vol. 76 num. 4 lang. en
Hierdie artikel handel oor die ontstaan van die moderne versamelingsleer wat, volgens Meschkowski, saamval met die eerste bewys wat Cantor in 1874 gepubliseer het vir die ooraftelbaarheid van die reële getalle. Later het Cantor sy bekende dia-gonaalbewys ontwikkel, wat die kern van hierdie artikel vorm. Die beredenering van die onderhawige artikel is gerig op die implisiete veronderstelling van die diagonaalbewys, naamlik die aanvaarding van die aktueel-oneindige (wat meer gepas die opeens-oneindige genoem kan word). Sonder hierdie aanname kan nie tot ooraftelbaarheid gekonkludeer word nie. Verskeie wiskundiges en wiskundige tradisies het gedurende die twintigste eeu die gebruik van die opeens-oneindige in die wiskunde bevraagteken. In die besonder word nader ingegaan op twee prominente teenstanders van die opeens-oneindige, naamlik Kaufmann en Wolff. Die sirkelredenasie wat in albei benaderings opgesluit lê, word uitgewys en as alternatief word 'n verantwoording van die gebruik van die opeens-oneindige verduidelik wat nie dit wat bewys wil word as uitgangspunt neem nie. Tegelyk word die beweerde eksaktheid (en neutraliteit) van die wiskunde bevraagteken (in die gees van 'Koers' as Christelik-wetenskaplike tydskrif). Hierdie besinning sien egter daarvan af om nader op die aard van die wiskunde in te gaan (deur byvoorbeeld ook die topologie, kategorieteorie en toposteorie te betrek) - wat ons gedagtegang sou heenvoer na die kontemporêre opvattings van persone soos Tait, Penelope en Shapiro, onder meer in hulle rol as redakteurs van en bydraers tot die omvangryke "Handbook of Philosophy of Mathematics and Logic" (2005).<hr/>The focus of this article is the rise of modern set theory which, according to Meschkowski, coincides with the first proof given in 1874 by Cantor of the non-denumerability of the real numbers. Later on he developed his well-known diagonal proof, which occupies a central position in this article. The argument of this article is directed towards the implicit supposition of the diagonal proof, to wit the acceptance of the actual infinite (preferably designated as the at once infinite). Without this assumption no conclusion to non-denumerability is possible. Various mathematicians and mathematical traditions of the twentieth century questioned the use of the actual infinite. A closer investigation is conducted in respect of two opponents of the actual infinite, namely Kaufmann and Wolff. The circular reasoning contained in their approach is highlighted and as alternative a non-circular understanding of the at once infinite is explained. At the same time the assumed exact nature (and neutrality) of mathematics is questioned (in the spirit of Koers' as a Christian academic journal). This contemplation disregards the question of what mathematics is (for example by including topology, category theory and topos theory), which would have diverted our attention to contemporary views of figures such as Tait, Penelope and Shapiro who, among others, acts as the editors of and contributors to the encompassing work 'Handbook of Philosophy of Mathematics and Logic' (2005).
Understanding beyond language: Perceiving meaning in reality]]>
This article is an attempt to develop a counter-argument to the contention that meaning is bound by language. Locating itself within the realist ontology of language developed by Saint Anselm of Canterbury, it will be argued that language comprises representations of entities perceived both extra to the perceiver and through introspection. Thus, a language game cannot be a closed system in the sense that by its very existence representations of extralinguistic being are contained therein. If truth is defined as that which is the case, the task of the perceiver becomes apprehension of being beheld without the cloud imposed by symbols: representations are not what they represent, instead they serve as windows onto a view of what is. Following exploration of psychological studies on contemplation, it is argued that it is in desymbolised moments of attentive awareness of being that meaning, unfiltered by the representativeness of language (and indeed, other symbolic systems), can arise. It will be proposed that in contemplative traditions, being is not reduced in perception, and the moment of meaning comes to the fore in the engagement and encounter with being.<hr/>Hierdie artikel is 'n poging om 'n teenargument te ontwikkel vir die standpunt dat betekenis ingeperk word deur taal. Deur die argument binne die werklikheidsontologie van Sint Anselmus van Canterbury te plaas, sal geargumenteer word dat taal representasies bevat van entiteite wat buite die waarnemer en ook deur introspeksie waargeneem word. 'n Taalspeletjie kan dus nie 'n geslote sisteem wees sodat deur sy blote bestaan representasies van buite-linguistiese syn daarin vervat is nie. Indien waarheid gedefinieer word as dit wat is, word die taak van die waarnemer bewuswording van syn sonder die wolk wat deur representasie opgelê word. Representasies of simbole is nie dit wat hulle voorstel nie; hulle dien eerder as vensters op dit wat is. In die lig van psigologiese studie oor nadenke word geargumenteer dat ongesimboliseerde oomblikke van aandagtige bewustheid van syn, betekenis na vore laat kom wat nie deur die representatiewe aard van taal (en inderdaad ook ander simboliese stelsels) gefiltreer is nie. Die stelling word gemaak dat in kontemplatiewe (nadenkende) tradisies die syn nie gereduseer word tot gewaarwording nie, en dat die oomblik van betekenis na vore kom in die betrokkenheid by en die ont-moeting met die syn.
"In order to breathe": Transformative mimesis as a condition for commitment in the poetry of Antjie Krog]]>
Betrokke skryfwerk benadruk 'n tipe verhouding tussen die teks, die werklikheid en die leser en dit veronderstel mimesis. Mimesis is egter 'n oënskynlik uitgediende konsep in die literêre estetika. Daarom is dit noodsaaklik om mimesis konseptueel te rehabiliteer ten einde wesenlike literêre betrokkenheid te kan verreken. Sodanige rehabilitasie kan gedoen word via Paul Ricoeur se teorie van drievoudige mimesis, ook bekend as die mimetiese boog. Die mimetiese boog laat 'n siening van mimesis toe wat nóg estetiese outonomie, nóg estetiese heteronomie privilegeer. Daardeur word die invloedsfeer van kuns in die samelewing behou, sonder dat kuns se eiesoortige doelwitte en karaktertrekke prysgegee word. Die drievoudige mimetiese proses dui gevolglik op 'n transformerende mimesis wat as die moontlikheidsvoorwaarde van literêre betrokkenheid self dien. Die beginsels van transformerende mimesis is op 'n duidelike en insiggewende wyse teenwoordig in die poësie van Antjie Krog. Haar poësie kan derhalwe as eksemplariese-betrokke kuns beskou word.<hr/>Committed writing makes salient a type of relationship between text, reality and reader which presupposes mimesis. Mimesis is, however, a seemingly outdated concept in literary aesthetics. Therefore, it is necessary to rehabilitate mimesis conceptually in order to account for actual literary commitment. This rehabilitation can be done via Paul Ricoeur's theory of a threefold mimesis, also known as mimetic arc. The mimetic arc allows a view of mimesis that privileges neither aesthetic autonomy nor aesthetic heteronomy. Thereby the power of art to influence society is preserved without compromising its unique aesthetic goals and characteristics. The threefold mimetic process consequently points towards a transformative mimesis, which acts as the condition for the possibility of literary commitment itself. The principles of transformative mimesis are present in the poetry of Antjie Krog in a salient and enlightening way, making her poetry exemplary committed art.
The radicalisation of a Swedish ecclesiastical critic of apartheid - Gunnar Helander]]>
From the 1950s through the 1980s, both the government of Sweden and various non-governmental agencies in that country stood at the forefront of the international campaign against apartheid. To a considerable extent, representatives of the Church of Sweden Mission were involved in this struggle. Among them was Gunnar Helander (1915-2006), a missionary in Natal and on the Witwatersrand from 1938 until 1956. After he returned permanently to Sweden, his role escalated and became known internationally, especially due to his prominence in the leadership of the International Defence and Aid Fund. Between 1949 and 1986 Helander wrote seven novels set in South Africa. In these works one can trace the unfolding of his position on apartheid, which evolved from mild criticism of race relations in South Africa to advocacy of international subversion of the P.W. Botha regime.<hr/>Vanaf die vyftiger- tot die tagtigerjare van die vorige eeu het die Sweedse regering, asook talle nie-regeringsorganisasies in hierdie land, aan die voorpunt gestaan van die internasionale stryd teen apartheid. Verskillende verteenwoordigers van die Church of Sweden Mission was in 'n groot mate aktief in hierdie stryd betrokke. Onder hulle was Gunnar Helander (1915-2006) wat as 'n sendeling tussen 1938 en 1956 in Natal en aan die Witwatersrand gewerk het. Na sy permanente terugkeer na Swede in 1956 het die rol wat hy gespeel het egter vergroot en hy het ook internasionaal bekend geword, veral vanweë sy betrokkenheid in die leierskap van die International Defence and Aid Fund. Tussen 1949 en 1986 het Helander ook sewe romans geskryf wat in Suid-Afrika afspeel. In hierdie werke kan 'n mens die ontwikkeling van sy denke oor apartheid volg, wat gegroei het van aanvanklike matige kritiek op rasseverhoudings in Suid-Afrika tot die bepleiting vir internasionale omverwerping van die P. W. Botha-regering.
Concerns about the future of creation order]]>
The theological background to the notion of the law of nature/ creation order is indispensable to the reformational tradition, which recognises that these laws are the Creator's will, and therefore holds a "necessity" view of these laws. There has, however, been a longstanding debate about the nature of law within the reformational tradition, where its origin and its status as boundary between God and creation have been questioned. In this article I will investigate how Trinitarian theology, specifically that of Robert W. Jenson, relates to process philosophy and theology, and how together they create some theological concerns about the future of creation order. Some of the concerns include the following: that the necessity of order is questioned (the disappearance of a Creator who wills these laws); that order is temporal and in constant change; and that the boundary between God and creation is weakened. I will raise some objections to these aspects, but will also highlight some questions the reformational tradition has to answer in terms of its understanding of the immanence of God and of the implicated theological basis for the creation order. These questions are of the utmost importance for the understanding of the future of creation order.<hr/>Die teologiese agtergrond van die idee van 'n skeppingsorde is onontbeerlik vir die reformatoriese tradisie. Volgens hierdie tradisie is die natuurwette die Skepper se wil en daarom word hierdie orde as noodsaaklik beskou. 'n Voortslepende debat binne die reformatoriese tradisie bestaan egter lank reeds ten opsigte van die aard van die skeppingsordening, waarvolgens die oorsprong en status daarvan as skeiding tussen God en die skepping bevraagteken word. Ek gaan in hierdie artikel ondersoek instel na die Trinitariese teologie, spesifiek hoe dié van Robert W. Jenson verband hou met prosesfilosofie en -teologie, asook hoe dit gesamentlik sekere teologiese bekommernise oor die toekoms van 'n skeppingsorde laat ontstaan. Sommige van hierdie kwessies sluit in dat die noodsaaklikheid van 'n skeppingsorde bevraagteken word (die verdwyning van 'n Skepper wat hierdie ordeninge wil); dat orde tydelik is en gedurig verander; en dat die grens tussen God en skepping vervaag. Ek sal sekere besware oor hierdie kwessies opper, maar ek sal ook sekere vrae uitlig wat die reformatoriese tradisie moet beantwoord in terme van hulle begrip van die immanensie van God en van die geïmpliseerde teologiese grondslag van die skeppingsorde. Hierdie vrae is van die uiterste belang vir insig oor die toekoms van 'n skeppingsorde.
Values and ethics enter the real world: A framework for public leadership and governance]]>
Indications are that an ethical problem exists regarding the internalisation of norms and values in the public sector. This results in an unacceptable number of public scandals related to malfeasance and it indicates that mechanisms to curb ethical violations are not always effective. All over the world governments experience such ethical violations. This article argues for a paradigm shift in public leadership and governance. What is required is a framework for the internalisation of values, ethics and norms to accentuate accountability. It is argued that answers to malfeasance do not lie in the ordinary process of education and training to conscientise public leaders about their role and compliance to policies, rules and regulations. Instead the solution is contained in the internalisation of values and ethics of public leadership and governance, and ensuring that these are upheld at all times. There should also be sanctions for unaccountability. Negotiating the reasons for not meeting set goals after the fact is a practice that compromises accountability. It is emphasised that accountability can thrive only in situations wherein values and ethics are rendered practical through public leadership and governance.<hr/>Genoegsame bewyse bestaan dat daar 'n etiese probleem in die openbare sektor is met betrekking tot die internalisering van norme en waardes. Dit het tot gevolg dat 'n onaanvaarbare hoeveelheid openbare skandale in verband met met ampsoortredings voorkom. Dit toon ook aan dat meganismes om etiese oortredings aan bande te lê, nie altyd doeltreffend is nie. Wêreldwyd ervaar regerings soortgelyke etiese oortredings. Hierdie artikel betoog vir 'n paradigmaskuif in openbare leierskap en staatsbestuur. 'n Strategie vir die internalisering van waardes, etiek en norme word benodig om aanspreeklikheid te beklemtoon. Daar word aangevoer dat antwoorde hiervoor nie te vind is in die gewone proses van onderrig en opleiding waar openbare leiers oor hulle rolle en nakoming van beleide, reëls en regulasies attent gemaak word nie. Dit is meer waarskynlik dat die antwoord lê in die internalisering van waardes en etiek van openbare leierskap en staatsbestuur, en die versekering dat dit te alle tye toegepas word. Daar behoort ook meetbare sanksies in plek te wees in gevalle van onverantwoordbaarheid. Om agterna oor die redes vir die nie-bereiking van doelwitte te onderhandel, is 'n praktyk wat aanspreeklikheid ondermyn. Daar word verder beklemtoon dat aanspreeklikheid slegs kan floreer wanneer waardes en etiek deur openbare leierskap en staatsbestuur prakties uitgeleef word.
Education of quality to the poor]]>
Quality education often eludes South African learners from poverty-stricken environments. There are, however, some notable exceptions. This article looks at how quality education based on social capital is provided to the poor. The author reports on a qualitative investigation based on both focus group and individual interviews conducted at a resource-poor KwaZulu-Natal school serving learners from Grade R to 9. The findings show that quality education at the research site relates to the moral agency of the school principal and teaching staff. Through their ethics of being and doing, the school principal and teaching staff ensure that sufficient resources, sound home-school relations, and a high premium on moral values result in a receptive learner corps. This environment encourages these learners to act with diligence, honesty, politeness, respect and service to the community. The findings contribute to research that maintains that quality education is indicative of the school principal and teachers' ethics of being and of doing.<hr/>Gehalte-onderwys is nie vrylik beskikbaar aan leerders uit arm omgewings nie. Daar is egter merkwaardige uitsonderings. Hierdie artikel ondersoek hoe gehalte-onderwys wat op sosiale kapitaal gegrond is aan arm leerders voorsien word. Die outeur doen verslag oor 'n kwalitatiewe ondersoek gebaseer op individuele en fokusgroeponderhoude wat gevoer is by 'n arm KwaZulu-Natalse skool vir leerders van graad R tot 9. Bevindings dui daarop dat gehalte-onderwys by hierdie navorsingsterrein verband hou met die morele bemiddeling van die skoolhoof en onderwysers. Deur middel van hulle etiek van wees en doen, verseker die skoolhoof en onderwysers dat voldoende hulpmiddels, gesonde verhoudings tussen die huis en skool, asook 'n hoë premie op morele waardes 'n ontvanklike leerderkorps tot gevolg het. Hierdie milieu bemagtig leerders met ywer, eerlikheid, hoflikheid, respek en bereidheid tot gemeenskapsdiens. Die bevindings dra by tot navorsing wat toon dat gehalte-onderwys 'n aanduiding is van die skoolhoof en onderwysers se etiek van wees en doen.
A missionary of a different kind]]>
Van die Kaap tot Gelderland]]>
Language rights: The way forward]]>
Evolution of language rights]]>
Caring for the chronically and terminally ill]]>