From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader (...) immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary. (shrink)

Volume 1 of this biography of L. E. J. Brouwer was published in 1999.1 The volume under review here covers the period from the early nineteen twenties until Brouwer's death in 1966. It also includes a short epilogue that discusses the disposition of Brouwer's estate after his death, his influence on others, the paths of some of his students and colleagues, and other matters. Van Dalen notes in the Preface that in preparing this volume he consulted some historical studies that (...) appeared after the first volume was published. He also used new material from various archives. The biography contains interesting quotations from unpublished materials in the Brouwer Archive and from correspondence. The bibliographical references to Brouwer's publications, it should be noted, are somewhat different in this volume. This volume, like the first, contains some nice photographs and reproductions. I noted that there were many typographical errors in the earlier book but Volume 2 is relatively free of them.As is the case in Volume 1, the discussion of Brouwer's mathematical and philosophical work is woven into the narrative of Brouwer's life and times. The story in this volume starts with Brouwer's first contacts with Paul Alexandrov and Paul Urysohn in 1923. The interaction began when Urysohn announced that he had found a mistake in Brouwer's definition of dimension in Brouwer's 1913 paper on natural dimension. Was it just a slip of the pen, as Brouwer always maintained, or something more substantial? Urysohn and Alexandrov ultimately came to agree with Brouwer on the matter, and Urysohn was prepared to grant Brouwer priority for the definition of dimension. There were, however, ups and downs along the way. Karl Menger, through his own work in topology and dimension theory, soon got into the picture, and Brouwer and Menger were to …. (shrink)

The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.

In Norway, research ethics committees in medicine are organized as interdisciplinary regional committees. Since 1999, Norway requires that one member of each ethics committee be a psychologist. Competence in psychology is considered relevant not only when evaluating psychology projects. As discussed in this article, a competence in psychology is also relevant for evaluating a number of issues common to all research involving human subjects as well as in the evaluation of protocols where other professionals have employed psychological methodologies.

We discuss a number of topics that are central in Brouwer's intuitionism. A complete treatment is beyond the scope of the paper, the reader may find it a useful introduction to Brouwer's papers.

There are basically two ways to view intuitionistic logic: as a philosophical‐foundational issue in mathematics; or as a technical discipline within mathematical logic. Considering first the philosophical aspects, for they will provide the motivation for the subject, this chapter follows L. E. J. Brouwer, the founding father of intuitionism. Although Brouwer himself contributed little to intuitionistic logic as seen from textbooks and papers, he did point the way for his successors.

The original Brouwerian counter examples were algorithmic in nature; after the introduction of choice sequences, Brouwer devised a version which did not depend on algorithms. This is the origin of the creating subject technique. The method allowed stronger refutations of classical principles. Here it is used to show that negative dense subsets of the continuum are indecomposable.

Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such (...) as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. (shrink)

Dedicated to Dana Scott on his sixtieth birthday.It is common knowledge that for a short while Hermann Weyl joined Brouwer in his pursuit of a revision of mathematics according to intuitionistic principles. There is, however, little in the literature that sheds light on Weyl's role and in particular on Brouwer's reaction to Weyl's allegiance to the cause of intuitionism. This short episode certainly raises a number of questions: what made Weyl give up his own program, spelled out in “Das Kontinuum”, (...) how did Weyl come to be so well-informed about Brouwer's new intuitionism, in what respect did Weyl's intuitionism differ from Brouwer's intuitionism, what did Brouwer think of Weyl's views,…? To some of these questions at least partial answers can be put forward on the basis of some of the available correspondence and notes. The present paper will concentrate mostly on the historical issues of the intuitionistic episode in Weyl's career.Weyl entered the foundational controversy with a bang in 1920 with his sensational paper “On the new foundational crisis in mathematics”. He had already made a name for himself in the foundations of mathematics in 1918 with his monograph “The Continuum” [18]; this contained in addition to a technical logical-mathematical construction of the continuum, a fairly extensive discussion of the shortcomings of the traditional construction of the continuum on the basis of arbitrary—and hence also impredicative—Dedekind cuts. (shrink)

This chapter contains sections titled: Logic: The Proof Interpretation Analysis: Choice Sequences Further Semantics.

This article analyzes the pediatric material in the Arabic commentaries (written tenth–fifteenth centuries) on the Hippocratic Aphorisms by exploring the traces of its late-antique origins and highlighting the influences of contemporary Islamic sources. This study demonstrates, first, how the commentaries assimilate Galenic pediatric theory through intricate elaborations and innovations; and second, that the commentators on the Aphorisms exhibit a strict theoretical interest in the causes and nature of childood diseases as opposed to their remedies. Consequently, it shows that therapeutic pediatric (...) material was restricted to other nonexegetical genres, such as the encyclopedias of Ibn Sīnā and Ibn Rabban al-Ṭabarī. The commentary material is thus a unique example of medieval Islamic theoria or theoretical medicine, which transmitted and transformed Galenic and early medieval theoretical explanations of childhood illnesses through the centuries. (shrink)

Until recently, only two Arabic translations of Ptolemy’s Almagest were thought to have survived, one by al-Ḥajjāj made under the caliph al-Maʾmūn and one by Isḥāq b. Ḥunayn, later revised by Thābit b. Qurra, prepared in the second half of the third/ninth century. In the 2010s, a third Arabic version of the Almagest, authored by Thābit b. Qurra alone, was first shown by Dirk Grupe to be extant in a partial Latin translation in a Dresden manuscript, and then in an (...) Arabic manuscript in Jaipur that breaks off after chapter VI.2. We introduce here a second manuscript of this Thābit version, extant in the Khuda Bakhsh Library in Patna, which is around four centuries older than the Jaipur manuscript, was copied from a manuscript by the hand of al-Bīrūnī, and extends the text till the middle of Book VIII. After a general introduction, we provide a detailed description of this manuscript. (shrink)

Conducting research in a prison setting is ethically challenging. Because history is full of unethical research conducted in prison settings, researchers are often afraid of doing research in this area. It is argued that too much emphasis has been put on the protection of prison inmates as a vulnerable population. Consequently, too little research is being conducted where the focus is on those factors which serve to make the prison population vulnerable. In this paper ethical questions, emerging when conducting a (...) study on literacy and mental health among Norwegian prison inmates, are presented and discussed. Relevant questions relate to topics which include ethical clearance of the research protocol, the consent procedure, clarification of roles and the publication of the results. The ethical questions are discussed in relation to the four principles of ‘respect for the client's rights and dignity’, ‘competence’, ‘responsibility’ and ‘integrity’ set out in the meta-code of ethics, formulated by the European Federation of Professional Psychologists Associations. The wider relationships between ethics in society, research ethics in general, and ethics when conducting research in a prison setting are also considered. (shrink)

Beth models of analysis are used in model theoretic proofs of the disjunction and (numerical) existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields. The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The (...) book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications. (shrink)

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of (...) mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict. It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century. (shrink)

Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)

Although the main responsibility for informed consent of medical procedures rests with doctors, nurses’ roles are also important, especially as patient advocates. Nurses’ preparation for this role in settings with a hierarchical and communal culture has received little attention. We explored the views of hospital managers and nurses regarding the roles of nurses in informed consent and factors influencing these roles. We conducted a qualitative study in a private, multispecialty hospital in Indonesia. Semi-structured interviews were conducted with seven managers. Two (...) rounds of focus group discussions with nurses (n = 27) were conducted. Constant comparative approach was used in the analysis. Nurses can act as manager, witness, information giver, and advocate in the informed consent process. These roles are influenced by nurses’ preparedness, hospital culture and policy, patients’ understanding, family involvement, and cost-related issues. In preparation for these tasks, nurses should acquire communication skills, clinical knowledge, and legal and ethical knowledge. (shrink)

On October 4, 1937, Zermelo composed a small note entitled “Der Relativismus in der Mengenlehre und der sogenannte Skolemsche Satz” in which he gives a refutation of “Skolem's paradox”, i.e., the fact that Zermelo-Fraenkel set theory—guaranteeing the existence of uncountably many sets—has a countable model. Compared with what he wished to disprove, the argument fails. However, at a second glance, it strongly documents his view of mathematics as based on a world of objects that could only be grasped adequately by (...) infinitary means. So the refutation might serve as a final clue to his epistemological credo.Whereas the Skolem paradox was to raise a lot of concern in the twenties and the early thirties, it seemed to have been settled by the time Zermelo wrote his paper, namely in favour of Skolem's approach, thus also accepting the noncategoricity and incompleteness of the first-order axiom systems. So the paper might be considered a late-comer in a community of logicians and set theorists who mainly followed finitary conceptions, in particular emphasizing the role of first-order logic. However, Zermelo never shared this viewpoint: In his first letter to Gödel of September 21, 1931, he had written that the Skolem paradox rested on the erroneous assumption that every mathematically definable notion should be expressible by a finite combination of signs, whereas a reasonable metamathematics would only be possible after this “finitistic prejudice” would have been overcome, “a task I have made my particular duty”. (shrink)

Although the main responsibility for informed consent of medical procedures rests with doctors, nurses’ roles are also important, especially as patient advocates. Nurses’ preparation for this role in settings with a hierarchical and communal culture has received little attention. We explored the views of hospital managers and nurses regarding the roles of nurses in informed consent and factors influencing these roles. We conducted a qualitative study in a private, multispecialty hospital in Indonesia. Semi-structured interviews were conducted with seven managers. Two (...) rounds of focus group discussions with nurses (n = 27) were conducted. Constant comparative approach was used in the analysis. Nurses can act as manager, witness, information giver, and advocate in the informed consent process. These roles are influenced by nurses’ preparedness, hospital culture and policy, patients’ understanding, family involvement, and cost-related issues. In preparation for these tasks, nurses should acquire communication skills, clinical knowledge, and legal and ethical knowledge. (shrink)

Background: In Southeast Asia, the process of obtaining informed consent is influenced by both culture and policy at the hospital and national level. Both physicians and nurses play vital roles in this process, but physicians influence the roles of nurses. Objectives: Since the physicians and nurses often have different perspectives, it is important to investigate their views about the informed consent process and nurses’ roles therein and whether there is a difference between ideal and experienced practice (reality), and whether this (...) differs across hospitals. Methods: A questionnaire was developed and a survey was conducted among physicians and nurses. Using exploratory factor analysis a three factor structure was determined: ‘nurses’ roles’, ‘barriers in informed consent’, and ‘adequacy of information’. Non-parametric tests were applied to compare nurses and physicians, and hospital setting. Participants and research context: Responses were obtained from 129 physicians and 616 nurses from two Indonesian hospitals. Those hospitals differ in ownership, location, and size. Ethical consideration: The study was reviewed by the hospital ethical committee. Participation was voluntary and confidentiality was ensured by keeping the responses anonymous. Findings: Physicians and nurses differ significantly on all three factors. The scores reflecting disparity between ideal and reality regarding nurses’ roles varied across professions, while barriers in informed consent differed between hospitals. Discussion: The differences between ideal and reality indicated that improvement in the informed consent process and nurses’ roles therein is called for. Varying views between physicians and nurses on nurses’ roles may hinder collaboration. The differences between hospital settings showed interventions may have to be customized for different settings. Conclusion: Views on nurses’ roles vary across professions. Views on barriers in informed consent vary across hospitals. Therefore interprofessional education is needed to promote interprofessional collaboration and intervention to improve informed consent practice should be tailored to the hospital context. (shrink)