It is widely held among philosophers that the conservation of energy is true and important, and widely held among philosophers of science that conservation laws and symmetries are tied together by Noether's first theorem. However, beneath the surface of such consensus lie two slights to Noether's first theorem. First, there is a 325+-year controversy about mind-body interaction in relation to the conservation of energy and momentum, with occasional reversals of opinion. The currently popular Leibnizian view, dominant since the (...) late 19th century, claims to find an objection to broadly Cartesian views in their implication of energy non-conservation. Here energy conservation is viewed as an oracle, an unchallengeable black box. But Noether's first theorem and its converse show that conservation and symmetry of the laws stand or fall together. Absent some basis for expecting conservation in brains that has a claim on the Cartesian, the objection is circular. An empirically based argument is possible, but is a different argument with little force except insofar as it is rooted in neuroscience. Second, General Relativity has a 100+-year-long controversy about whether gravitational energy exists and is objectively localized. The usual view is that gravitational energy exists but is not objectively localized, though some deny its existence. Without positive answers to both questions, generally applicable conservation laws do not exist: energy is not conserved. This conclusion is startling in itself and a problem for conserved quantity theories of causation. Yet Noether's first theorem applies to General Relativity, which has uncountably many symmetries of its laws and so has conservation laws, indeed uncountably many of them. Many authors downplay these laws due to their quirky properties; some authors even attempt to explain the laws' supposed nonexistence in terms of an absence of symmetries of the geometry, which is a distraction. Thus Noether's first theorem is widely ignored, left uninterpreted, or distorted in relation to General Relativity. Taking the theorem seriously seems possible, however, restoring the conservation of energy, or rather, energies. How do these controversies relate? One sometimes finds claims that General Relativity's supposed lack of conservation laws answers Leibniz on behalf of Descartes. Taking seriously the superabundance of formal conservation laws in General Relativity, however, suggests that General Relativity resists mind-to-body causation. This conclusion can be proven apart from interpretive controversies. The resistance is, however, finite and tends to be swamped by larger world-view considerations. (shrink)

The study of human cognition and the study of artificial intelligence (AI) have a symbiotic relationship, with advancements in one field often informing or creating new work in the other. Human cognition has many capabilities modern AI systems cannot compete with. One such capability is the detection, identification, and resolution of knowledge gaps (KGs). Using these capabilities as inspiration, we examine how to incorporate detection, identification, and resolution of KGs in artificial agents. We present a paradigm that enables research on (...) the understanding of KGs for visual-linguistic communication. We leverage and enhance and existing KG taxonomy to identify possible KGs that can occur for visual question answer (VQA) tasks and use these findings to develop a classifier to identify questions that could be engineered to contain specific KG types for other VQA datasets. Additionally, we examine the performance of different VQA models through the lens of KGs. (shrink)

The study of human cognition and the study of artificial intelligence (AI) have a symbiotic relationship, with advancements in one field often informing or creating new work in the other. Human cognition has many capabilities modern AI systems cannot compete with. One such capability is the detection, identification, and resolution of knowledge gaps (KGs). Using these capabilities as inspiration, we examine how to incorporate detection, identification, and resolution of KGs in artificial agents. We present a paradigm that enables research on (...) the understanding of KGs for visual-linguistic communication. We leverage and enhance and existing KG taxonomy to identify possible KGs that can occur for visual question answer (VQA) tasks and use these findings to develop a classifier to identify questions that could be engineered to contain specific KG types for other VQA datasets. Additionally, we examine the performance of different VQA models through the lens of KGs. (shrink)

In the described case, the consult requester, nurse Gloria, wants help with the question: “is it ethically justifiable to compel tube feeding over the objection of a young adult with anorexia nervo...

We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.In 2+1 dimensional spacetime, a velocity of the particle and spin tensor are dependent to each other and the chirality can not be (...) introduced. The free particle has 7 constants of motion: The momentum three vector, the charge, the energy in proper time, the scalar constant spin or magnetic polarization and the two components of total angular momentum. Two component electric polarizations oscillate with Zitterbewegung frequency.In 1+1 dimensional spacetime we have an independent velocity vector and a scalar spin tensor. The free particle has 5 integrals of motion: The momentum two vector, the charge, the energy in proper time, and the scalar total angular momentum. The normal component of the velocity or the scalar electric polarization oscillates with Zitterbewegung frequency.In 3+1 dimensional spacetime, the particle has an independent velocity vector, spin tensor and chirality. The free particle has 12 integrals of motion: The momentum four vector, the charge, the energy in proper time or mass, the three vector spin or magnetic polarizations and three components of total angular momentum. The parallel component of velocity into momentum and the normal components of the spin tensor or the spin three vector are constants of motion for the free particle. The chirality and electric polarizations oscillate with the Zitterbewegung frequency. The system is superintegrable in all dimensions. (shrink)

Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the (...) usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization. (shrink)

In relativistic classical and quantum mechanics with Poincaré-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. The formulation of a covariant canonical framework for the evolving events leads to a dynamical theory in which mass conservation is demoted from a priori constraint to the status of conserved Noether current for a certain class of interactions. In pre-Maxwell electrodynamics—the local gauge theory associated with this framework —events induce five local off-shell fields, which mediate interactions between instantaneous (...) events, not between the worldlines which represent entire particle histories. The fifth field, required to compensate for dependence of gauge transformations on the evolution parameter, enables the exchange of mass between particles and fields. In the equilibrium limit, these pre-Maxwell fields are pushed onto the zero-mass shell, but during interactions there is no mechanism regulating the mass that photons may acquire, even when event trajectories evolve far into the spacelike region. This feature of the off-shell formalism requires the application of some ad hoc mechanism for controlling the photon mass in two opposite physical domains: the low energy motion of a charged event in classical Coulomb scattering, and the renormalization of off-shell quantum electrodynamics. In this paper, we discuss a nonlocal, higher derivative correction to the photon kinetic term, which provides regulation of the photon mass in a manner which preserves the gauge invariance and Poincaré covariance of the original theory. We demonstrate that the inclusion of this term is equivalent to an earlier solution to the classical Coulomb problem, and that the resulting quantum field theory is renormalized. (shrink)

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress (...) that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. (shrink)

How does metaphysical necessity relate to the modal force often associated with natural laws? Fine argues that natural necessity can neither be obtained from metaphysical necessity via forms of restriction nor of relativization — and therefore pleads for modal pluralism concerning natural and metaphysical necessity. Wolff, 898–906, 2013) aims at providing illustrative examples in support of applying Fine’s view to the laws of nature with specific recourse to the laws of physics: On the one hand, Wolff takes it that equations (...) of motion can count as examples of physical laws that are only naturally but not metaphysically necessary. On the other hand, Wolff argues that a certain conservation law obtainable via Noether’s second theorem is an instance of a metaphysically necessary physical law. I show how Wolff’s example for a putatively metaphysically necessary conservation law fails but argue that so-called topological currents can nevertheless count as metaphysically necessary conservation laws carrying physical content. I conclude with a remark on employing physics to answer questions in metaphysics. (shrink)

Continuity as appears to us immediately by intuition differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmetical continuum, a formal set-theoretic entropy is assigned to the arithmetical continuum. Secondly, (...) by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the arithmetical continuum in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole, indicating that this apparently physical quantity might have a pure set-theoretic origin, too. (shrink)

A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with (...) spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, our reformulation retains the potentially important antisymmetric contribution. (shrink)

Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt (Etesi in Found Sci 25:327–340, 2020), the aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness present in the set of real numbers, a set-theoretic entropy is assigned to it using the Kullback–Leibler relative entropy of a pair of Riemannian (...) manifolds. Then exploiting the non-negativity of this relative entropy an abstract Hawking-like area theorem is derived. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the set of real numbers in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too. (shrink)

Emmy Noether’s many articles around the time that Felix Klein and David Hilbert were arranging her invitation to Göttingen include a short but brilliant note on invariants of finite groups highlighting her creativity and perspicacity in algebra. Contrary to the idea that Noether abandoned Paul Gordan’s style of mathematics for Hilbert’s, this note shows her combining them in a way she continued throughout her mature abstract algebra.

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument (...) as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

The gap in the mathematical derivation of Noether’s theorem, and also of the Ward-Takahashi identities, caused by performing variation before quantization is closed by introduction of variational calculus for operator fields. It is demonstrated that both Noether’s theorem and the Ward-Takahashi identities retain full validity in quantum field theory.

Guided by the example of gauge transformations associated with classical Yang-Mills fields, a very general class of transformations is considered. The explicit representation of these transformations involves not only the independent and the dependent field variables, but also a set of position-dependent parameters together with their first derivatives. The stipulation that an action integral associated with the field variables be invariant under such transformations gives rise to a set of three conditions involving the Lagrangian and its derivatives, together with derivatives (...) of the functions that define the transformations. These invariance identities constitute an extension of the classical theorem of Noether to general transformations of this kind. An application to the case of gauge fields demonstrates the existence of two distinct types of conservation laws for such fields. (shrink)

There are only five letters and two postcards which were written by Emmy Noether to P.S. Alexandroff that have been preserved. These will be edited in this paper. More than any other source, these letters and postcards give an insight into Emmy Noether's privacy, and her sympathy for the problems of her pen pal and colleagues. They illuminate her judgement of different colleagues, students, «mathematical grandchildren» and their papers. They also inform about relationships within the mathematicians' community and (...) the working atmosphere in Goettingen and the US after 1933. The author thanks Prof. Dr. Walter Purkert, Bonn, for the reference to the writings of Emmy Noether, and Prof. Dr. Albert Shiryaev, Moscow, for the kind publication permission. (shrink)

In 1918, Emmy Noether published a (now famous) theorem establishing a general connection between continuous 'global' symmetries and conserved quantities. In fact, Noether's paper contains two theorems, and the second of these deals with 'local' symmetries; prima facie, this second theorem has nothing to do with conserved quantities. In the same year, Hermann Weyl independently made the first attempt to derive conservation of electric charge from a postulated gauge symmetry. In the light of Noether's work, it is (...) puzzling that Weyl's argument uses local gauge symmetry. This paper explores the relationships between Weyl's work, Noether's two theorems, and the modern connection between gauge symmetry and conservation of electric charge. This includes showing that Weyl's connection is essentially an application of Noether's second theorem, with a novel twist. (shrink)

Internal global symmetries exist for the free non-relativistic Schrodinger particle, whose associated Noether charges---the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate---are exhibited. Analogous symmetries in classical electromagnetism are also demonstrated.

ABSTRACTThe unprecedented progress in bio‐medical sciences and technology during the last few decades has resulted in great transformations in the concepts of health and disease, health systems and healthcare organisation and practices. Those changes have been accompanied by the emergence of a broad range of ethical dilemmas that confront health professionals more frequently. The classical Hippocratic ethical principles, though still retaining their relevance and validity, have become insufficiently adequate in an increasing range of problems and situations. Healthcare that has been (...) practised for centuries on the basis of a direct doctor‐patient relationship has been increasingly transformed into a more complex process integrating the health‐team, the patient and the community. Systematic review of the specialised literatures revealed that Healthcare Ethics education has become a basic requirement for any training programme for health professionals, and should cover the different stages of undergraduate, postgraduate and continuing education. Both theoretical foundations and practical skills are required for the appropriate ethical reasoning, ethical attitude and decision‐making abilities. There is growing evidence that physicians’ professional and moral development is not only determined by the formal curriculum of ethics; rather more, it is determined by the moral environment of the professional practice, the ‘hidden curriculum’ which deserves serious consideration by medical education. (shrink)

For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden. „She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine – of all that is characterized by the term ‚Begriffliche Mathematik‘.“2 The aim of this paper is to illuminate this “new direction”, which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its (...) roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831–1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a “free creation of the human spirit”3. They thus stand for an abstract perspective of mathematics in their entirety, described as ‘modern algebra’ in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on “general mathematical concepts” [allgemein‐mathematische Begriffe]4, was the success of a cultural movement whose most important protagonists included Emmy Noether (1882–1935) and her pupil Bartel L. van der Waerden (1903–1996). With the use of the term ‘conceptual’, a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the “working and conceptual methods” [Arbeits‐ und Auffassungsmethoden]5 of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term “conceptual world” [Begriffswelt]6 in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School. (shrink)

The unique collaborative effort of a professor of English and a professor of philosophy, Current Issues and Enduring Questions is a balanced and flexible book that provides the benefits of the authors’ dual expertise in effective persuasive writing and rigorous critical thinking. Refined through eight widely adopted editions, it has been revised to address current student interests and trends in argument, research, and writing. Its comprehensive coverage of classic and contemporary approaches to argument includes Aristotle, Toulmin, and a range of (...) alternative views, making it an extraordinarily versatile text. Readings on contemporary controversies (including environmental stewardship, student-teacher relationships, cyber bullying, and the limits of reproductive rights) and classical philosophical questions (such as How free is the will of the individual?) are sure to spark student interest and lively discussion and writing. No other text and reader offers such an extensive resource for teaching argument. (shrink)

This paper argues that Noether's axiomatic method in algebra cannot be assimilated to Weyl's late view on axiomatics, for his acquiescence to a phenomenological epistemology of correctness led Weyl to resist Noether's principle of detachment.

Virtue is among the most venerable concepts in philosophy, and has recently seen a major revival. However, new challenges to conceptions of virtue have also arisen. In _Current Controversies in Virtue Theory_, five pairs of cutting-edge philosophers square off over central topics in virtue theory: the nature of virtue, the connection between virtue and flourishing, the connection between moral and epistemic virtues, the way in which virtues are acquired, and the possibility of attaining virtue. Mark Alfano guides his readers through (...) these essays, with a synthetic introduction, succinct abstracts of each debate, suggested further readings and study questions for each controversy, and a list of further controversies to be explored. (shrink)

Substantial advances in our understanding of the neural bases of emotional processing have been made over the past decades. Overall, studies in humans and other animals highlight the key role of the amygdala in the detection and evaluation of stimuli with affective value. Nonetheless, contradictory findings have been reported, especially in terms of the exact role of this structure in the processing of different emotions, giving rise to different neural models of emotion. For instance, although the amygdala has traditionally been (...) considered as exclusively involved in fear (and possibly anger), more recent work suggests that it may be important for processing other types of emotions, and even nonemotional information. A review of the main findings in this field is presented here, together with some of the hypotheses that have been put forward to interpret this literature and explain its inconsistencies. (shrink)

Analysis of Emmy Noether’s 1918 theorems provides an illuminating method for testing the consequences of “coordinate generality”, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether’s first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the (...) father of the whole business, A. Einstein (an apparent shift in Einstein’s thinking on the significance of general covariance between 1916 and 1918 is highlighted). (shrink)

_Current Issues in Business Ethics_ analyzes the questions which underlie business activities, arguing that the prime object for a legitimate business must be sustainability. It also looks at the issues between individuals and business and asks whether businesses can support their employees as an alternative to family and church. Finally it assesses the impact of most recent trends in business looking at: * the activities of multinational companies * the changing gender balance * privatization * the loss of power of (...) the trade unions. (shrink)

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Specific attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the (...) father of the whole business, A. Einstein. (shrink)

In this outstanding collection of essays, Isaiah Berlin, one of the great thinkers of the twentieth century, discusses the importance in the history of thought of dissenters whose ideas still challenge conventional wisdom--among them Machiavelli, Vico, Montesquieu, Herzen, and Sorel. With his unusual powers of imaginative re-creation, Berlin brings to life original minds that swam against the current of their times.

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom for (...) stability, along with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions imply that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed. (shrink)

_Current Issues in Business Ethics_ analyzes the questions which underlie business activities, arguing that the prime object for a legitimate business must be sustainability. It also looks at the issues between individuals and business and asks whether businesses can support their employees as an alternative to family and church. Finally it assesses the impact of most recent trends in business looking at: * the activities of multinational companies * the changing gender balance * privatization * the loss of power of (...) the trade unions. (shrink)

In May 2023, the world’s first whole-eye and partial-face transplant was performed, representing the first known whole-eye transplant in history and the “only successful combined transplant case of...

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the (...) conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder’s experimental results are remarked. (shrink)

The economic and debt crisis threaten many eurozone countries and the very existence of the common currency, the euro. The crisis has meant that some special mechanisms have had to be created (EFSF, ESM) and the introduction of special procedures in heavily indebted countries. The deepening of the crisis and the economic recession in the euro area have resulted in the growth of nationalism and anti-European sentiments in EU member states. Resolving the crisis, however, requires further convergence of the eurozone (...) countries, the formation of a fiscal union and a banking union. At the same time, the crisis has shown that the grand theories of European integration, neo-functionalism and liberal intergovernmentalism, have failed to provide answers to the questions raised by the crisis, and this has led to the growing importance of social constructivism. (shrink)