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.

Becoming a teacher: emerging teacher identity in mathematics teacher education

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.

Novel conditional mouse models for targeted kidney research : Emphasis on the analysis of the biological function of nephrin

Nephrin is a transmembrane protein belonging to the immunoglobulin superfamily and is expressed primarily in the podocytes, which are highly differentiated epithelial cells needed for primary urine formation in the kidney. Mutations leading to nephrin loss abrogate podocyte morphology, and result in massive protein loss into urine and consequent early death in humans carrying specific mutations in this gene. The disease phenotype is closely replicated in respective mouse models. The purpose of this thesis was to generate novel inducible mouse-lines, which allow targeted gene deletion in a time and tissue-specific manner. A proof of principle model for succesful gene therapy for this disease was generated, which allowed podocyte specific transgene replacement to rescue gene deficient mice from perinatal lethality. Furthermore, the phenotypic consequences of nephrin restoration in the kidney and nephrin deficiency in the testis, brain and pancreas in rescued mice were investigated. A novel podocyte-specific construct was achieved by using standard cloning techniques to provide an inducible tool for in vitro and in vivo gene targeting. Using modified constructs and microinjection procedures two novel transgenic mouse-lines were generated. First, a mouse-line with doxycycline inducible expression of Cre recombinase that allows podocyte-specific gene deletion was generated. Second, a mouse-line with doxycycline inducible expression of rat nephrin, which allows podocyte-specific nephrin over-expression was made. Furthermore, it was possible to rescue nephrin deficient mice from perinatal lethality by cross-breeding them with a mouse-line with inducible rat nephrin expression that restored the missing endogenous nephrin only in the kidney after doxycycline treatment. The rescued mice were smaller, infertile, showed genital malformations and developed distinct histological abnormalities in the kidney with an altered molecular composition of the podocytes. Histological changes were also found in the testis, cerebellum and pancreas. The expression of another molecule with limited tissue expression, densin, was localized to the plasma membranes of Sertoli cells in the testis by immunofluorescence staining. Densin may be an essential adherens junction protein between Sertoli cells and developing germ cells and these junctions share similar protein assembly with kidney podocytes. This single, binary conditional construct serves as a cost- and time-efficient tool to increase the understanding of podocyte-specific key proteins in health and disease. The results verified a tightly controlled inducible podocyte-specific transgene expression in vitro and in vivo as expected. These novel mouse-lines with doxycycline inducible Cre recombinase and with rat nephrin expression will be useful for conditional gene targeting of essential podocyte proteins and to study in detail their functions in the adult mice. This is important for future diagnostic and pharmacologic development platforms.

Biological Control of Oilseed Rape Pests with Entomopathogenic Nematodes

Biological control techniques attract increasing attention as one of the sustainable alternatives to pesticide use in integrated pest management programs. In order to develop sustainable pest management methods for arable crops based on entomopathogenic nematodes (EPN), their efficacy and persistence needed to be investigated, and an economically feasible delivery system had to be developed. In this study, first a survey of entomopathogens was conducted, and a system approach was tested, using the oilseed Brassica (OSB) growing system (OSB, spring wheat, and red clover) as a model. The system approach aimed at determining the potential of Steinernema feltiae (Filipjev) for the control of OSB pests, developing OSB rotation schemes that support EPN persistence, and investigating the impact of the selected biotic and abiotic factors on efficacy and persistence of EPN. This study employed abductive logic (which employs constant interplay between the theory and empirical observation), quantitative methods, and a case study on OSB. Laboratory and field experiments were carried out, and two types of pathogen surveys. A horizontal survey included OSB fields across Estonia, Germany, Poland, Sweden and the UK, while a vertical survey included sampling from two sets of differently managed experimental fields during three years. A new approach was introduced for measuring occurrence, where the prevalence and relative intensity of entomopathogens, biotic agents, and unidentified insect antagonists were determined. The effect of dose, timing, and the application method on S. feltiae in the control of pests in OSB, and the potential of a controlled release delivery system (CRS) were evaluated in the field. Studies on the impact of selected biotic and abiotc factors (Brassica plant, bait insects, developmental stages of Meligethes aeneus Fab., Isaria fumosorosea Wize (Ifr), and organic and synthetic fertilizers) on the efficacy of S. feltiae were conducted in the laboratory. Persistence of S. feltiae in the OSB growing system, and the effect of dose, timing, and the application method, was assessed in the field as part of the efficacy experiments. The impact of selected biotic and abiotic factors on S. feltiae persistence was assessed in laboratory experiments. The pathogen survey showed that the occurrence of entomopathogens is low in the OSB growing system, and that a management system causing less disturbance (ICM) to the soil increases the relative intensity of insect parasitic nematodes and other insect antagonists. A longer study period is required to show any possible impact of ICM on the relative intensity of entomopathogenic fungi, or on the prevalence of entomopathogens. Two different measures of the occurrence yielded different results: the relative intensity revealed the difference between the two different crop management methods, while prevalence did not. The highest efficacy of S. feltiae was achieved by using a low dose and targeting all stages of M. aeneus. When only the larval stage was targeted, the application method and dose had no significant effect. The CRS decreased the pest abundance significantly more than the surface application method. S. feltiae persisted in the OSB fields in Finland for several months, but did not survive the winter. The strain survived for 7 months when it was applied in autumn in Germany, but its populations declined rapidly after winter. The examined biotic and abiotic factors had variable impacts on S. feltiae efficacy and persistence. The two measures, prevalence and relative intensity of entomopathogens, gave valuable information for their use in biocontrol programs. The recommended biocontrol strategy for OSB growing in Finland is inundation and seasonal inoculation of EPN. The impact of some biotic and abiotic factors on S. feltiae efficacy and persistence is significant, and can be used to improve the efficacy of EPN. The CRS is a novel alternative for EPN application, and should also be considered for use on other crops. Keywords: Biological control, inundation, inoculation, conservation, formulation, slow release method, crop rotation, Entomopathogenic nematodes, Steinernema feltiae, oilseed rape pests, Meligethes aeneus, Phyllotreta spp., occurrence, prevalence, intensity, efficacy, persistence, field, Isaria fumosorosea, biotic factors, abiotic factors, interaction, impact, insect stages, integrated crop management, standard (conventional) crop management

Organic contaminants - occurrence and biological effects in the Baltic Sea

The Baltic Sea was studied with respect to selected organic contaminants and their ecotoxicology. The research consisted of analyses of total hydrocarbons, polycyclic aromatic hydrocarbons, bile metabolites, hepatic ethoxyresorufin-O-deethylase (EROD) activity, polychlorinated biphenyls (PCBs) and organochlorine pesticides (OCPs). The contaminants were measured from various matrices, such as seawater, sediment and biota. The methods of analysis were evaluated and refined to comparability of the results. Polyaromatic hydrocarbons, originating from petroleum, are known to be among the most harmful substances to the marine environment. In Baltic subsurface water, seasonal dependence of the total hydrocarbon concentrations (THCs) was seen. Although concentrations of parent polycyclic aromatic hydrocarbons (PAHs) in sediment surface varied between 64 and 5161 ug kg-1 (dw), concentrations above 860 ug kg-1 (dw) were found in all the studied sub-basins of the Baltic Sea. Concentrations commonly considered to substantially increase the risk of liver disease and reproductive impairment in fish, as well as potential effects on growth (above 1000 ug kg-1 dw), were found in all the studied sub-basins of the Baltic Sea except Kattegat. Thus, considerable pollution in sediments was indicated. In bivalves, the sums of 12 PAHs varied on a wet weight basis between 44 and 298 ug kg-1 (ww). The predominant PAHs were high molecular weight and the PAH profiles of M. balthica differed from those found in sediment from the same area. The PAHs were both pyrolytic and petrogenic in origin, and a contribution from diesel engines was found, which indicates pollution of the Baltic Sea, most likely caused by the steadily increasing shipping in the area. The HPLC methods developed for hepatic EROD activity and bile metabolite measurements proved to be fast and suitable for the study of biological effects. A mixed function oxygenase enzyme system in Baltic Sea perch collected from the Gulf of Finland was induced slightly: EROD activity in perch varied from 0.30 14 pmol min-1 mg-1 protein. This range can be considered to be comparable to background values. Recent PAH exposure was also indicated by enhanced levels (213 and 1149 ug kg-1) of the bile metabolite 1-hydroxypyrene. No correlation was indicated between hepatic EROD activity and concentration of 1-hydroxypyrene in bile. PCBs and OCPs were observed in Baltic Sea sediment, bivalves and herring. Sums of seven CBs in surface sediment (0 5 cm) ranged from 0.04 to 6.2 ug kg-1 (dw) and sums of three DDTs from 0.13 to 5.0 ug kg-1 (dw). The highest levels of contaminants were found in the most eastern area of the Gulf of Finland where the highest total carbon and nitrogen content was found and where the lowest percentage proportion of p,p -DDT was found. The highest concentrations of CBs and the lowest concentration of DDTs were found in M. balthica from the Gulf of Finland. The highest levels of DDTs were found in M. balthica from the Hanö Bight, which is the outer part of the Bornholm Basin close to the Swedish mainland. In bivalves, the sums of seven CBs were 72 108 ug kg-1 (lw) and the sums of three DDTs were 66 139 ug kg-1 (lw). Results from temporal trend monitoring showed, that during the period 1985 2002, the concentrations of seven CBs in two-year-old female Baltic herring were clearly decreased, from 9 16 to 2 6 ug kg-1 (ww) in the northern Baltic Sea. At the same time, concentrations of three DDTs declined from 8 15 to 1 5 ug kg-1 (ww). The total concentration of the fat-soluble CBs and DDTs in Baltic herring muscle was shown to be age-dependent; the average concentrations in ten-year-old Baltic herring were three to five-fold higher than in two-year-old herring. In Baltic herring and bivalves, as well as in surface sediments, CB 138 and CB153 were predominant among CBs, whereas among DDTs p,p'-DDD predominated in sediment and p,p'-DDE in bivalves and Baltic herring muscle. Baltic Sea sediments are potential sources of contaminants that may become available for bioaccumulation. Based on ecotoxicological assessment criteria, cause for concern regarding CBs in sediments was indicated for the Gulf of Finland and the northern Baltic Proper, and for the northern Baltic Sea regarding CBs in Baltic herring more than two years old. Statistical classification of selected organic contaminants indicated high-level contamination for p,p'-DDT, p,p'-DDD, p,p'-DDE, total DDTs, HCB, CB118 and CB153 in muscle of Baltic herring in age groups two to ten years; in contrast, concentrations of a-HCH and g-HCH were found to be moderate. The concentrations of DDTs and CBs in bivalves is sufficient to cause biological effects, and demonstrates that long-term biological effects are still possible in the case of DDTs in the Hanö Bight.

Synthesis, Reactivity and Biological Activity of 17β-HSD1 Inhibitors Based on a Thieno[2,3-d]pryrimidin-4(3H)-one Core

Breast cancer is the most common cancer in women in Western countries. In the early stages of development most breast cancers are hormone-dependent, and estrogens, especially estradiol, have a pivotal role in their development and progression. One approach to the treatment of hormone-dependent breast cancers is to block the formation of the active estrogens by inhibiting the action of the steroid metabolising enzymes. 17beta-Hydroxysteroid dehydrogenase type 1 (17beta-HSD1) is a key enzyme in the biosynthesis of estradiol, the most potent female sex hormone. The 17beta-HSD1 enzyme catalyses the final step and converts estrone into the biologically active estradiol. Blocking 17beta-HSD1 activity with a specific enzyme inhibitor could provide a means to reduce circulating and tumour estradiol levels and thus promote tumour regression. In recent years 17beta-HSD1 has been recognised as an important drug target. Some inhibitors of 17beta-HSD1 have been reported, however, there are no inhibitors on the market nor have clinical trials been announced. The majority of known 17beta-HSD1 inhibitors are based on steroidal structures, while relatively little has been reported on non-steroidal inhibitors. As compared with 17beta-HSD1 inhibitors based on steroidal structures, non-steroidal compounds could have advantages of synthetic accessibility, drug-likeness, selectivity and non-estrogenicity. This study describes the synthesis of large group of novel 17beta-HSD1 inhibitors based on a non-steroidal thieno[2,3-d]pyrimidin-4(3H)-one core. An efficient synthesis route was developed for the lead compound and subsequently employed in the synthesis of thieno[2,3-d]pyrimidin-4(3H)-one based molecule library. The biological activities and binding of these inhibitors to 17beta-HSD1 and, finally, the quantitative structure activity relationship (QSAR) model are also reported. In this study, several potent and selective 17beta-HSD1 inhibitors without estrogenic activity were identified. This establishment of a novel class of inhibitors is a progressive achievement in 17beta-HSD1 inhibitor development. Furthermore, the 3D-QSAR model, constructed on the basis of this study, offers a powerful tool for future 17beta-HSD1 inhibitor development. As part of the fundamental science underpinning this research, the chemical reactivity of fused (di)cycloalkeno thieno[2,3-d]pyrimidin-4(3H)-ones with electrophilic reagents, i.e. Vilsmeier reagent and dimethylformamide dimethylacetal, was investigated. These findings resulted in a revision of the reaction mechanism of Vilsmeier haloformylation and further contributed to understanding the chemical reactivity of this compound class. This study revealed that the reactivity is dependent upon a stereoelectronic effect arising from different ring conformations.

Discovering hidden structures in molecular data using a Bayesian partition model approach

Advancements in the analysis techniques have led to a rapid accumulation of biological data in databases. Such data often are in the form of sequences of observations, examples including DNA sequences and amino acid sequences of proteins. The scale and quality of the data give promises of answering various biologically relevant questions in more detail than what has been possible before. For example, one may wish to identify areas in an amino acid sequence, which are important for the function of the corresponding protein, or investigate how characteristics on the level of DNA sequence affect the adaptation of a bacterial species to its environment. Many of the interesting questions are intimately associated with the understanding of the evolutionary relationships among the items under consideration. The aim of this work is to develop novel statistical models and computational techniques to meet with the challenge of deriving meaning from the increasing amounts of data. Our main concern is on modeling the evolutionary relationships based on the observed molecular data. We operate within a Bayesian statistical framework, which allows a probabilistic quantification of the uncertainties related to a particular solution. As the basis of our modeling approach we utilize a partition model, which is used to describe the structure of data by appropriately dividing the data items into clusters of related items. Generalizations and modifications of the partition model are developed and applied to various problems. Large-scale data sets provide also a computational challenge. The models used to describe the data must be realistic enough to capture the essential features of the current modeling task but, at the same time, simple enough to make it possible to carry out the inference in practice. The partition model fulfills these two requirements. The problem-specific features can be taken into account by modifying the prior probability distributions of the model parameters. The computational efficiency stems from the ability to integrate out the parameters of the partition model analytically, which enables the use of efficient stochastic search algorithms.

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

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.