally charged time. Following this, an overview is provided of the information that these leaflets should contain, along with guidance on effective presentation of this information. (shrink)