31 resultados para Mathematics history

em Helda - Digital Repository of University of Helsinki


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This study examines the scholarly reception history of an early Irish text, Buile Shuibhne (The Frenzy of Suibhne), by focusing on the various theoretical and methodological presuppositions which have determined the scholars’ understanding of the text’s religious allegorical significance in the course of the 20th century. The reception-oriented inquiry takes the intersubjective aspect of literary interpretation as the basis for accentuating the importance of communally shared presumptions and reading strategies in the explication of interpretive variety. The materials of the study have been divided into four frameworks of interpretation: historical, pre-Christian, Christian and anthropological. This heuristic division does not denote mutually exclusive paradigms, but rather refers to perceived similarities within each group regarding the questions posed, and the evidence adduced, in textual analysis. The historical framework concentrates on the issues of the origins of the tale and the possible historicity of its main protagonist. The pre-Christian framework covers the theories of the shamanic, Indo-European and Celtic elements in the text, whereas the Christian framework includes readings emphasising the biblical, monastic and ascetic aspects of the tale. The anthropological framework in turn focuses on the parallels drawn between the narrative and the universal structure of the rites of passage. In addition to the examination of these four frameworks, the study also links the question of methodology with wider issues of authorship and textual integrity, and critically reconsiders the manner in which J.G. O'Keeffe's 1913 edition of the text has been reified in previous scholarship as a representation of a 12th century authorial original. The overall objective of the present case-study is to relate theoretical conceptions of literary theory, comparative religion and historiography to the study of early Irish narrative material by considering the communal and institutional dimension of meaning-making, and the implications of comparative methodology for historical research. In this aim, the prevailing methodological presuppositions informing the scholarly discourse on Buile Shuibhne are set against the wider context of Celtic Studies scholarship, in order to draw attention to the need to critically reflect upon the operations of knowledge production in future research.

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One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

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The study is an examination of how the distant national past has been conceived and constructed for Finland from the mid-sixteenth century to the Second World War. The author argues that the perception and need of a national 'Golden Age' has undergone several phases during this period, yet the perceived Greatness of the Ancient Finns has been of great importance for the growth and development of the fundamental concepts of Finnish nationalism. It is a question reaching deeper than simply discussing the Kalevala or the Karelianism of the 1890s. Despite early occurrences of most of the topics the image-makers could utilize for the construction of an Ancient Greatness, a truly national proto-history only became a necessity after 1809, when a new conceptual 'Finnishness' was both conceived and brought forth in reality. In this process of nation-building, ethnic myths of origin and descent provided the core of the nationalist cause - the defence of a primordial national character - and within a few decades the antiquarian issue became a standard element of the nationalist public enlightenment. The emerging, archaeologically substantiated, nationhood was more than a scholarly construction: it was a 'politically correct' form of ethnic self-imaging, continuously adapting its message to contemporary society and modern progress. Prehistoric and medieval Finnishness became even more relevant for the intellectual defence of the nation during the period of Russian administrative pressure 1890-1905. With independence the origins of Finnishness were militarized even further, although the 'hot' phase of antiquarian nationalism ended, as many considered the Finnish state reestablished after centuries of 'dependency'. Nevertheless, the distant past of tribal Finnishness and the conceived Golden Age of the Kalevala remained obligating. The decline of public archaeology is quite evident after 1918, even though the national message of the antiquarian pursuits remained present in the history culture of the public. The myths, symbols, images, and constructs of ancient Finnishness had already become embedded in society by the turn of the century, like the patalakki cap, which remains a symbol of Finnishness to this day. The method of approach is one of combining a broad spectrum of previously neglected primary sources, all related to history culture and the subtle banalization of the distant past: school books, postcards, illustrations, festive costumes, drama, satirical magazines, novels, jewellery, and calendars. Tracing the origins of the national myths to their original contexts enables a rather thorough deconstruction of the proto-historical imaginary in this Finnish case study. Considering Anthony D. Smith's idea of ancient 'ethnies' being the basis for nationalist causes, the author considers such an approach in the Finnish case totally misplaced.

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The Uppsala school of Axel Hägerström can be said to have been the last genuinely Swedish philosophical movement. On the other hand, the Swedish analytic tradition is often said to have its roots in Hägerström s thought. This work examines the transformation from Uppsala philosophy to analytic philosophy from an actor-based historical perspective. The aim is to describe how a group of younger scholars (Ingemar Hedenius, Konrad Marc-Wogau, Anders Wedberg, Alf Ross, Herbert Tingsten, Gunnar Myrdal) colonised the legacy of Hägerström and Uppsala philosophy, and faced the challenges they met in trying to reconcile this legacy with the changing philosophical and political currents of the 1930s and 40s. Following Quentin Skinner, the texts are analysed as moves or speech acts in a particular historical context. The thesis consists of five previously published case studies and an introduction. The first study describes how the image of Hägerström as the father of the Swedish analytic tradition was created by a particular faction of younger Uppsala philosophers who (re-) presented the Hägerströmian philosophy as a parallel movement to logical empiricism. The second study examines the confrontations between Uppsala philosophy and logical empiricism in both the editorial board and in the pages of Sweden s leading philosophical journal Theoria. The third study focuses on how the younger generation redescribed Hägerströmian legal philosophical ideas (Scandinavian Legal Realism), while the fourth study discusses how they responded to the accusations of a connection between Hägerström s value nihilistic theory and totalitarianism. Finally, the fifth study examines how the Swedish social scientist and Social Democratic intellectual Gunnar Myrdal tried to reconcile value nihilism with a strong political programme for social reform. The contribution of this thesis to the field consists mainly in a re-evaluation of the role of Uppsala philosophy in the history of Swedish philosophy. From this perspective the Uppsala School was less a collection of certain definite philosophical ideas than an intellectual legacy that was the subject of fierce struggles. Its theories and ideas were redescribed in various ways by individual actors with different philosophical and political intentions.

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Between 1935 and 1970 the state-funded Irish Folklore Commission (Coimisiún Béaloideasa Éireann) assembled one of the great folklore collections of the world under the direction of Séamus Ó Duilearga (James Hamilton Delargy). The aim of this study is to recount and assess the work and achievement of this commission. The cultural, linguistic, political and ideological factors that had a bearing on the establishment and making permanent of the Commission and that impinged on many aspects of its work are here elucidated. The genesis of the Commission is traced and the vision and mission of Séamus Ó Duilearga are outlined. The negotiations that preceded the setting up of the Commission in 1935 as well as protracted efforts from 1940 to 1970 to place it on a permanent foundation are recounted and examined at length. All the various collecting programmes and other activities of the Commission are described in detail and many aspects of its work are assessed. This study also deals with the working methods and conditions of employment of the Commission s field and Head Office staff as well as with Séamus Ó Duilearga s direction of the Commission. In executing this work extensive use has been made of primary sources in archives and libraries in Ireland, Sweden, Finland, Estonia, and North America. This is the first major study of this world-famous institute, which has been praised in passing in numerous publications, but here for the first time its work and achievement are detailed comprehensively and subjected to scholarly scrutiny. This study should be of interest not only to students of Irish oral tradition but to folklorists everywhere. The history of the Irish Folklore Commission is a part of a wider history, that of the history of folkloristics in Europe and North America in particular. Moreover, this work has relevance for many areas of the developing world today, where conditions are not dissimilar to those that pertained in Ireland in the 1930's when this great salvage operation was funded by the young, independent Irish state. It is also hoped that this work will be of practical assistance to scholars and the general public when utilising these collections, and that furthermore it will stimulate research into the assembling of other national collections of folklore as well as into the history of folkloristics in other countries, subjects which in recent years are beginning to attract more and more scholarly attention.

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The research is related to the Finnish Jabal Harun Project (FJHP), which is part of the research unit directed by Professor Jaakko Frösén. The project consists of two interrelated parts: the excavation of a Byzantine monastery/pilgrimage centre on Jabal Harun, and a multiperiod archaeological survey of the surrounding landscape. It is generally held that the Near Eastern landscape has been modified by millennia of human habitation and activity. Past climatic changes and human activities could be expected to have significantly changed also the landscape of the Jabal Harun area. Therefore it was considered that a study of erosion in the Jabal Harun area could shed light on the environmental and human history of the area. It was hoped that it would be possible to connect the results of the sedimentological studies either to wider climatic changes in the Near East, or to archaeologically observable periods of human activity and land use. As evidence of some archaeological periods is completely missing from the Jabal Harun area, it was also of interest whether catastrophic erosion or unfavourable environmental change, caused either by natural forces or by human agency, could explain the gaps in the archaeological record. Changes in climate and/or land-use were expected to be reflected in the sedimentary record. The field research, carried out as part of the FJHP survey fieldwork, included the mapping of wadi terraces and cleaning of sediment profiles which were recorded and sampled for laboratory analyses of facies and lithology. To obtain a chronology for the sedimentation and erosion phases also OSL (optically stimulated luminescence) dating samples were collected. The results were compared to the record of the Near Eastern palaeoclimate, and to data from geoarchaeological studies in central and southern Jordan. The picture of the environmental development was then compared to the human history in the area, based on archaeological evidence from the FJHP survey and the published archaeological research in the Petra region, and the question of the relationship between human activity and environmental change was critically discussed. Using the palaeoclimatic data and the results from geoarchaeological studies it was possible to outline the environmental development in the Jabal Harun area from the Pleistocene to the present.It is appears that there was a phase of accumulation of sediment before the Middle Palaeolithic period, possibly related to tectonic movement. This phase was later followed by erosion, tentatively suggested to have taken place during the Upper Palaeolithic. A period of wadi aggradation probably occurred during the Late Glacial and continued until the end of the Pleistocene, followed by significant channel degradation, attributed to increased rainfall during the Early Holocene. It seems that during the later Holocene channel incision has been dominant in the Jabal Harûn area although there have been also small-scale channel aggradation phases, two of which were OSL-dated to around 4000-3000 BP and 2400-2000 BP. As there is no evidence of tectonic movements in the Jabal Harun area after the early Pleistocene, it is suggested that climate change and human activity have been the major causes of environmental change in the area. At a brief glance it seems that many of the changes in the settlement and land use in the Jabal Harun area can be explained by climatic and environmental conditions. However, the responses of human societies to environmental change are dependent on many factors. Therefore an evaluation of the significance of environmental, cultural, socio-economic and political factors is needed to decide whether certain phenomena are environmentally induced. Comparison with the wider Petra region is also needed to judge whether the phenomena are characteristic of the Jabal Harun area only, or can they be connected to social, political and economic development over a wider area.

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This research examines three aspects of becoming a teacher, teacher identity formation in mathematics teacher education: the cognitive and affective aspect, the image of an ideal teacher directing the developmental process, and as an on-going process. The formation of emerging teacher identity was approached in a social psychological framework, in which individual development takes place in social interaction with the context through various experiences. Formation of teacher identity is seen as a dynamic, on-going developmental process, in which an individual intentionally aspires after the ideal image of being a teacher by developing his/her own competence as a teacher. The starting-point was that it is possible to examine formation of teacher identity through conceptualisation of observations that the individual and others have about teacher identity in different situations. The research uses the qualitative case study approach to formation of emerging teacher identity, the individual developmental process and the socially constructed image of an ideal mathematics teacher. Two student cases, John and Mary, and the collective case of teacher educators representing socially shared views of becoming and being a mathematics teacher are presented. The development of each student was examined based on three semi-structured interviews supplemented with written products. The data-gathering took place during the 2005 2006 academic year. The collective case about the ideal image provided during the programme was composed of separate case displays of each teacher educator, which were mainly based on semi-structured interviews in spring term 2006. The intentions and aims set for students were of special interest in the interviews with teacher educators. The interview data was analysed following the modified idea of analytic induction. The formation of teacher identity is elaborated through three themes emerging from theoretical considerations and the cases. First, the profile of one s present state as a teacher may be scrutinised through separate affective and cognitive aspects associated with the teaching profession. The differences between individuals arise through dif-ferent emphasis on these aspects. Similarly, the socially constructed image of an ideal teacher may be profiled through a combination of aspects associated with the teaching profession. Second, the ideal image directing the individual developmental process is the level at which individual and social processes meet. Third, formation of teacher identity is about becoming a teacher both in the eyes of the individual self as well as of others in the context. It is a challenge in academic mathematics teacher education to support the various cognitive and affective aspects associated with being a teacher in a way that being a professional and further development could have a coherent starting-point that an individual can internalise.

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Historical sediment nutrient concentrations and heavy-metal distributions were studied in five embayments in the Gulf of Finland and an adjacent lake. The main objective of the study was to examine the response of these water bodies to temporal changes in human activities. Sediment cores were collected from the sites and dated using 210Pb and 137Cs. The cores were analyzed for total carbon (TC), total nitrogen (TN), total phosphorus (TP), organic phosphorus (OP), inorganic phosphorus (IP), biogenic silica (BSi), loss on ignition (LOI), grain size, Cu, Zn, Al, Fe, Mn, K, Ca, Mg and Na. Principal component analysis (PCA) was used to summarize the trends in the geochemical variables and to compare trends between the different sites. The links between the catchment land use and sediment geochemical data were studied using a multivariate technique of redundancy analysis (RDA). Human activities produce marked geochemical variations in coastal sediments. These variations and signals are often challenging to interpret due to various sedimentological and post-depositional factors affecting the sediment profiles. In general, the sites studied here show significant upcore increases in sedimentation rates, TP and TN concentrations. Also Cu, which is considered to be a good indicator of anthropogenic influence, showed clear increases from 1850 towards the top part of the cores. Based on the RDA-analysis, in the least disturbed embayments with high forest cover, the sediments are dominated by lithogenic indicators Fe, K, Al and Mg. In embayments close to urban settlement, the sediments have high Cu concentrations and a high sediment Fe/Mn ratio. This study suggests that sediment accumulation rates vary significantly from site to site and that the overall sedimentation can be linked to the geomorphology and basin bathymetry, which appear to be the major factors governing sedimentation rates; i.e. a high sediment accumulation rate is not characteristic either to urban or to rural sites. The geochemical trends are strongly site specific and depend on the local geochemical background, basin characteristics and anthropogenic metal and nutrient loading. Of the studied geochemical indicators, OP shows the least monotonic trends in all studied sites. When compared to other available data, OP seems to be the most reliable geochemical indicator describing the trophic development of the study sites, whereas Cu and Zn appear to be good indicators for anthropogenic influence. As sedimentation environments, estuarine and marine sites are more complex than lacustrine basins with multiple sources of sediment input and more energetic conditions in the former. The crucial differences between lacustrine and estuarine/coastal sedimentation environments are mostly related to Fe. P sedimentation is largely governed by Fe redox-reactions in estuarine environments. In freshwaters, presence of Fe is clearly linked to the sedimentation of other lithogenic metals, and therefore P sedimentation and preservation has a more direct linkage to organic matter sedimentation.

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Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.