From Nobel Laureate Robert M. Solow comes this second edition of his classic text, Growth Theory, to which he has added six new chapters. The book begins with the author's Nobel Prize Lecture "Growth Theory and After", followed by the six original chapters of the first edition. The author maintains that basic growth theory is still best summarized in these chapters.The publication of the first edition in 1970 coincided with a worldwide productivity slowdown; during that time very little work (...) occurred on growth theory. It wasn't until the 1980s that a surge of new research appeared, including the work of Roemer, Lucas, Grossman/Helpman, Aghion, and Howitt. The second half of the book deals with this relatively recent surge, often referred to as "the new endogenous growth theory." As a bridge to the six new chapters, Solow includes an essay entitled "Intermezzo" in which he discusses this transition. The author recasts his model to help the reader compare the relationships among all models; he deals rather tersely, for reasons explained in the book, with "AK" theory, convergence, and international cross-section studies rather tersely. The author concludes by drawing some lessons from the new growth theory and suggests where gaps may be filled in future research. Although Solow disagrees strongly with much of the recent research, he is quick to acknowledge some of its outstanding contributions.This second edition is essential reading for graduate courses in macroeconomics as well as courses on growth theory at both undergraduate and graduate levels. No other book provides this broad overview of the whole field and its evolution. (shrink)

The truth of it all -- The forward-backward method -- On definitions and mathematical terminology -- Quantifiers I: the construction method -- Quantifiers II: the choose method -- Quantifiers III: specialization -- Quantifiers IV: nested quantifiers -- Nots of nots lead to knots -- The contradiction method -- The contrapositive method -- The uniqueness methods -- Induction -- The either/or methods -- The max/min methods.

The seventeen seminal essays by Robert J. Gordon collected here, including three previously unpublished works, offer sharply etched views on the principal topics of macroeconomics - growth, inflation, and unemployment. The author re-examines their salient points in a uniquely creative, accessible introduction that serves on its own as an introduction to modern macroeconomics. Each of the four parts into which the essays are grouped also offers a new introduction. The papers in Part I explore different key aspects of the history, (...) theory, and measurement of productivity growth. The essays in Part II investigate the sources of business cycles and productivity fluctuations. Those in Part III cover the effects of supply shocks in macroeconomics. The final group presents empirical studies of the dynamics of inflation in the United States. The foreword by Nobel Laureate Robert M. Solow comments on the abiding importance of these essays drawn from 1968 to the present. (shrink)

The field of economics proves to be a matter of metaphor and storytelling - its mathematics is metaphoric and its policy-making is narrative. Economists have begun to realize this and to rethink how they speak. This volume is the result of a conference held at Wellesley College, involving both theoretical and applied economists, that explored the consequences of the rhetoric and the conversation of the field of economics.

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

The technological progress makes great contribution to the rapid economic growth of China during its past three decades of reform and opening up. An empirical analysis conducted over China’s total factor productivity certifies this conclusion but it also reveals that China’s TFP growth rate is not very high. We further explore the various stages of change of China’s total factor productivity and the causes of these changes and finally take an analytical calculation over the present flaws of China’s innovation system (...) and offer some advices. (shrink)

His first point is that knowledge about economic development is very limited. Much of economic growth has to be attributed to the "residual" -- "the measure of our ignorance," as Robert Solow calls it. In the best studied case, the United States, two-thirds of the rise in per capita income falls within this category. Similarly, the Asian NICs provide "no obvious lessons," having followed "varied and ambiguous" paths that surely do not conform to what "current orthodoxy says are (...) the key to growth." Krugman recommends "humility" in the face of the limits of understanding, and caution about "sweeping generalizations.". (shrink)

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...) for t-norms without non-trivial zero divisors, $\neg$ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation. (shrink)

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

We prove a representation theorem for residuated algebras: each residuated algebra is isomorphically embeddable into a powerset residuated algebra. As a consequence, we obtain a completeness theorem for the Generalized Lambek Calculus. We use a Labelled Deductive System which generalizes the one used by Buszkowski [4] and Pankrat'ev [17] in completeness theorems for the Lambek Calculus.

We share Nair-Collins and Joffe's (2023) concern with the accuracy of the “whole brain-death” diagnosis, which fails to take into account current understandings of residual brain function (neurohor...

We introduce a new product bilattice con- struction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lat- tice factors. Finally, we show how (...) to employ our product construction to define first-order definable classes of bi- lattices corresponding to any first-order definable subclass of residuated lattices. (shrink)

The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some (...) parts of the theory of join-completions of residuated \-groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices. (shrink)

We present an algebraic approach to canonical embeddings of arbitrary residuated algebras into powerset residuated algebras. We propose some construction of powerset residuated algebras and prove a representation theorem for symmetric residuated algebras.

This essay reflects on the concept of “hydropower” – the corrosive power of seawater to amalgamate Life and Nonlife in the context of migrant deaths in the waters of the Mediterranean. Through a focus on drowned bodies’ dissolution and eventual sedimentation into their deep-sea surroundings, my approach interrelates the order of biopolitical violence enacted by Europe’s restrictive migration policies and the thick time of the geophysical. The degradation of bodies under the influence of hydropower reveals residual ontologies marked by (...) porousness between embodied forms of Life and their geophysical environments, putting significant pressure on the putatively watertight divide between Life and Nonlife in the Anthropocene. Parsed from the lens of residuality, hydropower reveals humans’ full ontological coincidence with matter writ large, their endurance and solubility in geological life forces, but also the necessity to think agency in terms of human/inhuman continuity in excess of biopower’s regimenting forces. Against the attempted biopolitical suppression of a certain form of humanity, the residual dwelling enacted by hydropower champions the inclusion of new constellations of matter in our political thought processes. (shrink)

Residual categories such as »not elsewhere categorized« densely populate modern information systems. This article roughly categories two types of modern information surveillance and notification systems, statistical and event-based. It examines the nature of residual categories arising from each, and proposes some methodological considerations for how these impact moral order within information infrastructure. The article concludes with comments about how the inclusion of lived experience might ameliorate a sort of moral gridlock often encountered today in large-scale information systems.

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

We present a unified vision of human knowledge, the external world and ourselves in the frame of an overall unity of Everything. Two main sources of knowledge are considered to this goal: an admittedly reductionist version of Modern Science and a few key elements of Oriental Philosophy. Our view is based on an analogy between the fundamental unity of Vedic ontology and the Grand Unification scheme of Particle Physics traced along the evolution of the Universe. Our key statement is that (...) these two sources of knowledge describe the same ontological story of separation, from an original One down to the multiplicity of the phenomenological world. We further substantiate this vision by drawing an analogy between the Residue of the Vedic sacrifice and the post-Big-Bang cosmological Matter-Antimatter Asymmetry. We also discuss a Big-Bang analogy between the postulated field of Inflationary Cosmology (the Inflaton) and the Vedic dissolution-decomposition of the cosmic progenitor Prajapati – whose body, according to Brahmanas texts, provides the material substrate of which the Universe is built. (shrink)

This paper will examine the concepts of integrity and moral residue as they relate to nursing practice in the current health care environment. I will begin with my definition and conception of ethical practice, and, based on that, will go on to argue for the importance of recognizing that nurses often find themselves in the position of compromising their moral integrity in order to maintain their self‐survival in the hospital or health care environment. I will argue that moral integrity is (...) necessary to a moral life, and is relational in nature. When integrity is threatened, the result is moral distress, moral residue, and in some cases, abandonment of the profession. The solution will require more than teaching bioethics to nursing students and nurses. It will require changes in the health care environment, organizational culture and the education of nurses, with an emphasis on building a moral community as an environment in which to practise ethically. (shrink)

A range of current truth-value realist philosophies of mathematics allow one to reduce the Benacerraf Problem to a problem concerning mathematicians' ability to recognize which conceptions of pure mathematical structures are coherent – in a sense which can be cashed out in terms of logical possibility. In this paper I will clarify what it takes to solve this `residual' access problem and then present a framework for solving it.

We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields (and also algebraically closed valued fields). We lay some groundwork for extending these results to a power-bounded T-convex (...) theory. (shrink)

Logics designed to deal with vague statements typically allow algebraic semantics such that propositions are interpreted by elements of residuated lattices. The structure of these algebras is in general still unknown, and in the cases that a detailed description is available, to understand its significance for logics can be difficult. So the question seems interesting under which circumstances residuated lattices arise from simpler algebras in some natural way. A possible construction is described in this paper.Namely, we consider pairs consisting of (...) a Brouwerian algebra and an equivalence relation. The latter is assumed to be in a certain sense compatible with the partial order, with the formation of differences, and with the formation of suprema of pseudoorthogonal elements; we then call it an s-equivalence relation. We consider operations which, under a suitable additional assumption, naturally arise on the quotient set. The result is that the quotient set bears the structure of a residuated lattice. Further postulates lead to dual BL-algebras. In the case that we begin with Boolean algebras instead, we arrive at dual MV-algebras. (shrink)

This article focuses on three scenarios in which residual biological materials are turned into research collections during the procedure of procuring these materials for diagnostic, therapeutic or other non-research purposes. These three scenarios differ from each other primarily because they employ different models of consent: (a) precautionary consent, which may be secured during the collecting procedure; (b) the presumed consent model, which may be applied during the collection of materials; and (c) consent for research use of identifiable human biological (...) materials, which may be skipped entirely. These scenarios offer additional sources of biological samples for research purposes and at the same time seem to offer even more flexibility in terms of stringency of consent as compared with the more traditional models of broad consent in prospective research collections and the waiver of consent in retrospective research. Our discussion leads us to think that precautionary consent is preferable to presumed consent and no consent when handling issues of consent in the use of residual human biological materials for research. However, such precautionary consent should not be construed as blanket, unrestricted consent for any future use. (shrink)

Residual useful lifetime prediction plays a key role of failure prediction and health management in equipment. Aiming at the problems of residual life prediction without comprehensively considering multistage and individual differences in equipment performance degradation at present, we explore a prediction model that can fit the multistage random performance degradation. Degradation modeling is based on the random Wiener process. Moreover, according to the degradation monitoring data of the same batch of equipment, we apply the expectation maximization algorithm to (...) estimate the prior distribution of the model. The real-time remaining life distribution of the equipment is acquired by merging prior information of real-time degradation data and historical degradation monitoring data. The accuracy of the proposed model is demonstrated by analyzing a practical case of metalized film capacitors, and the result shows that a better RUL estimation accuracy can be provided by our model compared with existing models. (shrink)

Patients with severe disorders of consciousness are thought to be unaware of themselves or their environment. However, research suggests that a minority of patients diagnosed as having a disorder of consciousness remain aware. These patients, designated as having “cognitive motor dissociation”, can demonstrate awareness by imagining specific tasks, which generates brain activity detectable via functional neuroimaging. The discovery of consciousness in these patients raises difficult questions about their well-being, and it has been argued that it would be better for these (...) patients if they were allowed to die. Conversely, I argue that CMD patients may have a much higher level of well-being than is generally acknowledged. It is far from clear that their lives are not worth living, because there are still significant gaps in our understanding of how these patients experience the world. I attempt to fill these gaps, by analyzing the neuroscientific research that has taken place with these patients to date. Having generated as comprehensive a picture as possible of the capacities of CMD patients, I examine this picture through the lens of traditional philosophical theories of well-being. I conclude that the presumption that CMD patients do not have lives worth living is not adequately supported. (shrink)

One of the debated issues regarding Residual Normality (RN) is frequency sensitivity in Williams syndrome (WS). We present some data on frequency sensitivity in Hungarian WS subjects. Based on vocabulary measures, we suggest that instead of the across-the-board frequency insensitivity proposed by some, a higher frequency threshold characterizes these subjects’performance. Results from a category fluency task show that whereas frequency sensitivity in WS is in line with controls, error patterns imply a qualitatively distinct, looser categorical organization. Regarding the much-debated (...) issue of morphological overgeneralizations, our data suggest that frequency sensitivity cuts across the divisions proposed by dual-process theories. In general, some of the frequency effects are the same as in typically developing populations, but with a delayed pattern. Frequency may be interpreted as supporting RN, but in WS it operates with higher thresholds that might be a general processing feature of WS individuals. (shrink)

Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the (...) extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. (shrink)

In this arresting book, Wai Chee Dimock takes on the philosophical tradition from Kant to Rawls, challenging its conception of justice as foundational, self-evident, and all-encompassing. The idea of justice is based on the premise that the world can be resolved into commensurate terms: punishment equal to the crime, redress equal to the injury, benefit equal to the desert. Dimock focuses, however, on what remains unexhausted, unrecovered, and noncorresponding in the exercise of justice. To honor these "residues," she turns to (...) literature, which, in its linguistic density, transposes the clean abstractions of law and philosophy into persistent shadows, the abiding presence of the incommensurate. Justice can only be a partial answer to the phenomenon of human conflict. In arguing for justice as an _incomplete_ virtue, Dimock draws upon legal history, political philosophy, linguistics, theology, and feminist theory; she discusses Aristotle and Augustine, Locke and Luther, Marx and Durkheim, Michael Sandel and Carol Gilligan, Noam Chomsky and Mary Ann Glendon. She also examines an unusual configuration of nineteenth-century American authors, pairing figures such as Herman Melville and Rebecca Harding Davis, Walt Whitman and Susan Warner. The result is a book both passionate and scholarly. It invites us to rethink the meanings of literature, law, and philosophy, and to imagine a language of community more supple and more nuanced than the language of justice. (shrink)

In this arresting book, Wai Chee Dimock takes on the philosophical tradition from Kant to Rawls, challenging its conception of justice as foundational, self-evident, and all-encompassing. The idea of justice is based on the premise that the world can be resolved into commensurate terms: punishment equal to the crime, redress equal to the injury, benefit equal to the desert. Dimock focuses, however, on what remains unexhausted, unrecovered, and noncorresponding in the exercise of justice. To honor these "residues," she turns to (...) literature, which, in its linguistic density, transposes the clean abstractions of law and philosophy into persistent shadows, the abiding presence of the incommensurate. Justice can only be a partial answer to the phenomenon of human conflict. In arguing for justice as an _incomplete_ virtue, Dimock draws upon legal history, political philosophy, linguistics, theology, and feminist theory; she discusses Aristotle and Augustine, Locke and Luther, Marx and Durkheim, Michael Sandel and Carol Gilligan, Noam Chomsky and Mary Ann Glendon. She also examines an unusual configuration of nineteenth-century American authors, pairing figures such as Herman Melville and Rebecca Harding Davis, Walt Whitman and Susan Warner. The result is a book both passionate and scholarly. It invites us to rethink the meanings of literature, law, and philosophy, and to imagine a language of community more supple and more nuanced than the language of justice. (shrink)

In response to our target article, many of the commentators concentrated on our notion of Residual Normality. In our response, we focus on the questions raised by this idea. However, we also examine broader issues concerning the importance of incorporating a realistic theory of the process of development into explanations of developmental deficits.

Growth mixture models are regularly applied in the behavioral and social sciences to identify unknown heterogeneous subpopulations that follow distinct developmental trajectories. Marcoulides and Trinchera recently proposed a mixture modeling approach that examines the presence of multiple latent classes by algorithmically grouping or clustering individuals who follow the same estimated growth trajectory based on an evaluation of individual case residuals. The purpose of this article was to conduct a simulation study that examines the performance of this new approach for determining (...) the number of classes in growth mixture models. The performance of the approach to correctly identify the number of classes is examined under a variety of longitudinal data design conditions. The findings demonstrated that the new approach was a very dependable indicator of classes across all the design conditions considered. (shrink)

Progress in understanding the mind-body problem can be made without attempting to solve it as one unified problem, which it is not. Pepper's "Identity Theory" solution to the problem is now seen as not necessarily clarifying for the question of dualism. Residual asymmetrical dualism is proposed as a theory offering one very good way to think about this set of problems in a variety of modes of inquiry. These include neurophysiological research on the amygdala by LeDoux, research in the (...) phenonenon of hearing and learning while under general anesthetic, Gendlin's methods of focusing upon the body during therapeutic procedures and during creative composition of poetry, and Dewey's position concerning "primary experience" versus a "secondary pseudo-environment" inhabited by the civilized human. Residual asymmetrical dualism is not a value-neutral theory: it is based on a determination that bodily intelligence must ultimately guide mental functioning if survival and well-being are to be secured. It leads to take actions within society to carry out whatever steps are needed to alleviate the mind-body split whenever such a split is harmful to human interaction. (shrink)

This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids. An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if its finitely subdirectly irreducible members form an elementary class. A syntactic characterization of this hypothesis is proved, and examples are discussed.