A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Prior knowledge structures (or schemas) confer multiple behavioral benefits. First, when we encounter information that fits with prior knowledge structures, this information is generally better learned and remembered. Second, prior knowledge can support prospective planning. In humans, memory enhancements related to prior knowledge have been suggested to be supported, in part, by computations in prefrontal and medial temporal lobe cortex. Moreover, animal studies further implicate a role for the hippocampus in schema-based facilitation and in the emergence of prospective planning signals (...) following new learning. To date, convergence across the schema-enhanced learning and memory literature may be constrained by the predominant use of hippocampally dependent spatial navigation paradigms in rodents, and non-spatial list-based learning paradigms in humans. Here, we targeted this missing link by examining the effects of prior knowledge on human navigational learning in a hippocampally dependent virtual navigation paradigm that closely relates to foundational studies in rodents. Outside the scanner, participants overlearned Old Paired Associates (OPA – item-location associations) in multiple spatial environments, and they subsequently learned New Paired Associates (NPA – new item-location associations) in the environments while undergoing fMRI. We hypothesized that greater OPA knowledge precision would positively affect NPA learning, and that the hippocampus would be instrumental in translating this new learning into prospective planning of navigational paths to NPA locations. Behavioral results revealed that OPA knowledge predicted one-shot learning of NPA locations, and neural results indicated that one-shot learning was predicted by the rapid emergence of performance-predictive prospective planning signals in hippocampus. Prospective memory relationships were not significant in parahippocampal cortex and were marginally dissociable from the primary hippocampal effect. Collectively, these results extend understanding of how schemas impact learning and performance, showing that the precision of prior spatial knowledge is important for future learning in humans, and that the hippocampus is involved in translating this knowledge into new goal-directed behaviors. (shrink)

We used a participatory approach and a rural livelihoods framework to explore the knowledge and capacity of southeast Queensland graziers to adapt to climate change. After being presented with information on climate change projections, participants identified biophysical and socio-economic opportunities and challenges to adaptation. Graziers identified key opportunities as components of resilience, and in many cases were options that they had some knowledge of either from their own region or elsewhere in the grazing industry. The major constraint to adaptation was (...) the lack of financial capital: with low profitability of the industry and high land costs restricting their capacity to diversify and exploit economies of scale. These constraints were exacerbated by the pressure many graziers experienced from the demand for land as a result of urban expansion. While the focus of the workshop was on the impact of climate change and capacity to adapt, many of the issues raised by graziers were pressures not solely related to climate change. Adaptation needs to be considered in light of the appropriate level and spatial scale required to tackle the issues identified. Policy needs to support good natural resource management, rural amenity, and food and fibre production close to urban population and markets in the face of urban encroachment. (shrink)

1 Evidence-based policy requires researchers to provide the answers to ecological questions that are of interest to policy makers. To find out what those questions are in the UK, representatives from 28 organizations involved in policy, together with scientists from 10 academic institutions, were asked to generate a list of questions from their organizations. 2 During a 2-day workshop the initial list of 1003 questions generated from consulting at least 654 policy makers and academics was used as a basis for (...) generating a short list of 100 questions of significant policy relevance. Short-listing was decided on the basis of the preferences of the representatives from the policy-led organizations. 3 The areas covered included most major issues of environmental concern in the UK, including agriculture, marine fisheries, climate change, ecosystem function and land management. 4 The most striking outcome was the preference for general questions rather than narrow ones. The reason is that policy is driven by broad issues rather than specific ones. In contrast, scientists are frequently best equipped to answer specific questions. This means that it may be necessary to extract the underpinning specific question before researchers can proceed. 5 Synthesis and applications. Greater communication between policy makers and scientists is required in order to ensure that applied ecologists are dealing with issues in a way that can feed into policy. It is particularly important that applied ecologists emphasize the generic value of their work wherever possible. (shrink)

One of the widespread confusions concerning the history of the 1887 Michelson-Morley experiment has to do with the initial explanation of this celebrated null result due independently to FitzGerald and Lorentz. In neither case was a strict, longitudinal length contraction hypothesis invoked, as is commonly supposed. Lorentz postulated, particularly in 1895, any one of a certain family of possible deformation effects for rigid bodies in motion, including purely transverse alteration, and expansion as well as contraction; FitzGerald may well have had (...) the same family in mind. A careful analysis of the Michelson-Morley experiment (which reveals a number of serious inadequacies in many text-book treatments) indeed shows that strict contraction is not required. (shrink)

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker “paradox” in quantum mechanics.

Neural engineering technologies such as implanted deep brain stimulators and brain-computer interfaces represent exciting and potentially transformative tools for improving human health and well-being. Yet their current use and future prospects raise a variety of ethical and philosophical concerns. Devices that alter brain function invite us to think deeply about a range of ethical concerns—identity, normality, authority, responsibility, privacy, and justice. If a device is stimulating my brain while I decide upon an action, am I still the author of the (...) action? Does a device make the interiority of my experience accessible to others? Will the device change the way I think of myself and others think of me? Such fundamental questions arise even when a device is designed for only a relatively circumscribed purpose, such as restoring functioning via a smart prosthetic. We are part of a National Science Foundation-funded Engineering Research Center tasked with investigating philosophical and social implications of neural engineering research and technologies. Neural devices already in clinical use, such as deep brain stimulators for Parkinson's disease or essential tremor, have spurred healthy debate about such implications. Devices currently under development—such as the BrainGate System of implanted brain sensors coupled to robotics in persons with paralysis, exoskeletons for augmented movement, transcranial do-it-yourself stimulators, closed-loop brain stimulating systems, or even brain-to-brain interfacing—promise to extend and deepen these debates. At our center, brain-computer interfaces are the principal focus of work. Even acknowledging that the clinical translation of neural devices and seamless integration by end users may still largely reside in the future, the potential these devices hold calls for careful early analysis. The launching of the Brain Research through Advancing Innovative Neurotechnologies Initiative in April 2013 provides further impetus for this work. (shrink)

The Past Hypothesis defended by David Wallace in his 2011 account of macroscopic irreversibility is technically distinct from, but in the same spirit as, that of David Albert in his 2000 book Time and Chance. I am concerned in this essay with the role of objective probability in both accounts, which I find obscure. Most of the analysis will be devoted to the classical treatments by both authors, but a final section will question whether Wallace's quantum version involving unitary dynamics (...) removes this obscurity. (shrink)

Domain constraint, the requirement that analogues be selected from "the same category," inheres in the popular saying "you can't compare apples and oranges" and the textbook principle "the greater the number of shared properties, the stronger the argument from analogy." I identify roles of domains in biological, linguistic, and legal analogy, supporting the account of law with a computer word search of judicial decisions. I argue that the category treatments within these disciplines cannot be exported to general informal logic, where (...) the relevance of properties, not their number, must be the logically prior criterion for evaluating analogical arguments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:When Our Fathers Fall:A Thomistic-Confudan Approach to Lay Moral Correction of ClergyJoshua R. BrownIn this article, I seek to draw upon the resources of Thomas Aquinas and early Confucian philosophy in order to answer the following question: what are the responsibilities of lay Catholics to our priests and bishops as regards their personal moral rectification? This justifiably provokes two questions in reaction: why is this question worth pursuing, and (...) why pursue it via a comparative reading of Aquinas and Confucian philosophy?As to the first of these, the question I pose here is a specification of the larger responsibilities that fall to Christians according to the Scriptures. Galatians 5:1–2 puts the matter this way: "Brothers, even if a person is caught in some transgression, you who are spiritual should correct that one in a gentle spirit, looking to yourself, so that you may also not be tempted. Bear one another's burdens and so you will fulfill the law of Christ."1 In the theological tradition, "bearing one another's burdens" has been neatly and aptly represented in the principle of fraternal correction. The question I am focused on here, then, is how is fraternal correction properly offered from laity to clerics.Ultimately, articulating the shape or form of virtuous lay correction of clergy is actually a rather knotty problem. This is because the manner of the relationship between laity and clergy is not simply understood in terms [End Page 1025] of the bonds of Christian fraternity. Certainly, all Christians are brothers and sisters in Christ, for through His grace we have been adopted into the inheritance of the Kingdom of God as children of God (see Eph 5:1–5; 1 John 3:1–3). Yet the Church also recognizes that priests and bishops possess not simply a fraternal but also a paternal relationship to laity. As St. Paul again puts it to the church in Corinth, "I became your father in Christ Jesus through the gospel. Therefore, I urge you, be imitators of me" (1 Cor 4:15–16).I propose here that, although fraternal correction is a still useful concept for understanding how laity can morally correct clergy, it has an obvious weakness in that it corresponds to a particular relational analogy, that of fraternity, within which the difference in authority is not as great as the parent–child bond. Thus, fraternal correction is exceptionally useful for understanding how relationships with more or less equal rank of authority can function in terms of moral remonstration, such as how a lay Christian might fraternally correct another lay Christian, or a cleric fraternally correct a cleric. However, when it comes to clergy–laity relations, the shape of fraternal correction is far less clear, for there is a just and genuine disparity between them in the order of ecclesial, magisterial authority underlying the relationship, even if there is equality in other important respects.I argue here that lay responsibilities for correcting clergy can be fruitfully understood in terms of filial remonstration as understood by the Confucian philosophical tradition. Of course, there is one tremendous dissimilarity between Confucian views on the responsibilities for filial remonstration and those pertaining to the laity–clergy relationship: the former occur within and flow from the natural foundation of the parent–child bond, while the latter are not based on blood relations and natural duties. Yet, the same can be said about the language of fraternal correction, which draws upon the analogous duties of blood-kin applied to the spiritual fraternity of the Christian life. And so, it must be admitted that although the father–child relationship is used only analogously to describe the priest–laity relationship, it also accurately depicts the reality of that relationship. As John Paul II observed, priestly celibacy entails "a singular sharing in God's fatherhood and in the fruitfulness of the Church."2 The call of the priest to the celibate life is thus a call to fatherhood, indeed, a call to imitate and participate in the paternity of the triune God in a special and spiritual way. It seems clear that only a materialistic conception of things that denies the spiritual its proper... (shrink)

I defend a neo-Aristotelian ethical theory I call "naturalized virtue ethics," or NVE. This is a naturalistic, teleological theory. Human beings are a species of social animal for whom there is a characteristic form of life. An individual human being may be evaluated as a good or bad specimen according to how well that individual realizes the human form of life. To be a good human being, one must possess those traits of character that reliably enable one to achieve the (...) ends of creatures like us. ;In Chapter 1, I present reasons for why we should prefer ethical naturalism. ;In Chapter 2, I discuss what to many is still a contentious issue: natural teleology. NVE is teleological. Teleology, both in ethics and in science, has often been looked upon with suspicion. I argue that the teleology operative in NVE is natural, or naturalizable. NVE is on a metaphysically sound foundation. ;In Chapter 3, I further explicate NVE and show how several of the standard virtues are justified by the lights of NVE. I also show the further applications of the theory to issues of distributive justice and law. These examples provide tests of the descriptive and explanatory adequacy of NVE, a test the theory passes. ;In Chapter 4, I consider the charge that ethical naturalism commits some one or other egregious metaethical mistake. This sort of mistake has been associated variously with the fact/value gap, the is/ought gap, and the naturalistic fallacy. I discuss these issues in their general form and relative to NVE, showing that there are no problems here for NVE. ;In Chapter 5, I place NVE is the space of contemporary virtue theories and also contrast it with eudaimonistic or welfare-based ethics and with evolutionary ethics. NVE is a good-based virtue theory, but it is neither a kind of eudaimonism nor an evolutionary ethics. Considerations of evolution lead us to certain criticisms of ethical theories like NVE. Contra the critics, I show NVE's compatibility with neo-Darwinism. I then suggest further research. (shrink)

I must begin by confessing that I owe to the deficiencies of voice-mail a valuable occasion to re-think the purpose of this lecture. For I left on the voice-mail of Professor Martin the title of the lecture: “Augustine and a Crisis of Wealth in Late Antiquity.” I received—again by voice-mail—a delighted reply. He fully approved of my title: “Augustine and a Crisis of Wills in Late Antiquity.” I realized, to my shame, that I had awoken false expectations in the heart (...) of a great Augustinian scholar. Of course, “Wills” is what a St Augustine Lecture should be about. It was on the Will that Augustine wrote with greatest passion and tenacity, and with the gravest long-term consequences. And I had offered, for the occasion of a St. Augustine Lecture, not “Will” but merely “Wealth.”. (shrink)

I should like to offer my greatest thanks to Paul Griffiths for providing the opportunity for this exchange, and to commentators Gillian Brown, Steven Fuller, Stefan Linquist, and Erika Milam for their generous and thought-provoking comments. I shall do my best in this space to respond to some of their concerns.

In lieu of an abstract, here is a brief excerpt of the content:Interpreting from the IntersticesThe Role of Justice in a Liberal Democracy—Lessons from Michael Walzer and Emmanuel LevinasNicholas R. Brown (bio)1As anyone who is familiar with more recent theological debate can attest, the appraisal of the liberal democratic tradition has undergone a radical reevaluation in the wake of Stanley Hauerwas’s and Alasdair MacIntyre’s scathing critiques. As a result of their blistering assault, religious ethicists and philosophers now find themselves (...) operating within a discursive milieu that is almost the photo negative of the one they previously inhabited. For what has followed After Virtue and After Christendom is a situation in which compliance with liberal democratic norms is now perceived as actively inveighing against justice rather than as an integral prerequisite to its pursuit.There are cracks, however, beginning to emerge in the MacIntyre/Hauerwas edifice. For what is becoming disputed and increasingly so among a growing chorus of religious ethicists and philosophers is whether their critical reading of liberal democracy offers the most [End Page 155] helpful or even the most biblical way to think through its own moral dimensions as well as those undergirding its relationship with justice.It is the emergence of these criticisms that forms the basis for this essay. For the thesis that I wish to advance below is that liberal democracy offers religious ethicists and philosophers alike a moral framework and vocabulary from which it is possible to comprehend and enact the normative precepts encapsulated within a biblical understanding of justice. Accordingly, some aspects of my argument will build upon the rhetorical trajectories that have been already charted by the ethicists and philosophers I mention above.What distinguishes my approach, however, is that I will proceed from a more focused examination of some of the ethical and political undercurrents found within contemporary Jewish thought. More specifically, I want to probe the ethical philosophy of Emmanuel Levinas and the political philosophy of Michael Walzer, for I believe the juxtapositional methodology of interpretation which informs each of their perspectives is illustrative of an interstitial hermeneutic that helps further illuminate the moral compatibility between biblical and democratic accounts of justice.2By now, MacIntyre’s and Hauerwas’s critiques of the liberal democratic tradition have been so thoroughly documented, discussed, and dissected that a review of their perspectives cannot help but have a certain pleonastic quality.Probably the most significant and disturbing problem that MacIntyre and Hauerwas see belying the liberal democratic tradition stems from its conception of time and space, or more precisely, its lack thereof. For what they discover upon a more careful probing of its moral and epistemological underpinnings is a pursuit of transcendence not dissimilar to Gnostic metaphysics. In the case of liberalism, however, the existential encumbrances to be excised are not corporeal and carnal in nature, but historical and social. [End Page 156]Such conditionalities, surmise liberal theorists, are so shot through with conceptual prejudices that they comprise an interpretative straight-jacket that vitiates against the kind of objectivity necessary to engage in a nonparochial process of moral and political discernment. For it is precisely this ability “to be able to stand back from any and every situation in which one is involved, from any and every characteristic that one may possess, and to pass judgment on it from a purely universal and abstract point of view that is totally detached from all social particularity” which MacIntyre sees as constituting “the essence of moral agency” of modern liberalism (AV 31–32). Therefore, “liberalism is successful,” maintains Hauerwas, “exactly because... [it] provide[s] that philosophical account of society designed to deal with” the moral and political implications such a social and historical denuding portends, namely “a system of rules that will constitute procedures for resolving disputes as they pursue their various interests.”1However, what liberalism defines as success MacIntyre and Hauerwas see as anything but. Instead, both judge its “system of rules” to be an insidious prescription for a particularly virulent form of moral nihilism and political bankruptcy. For by stripping moral and political discourse of their historical and social referents, liberalism, ironically and tragically, eviscerates itself of the very heuristic and discursive practices necessary to make those... (shrink)

When I was asked to propose a topic for my presidential address, the subject I chose, moral imperatives and conundrums of conscience, seemed to me particularly appropriate and timely. This was in part because of the problems of conscience caused for many members of the Academy by the decision to hold the annual meeting in Arizona, whose restrictive laws on immigration seemed to many to violate basic principles of right and justice and hence to warrant a boycott. Long, thoughtful, and (...) impassioned discussion of the issues revealed their complexity. Although the final decision disappointed many members, all recognized its virtue in supporting the Arizonans who were struggling to accomplish revocation of legislation they believed wrong. There was more. The crises in the leadership of the Academy during two of my years as a presidential officer raised issues of conscience and morality for all who worked to achieve equitable, just, and rational solutions to our problems and conflicts. On both issues, the site of the meeting and the governance of the Academy, colleagues adopted and defended positions that demonstrated the variety and strength of their convictions and the diversity of their reasons for holding them. (shrink)

The aim of this paper is to illustrate four properties of the non-relativistic limits of relativistic theories: that a massless relativistic field may have a meaningful non-relativistic limt, that a relativistic field may have more than one non-relativistic limit, that coupled relativistic systems may be "more relativistic" than their uncoupled counterparts, and that the properties of the non-relativistic limit of a dynamical equation may differ from those obtained when the limiting equation is based directly on exact Galilean kinematics. These properties (...) are demonstrated through an examination of the non-relativistic limit of the familiar equations of first-quantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admits non-relativistic limits are given, particular attention being given to a gauge-invariant formulation of the limiting process especially as it applied to the electromagnetic potentials. The difference between the properties of a limiting theory and an exactly Galilean covariant theory based on the same dynamical equation is demonstrated by examination of the Pauli equation. (shrink)

Stimuli such as surprised faces are ambiguous in that they are associated with both positive and negative outcomes. Interestingly, people differ reliably in whether they evaluate these and other ambiguous stimuli as positive or negative, and we have argued that a positive evaluation relies in part on a biasing of the appraisal processes via reappraisal. To further test this idea, we conducted two studies to evaluate whether increasing the cognitive accessibility of reappraisal through a brief emotion regulation task would lead (...) to an increase in positive evaluations of ambiguity. Supporting this prediction, we demonstrated that cuing reappraisal, but not in three other forms of emotion regulation (Study 1a-d; n = 120), increased positive evaluations of ambiguous faces. In a sign of robustness, we also found that the effect of reappraisal generalised from ambiguous faces to ambiguous scenes (Study 2; n = 34). Collectively, these findings suggest that reappraisal may play a key role in determining responses to ambiguous stimuli. We discuss these findings in the context of affective flexibility, and suggest that valence bias (i.e. the tendency to evaluate ambiguity more positively or negatively) represents a novel approach to measuring implicit emotion regulation. (shrink)

"By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis. I found it to be challenging, fascinating, infuriating, and provocative, but certainly not dull."--James H, Brown, University of New Mexico "This book is unquestionably mandatory reading not only for every living biologist but for generations of biologists to come."--Jack P. Hailman, Animal Behaviour , review of the (...) first edition "An important contribution to modern evolutionary thinking. It fortifies the place of Evolutionary Theory among the other well-established natural laws."--R.Gessink, TAXON. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:242 HISTORY OF PHILOSOPHY his political and religious predispositions prodded him to demonstrate that the roots of modern science were in the Christian Middle Ages. Sarton's particular foibles are best understood by referring them to his pacifist commitments and the moralistic assumption that the values of science are transferable to other human endeavors. Categories such as inductivism, conventionalism and Popperianism are of little help in gaining historical understanding. For (...) this, they are in fact Platonic ideals which have little heuristic value. I would venture that a truly historical historiography of science would aid us in spotting errors in the past and help us in the future. My guess is that a good analysis would reveal a major source of trouble to have stemmed from preconceived notions which the history of science was meant to illustrate. Surely some of them have been philosophical in character, and even Baconian or conventionalist. But until recent times, most of these preconceptions have stemmed from religious, nationalistic, or personal motivations, or from scientists who wanted support for a particular concept. I agree with Agassi only in the suggestion that a parti pris was at the root of our troubles. Why, then, substitute a Popperian preconception for a conventionalist one? Why not, on the contrary, combat their distorting influence and reduce their impact? This is in fact what has happened in recent times. As the history of science has fallen into the hands of a gradually organized profession, the blatant motivations --of any type--which colored past historical writings have slowly receded. By a constant and critical confrontation of opposing views among specialists, the purpose for examining the history of science has slowly been transformed. The older external motivations have given way to an interest in the subject for its own sake and a gradual transformation has been in the making for the last few decades. As happens in other human endeavors, professionalization has already raised the standards in the discipline and there is every reason to think it will continue to do so in the future. We need not really be as pessimistic as Agassi, nor embrace his particular salvation. ROGEa HAm~ University o] Cali]ornia, Berkeley A MEDIEVAL ANALYSIS OF INFINITY IN THE COURSEof arguing that time must have had a beginning, St. Bonaventure (1221-74) put forward a demonstration which in some ways seems to anticipate Cantor's definition of infinity.1 Bonaventure pointed out that, if the world were infinitely old, then there would have been an infinite number of annual revolutions of the sun around the ecliptic. But during each such period there occur (roughly) twelve revolutions of the moon, i.e. lunar months or lunations. Thus there would be one infinity which was twelve times another--which, says Bonaventure, is impossible. This attempted proof might be formulated as the following For other adumbrationsof this definition,see I. Thomas,"A TwelfthCentury Paradoxof the Infinite,"Journal o] Symbolic Logic, XXIII (1958), 133-134, and W. & M. Kneale, The Development of Logic (Oxford,1962),p. 440. NOTES AND DISCUSSIONS 243 reductio ad absurdum, in which a revolution of the sun is specified as the period between successive vernal equinoxes. If there could be an infinite set of past lunations, then clearly it could be put in a one-to-one correspondence with a proper sub-set of itself--viz., with the set of past lunar months during which vernal equinoxes occurred. But this consequence is preposterous; no set could be so correlated with its own sub-set. Therefore the set of past lunar months cannot be infinite, and the world must have had a beginning. The passage, which is found in Bonaventure's commentary on the Sentences of Peter Lombard, reads as follows :2 Si mundus est aeternus, revolutiones solis in orbe suo sunt infmitae ; rursus, pro una revolutions solis necesse est fuisse duodecim ipsius lunae: ergo plus revoluta est luna quam sol; et sol infinities: ergo infinitorum ex ea parle, qua infinita sunt, est reperire excessum. Hoe autem est impossibile : ergo etc. PA~-r~asoN BROWN Harpur College, State University o] New York Sententiarum L/b. H, Dist. I, P.I, Art. I, Quaest. II, as found in S. Bonaventurme, Opera Omnla... (shrink)

R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.