Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Radiative transfer, interception and scattering in coniferous forests : models and applications for production ecology and remote sensing

This work develops methods to account for shoot structure in models of coniferous canopy radiative transfer. Shoot structure, as it varies along the light gradient inside canopy, affects the efficiency of light interception per unit needle area, foliage biomass, or foliage nitrogen. The clumping of needles in the shoot volume also causes a notable amount of multiple scattering of light within coniferous shoots. The effect of shoot structure on light interception is treated in the context of canopy level photosynthesis and resource use models, and the phenomenon of within-shoot multiple scattering in the context of physical canopy reflectance models for remote sensing purposes. Light interception. A method for estimating the amount of PAR (Photosynthetically Active Radiation) intercepted by a conifer shoot is presented. The method combines modelling of the directional distribution of radiation above canopy, fish-eye photographs taken at shoot locations to measure canopy gap fraction, and geometrical measurements of shoot orientation and structure. Data on light availability, shoot and needle structure and nitrogen content has been collected from canopies of Pacific silver fir (Abies amabilis (Dougl.) Forbes) and Norway spruce (Picea abies (L.) Karst.). Shoot structure acclimated to light gradient inside canopy so that more shaded shoots have better light interception efficiency. Light interception efficiency of shoots varied about two-fold per needle area, about four-fold per needle dry mass, and about five-fold per nitrogen content. Comparison of fertilized and control stands of Norway spruce indicated that light interception efficiency is not greatly affected by fertilization. Light scattering. Structure of coniferous shoots gives rise to multiple scattering of light between the needles of the shoot. Using geometric models of shoots, multiple scattering was studied by photon tracing simulations. Based on simulation results, the dependence of the scattering coefficient of shoot from the scattering coefficient of needles is shown to follow a simple one-parameter model. The single parameter, termed the recollision probability, describes the level of clumping of the needles in the shoot, is wavelength independent, and can be connected to previously used clumping indices. By using the recollision probability to correct for the within-shoot multiple scattering, canopy radiative transfer models which have used leaves as basic elements can use shoots as basic elements, and thus be applied for coniferous forests. Preliminary testing of this approach seems to explain, at least partially, why coniferous forests appear darker than broadleaved forests in satellite data.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Peliprojektin aikataulutus

Tässä pro gradu -tutkielmassa aikataulutetaan itsenäisen pelinkehittäjän peliprojekti. Aikataulutus on matematiikan ala, jonka tavoitteena on järjestää projektitehtävät optimaaliseen järjestykseen asetetun tavoitteen mukaan. Käytännössä tavoite voi olla esimerkiksi mimimoida painotetun valmistumisajan summaa. Tutkielma koostuu neljästä pääosiosta: aikataulutuksen teoriasta, aikataulutettavan datataulukon muodostuksesta, laskennallisista esimerkeistä ja aikataulutusohjelman esittelystä. Teoriaosuudessa esitetään peliprojektin aikataulutukseen tarvittavat matemaattiset merkinnät ja lemmat todistuksineen. Tutkielman teoriaosuuden todistukset ovat peräisin Michael Pinedon kirjasta Scheduling - Theory, Algorithms, and Systems vuodelta 2008. Pinedon teos on tutkielman keskeisin kirjallisuuslähde. Tutkielman toisessa pääosiossa esitetään, miten peliprojektista saadaan muodostettua aikataulutettava datataulukko. Datataulukon mallinnuksessa apuna toimi turkulainen pelinkehittäjä Timo Naskali. Yhteistyössä Naskalin kanssa peliprojekti saatiin mallinnettua mahdollisimman tarkasti laskettavissa olevaksi datataulukoksi ilman liiallisia yksinkertaistuksia. Peliprojektin mallintamisen lisäksi tutkielmassa tullaan käymään läpi paljon erilaisia esimerkkitehtäviä, joissa sovelletaan esiteltyä teoriaa. Esimerkit on tehty hyvin selkeiksi kirjaamalla ylös paljon laskujen välivaiheita. Esimerkkitehtävien vaikeustaso kasvaa kappaleen edetessä, sillä monimutkaisempia tilanteita tarkasteltaessa datataulukoihin joudutaan lisäämään uusia parametrejä. Viimeisessä esimerkkitehtävässä käytössä on jo koko mallinnettu datataulukko. Tutkielmaa varten koodattiin myös aikataulutusohjelma, joka mahdollistaa isojen datataulukoiden laskemisen tietokoneen avulla. Aikataulutusohjelmassa on graafinen käyttöliittymä, mutta ohjelma tallentaa tulokset myös tekstitiedostoksi. Tutkielman loppuosassa käsitellään aikataulutuksesta saatavaa hyötyä. Johtopäätöksissä pohditaan myös potentiaalisia jatkomahdollisuuksia tutkielman aiheeseen.

Lukion pitkä matematiikka ja wxMaxima

Tässä tutkielmassa tutkitaan lukion pitkän matematiikan pakollisia kursseja ja on keskitytty juuri sellaisiin matematiikan alueisiin, joita voi ratkaista wxMaximan avulla. Tutkielmassa ei ollenkaan opeteta wxMaximan käyttöä, mutta ohessa on kirjoittajan tekemä kandin työ, wxMaximan pikaopas, jossa neuvotaan wxMaximan käyttöä. Tutkielmasta on kuitenkin jätetty pois geometrian, trigonometrian ja vektorien osuudet, koska kolmioita ja vektoreita on hankala piirtää wxMaximan avulla. Näin ollen myös trigonometriset laskut on jätetty pois raja-arvon, derivaatan ja integraalin yhteydestä. Tutkielmasta on jätetty pois myös lukujonot, lukuteoria ja todistaminen. Sen sijaan tutkielmaan on otettu pitkän matematiikan syventävistä kursseista puolisuunnikassääntö, Newtonin menetelmä ja laajennettu raja-arvon sekä integraalin osa-alueita. Ekstra asiaa kohdissa käsitellään asioita, jotka ovat kokonaan lukion pitkän matematiikan kurssien opetuksen ulkopuolella. Tutkielman toisessa luvussa kerrotaan, mitä lukion opetussuunnitelman perusteet eli OPSin (2015) kurssien sisältöjä, tutkielman luvat vastaavat. Kurssien OPS (2015) tavoitteissa kerrotaan vain se osuus OPSin kurssien sisällöistä, joita tässä tutkielmassa käsitellään. Mukaan on laadittu myös tuntisuunnitelma, kuinka monta tuntia mihinkin lukuun voisi käyttää aikaa, jos tutkielmaa käytettäisiin pitkän matematiikan kertauskurssina lukiossa. Tutkielman lopussa on kaikkiin tehtäviin vastaukset. Ensin löytyy pelkät loppuvastaukset ja sitten on täydelliset vastaukset, jotka on tehty wxMaximalla. Varmaan moniin laskuihin löytyisi toinenkin tapa ratkaista ne. Tällaisen tutkielman tekeminen on ajan kohtainen, sillä vuonna 2019 matematiikan yo-kirjoitukset muuttuvat sähköiseen muotoon. wxMaxima on valittu juuri yhdeksi ohjelmaksi, jota voi käyttää sähköisissä kirjoituksissa.

Lukion pitkä matematiikka ja wxMaxima

Tässä tutkielmassa tutkitaan lukion pitkän matematiikan pakollisia kursseja ja on keskitytty juuri sellaisiin matematiikan alueisiin, joita voi ratkaista wxMaximan avulla. Tutkielmassa ei ollenkaan opeteta wxMaximan käyttöä, mutta ohessa on kirjoittajan tekemä kandin työ, wxMaximan pikaopas, jossa neuvotaan wxMaximan käyttöä. Tutkielmasta on kuitenkin jätetty pois geometrian, trigonometrian ja vektorien osuudet, koska kolmioita ja vektoreita on hankala piirtää wxMaximan avulla. Näin ollen myös trigonometriset laskut on jätetty pois raja-arvon, derivaatan ja integraalin yhteydestä. Tutkielmasta on jätetty pois myös lukujonot, lukuteoria ja todistaminen. Sen sijaan tutkielmaan on otettu pitkän matematiikan syventävistä kursseista puolisuunnikassääntö, Newtonin menetelmä ja laajennettu raja-arvon sekä integraalin osa-alueita. Ekstra asiaa kohdissa käsitellään asioita, jotka ovat kokonaan lukion pitkän matematiikan kurssien opetuksen ulkopuolella. Tutkielman toisessa luvussa kerrotaan, mitä lukion opetussuunnitelman perusteet eli OPSin (2015) kurssien sisältöjä, tutkielman luvat vastaavat. Kurssien OPS (2015) tavoitteissa kerrotaan vain se osuus OPSin kurssien sisällöistä, joita tässä tutkielmassa käsitellään. Mukaan on laadittu myös tuntisuunnitelma, kuinka monta tuntia mihinkin lukuun voisi käyttää aikaa, jos tutkielmaa käytettäisiin pitkän matematiikan kertauskurssina lukiossa. Tutkielman lopussa on kaikkiin tehtäviin vastaukset. Ensin löytyy pelkät loppuvastaukset ja sitten on täydelliset vastaukset, jotka on tehty wxMaximalla. Varmaan moniin laskuihin löytyisi toinenkin tapa ratkaista ne. Tällaisen tutkielman tekeminen on ajan kohtainen, sillä vuonna 2019 matematiikan yo-kirjoitukset muuttuvat sähköiseen muotoon. wxMaxima on valittu juuri yhdeksi ohjelmaksi, jota voi käyttää sähköisissä kirjoituksissa.

Measuring attitudes in translation: a study of Nokia business reports

Background Contemporary Finnish, spoken and written, reveals loanwords or foreignisms in the form of hybrids: a mixture of Finnish and foreign syllables (alumiinivalua). Sometimes loanwords are inserted into the Finnish sentence in their raw form just as they are found in the source language (pulp, after sales palvelu). Again, sometimes loanwords are calques, which appear Finnish but are spelled and pronounced in an altogether foreign manner (Protomanageri, Promenadi kampuksella). Research Questions What role does Finnish business translation play in the migration of foreignisms into Finnish if we consider translation "as a construct of solutions determined by the ideological constraints and conflicts characterizing the target culture" (Robyns 1992: 212)? What attitudes do the Finns display toward the presence of foreignisms in their language? What socio-economic or ideological conditions (Bassnett 1994: 321) are responsible for these attitudes? Are these conditions dynamic? What tools can be used to measure such attitudes? This dissertation set out to answer these and similar questions. Attitudes are imperialist (where otherness is both denied and transformed), defensive (where otherness is acknowledged, transformed, and vilified), transdiscursive (a neutral attitude to both otherness and transformation), or finally defective (where alien migration is acknowledged and "stimulated") (Robyns 1994: 60). Methodology The research method follows Rose's schema (1984: 8): (a) take an existing theory, (b) develop from it a proposition specific enough to be tested, (c) devise a scheme that tests this proposition, (d) carry through the scheme in practice, (e) draw up results and discuss conclusions in relation to the original theory. In other words, the method attempts an explanation of a Finnish social phenomenon based on systematic analyses of translated evidence (Lewins 1992: 4) whereby what really matters is the logical sequence that connects the empirical data to the initial research questions raised above and, ultimately to its conclusion (Yin 1984: 29). Results This research found that Finnish translators of the Nokia annual reports used a foreignism whenever possible such as komponentin instead of rakenneosa, or investoida instead of sijoittaa, and often without any apparent justification (Pryce 2003: 203-12) more than the translator's personal preference. In the old documents (minutes of meetings of the Board of Directors of Osakeyhtio H. Saastamoinen, Ltd. dated 5 July 1912-1917, a NOPSA booklet (1932), Enzo-Gutzeit-Tornator Oy document (1938), Imatra Steel Oy Annual Report 1964, and Nokia Oy Annual Report 1946), foreignisms under Haugen's (1950: 210-31) Classification #1 occurred an average of 0.6 times, while in the new documents (Nokia 1998 translated Annual Reports) they occurred an average of 6.5 times. That big difference, suggests transdiscursive and defective attitudes in Finnish society toward the other. In the 1850s, Finnish attitudes toward alien persons and cultures were hardened, intolerant and prohibitive because language politics were both nascent and emerging, and Finns adopted a defensive stance (Paloposki 2002: 102 ff) to protect their cultural and national treasures such as language and folklore. Innovation The innovation here is that no prior doctoral level research measured Finnish attitudes toward foreignisms using a business translation approach. This is the first time that Haugen's classification has been modified and applied in target language analysis. It is hoped that this method would be replicated in similar research in the future. Applications For practical applications, researchers with interest in languages, language development, language influences, language ideologies, and power structures that affect national language policies will find this thesis useful, especially the model for collecting, grouping, and analyzing foreignisms that has been demonstrated here. It is intended to document for posterity current attitudes of Finns toward the other as revealed in business translations from 1912-1964, and in 1998. This way, future language researchers would be able to explore a time-line of Finnish language development and attitudes toward the other. Communication firms may also find this research interesting. In future, could the model we adopted be used to analyze literary texts or religious texts for example? Future Trends Though business documents show transdiscursive attitudes, other segments of Finnish society may show defensive or imperialist attitudes. When the ideology of industrialization changes in the future, will Finnish attitudes toward the other change as well? Will it then be possible to use the same kind of analytical tools to measure Finnish attitudes? More broadly, will linguistic change continue in the same direction of transdiscursive attitudes, or will the change slow down or even reverse into xenophobic attitudes? Is this our model culture-specific or can it be used in the context of other cultures? Conclusion There is anger against foreignisms in Finland as newspaper publications and television broadcasts show, but research shows that a majority of Finns consider foreignisms and the languages from which they come as sources of enrichment for Finnish culture (Laitinen 2000, Eurobarometer series 41 of July 1994, 44 of Spring 1996, 50 of Autumn 1998). Ideologies of industrialization and globalization in Finland have facilitated transdiscursive tendencies. When Finland's political ideology was intolerant toward foreign influences in the 1850s because Finland was in the process of consolidating her nascent country and language, attitudes toward the importation of loanwords also became intolerant. Presently, when industrialization and globalization became the dominant ideologies, we see a shift in attitudes toward transdiscursive tendencies. Ideology is usually unseen and too often ignored by translation researchers. However, ideology reveals itself as the most powerful factor affecting language attitudes in a target culture. Key words Finnish, Business Translation, Ideology, Foreignisms, Imperialist Attitudes, Defensive Attitudes, Transdiscursive Attitudes, Defective Attitudes, the Other, Old Documents, New Documents.

Productivity of the suffixes -ness and -ity in 17th-century English letters : A sociolinguistic approach

Tässä työssä tutkitaan englannin kielen substantiivijohtimien -ness ja -ity produktiivisuutta 1600-luvulla kirjoitetuissa kirjeissä. Näitä lähes synonyymisiä johtimia käytetään yleensä merkitykseltään abstraktien substantiivien muodostamiseen adjektiiveista (esim. productive 'produktiivinen' > productiveness tai productivity 'produktiivisuus'). Johtimista -ity on lainautunut englantiin ranskasta ja myöhemmin myös latinasta; se on sekä fonologialtaan että semantiikaltaan läpinäkymättömämpi kuin kotoperäinen -ness. Lisäksi -ity-johdinta on käytetty enimmäkseen formaaleissa tilanteissa ja tieteellisissä teksteissä, kun taas -ness on ollut yleiskäyttöisempi. Tutkielman lähestymistapa on sosiolingvistinen: oletetaan, että johtimien produktiivisuus (eli valmius muodostaa uusia johdoksia) voi vaihdella eri sosiaaliryhmissä. Sosiolingvistiikkaa ei ole aiemmin juurikaan sovellettu produktiivisuuden tutkimiseen. Tutkimusaineistona on Helsingin yliopiston VARIENG-tutkimusyksikön laatima Corpus of Early English Correspondence, varhaisista englanninkielisistä kirjeistä koostuva korpus eli elektroninen tekstikokoelma, joka on suunniteltu historiallisen sosiolingvistiikan tarpeisiin. Korpuksen 1600-luvun kirjeitten yhteenlaskettu pituus on noin 1,4 miljoonaa sanaa, ja ne on kirjoitettu vuosina 1600-1681. Tutkielman tärkeimpänä produktiivisuusmittarina käytetään johtimien avulla muodostettujen eri sanojen eli tyyppien lukumäärää. Hypoteesina on, että -ity-tyyppien määrä on keskimääräistä pienempi huonosti koulutettujen sosiaaliryhmien kirjeissä. Näitä olivat 1600-luvulla naiset sekä alhaisimmat yhteiskuntaryhmät, kuten talonpojat ja käsityöläiset. Johtimen -ness tyyppimäärissä ei odoteta esiintyvän sosiolingvististä variaatiota. Tutkielmassa käsitellään myös tyyppimäärien vertailuun liittyviä metodologisia ongelmia. Koska vaikkapa naisilta ja miehiltä on eri määrä dataa, ei heidän tyyppimääriään voida suoraan verrata keskenään. Esimerkiksi tyyppimäärien normalisointi tuhatta sanaa kohti ei myöskään ole mahdollista, koska tyyppien lukumäärä ei kasva lineaarisesti korpuksen kasvaessa. Tutkielmassa esitetään kielitieteessä harvoin käytetty tilastotieteellinen menetelmä, jonka avulla korpuksen eri osista saatuja tyyppimääriä voidaan verrata koko korpukseen ja testata, ovatko ne tilastollisesti merkittävän pieniä tai suuria. Toisin kuin monet yleisemmät menetelmät, tämä tyyppikertymiin ja permutaatiotesteihin perustuva metodi ei vaadi yksinkertaistavien oletuksien tekemistä. Tutkimustulokset vahvistavat hypoteesin oikeaksi: naisten -ity-tyyppien lukumäärä on tilastollisesti merkittävän alhainen, kun taas -ness-tyyppien määrissä ei ole tilastollisesti merkittäviä eroja. Alhaisimpien yhteiskuntaryhmien osalta tuloksia ei saada, koska niiltä on korpuksessa liian vähän dataa. Analyysissä paljastuu myös yllättävä eroavaisuus: korpuksen ajallisesti ensimmäisessä puoliskossa (1600-1639) on merkittävän vähän -ity-tyyppejä. Tämä voidaan tulkita kielelliseksi muutokseksi: -ity-johtimen produktiivisuus kasvaa kirjeissä 1600-luvun aikana. Saattaa olla, että johtimen produktiivisuus on ensin kasvanut formaalimmissa tekstilajeissa, joista lisääntynyt käyttö on sitten levinnyt myös kirjeisiin, ehkäpä 1640-luvun sisällissodan synnyttämien kontaktiverkostojen siivittämänä. Tuloksien perusteella voidaan sanoa, että sosiolingvistinen vaihtelu on merkittävä tekijä ainakin joittenkin johtimien produktiivisuudessa, joten vaihtelua on syytä tutkia enemmänkin. Tutkimuksessa käytetty metodi mahdollistaa osakorpuksien tyyppimäärien luotettavan vertailun melko pienissäkin korpuksissa, joten se soveltuu hyvin niin historialliseen kielitieteeseen kuin sosiolingvistiikkaankin.

Language change as an evolutionary process

In the thesis it is discussed in what ways concepts and methodology developed in evolutionary biology can be applied to the explanation and research of language change. The parallel nature of the mechanisms of biological evolution and language change is explored along with the history of the exchange of ideas between these two disciplines. Against this background computational methods developed in evolutionary biology are taken into consideration in terms of their applicability to the study of historical relationships between languages. Different phylogenetic methods are explained in common terminology, avoiding the technical language of statistics. The thesis is on one hand a synthesis of earlier scientific discussion, and on the other an attempt to map out the problems of earlier approaches in addition to finding new guidelines in the study of language change on their basis. Primarily literature about the connections between evolutionary biology and language change, along with research articles describing applications of phylogenetic methods into language change have been used as source material. The thesis starts out by describing the initial development of the disciplines of evolutionary biology and historical linguistics, a process which right from the beginning can be seen to have involved an exchange of ideas concerning the mechanisms of language change and biological evolution. The historical discussion lays the foundation for the handling of the generalised account of selection developed during the recent few decades. This account is aimed for creating a theoretical framework capable of explaining both biological evolution and cultural change as selection processes acting on self-replicating entities. This thesis focusses on the capacity of the generalised account of selection to describe language change as a process of this kind. In biology, the mechanisms of evolution are seen to form populations of genetically related organisms through time. One of the central questions explored in this thesis is whether selection theory makes it possible to picture languages are forming populations of a similar kind, and what a perspective like this can offer to the understanding of language in general. In historical linguistics, the comparative method and other, complementing methods have been traditionally used to study the development of languages from a common ancestral language. Computational, quantitative methods have not become widely used as part of the central methodology of historical linguistics. After the fading of a limited popularity enjoyed by the lexicostatistical method since the 1950s, only in the recent years have also the computational methods of phylogenetic inference used in evolutionary biology been applied to the study of early language history. In this thesis the possibilities offered by the traditional methodology of historical linguistics and the new phylogenetic methods are compared. The methods are approached through the ways in which they have been applied to the Indo-European languages, which is the most thoroughly investigated language family using both the traditional and the phylogenetic methods. The problems of these applications along with the optimal form of the linguistic data used in these methods are explored in the thesis. The mechanisms of biological evolution are seen in the thesis as parallel in a limited sense to the mechanisms of language change, however sufficiently so that the development of a generalised account of selection is deemed as possibly fruiful for understanding language change. These similarities are also seen to support the validity of using phylogenetic methods in the study of language history, although the use of linguistic data and the models of language change employed by these models are seen to await further development.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

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.

Nykytaiteen alkukuvat : Postjungilainen estetiikka nykykuvataiteen tulkintavälineenä

Tutkimus tarkastelee analyyttisen psykologian isän C. G. Jungin teorian sekä jungilaisten ja postjungilaisten teorioiden soveltuvuutta nykykuvataiteen tarkasteluun. Tutkimus esittelee jungilaista estetiikkaa kattavasti suomeksi ja soveltaa sitä postjungilaisesti nykykuvataiteen tulkintaan. Kumpaakaan ei ole aiemmin tehty estetiikan alalla Suomessa. Tutkimusaineistona on käytetty painettujen lähteiden lisäksi esimerkiksi haastatteluita ja aiheeseen liittyviä seminaareja. Jung ei itse muodostanut yhtenäistä taiteen tulkintateoriaa. Sekä psykologian että taidefilosofian puolella on viitattu yleisellä tasolla joihinkin jungilaisiin tulkintamahdollisuuksiin, mutta jungilaista estetiikkaa ei ole kehitetty kuvataiteen tulkintaan eikä varsinkaan nykykuvataiteen tulkintaan soveltuvaksi välineeksi. Kirjallisuuden tutkimuksen puolella jungilaisen näkökulman soveltaminen tulkintaan on yleisempää, myös Suomessa. Suomessa Jung-tutkimus on kuitenkin vähäistä ja pintapuolista sekä yleisesti ottaen että erityisesti työn aiheen kannalta. Työn alussa esitellään tutkimuksellinen ja teoreettinen kansainvälinen ja kansallinen viitekehys. Tämän jälkeen esitellään tutkimuksen kannalta tärkeät jungilaiset käsitteet, kuten arkkityyppi, kollektiivinen tiedostamaton ja symboli. Aiheelle keskeistä jungilaista symboli-käsitettä tarkastellaan laajasti ja pohditaan tämän sijoittumista taiteen tutkimuksen kentällä suhteessa esimerkiksi muihin estetiikan symbolikäsityksiin. Tutkielmassa yhdistellään jungilaisten ja postjungilaisten ajattelijoiden teorioita ja tutkimusmetodeja ja sovelletaan tästä ajattelumatriisista johdettua postjungilaista taiteen tulkintavälinettä kulttuurisidonnaisen nykykuvataiteen tulkintaan. Tässä tutkimuksessa postjungilaista estetiikkaa sovelletaan taiteen tulkintaan innovatiivisesti ja tieteellisesti tukeutumatta vain mielleyhtymiin. Työssä kehitellään erityisesti myös terapiassa käytettyä jungilaista amplifikaatio-menetelmää nykykuvataiteen tulkintavälineeksi, minkä jälkeen amplifikaatio-menetelmän sovelluksella tulkitaan Maaria Wirkkalan Vakain aikein (2006) -installaatioteosta. Työssä keskitytään yhteisölliseen ja kollektiiviseen näkökulmaan teostulkinnassa. Taiteesta voidaan tätä kautta löytää jotain ajatonta ja yhteistä. Postjungilaisen nykytaiteen tulkinnan avulla voi tunnistaa ja nostaa näitä asioita keskusteluun. Amplifikaatiota ei ole aiemmin sovellettu samalla tavalla. Lopuksi käsitellään tämän postjungilaisen taideteostulkinnan tuloksia ja jäsennetään niitä suhteessa teoreettisen viitekehyksen käsitteisiin sekä tarkastellaan jatkotutkimusmahdollisuuksia. Tutkimus osoittaa, että esitelty postjungilainen tarkastelu sopii nykykuvataiteen tulkintavälineeksi erityisesti kun halutaan järjestelmällisesti etsiä ja tarkastella nykykuvataideteosten yliyksilöllisiä viittausmahdollisuuksia. Avainsanat: Estetiikka, taidefilosofia, taide, tulkinta, Jung, jungilaisuus, postjungilaisuus, nykytaide, nykykuvataide, kuvataide, tiedostamaton, kollektiivinen, kollektiivinen tiedostamaton, arkkityypit, symbolit, amplifikaatio

Konstruktioiden dynamiikkaa

Dynamic constructions Dynamic constructions is a study of the dynamism of Finnish grammar. Dynamism as a linguistic phenomenon is studied on both the diachronic and synchronic level. The study therefore focuses not only on the temporal changes of grammar but also on the conventionality of grammatical structures and on the interplay between closely related constructions. Dynamism is also treated as a phenomenon occurring between different varieties of Finnish. All in all, dynamism is shown to be a key feature of the nature of grammar. The study is set within the framework of cognitive linguistics and construction grammar. Both theories emphasise the role of constructions pairings of form with semantic or discourse function in the composition and development of grammar. The grammar of a language is understood to be a structured inventory of such constructions. I argue that the constructions are best studied in their original contexts of use. Thus, the study is usage-based in a strict sense. The data is compiled from various corpora consisting of both written and spoken as well as standard and non-standard Finnish. The dissertation consists of an introduction and four empirical studies. The four papers examine various Finnish constructions and thereby shed light on different aspects of the dynamism of a grammar. The first paper focuses on the diachronic development of the Finnish temporal converb essa. The second paper discusses a specific construction which includes the essa converb, that is, the mikäs on ollessa construction. Some closely related constructions and their semantic interplay are also examined. The third paper extensively studies what is generally regarded as an ellipsis of the negation verb in Finnish. By using present day Finnish data, I show that the omission of the negation verb is not an instance of mere ellipsis but rather a construction. The final paper combines the themes of the second and the third paper by focusing on closely related constructions of the negative ellipsis construction.

Kehittävän kuntoutuksen mahdollisuudet. : Tutkimus Aslak -kuntoutuksen työkytkennän ja asiakkuuden rakentumisesta.

The possibilities of developmental rehabilitation. A study on the construction of work relatedness and the customer in Aslak rehabilitation The challenge of work-related rehabilitation is to anticipate the factors threatening work ability and to affect them. The purpose of this study was to analyze how work-related rehabilitation is constructed in practice and what are the challenges and, at the same time, the possibilities of an innovative transformation of rehabilitation when trying to achive this goal. The theoretical basis is cultural-historical activity theory and developmental work research. Based on a historical analysis, I studied rehabilitation activity empirically using the data gathered from one Aslak programme (Aslak = occupationally oriented medical rehabilitation) over two years. I described and analysed the construction of Aslak using ethnographic data and interviews. The data includes audio- and video-recordings of the Aslak course, fieldnotes, documents and other materials used in the course. The study aimed to reveal rehabilitation practices from different perspectives carried out by different stakeholders and participants in the Aslak course. It focused on the Aslak trajectory produced by a multiorganizational subject. I analyzed the rehabilitation activity using the method of ethnographic analysis of infrastructure. The method of analyzing the construction of the object of rehabilititation the customer was a membership categorization analysis (MCD) based on the ethnomethodological research tradition. I analyzed the meanings denoting customers given by different parties during one Aslak process and the relations between the meanings. Based on this analysis, I studied the disturbances, ruptures, and innovations in the rehabilitation activity. The results of the study show that the infrastructure of Aslak has different basic ideas. Aslak is constructed most explicitly on the infrastructure of medical rehabilitation. The second layer has been provided with some tools of identifying and preventing well-defined occupation-specific load factors. However, it has failed to perform a new structure, as Aslak has encountered, at the same time, rapid changes in working life. The study identified some promising markers representing new kinds of work-related rehabilitation ideas, but they proved to be incomplete and fragile. As a consequence of the multilayered infrastructure, the contents of the Aslak course were split into fragmented phases and disconnected themes, which were blocked in by the master idea of medical orientation. Its relationship to work remained weak and obscure. The categorizations of customers in Aslak were manifold and contradictory. According to the results, the possibilities for transforming work-related rehabilitation lie both in changing the orientation to the customer to be more relevant to changing working life and forging the infrastructural innovations related to this change. The results showed that a new work-relatedeness would be difficult but possible to construct. What is needed is the construction of an infrastructure that will support a coherent master idea of work-related rehabilitation over the entire trajectory of a process. A shared idea of a rehabilitation object must be constructed in close collaboration between different stakeholders, such as Kela (the Social Insurance Institution of Finland), occupational health services, work organizations, and rehabilitation institutes. Key words: Aslak rehabilitation, work-related rehabilitation, development of rehabilitation, customer of rehabilitation, developmental work research, analysis of infrastructure, membership category analysis

Liikkumisen ja kokemusten yhteys virtuaaliympäristöissä

The aim of this study was to build a model and analyze how users move in a virtual environment and to explore the experiential dimensions connected with different ways of moving. Due to the lack of previous research on this subject, this was an explorative study. This study also aimed to identify different ways how users move in virtual environments and the background variables connected to them. It was hypothesized that fluent movement in virtual environments is connected to high presence, skill and challenge assessments. Test participants (n = 68) were mostly highly educated young adults. A virtual environment was built using a CAVE -type virtual reality interface. The task was to search for objects that do not belong into a normal house. The participants movement in the virtual house was recorded on a computer. Movement was modelled using a cluster analysis of information entropy based movement measurements, acceleration, amount of stops and time spent being stationary. The experiential dimensions were measured using the EVEQ -questionnaire. We were able to identify four different ways of moving in virtual environments. In respect of background variables, the four groups differed only in the amount of weekly computer usage. However, fluent movement in virtual environments was connected to a high sense of presence. Furthermore, participants who moved fluently in the environment assessed their skills as being high and regarded the use of virtual environment as challenging. The results indicate that different ways of moving affects how people experience virtual environments. Consequently the participants assessment of their skills and level of challenge have an impact on the affective evaluation of the situation at hand. Entropy measures have not been previously applied when studying movement, and in addition the role of movement on the experiential dimensions of virtual environments is an unexplored subject. The movement analysis method introduced here is applicable to other research problems. Finally, this study expands on our knowledge of the special characteristics connected with the experiential dimensions of virtual environments.