Drawing on letters, orations and disputations, this book argues that during the seventeenth century, the Amsterdam Athenaeum, despite the revolutionary debates of the time, and despite the intellectual liberalism characteristic of Amsterdam, remained traditional in its teaching.

The original essays in this volume present new research on unstructured theories of content, which have traditionally played a central role in linguistics and philosophy of language. The volume explores a wide range of themes related to unstructured content, including both the continued controversy over whether unstructured theories individuate contents too coarsely and various applications of unstructured theories to topics like rationality, epistemic commitment, semantic expressivism, relevance, and propositional attitude ascriptions. It contains contributions from different theoretical perspectives, including both those (...) sympathetic to unstructured theories of content and those who are skeptical, as well as from different methodological backgrounds, with philosophy, logic, and linguistics all represented. With contributions from leading scholars in philosophy and linguistics, this volume will be of interest to anyone working in logic, metaphysics, or the philosophy of mind. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...) precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

Irrespective of the short academic history of Christian spirituality, a vast number of academic and popular publications ensued and is still dynamically growing. Many definitions have been proposed to define (Christian) spirituality. Spirituality is also no longer connected only to religion, although in this research the focus will fall on Christian spirituality. This research intends to partake in the continuing academic dialogue to define Christian spirituality. Christian spirituality is interpreted from the perspective of the divine-human conversation. This research consists of (...) three sections. In the first section, a working definition of Christian spirituality is formulated. In the second section, various aspects that constitute spiritualities are distinguished and discussed. In the last section, the constituents of Christian spirituality are pointed out and are reviewed from a conversational perspective. The focus will be on ‘the experience of the divine’ when living a life that resonates with the Christian life. (shrink)

Lexical diversity, the amount of lexical variation shown by a particular concept, varies between concepts. For the conceptdrunk, for instance, nearly 3000 English expressions exist, includingblitzed, intoxicated, andhammered. For the conceptsober, however, a significantly smaller number of lexical items is available, likesoberorabstinent. While earlier variation studies have revealed that meaning-related concept characteristics correlate with the amount of lexical variation, these studies were limited in scope, being restricted to one semantic field and to one dialect area, that of the Limburgish dialects (...) of Dutch. In this paper, we investigate whether the impact of concept characteristics, viz. vagueness, lack of salience and proneness to affect, is manifest in a similar way in other dialects and other semantic fields. In particular, by extending the scope of the earlier studies to other carefully selected semantic fields, we investigate the generalizability of the impact of concept characteristics to the lexicon as a whole. The quantitative approach that we employ to measure concept characteristics and lexical diversity methodologically advances the study of linguistic variation. Theoretically, this paper contributes to the further development of Cognitive Sociolinguistics by showcasing how meaning can be a source of lexical diversity. (shrink)

Lexical diversity, the amount of lexical variation shown by a particular concept, varies between concepts. For the concept drunk, for instance, nearly 3000 English expressions exist, including blitzed, intoxicated, and hammered. For the concept sober, however, a significantly smaller number of lexical items is available, like sober or abstinent. While earlier variation studies have revealed that meaning-related concept characteristics correlate with the amount of lexical variation, these studies were limited in scope, being restricted to one semantic field and to one (...) dialect area, that of the Limburgish dialects of Dutch. In this paper, we investigate whether the impact of concept characteristics, viz. vagueness, lack of salience and proneness to affect, is manifest in a similar way in other dialects and other semantic fields. In particular, by extending the scope of the earlier studies to other carefully selected semantic fields, we investigate the generalizability of the impact of concept characteristics to the lexicon as a whole. The quantitative approach that we employ to measure concept characteristics and lexical diversity methodologically advances the study of linguistic variation. Theoretically, this paper contributes to the further development of Cognitive Sociolinguistics by showcasing how meaning can be a source of lexical diversity. (shrink)

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

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)

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)

Via a historical reconstruction, this paper primarily demonstrates how the societal debate on genetically modified organisms (GMOs) gradually extended in terms of actors involved and concerns reflected. It is argued that the implementation of recombinant DNA technology out of the laboratory and into civil society entailed a “complex of concerns.” In this complex, distinctions between environmental, agricultural, socio-economic, and ethical issues proved to be blurred. This fueled the confusion between the wider debate on genetic modification and the risk assessment of (...) transgenic crops in the European Union. In this paper, the lasting skeptical and/or ambivalent attitude of Europeans towards agro-food biotechnology is interpreted as signaling an ongoing social request – and even a quest – for an evaluation of biotechnology with Sense and Sensibility. In this (re)quest, a broader-than-scientific dimension is sought for that allows addressing the GMO debate in a more “sensible” way, whilst making “sense” of the different stances taken in it. Here, the restyling of the European regulatory frame on transgenic agro-food products and of science communication models are discussed and taken to be indicative of the (re)quest to move from a merely scientific evaluation and risk-based policy towards a socially more robust evaluation that takes the “non-scientific” concerns at stake in the GMO debate seriously. (shrink)

A wide-ranging analysis of the economic world order and its ecological and theological dimensions, this unique and challenging work confronts us with the ...

In the present paper the story is told of the brief and far from tranquil encounter of L.E.J. Brouwer and A. Fraenkel. The relationship which started in perfect harmony, ended in irritation and reproaches.The mutual appreciation at the outset is beyond question. All the more deplorable is the sudden outbreak of an emotional disagreement in 1927. Looking at the Brouwer–Fraenkel episode, one should keep in mind that at that time the so-calledGrundlagenstreitwas in full swing. An emotional man like Brouwer, who (...) easily suffered under stress, was already on edgewhen Fraenkel's bookZehn Vorlesungen Über die Grundlegung der Mengenlehre, [Fraenkel 1927] was about to appear.With theGrundlagenstreitreaching (in print!) a level of personal abuse unusual in the quiet circles of pure mathematics, Brouwer was rather sensitive, where the expositions of his ideas were concerned. So when he thought that he detected instances of misconception and misrepresentation in the case of his intuitionism, he felt slighted. We will mainly look at Brouwer's reactions. since the Fraenkel letters have not been preserved.The late Mrs. Fraenkel kindly put the Brouwer letters that were in her possession at my disposal. I am grateful to the Fraenkel family for the permission to use the material.I am indebted to Andreas Blass for his valuable suggestions and corrections.Abraham Fraenkel (then still called Adolf) was one of the first non-partisan mathematicians, if not the first, who developed a genuine interest in intuitionism. (shrink)

Servant leadership is increasingly gaining interest inside and outside academia. This article builds and extends current theorizing by describing the process that introduces compassionate love as a practical translation for the need to serve, which was positioned by Greenleaf as the core of servant leadership. This article takes a virtues perspective and shows how servant leadership may encourage a more meaningful and optimal human functioning with a strong sense of community to current-day organizations. In essence, we propose that a leader’s (...) propensity for compassionate love will encourage a virtuous attitude in terms of humility, gratitude, forgiveness and altruism. This virtuous attitude will give rise to servant leadership behavior in terms of empowerment, authenticity, stewardship and providing direction. (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)

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.

. “Normal” Prisons in an “abnormal” society? A comparative perspective on South African prison law and practice. Criminal Justice Ethics: Vol. 6, No. 2, pp. 37-51. doi: 10.1080/0731129X.1987.9991816.

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)

Accounts and analyses of the formation of scholarly and scientific communities in the early modern period by means of memory and collective identity.