A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

Köyhyyden perintö : Tutkimus kulttuurisen tiedon sisällöistä ja jatkuvuuksista suomalaisissa elämäkerta- ja sananlaskuaineistoissa

The Legacy of Poverty. A Study of the substance and continuity of cultural knowledge in Finnish biographical and proverbial texts The study focuses on the idea of the cultural knowledge and shared understanding that ordinary people, folk , have of the concepts and ideas about rural based poverty in Finland. Throughout 19th century and well into 20th century, the majority of the population remained agrarian and poor. By the 1950s, most people still lived in rural areas and a majority of them earned their living primarily from agriculture and forestry. Urbanization proceeded rapidly from the 1960s onwards. Even though the Nordic welfare state was firmly established in Finland by the 1970s, old forms of agrarian poverty still remained in the culture. The source material for the study consists of 99 biographies and 502 proverbs. Biographical texts include written autobiographies and interviewed biographies. A primary analyzing concept is called a poverty speech. The poverty speech has been analyzed by providing answers to the following three questions: What connotations do people attach to poverty when they speak about it? What sort of social relations arise when people speak about poverty? How is the past experience of poverty constructed in the present and in the welfare state context? Cultural knowledge is a theoretical and analytical tool that enables people to categorize information. The three questions stated above are crucial in revealing the schematic structure that people use to communicate about agrarian poverty. Categories are analyzed and processed in terms of cultural themes that contain the ideals and stereotypes of spoken motif and sub-themes. The application of theoretical and analytical premises to the poverty speech has shown that there are four cultural themes. The first theme is Power. The social connotations in the poverty speech are mostly in relation to the better-off people. Poverty does not exist without an awareness of welfare, i.e. the understanding of a certain standard of welfare above that of one's own. The second theme is about family ties as a resource and welfare network. In poverty speech, marriage is represented as a means to upgrade one's livelihood. Family members are described as supporting one another, but at the same time as being antagonists. The third theme, Work represents the work ethic that is being connected to the poverty. Hard working as a representation is attached to eligibility for `a good life´ that in Finland was to become an owner-occupier of a cottage or a flat. The fourth theme is Security. The resentment of unfair treatment is expressed by using moral superiority and rational explanations. The ruling classes in the agrarian society are portrayed as being evil and selfish with no social conscience because they did not provide enough assistance to those who needed it. During the period when the welfare benefit system was undeveloped, the poor expected the wealthier people to make a contribution to the distribution of material wealth. In the premises of cultural knowledge, both oral and written traditions are about human thinking: they deal with topics, ideas and evaluations that are relevant to their bearers. Many elements expressed in poverty speech, such as classifications and customs derived from the rural world, have been carried over into the next generation in newer contexts and a different cultural environment. Keywords: cultural knowledge, cognitive categorization, poverty, life stories, proverbs

Museoesineitä Itä-Karjalasta : Väinö Tuomaalan jatkosodan aikana keräämä esinekokoelma ja sen syntyhistoria

Jatkosodan aikana kerättiin Suomen valtaamalta alueelta Itä-Karjalasta tuhansittain museoesineitä Suomen museoihin. Kansallismuseon kokoelmiin kerättiin esineitä lähinnä suomenheimoisilta mutta myös isovenäläisiltä. Tämän tutkimuksen kohteena on lähes 400:n esineen kokoelma, joka toimitettiin Kansallismuseoon vuosina 1941 1944 ja merkittiin kansallisuudeltaan venäläiseksi. Näistä venäläisistä esineistä suurimman osan keräsi alikersanttina palvellut Väinö Tuomaala. Tutkimukseni tarkastelee Väinö Tuomaalan kokoelmaa ja etsii syitä siihen, miksi kokoelma on sellainen kuin se on, miksi se ja koko venäläisten esineiden kokoelma syntyi ja mitkä seikat vaikuttivat Tuomaalan esinevalintoihin. Tutkimuksen teoria rakentuu museologisen kirjallisuuden varaan. Tutkimuksessa tarkastellaan Väinö Tuomaalan kokoelman keräyskonteksteja. Keräyskonteksteihin kuuluvat kokoelman kerääjä, keräysajankohta ja -paikka sekä yhteenkuuluvat esineet, eli muut venäläiset esineet. Kerääjän tarkastelussa huomioidaan hänen henkilöhistoriansa ja etsitään mahdollisia keruuseen vaikuttaneita tekijöitä. Keräysajankohdan tarkastelussa huomio kiinnittyy keruuympäristöön, eli vallitseviin olosuhteisiin ja aatteelliseen ilmapiiriin, joiden vaikutuksen alaisena keruu suoritettiin. Primääriaineisto koostuu Kansallismuseon alaisen Kulttuurien museon yleisetnografisten esineiden kokoelmaan kuuluvista 198:sta Väinö Tuomaalan keräämästä esineestä verifikaatteineen, jotka ovat osa 393 esinettä käsittävästä venäläisestä kokoelmasta. Aineisto sisältää myös eri arkistojen materiaalia. Kansallisarkiston Sörnäisten toimipisteestä, entisestä sota-arkistota, löytyneitä sotapäiväkirjoja ja Tuomaalan kantakorttia on tutkimuksessa käytetty jatkosodan tapahtumien esittämiseen. Museoviraston hallinto-osaston arkiston kirjeet ja pöytäkirjat ovat antaneet tietoa kulttuurikeruun organisoinnista. Väinö Tuomaalan arkistokokoelma Seinäjoella sisältää Tuomaalan keräämää perinneaineistoa, hänen puheitaan, lehtikirjoituksiaan ja kirjeenvaihtoaan. Myös Evijärven kunnantalon kotiseutuarkistosta löytyneet kirjeet ovat valottaneet Tuomaalan jatkosodan aikaista keruutoimintaa. Suomalaisen Kirjallisuuden Seuran arkistot ovat tarjonneet materiaalia jatkosodan aikaisesta kulttuurikeruusta. Koko venäläisten esineiden kokoelma syntyi sattumalta ja organisoimattoman toiminnan tuloksena, jossa aktiivisia toimijoita olivat yksittäiset kerääjät. Intohimoisesta suhtautumisesta kansatieteellistä keruuta kohtaan johtuen, Tuomaala olisi todenäköisesti kerännyt museoesineitä missä päin Itä-Karjalaa tahansa. Väinö Tuomaalan Itä-Karjalassa keräämä esinekokoelma oli luonnollinen jatke hänen kotiseudullaan aloittamalleen keräystoiminnalle. Tuomaalan jatkosodan aikana keräämä kokoelma on kerääjän mieltymysten mukainen yritys kerätä vanhaa itäkarjalaista, kansallista talonpoikaiskulttuuria. Tuomaala pyrki keräämään klassista kansatieteellistä aineistoa monipuolisesti kansankulttuurin eri elämänalueilta. Tuomaalan esinekeruussa näkyi vahvasti talonpoikaiskulttuurin ihannointi ja halu pelastaa osa siitä tuleville sukupolville. Yrityksen onnistumiseen vaikuttivat sodanajan olosuhteet sekä aatteellinen ilmapiiri. Esineiden saatavuudella oli merkittävä osa kokoelman muodostumiseen, samoin Tuomaalan käsityksillä heimokansoista, Suur-Suomesta ja venäläisistä. Keruuvalintoihin ja keruun jatkumiseen vaikuttivat myös Kansallismuseon henkilökunta ja työstä saatu tunnustus.

Pietismin kuva - ikkuna yksityiseen hengellisyyteen : Johann Arndtin opetukset pietistisen embleemin perustana

The image of Pietism a window to personal spirituality. The teachings of Johann Arndt as the basis of Pietist emblems The Pietist effect on spiritual images has to be scrutinised as a continuum initiating from the teachings of Johann Arndt who created a protestant iconography that defended the status of pictures and images as the foundation of divine revelation. Pietist artworks reveal Arndtian part of secret, eternal world, and God. Even though modern scholars do not regarded him as a founding father of Pietism anymore, his works have been essential for the development of iconography, and the themes of the Pietist images are linked with his works. For Arndt, the starting point is in the affecting love for Christ who suffered for the humankind. The reading experience is personal and the words point directly at the reader and thus appear as evidence of the guilt of the reader as well as of the love of God. Arndt uses bounteous and descriptive language which has partially affected promoting and picturing of many themes. Like Arndt, Philipp Jakob Spener also emphasised the heart that believes. The Pietist movement was born to oppose detached faith and the lack of the Holy Ghost. Christians touched by the teachings of Arndt and Spener began to create images out of metaphors presented by Arndt. As those people were part of the intelligentsia, it was natural that the fashionable emblematics of the 17th century was moulded for the personal needs. For Arndt, the human heart is manifested as a symbol of soul, personal faith or unbelief as well as an allegory of the burning love for Jesus. Due to this fact, heart emblems were gradually widely used and linked with the love of Christ. In the Nordic countries, the introduction of emblems emanated from the gentry s connections to the Central Europe where emblems were exploited in order to decorate books, artefacts, interiors, and buildings as well as visual/literal trademarks of the intelligentsia. Emblematic paintings in the churches of the castles of Venngarn (1665) and Läckö (1668), owned by Magnus Gabriel De la Gardie, are one of the most central interior paintings preserved in the Nordic countries, and they emphasise personal righteous life. Nonetheless, it was the books by Arndt and the Poet s Society in Nurnberg that bound the Swedish gentry and the scholars of the Pietist movement together. The Finnish gentry had no castles or castle churches so they supported county churches, both in building and in maintenance. As the churches were not private, their iconography could not be private either. Instead, people used Pietist symbols such as Agnus Dei, Cor ardens, an open book, beams, king David, frankincense, wood themes and Virtues. In the Pietist images made for public spaces, the attention is focused on pedagogical, metaphorical, and meaningful presentation as well as concealed statements.

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept taken from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical coherence and consistency . This investigation provides a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. This research analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Looking forward in this direction, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature: proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. Using quantitative qualitative methods, evidence is presented to justify a parallel study of different modalities of musical self-similarity. For this purpose, original arguments by Benoît B. Mandelbrot are revised, alongside a systematic critique of the literature on the subject. Furthermore, connecting Charles S. Peirce s synechism with Mandelbrot s fractality is one of the main developments of the present study. This study provides elements for explaining Bolognesi s (1983) conjecture, that states that the most primitive, intuitive and basic musical device is self-reference, extending its functions and operations to self-similar surfaces. In this sense, this research suggests that, with various modalities of self-similarity, synecdochic intersemiosis acts as system of systems in coordination with greater or lesser development of structural consistency, and with a greater or lesser contextual dependence.

Many Faces of Mao Zedong

The main aim of this work was to explore the use of Mao Zedong s (毛泽东, 1893—1976) visual image in contemporary Chinese art during the years 1976—2006. Chairman Mao is the most visually reproduced person in the People's Republic of China (PRC), and the presence of his image is still unquestionable at many levels. Although several scholars have provided insightful observations on this topic, research focusing on Mao's visual image has been neglected. Employing the interdisciplinary approach of visual studies and using image as the main concept, this research combines different theoretical frameworks, deriving from art history, image studies and social sciences, for each chapter in order to explain the origins, intentions and major strategies of the contemporary Chinese artists. The focus of this research was to elucidate how Mao's visual image, deriving from the Maoist era, is re-created and negotiated in contemporary Chinese art works. The material reproductions - the visual images in contemporary art - are created to be juxtaposed with the immaterial mental images of Mao that were created during the Maoist era through the original visual images of Mao. This complex interaction between visual and mental images is further exemplified by art works that do not include Mao's visual image, but still imply his mental image. The methods used derive from both sinology and art history. The research is based on extensive fieldwork in China, which was crucial for gathering new information and materials from this vigorous art scene. The topic is approached through a Chinese cultural, political and historical perspective that is necessary for a further understanding of how the original visual images of Mao obtained their omnipotent status and what kind of iconography was created. Close structural analysis, taking into account the format, style, techniques, composition, colors, materials and space used in the art works, is employed to demonstrate the great variety of visual images created. The analysis is further placed in a continuous dialogue both with the contemporary art works of Mao and with the original visual images of Mao from the past. In this study it is shown that contemporary Chinese art relating to Chairman Mao is a more versatile and multilayered phenomenon than is generally assumed. Although some of the art works seem to fit into the definition of superficial art, the study demonstrates that this reading of the art works is not adequate. The author argues that employing Mao's visual images in contemporary Chinese art is based on three main strategies used by artists: to create a visual dialogue with a traumatizing past, to employ transcontextual parody, and to explore the importance of Tian'anmen through site-dependent art. These strategies are not exclusionary, but instead interdependent and many art works employ more than one of them. In addition, these three main strategies include versatile methods used by artists that make the use of Mao's visual images even more multifaceted.

Jac. Ahrenberg ja historian perintö : Restaurointisuunnitelmat Viipurin ja Turun linnoihin 1800-luvun lopussa

Jac. Ahrenberg and Patrimony Restoration Plans for Viipuri and Turku Castles at the End of the 19th Century This dissertation examines the unrealized restoration plans for two castles in the Grand Duchy of Finland one located at Viipuri (Vyborg, nowadays in Russia), the other at Turku (in Swedish, Åbo) during the last decades of the 19th century. Both castles were used as prisons, barracks and warehouses. From the middle of the 19th century on, their restoration and transformation into museums and "national monuments" were demanded in the newspapers. The prison reform in the 1860s stimulated the documentation and debate concerning their future, but it was only at the beginning of the 1880s when their restoration became an official state-run project. The undertaking was carried out by Johan Jacob (Jac.) Ahrenberg (1847 1914), architect of the National Board of Public Buildings. By combining written sources with drawings and photographs, this dissertation examines the restoration projects, the two castles' significance and the ways in which they were investigated by scholars. The plans are analyzed in connection with restoration practices in France and Sweden and in the context of contemporary discussions concerning national art and patrimony. The thesis argues that these former castles of the Swedish crown were used to manifest the western roots of Finnish law and order, the lineage of power and the capacity of the nation to defend itself. However, because of their symbolism, their restoration became a politically delicate question concerning the role of the Swedish heritage in Finland's nation-building process. According to Jac. Ahrenberg's plans, the two castles were to be restored to their assumed appearance at the time of the Vasa dynasty. Consequently, the structures would have resembled castles in Sweden. It is suggested that one aim of the restoration plans was to transform the two buildings into monuments testifying to the common history of Sweden and Finland. They were meant to consolidate the Swedish basis of Finnish culture and autonomy and thus to secure them against the threatening implications of Russian imperialism. It seems that along with the changing ideals of architectural restoration and the need for an original Finnish architectural heritage, the political connotations associated with the castles were one reason why Jac. Ahrenberg's restoration plans were never realized.

Conservadurismo, negación y diáspora

This contribution deals with social and political aspects affecting cultural life in Jalisco (Mexico), during the last forty years. It is, especially, a critical view on the regional deterioration of experimental music, analysing ethnic, religion, gender and other social components in one of the culturally foremost states of Mexico.

Evil Gods and Reckless Saviours : Adaptation and Appropriation in Late Twentieth Century Jesus-Novels

Late twentieth century Jesus-novels search after a completely new picture of Jesus. Novels written for instance by Norman Mailer, José Saramago, Michèle Roberts, Marianne Fredriksson, and Ki Longfellow provide an inversive revision of the canonic Gospels. They read the New Testament in terms of the present age. In their adaptation the story turns often into a critique of the whole Christian history. The investigated contrast-novels end up with an appropriation that is based on prototypical rewriting. They aim at the rehabilitation of Judas, and some of them make Mary Magdalane the key figure of Christianity. Saramago describes God as a blood thirsty tyrant, and Mailer makes God combat with the Devil in a manichean sense as with an equal. Such ideas are familiar both from poststructuralist philosophy and post-metaphysical death-of-God theology. The main result of the intertextual analysis is that these scholars have adopted Nietzschean ideas in their writing. Quite unlike earlier Jesus-novels, these more recent novels present a revision that produces discontinuity with the original source text, the New Testament. The intertextual strategy is based on contradiction. The reader wittnesses contesting and challenging, the authors attack Biblical beliefs and attempt to dissolve Christian doctrines. An attack on Biblical slave morality and violent concept of God deprives Jesus of his Jewish Messianic identity, makes Old Testament law a contradiction of life, calls sacrificial soteriology a violent pattern supporting oppression, and presents God as a cruel monster who enslaves people under his commandments and wishes their death. The new Jesus-figure contests Mosaic Law, despises orthodox Judaism, abandons Jewish customs and even questions Old Testament monotheism. In result, the novels intentionally transfer Jesus out of Judaism. Furthermore, Jewish faith appears in a negative light. Such an intertextual move is not open anti-Semitism but it cannot avoid attacking Jewish worship. Why? One reason that explains these attitudes is that Western culture still carries anti-Judaic attitudes beneath the surface covered with sentiments of equality and tolerance. Despite the evident post-holocaust consciousness present in the novels, they actually adopt an arrogant and ironical refutation of Jewish beliefs and Old Testament faith. In these novels, Jesus is made a complete opposite and antithesis to Judaism. Key words: Jesus-novel, intertextuality, adaptation, slave morality, Nietzsche, theodicy, patriarchy.

Cattle Teeth in Graves : Interpretations of animal bones found in Finnish inhumation graves (ca AD 550-1700)

The nature of a burial is always ritualistic. This is often forgotten when dealing with Finnish inhumation burials containing animal bones. Only the animal bones found close to the deceased have traditionally been thought to have a ritualistic purpose. The animal bones found in the filling of the grave, which is still part of the burial, has on the other hand, often been neglected in the previous research. In this Master s thesis I will discuss the function and interpretation of animal bones in graves. The base of this study is six sites, all of different nature, from Finland. Luistari in Eura is from the western coast and is dated to Late Iron Age (and possibly Medieval period), the Medieval hamlet of Finno is situated in Espoo which is situated on the southern coast. Two town burials, Turku and Porvoo, are also included in this study. The graves from Turku are dated to Late Medieval period and Early Renaissance, whereas the cemetery in Porvoo is from the 18th century. Visulahti in Mikkeli is from the Late Iron Age and represents Eastern Finnish burial tradition, the same as Suotniemi from Käkisalmi parish, which is nowadays part of Russia. While parts of the animal bones had already been analysed before, the author also analysed animal bones for the purpose of the present Master´s thesis. The bones were compared to the burial contexts, when possible. Based on the comparisons I have made interpretations which might explain the existence of animal bones in the graves. The interpretations are among others sacrifice, commemoration meals and animal burials. The site could also have been a settlement site prior to the graves, thus the bones in the graves would belong to the settlement phase. When comparing the date of the studied sites, the town burials are later and the animal bones are probably related to previous or contemporary use of the sites as graveyards. On top of this there does not seem to be much difference in burial tradition between Eastern and Western Finland, although at least from the hamlet burials of Finno there are aspects that could be linked to Eastern burials. In making the interpretations I have taken into consideration the aspects of belief during different time periods when they could be accounted as relevant. Also the problems with bone preservation were relevant and challenging for the study. Often only the hardest substance of the skeleton, namely teeth, has been preserved. For this reason the quality of the archaeological documentation was a key issue in this study. In producing quality interpretations of the animal bones in graves, the bones, contexts and their relationship to the surrounding site should be documented with care.