This paper is part II of a trilogy on the transition from classical particle mechanics to relativistic continuum mechanics that one of the authors is working on. The first part, on the Trouton experiment, was published in the Stachel festschrift (Janssen 2003). This paper focuses on the Lorentz-Poincaré electron, and, in particular, on the "Poincaré pressure" or "Poincaré stresses" introduced to stabilize the electron. It covers both the original argument by Poincaré (1906) and a modern relativistic argument for adding (...) a negative pressure term to the system's energy-momentum tensor inspired by the work of Laue (1911a, b). It highlights the importance of a paper by Lorentz (1899) in this context and of the "electromagnetic mechanics" of Abraham (1903). (shrink)
In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts. 1 Rival theories of time 2 Relativity and the present 3 Special relativity: (...) one theory, three interpretations 4 Theories of principle and constructive theories 5 The relativity interpretation: explanatorily deficient? 6 The relativity interpretation: ontologically fragmented? 7 The space-time interpretation: does God need a preferred frame of reference? 8 The neo-Lorentzian interpretation: at what price? 9 The neo-Lorentzian interpretation: with what payoff? 10 Why we should prefer the space-time interpretation over the neo-Lorentzian interpretation 11 What about general relativity? 12 Squaring the tenseless space-time interpretation with our tensed experience. (shrink)
There is a striking difference between the methodology of the young Einstein and that of the old. I argue that Einstein’s switch in the late 1910s from a moderate empiricism to an extreme rationalism should at least in part be understood against the background of his crushing personal and political experiences during the war years in Berlin. As a result of these experiences, Einstein started to put into practice what, drawing on Schopenhauer, he had preached for years, namely to use (...) science as his means of escaping from “the merely personal.” Whatever the exact sources of Einstein’s about-face, the older man has left us with a highly misleading picture of how the younger man achieved the successes that we still celebrate today. This has had a harmful inﬂuence on theoretical physics. If the young Einstein’s successes are any guide as to how successful theoretical physics is done, close adherence to general features of the empirical data is much more and mathematical elegance is much less important than the old Einstein wanted us to believe. (shrink)
In the course of his work on optics and electrodynamics in systems moving through the ether, the 19th-century medium for light waves and electric and magnetic ﬁelds, Lorentz discovered and exploited the invariance of the free-ﬁeld Maxwell equations under what Poincaré later proposed to call Lorentz transformations. To account for the negative results of optical experiments aimed at detecting the earth’s motion through the ether, Lorentz, in effect, assumed that the laws governing matter interacting with light waves are Lorentz invariant (...) as well. Like Lorentz, Einstein ﬁrst encountered the Lorentz transformations in electrodynamics. Unlike Lorentz, for whom the transformation merely provided convenient mathematical substitutions, but like Poincaré, Einstein recognized that the Lorentz-transformed quantities are the measured quantities for the moving observer. More importantly, Einstein recognized that the Lorentz invariance of all physical laws had nothing to do with electrodynamics per se, but reﬂected the kinematics in a new relativistic space-time, to be named after Minkowski who worked out its geometry a few years later. (shrink)
I defend the widely held view challenged by Harvey Brown in his recent book that special relativity is preferable to those parts of Lorentz’s electron theory it replaced because various phenomena that special relativity reveals to be of purely kinematical origin were given a dynamical explanation in Lorentz’s theory. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other such phenomena that played a role in the early reception (...) of special relativity in the physics community: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in the -ray deﬂection.. (shrink)
With the discovery that the universe is expanding at an accelerating rate, Einstein’s cosmological constant, which he once supposedly called his biggest blunder, is making a remarkable comeback. Einstein’s introduction of this constant had little to do with cosmology. It was part of yet another failed attempt to eliminate absolute space from physics. It took the Dutch astronomer Willem de Sitter only a few days to blow the idea out of the water. It took Einstein over a year to concede (...) the point. In the process Einstein and De Sitter produced the ﬁrst two models of relativistic cosmology, the Einstein cylinder universe and the De Sitter hyperboloid universe. (shrink)
In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz's theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in (...) the early reception of special relativity in the physics literature: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in beta-ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. (shrink)
There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (shrink)
This paper will serve as the editorial note on Einstein's 1916 review article on general relativity in a planned volume with all of Einstein's papers in Annalen der Physik. It summarizes much of my other work on history of general relativity and draws heavily on the annotation of Einstein's writings and correspondence on general relativity for Vols. 4, 7, and 8 of the Einstein edition.
Readers of this volume will notice that it contains only a few papers on general relativity. This is because most papers documenting the genesis and early development of general relativity were not published in Annalen der Physik . After Einstein took up his new prestigious position at the Prussian Academy of Sciences in the spring of 1914, the Sitzungsberichte of the Berlin academy almost by default became the main outlet for his scientific production. Two of the more important papers on (...) general relativity, however, did find their way into the pages of the Annalen [35,41]. Although I shall discuss both papers in this essay, the main focus will be on , the first systematic exposition of general relativity, submitted in March 1916 and published in May of that year. (shrink)
In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a 'neo-Lorentzian interpretation' of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts.
Scientists working on the wave theory of light in the 19 th century took it for granted that there had to be a medium for the propagation of light waves. This medium was called the luminiferous [= “light carrying”] ether. One of the central questions about this medium concerned its state of motion. There were two options: (1) The ether is completely undisturbed by matter moving through it (stationary or immobile ether); (2) Matter drags along the ether in its vicinity (...) and/or in its interior (dragged-along ether). Stellar aberration provided the main argument for the first option (even though a special dragging effect in the case of transparent matter had to be built into the theory to account for refraction). Polarization provided the main argument for the second option. These two options and the arguments pro and con will be explained in more detail below. (shrink)
A substantial part of my reconstruction can aheady be found, in a very condensed form, in the annotauon for the relevant pages of the Einstein-Besso manuscript in Einstein CP4: doc. 14, pp. [41Ã¢â¬â 42]. The letter to Freundlich and other correspondence from the period 1915 Ã¢â¬â 1917 that I drew on for this paper appear in Einstein CPS. I wrote this paper in the context of a larger project of the Maxplanck-Institut flir Wissenschaflsgeschichte which aims at giving the most detailed (...) reconstruction yet of Einstein's path to general relativity. My paper does not necessarily reflect the views of the other members of the group working on this project. See Renn tk Sauer 1996 for a preliminary report on the gmup's findings. (shrink)
This paper takes as its point of departure two striking incongruities between scientiªc practice and trends in modern history and philosophy of science. (1) Many modern historians of science are so preoccupied with local scientiªc practices that they fail to recognize important non-local elements. (2) Many modern philosophers of science make a sharp distinction between explanation and evidence, whereas in scientiªc practice explanatory power is routinely used as evidence for scientiªc claims. I draw attention to one speciªc way in..
In 1907, Einstein set out to fully relativize all motion, no matter whether uniform or accelerated. After ﬁve failed attempts between 1907 and 1918, he ﬁnally threw in the towel around 1920, setting himself a new goal. For the rest of his life he searched for a classical ﬁeld theory unifying gravity and electromagnetism. As he struggled to relativize motion, Einstein had to readjust both his approach and his objectives at almost every step along the way; he got himself hopelessly (...) confused at times; he fooled himself with fallacious arguments and sloppy calculations; and he committed what he later allegedly called the biggest blunder of his career: he introduced the cosmological constant. There is a very uplifting moral to this somber tale. Although Einstein never reached his original destination, the harvest of his thirteen-year odyssey is quite impressive. First of all, what is left of absolute motion in general relativity is far more palatable than absolute motion in special relativity or Newtonian theory. And general relativity does seem to eliminate absolute space. More importantly, from a modern physics point of view, Einstein produced a spectacular new theory of gravity based on what he called the equivalence principle. This principle says that inertial and gravitational effects are due to one and the same structure, the inertio-gravitational ﬁeld, which in Einstein’s theory is represented by a metric tensor ﬁeld. In addition to laying the foundations of this theory, Einstein, among other things, launched relativistic cosmology, suggested the possibility of gravitational waves, gave the ﬁrst sensible deﬁnition of a space-time singularity, and caught on to the intimate connection between general covariance and energy-momentum conservation, an example of the general connection between symmetries and conservation laws of Noether’s theorems. These results more than make up for the—at least by the standards of modern philosophy of science—rather opportunistic way in which they were obtained.. (shrink)
1.1. The two postulates of special relativity and the tension between them. When Einstein first presented what came to be known as special relativity, he based the theory on two postulates or principles, called the “relativity postulate” or “relativity principle” and the “light postulate.” Both postulates are supported by a wealth of experimental evidence. The combination of the two, however, appears to lead to contradictions. To avoid such contradictions, Einstein argued, we need to change some of our fundamental ideas about (...) space and time. Einstein formulated the relativity postulate as follows: “The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good” (Einstein 1905r, 891). Such frames of reference are called inertial frames and an observer at rest in one of them is called an inertial observer. A few examples will suffice to understand both the concept of an inertial frame and the meaning of the relativity postulate. First consider a plane which starts out sitting on the tarmac, proceeds to fly through clear skies, and eventually hits turbulence. All the while a passenger is nursing a cup of coffee. Sipping coffee without spilling is easy during the smooth portion of the flight. This is because the laws governing the behavior of the coffee in the frame of reference of the plane flying at constant velocity are the same as in the frame of reference of the airport.1 In fact, these same laws hold in any frame moving uniformly (i.e., with constant velocity) with respect to the frame of the airport. Drinking coffee without spilling when the plane ride gets bumpy is much harder. The laws for the coffee in noninertial frames, such as the frame of a plane encountering turbulence, are more complicated than in inertial frames. As a second example consider a cruise ship that sets out from its port of origin, sails smoothly on a calm sea, and eventually is caught in a storm. All the while two passengers engage in a drawn-out tennis match on the ship’s upper deck.. (shrink)
The recently published Vol. 8 of Einstein’s Collected Papers brings together for the ﬁrst time all extant letters and postcards documenting the famous debate of 1916–18 between Einstein and the Leyden astronomer Willem de Sitter (1872–1934), over, as they referred to it, the relativity of inertia. It was in the course of this debate that the ﬁrst two relativistic cosmological models were proposed: the “Einstein cylinder world,” ﬁlled with a uniform static mass distribution; and the completely empty “De Sitter hyperboloid (...) world” (a name introduced in.. (shrink)
In this critical notice we argue against William Craig’s recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig’s defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz’s theory and its historical development is fatally ﬂawed and that his arguments for reviving this theory fail on many counts.
This comment makes four related points. First, explaining coordination is different from explaining cooperation. Second, solving the coordination problem is more important for the theory of games than solving the cooperation problem. Third, a version of the Principle of Coordination can be rationalized on individualistic grounds. Finally, psychological game theory should consider how players perceive their gaming situation.
In the Fall of 1900, Frederick T. Trouton started work on an ingenious experiment in his laboratory at Trinity College in Dublin. The purpose of the experiment was to detect the earth’s presumed motion through the ether, the 19th century medium thought to carry light waves and electric and magnetic ﬁelds. The experiment was unusual in that, unlike most of these so-called ether drift experiments, it was not an experiment in optics. Trouton tried to detect ether drift by charging and (...) discharging a capacitor in a torsion pendulum at its resonance frequency, which he hoped would set the system oscillating. (shrink)
Focal points seem to be important in helping players coordinate their strategies in coordination problems. Game theory lacks, however, a formal theory of focal points. This paper proposes a theory of focal points that is based on individual rationality considerations. The two principles upon which the theory rest are the Principle of Insufficient Reason (IR) and a Principle of Individual Team Member Rationality. The way IR is modelled combines the classic notion of description symmetry and a new notion of pay-off (...) symmetry, which yields different predictions in a variety of games. The theory can explain why people do better than pure randomization in matching games. (shrink)
How do people interleave attention when multitasking? One dominant account is that the completion of a subtask serves as a cue to switch tasks. But what happens if switching solely at subtask boundaries led to poor performance? We report a study in which participants manually dialed a UK-style telephone number while driving a simulated vehicle. If the driver were to exclusively return his or her attention to driving after completing a subtask (i.e., using the single break in the xxxxx-xxxxxx representational (...) structure of the number), then we would expect to see a relatively poor driving performance. In contrast, our results show that drivers choose to return attention to steering control before the natural subtask boundary. A computational modeling analysis shows that drivers had to adopt this strategy to meet the required performance objective of maintaining an acceptable lateral position in the road while dialing. Taken together these results support the idea that people can strategically control the allocation of attention in multitask settings to meet specific performance criteria. (shrink)
In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited (...) to have led directly to Heisenberg's Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation. (shrink)
I relate the story of how matrix mechanics grew out of the treatment of optical dispersion in the old quantum theory, paying special attention to the contributions of the American theoretical physicists John H. Van Vleck and John C. Slater. Van Vleck shares the credit with Max Born for being the first to publish a full derivation of the crucial Kramers dispersion formula using Bohr’s correspondence principle. Slater was one of the architects of the short-lived but influential Bohr-Kramers-Slater (BKS) theory (...) that helped popularize the so-called Ersatz- or virtual oscillators central both to the treatment of dispersion in the old quantum theory and to the transition to matrix mechanics. (shrink)
In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is (...) needed. And we will investigate to what extent non-monotonic epistemic logic can provide such an alternative logical framework. Finally we will show that our non-monotonic logical analysis of explanation is not only suitable for simple cases such as the electric circuit, but that it also sheds new light on more controversial causal explanations such as Milton Friedman's explanation of the business cycle. (shrink)
“Special relativity killed the classical dream of using the energy-momentumvelocity relations as a means of probing the dynamical origins of [the mass of the electron]. The relations are purely kinematical” (Pais, 1982, 159). This perceptive comment comes from a section on the pre-relativistic notion of electromagnetic mass in ‘Subtle is the Lord . . . ’, Abraham Pais’ highly acclaimed biography of Albert Einstein. ‘Kinematical’ in this context means ‘independent of the details of the dynamics’. In this paper we examine (...) the classical dream referred to by Pais from the vantage point of relativistic continuum mechanics. (shrink)
On many occasions, individuals are able to coordinate their actions. The first empirical evidence to this effect has been described by Schelling (1960) in an informal experiment. His results were corroborated many years later by Mehta et al. (1994a,b) and Bacharach and Bernasconi (1997). From the point of view of mainstream game theory, the success of individuals in coordinating their actions is something of a mystery. If there are two or more strict Nash equilibria, mainstream game theory has no means (...) of explaining why people tend to choose their part of one and the same equilibrium. Textbooks (see, e.g., Rasmusen, 1989 and Kreps, 1990) refer to the fact that players may use focal points (see Schelling (1960)) or social conventions (see Lewis (1969)). Both notions cannot easily be incorporated into mainstream game theory, however. The notion of social conventions has recently been extensively studied in the context of evolutionary game theory where a population of agents interacts with each other. The central focus of this paper, however, is on situations where a few players play a game only once and I study how they may coordinate their actions. (shrink)
The relationship between Albert Einstein’s special theory of relativity and Hendrik A. Lorentz’s ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell’s equations, the laws governing electromagnetic ﬁelds in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth’s motion through the ether, Lorentz, in effect, had to assume that the laws (...) governing the matter interacting with the ﬁelds are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz’s theory, it remained an unexplained coincidence that both the laws governing ﬁelds and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reﬂects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz’s interpretation. (shrink)
Scientists working on the wave theory of light in the 19th century took it for granted that there had to be a medium for the propagation of light waves. This medium was called the luminiferous [= “light carrying”] ether. One of the central questions about this medium concerned its state of motion. There were two options: (1) The ether is completely undisturbed by matter moving through it (stationary or immobile ether); (2) Matter drags along the ether in its vicinity and/or (...) in its interior (dragged-along ether). Stellar aberration provided the main argument for the first option (even though a special dragging effect in the case of transparent matter had to be built into the theory to account for refraction). Polarization provided the main argument for the second option. These two options and the arguments pro and con will be explained in more detail below. (shrink)
We report the results of a dual-task study in which participants performed a tracking and typing task under various experimental conditions. An objective payoff function was used to provide explicit feedback on how participants should trade off performance between the tasks. Results show that participants’ dual-task interleaving strategy was sensitive to changes in the difficulty of the tracking task and resulted in differences in overall task performance. To test the hypothesis that people select strategies that maximize payoff, a Cognitively Bounded (...) Rational Analysis model was developed. This analysis evaluated a variety of dual-task interleaving strategies to identify the optimal strategy for maximizing payoff in each condition. The model predicts that the region of optimum performance is different between experimental conditions. The correspondence between human data and the prediction of the optimal strategy is found to be remarkably high across a number of performance measures. This suggests that participants were honing their behavior to maximize payoff. Limitations are discussed. (shrink)
The results of an empirical study into the perceptions of “hands-on” experts concerning the welfare of (non-human) animals in traveling circuses in the Netherlands are presented. A qualitative approach, based on in-depth conversations with trainers/performers, former trainers/performers, veterinarians, and an owner of an animal shelter, conveyed several patterns in the contextual construction of perceptions and the use of dissonance reduction strategies. Perceptions were analyzed with the help of the Symbolic Convergence Theory and the model of the frame of reference, consisting (...) of knowledge, convictions, values, norms, and interests. The study shows that the debate regarding animals in circuses in the Netherlands is centered on the level of welfare that is required; the importance of animal welfare is not disputed. Arguments that were used differed according to the respondents’ specific backgrounds and can be placed on a gradient ranging from the conviction that the welfare of animals in circuses is sufficiently warranted and both human and animal enjoy the performance (right end), to the conviction that animal welfare in circuses is negative, combined with the idea that the goal of entertaining people does not outweigh that (left end). The study confirms that perceptions reflect people’s contexts, though the variety in scopes suggests that the (inter)relations between people and their context are complex in nature. Evidence of cognitive dissonance was abundant. Coping strategies were found to be used more by respondents towards the right end of the gradient, suggesting that those respondents experience more ambivalence. This encountered pattern of association between position on the gradient and frequency of dissonance reduction strategies calls for further research on the type of ambivalent feelings experienced. The authors argue that, to come to an agreement about the welfare of animals in circuses, including the way this welfare should be guaranteed, stakeholders from different contexts need to engage in a dialogue in which a distance is taken from right/wrong-schemes and that starts from acceptance of dilemmas and ambiguity. (shrink)
Many older people in western countries express a desire to live independently and stay in control of their lives for as long as possible in spite of the afflictions that may accompany old age. Consequently, older people require care at home and additional support. In some care situations, tension and ambiguity may arise between professionals and clients whose views on risk prevention or health promotion may differ. Following Antonovsky’s salutogenic framework, different perspectives between professionals and clients on the pathways that (...) lead to health promotion might lead to mechanisms that explain the origin of these tensions and how they may ultimately lead to reduced responsiveness of older clients to engage in care. This is illustrated with a case study of an older woman living in the community, Mrs Jansen, and her health and social care professionals. The study shows that despite good intentions, engagement, clear division of tasks and tailored care, the responsiveness to receive care can indeed not always be taken for granted. We conclude that to harmonize differences in perspectives between professionals and older people, attention should be given to the way older people endow meaning to the demanding circumstances they encounter (comprehensibility), their perceived feelings of control (manageability), as well as their motivation to comprehend and manage events (meaningfulness). Therefore, it is important that both clients and professionals have an open mind and attempt to understand each others’ perspective, and have a dialogue with each other, taking the life narrative of clients into account. (shrink)
The problem of simultaneous measurement of incompatible observables in quantum mechanics is studied on the one hand from the viewpoint of an axiomatic treatment of quantum mechanics and on the other hand starting from a theory of measurement. It is argued that it is precisely such a theory of measurement that should provide a meaning to the axiomatically introduced concepts, especially to the concept of observable. Defining an observable as a class of measurement procedures yielding a certain prescribed result for (...) the probability distribution of the set of values of some quantity (to be described by the set of eigenvalues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible observables. It is shown that such an extension is possible on the basis of a theory of measurement, under the proviso that in simultaneously measuring such observables there is a disturbance of the measurement results of the one observable, caused by the presence of the measuring instrument of the other observable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since overlooking it seems to prohibit an axiomatic description of simultaneous measurement of incompatible observables by quantum mechanics. (shrink)
To describe the content of practice guidelines on euthanasia and assisted suicide (EAS) and to compare differences between settings and guidelines developed before or after enactment of the euthanasia law in 2002 by means of a content analysis. Most guidelines stated that the attending physician is responsible for the decision to grant or refuse an EAS request. Due care criteria were described in the majority of guidelines, but aspects relevant for assessing these criteria were not always described. Half of the (...) guidelines described the role of the nurse in the performance of euthanasia. Compared with hospital guidelines, nursing home guidelines were more often stricter than the law in excluding patients with dementia (30% vs 4%) and incompetent patients (25% vs 4%). As from 2002, the guidelines were less strict in categorically excluding patients groups (32% vs 64%) and in particular incompetent patients (10% vs 29%). Healthcare institutions should accurately state the boundaries of the law, also when they prefer to set stricter boundaries for their own institution. Only then can guidelines provide adequate support for physicians and nurses in the difficult EAS decision-making process. (shrink)
Various restrictions on transformational grammars have been investigated in order to reduce their generative power from recursively enumerable languages to recursive languages.It will be shown that any restriction on transformational grammars defining a recursively enumerable subset of the set of all transformational grammars, is either too weak (in the sense that there does not exist a general decision procedure for all languages generated under such a restriction) or too strong (in the sense that there exists a recursive language that cannot (...) be generated by any transformational grammar thus restricted). In addition, some related problems will be discussed. (shrink)