Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of the Burnside Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of (...) the mathematical community at the turn of the twentieth century. (shrink)

H.B.G. Casimir's life, interests and works are intertwined with the important developments that have taken place in physics during this century. This book was compiled by his friends and admirers in honour of his 80th birthday and concentrates mainly on Casimir's achievements in the field of physics, though without ignoring the peripheral areas of the history and philosophy of physics in which he was greatly interested. The book is divided into four parts. Part I describes Casimir's teachers, Ehrenfest, Bohr and (...) Pauli, and will be of general interest due to the key role which these physicists played in modern developments. The articles do give new facts and provide new insights into the history of modern physics. Part II consists of essays on recent developments in various areas of physics in which Casimir has taken an active interest, such as the modern concept of time, statistical foundations of electrodynamic theory and field theory. The subjects covered in Part III have been selected because of Casimir's efforts in the industrial research area of physics. They cover past, present and future expectations in research. (shrink)

Jean-Paul Sartre, in describing the realization of his freedom, was often inclined to say mysterious things like ‘I am what I am not’, ‘I am not what I am’ (‘as I am already what I will be …, I am the self which I will be, in the mode of not being it’, ‘I make myself not to be the past … which I am’.) He was therefore plainly contradicting himself, but was this merely a playful literary figure (paradox), or (...) was he really being incoherent? By the latter judgment I do not mean to reject his statements entirely (like many of his Anglo-Saxon contemporaries); for I believe there is an intimate link between contradiction and freedom, as I shall explain in this paper. But a minor thing we must first have out of the way is the suggestion that Sartre's language was just a rhetorical trope, designed merely to express some banal platitude in a bemusing way: ‘I am not yet what I will be’, ‘I am no longer what I was’ are sane and sensible, for instance, but cannot be the meant content of Sartre's sayings, since, while they would indeed describe the reform of some character, they would be appropriate only before or after some metamorphosis, not, as Sartre clearly intended, in the midst of some process of riddance and conversion, whether radical or otherwise. Yet, in the turmoil of such a change, ‘I am not what I am’ (or the everyday ‘I am not myself’) still, surely, cannot be true, and if that is the case, Sartre must be being inocherent, and therefore, obfuscating and deliberately obscure, and hence, it seems, must properly be rejected by all right and clear thinking men. (shrink)

Background: Older, frail patients with multimorbidity are at an especially high risk for disease severity and death from COVID-19. The social restrictions proved challenging for the residents, their relatives, and the care staff. While these restrictions clearly impacted daily life in Norwegian nursing homes, knowledge about how the pandemic influenced nursing practice is sparse. Aim: The aim of the study was to illuminate ethical difficult situations experienced by Norwegian nurses working in nursing homes during the COVID-19 pandemic. Research design and (...) participants: The research design involved semistructured individual interviews conducted with 15 nurses working in 8 nursing homes in 3 health regions in Norway, within both urban and rural areas. Ethical considerations: Oral and written information about the study was provided before the participants gave their written consent. The transcribed interviews were de-identified. The study was approved by the Norwegian Centre for Research Data. Findings: Four ethical difficult situations were identified: (a) turning the nursing home into a prison; (b) using medication to maintain peace and order; (c) being left alone with the responsibility; and (d) s. impact on decision-making. Conclusions: The nurses’ ethical challenges were intertwined with external factors, such as national and local guidelines, and the nurses’ own internalized factors, which were connected to their subjective professionality. This duality inflicted emotional distress and gave nurses few opportunities to perform nursing in a professionally sound and safe manner. (shrink)

Background: Recent research demonstrates that people sometimes make different medical decisions for others than they would make for themselves. This finding is particularly relevant to end-of-life decisions, which are often made by surrogates and require a trade-off between prolonging life and maintaining quality of life. We examine the impact of decision role, patient age, decision maker age and multiple individual differences on these treatment decisions. Methods: Participants read a scenario about a terminally ill cancer patient faced with a choice between (...) an aggressive chemotherapy regimen that will extend life by two years and palliative treatments to control discomfort for one remaining month. Participants were randomly assigned to one of three decision roles (patient, physician, or an abstract other) and the scenario randomly varied whether the patient was described as 25 or 65-years old. Results: When deciding for a 65-year old patient, approximately 60% of participants selected aggressive chemotherapy regardless of decision role. When deciding for a 25-year old patient, however, participants were more likely to select chemotherapy for a patient (physician role) or another person (abstract other) than for themselves (70%, 67%, and 59%, respectively). In addition, confidence that powerful others (eg, physicians) control one’s health, as well as respondents’ age and race, consistently predicted treatment choices. Conclusions: Patient age appears to influence medical decisions made for others but not those that we make for ourselves. These findings may help to explain the discord that often occurs when younger cancer patients refuse life-extending treatments. (shrink)

The eleventh-century Byzantine compiler Cedrenus includes a unique story in the midst of his otherwise traditional and hagiographic material on the emperor Constantine. Mentioning the outbreak of war between the Roman and Persian empires, he describes the cause of the breakdown of peace somewhat as follows. A certain Metrodorus, who was of Persian origin, went to visit the Brahmins in India to study philosophy and won the reputation of being a holy man through his asceticism. He also built water mills (...) and baths, unknown to the Indians till that time. Having acquired this reputation, he entered the temples and took away many precious stones and pearls. He also received gifts from the king of the Indians. On his return to Byzantium he gave them to the emperor Constantine as being gifts of his own. When Constantine expressed his astonishment, Metrodorus said he had sent other gifts by the land route but that they had been detained by the Persians. Constantine then wrote a strong protest to Sapor demanding the gifts but received no reply; thus the peace was broken. This remarkable conte, more appropriate to the Arabian Nights than to sober history, is generally supposed to be referred to in a passage in Ammianus. Towards the end of a long section commenting on the personality and achievements of Julian, Ammianus turns briefly to the question of the ultimate responsibility for the Persian War which ended so disastrously for Julian and the Roman Empire: et quoniam eum obtrectatoribus novos bellorum tumultus ad perniciem rei communis insimulant concitasse, sciant docente veritate perspicue, non Iulianum sed Constantinum ardores Parthicos succendisse, cum Metrodori mendaciis avidius acquiescit, ut dudum rettulimus plane. (shrink)

The Peanese convention for the use of dots as brackets has the disadvantage that it gives only an awkward method for representing chains of indefinite length, such as the compound implicationSuch chains occur frequently in logical investigations of a metatheoretic nature, and it is convenient to have a systematic method of abbreviating them. The most obvious method of doing this would be to leave the parentheses out entirely, and to understand that in such cases the implication sign or other operation (...) appearing on the extreme left is the most inclusive; but this method, which has been followed by Quine, is at variance with our ordinary algebraic usage, in which we write a − b + c − d for ((a − b) + c) − d, and consequently leads to confusion. It is desirable to have a modification of the Peanese convention which gives a simple method of representing such chain implications, and at the same time avoids this difficulty.Such a modification is easily obtained by generalizing somewhat a procedure of Church. The latter author uses only a single dot, which he writes on the right of an operator to signify a bracket extending from that point to the end of the formula (or parenthesized expression). If dots are used only on the right of operations this is all that can be desired. But the essential idea of this device can be extended to the case where dots are used also on the left, as follows: let us suppose that a group of dots on the right of an operation or prefix denotes the beginning of a bracket which extends to the right until it meets a group with an equal or larger number of dots on the left of an operation; and that the scope of a group of dots on the left of an operation shall extend to the left until it reaches a larger group of dots on the right of some operation. (shrink)

Brian Wormald provides a fundamental reappraisal of one of the most complex and innovative figures of the late-Elizabethan and Jacobean age. In the centuries since his death, Francis Bacon (1561-1626) has been perceived and studied as a promoter and prophet of the philosophy of science--natural science--but he saw himself also as a clarifier and promoter of what he called "policy" or the study and improvement of the structure and function of civil states. Mr. Wormald shows that Bacon was concerned equally (...) with the knowledge of the world of nature and with that of policy. The junction between the two enterprises was effected by his work in history; and in the end it was Bacon's conception and practice of history that provided the answer to his efforts to advance policy and natural philosophy. (shrink)

The paper presents and applies Hilbert's Epsilon Calculus, first describing its standard proof theory, and giving it an intensional semantics. These are contrasted with the proof theory of Fregean Predicate Logic, and the traditional (extensional) choice function semantics for the calculus. The semantics provided show that epsilon terms are referring terms in Donnellan's sense, enabling the symbolisation and validation of argument forms involving E-type pronouns, both in extensional and intensional contexts. By providing for transparency in intensional constructions they support a (...) Model Conceptualism to contrast with traditional intensional logic's Modal Realism. But epsilon-terms also symbolise fictions, and through their difference from iota terms enable the solution of a number of outstanding puzzles about Direct Reference and de re beliefs. (shrink)

In the context of the motor skill literature on observational learning and hierarchical skill structuring, Byrne & Russon's findings call into question their standpoint that great apes imitate the behaviour of role models at the programme level. The authors impose a hierarchical model on their observations without properly considering alternative explanations. One such possibility, which stems from a constraints perspective that they dismiss, is put forward.