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.

Visions of Past Glory: Nationalism and the Construction of Early Finnish History

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

Tiedettä Pohjantähden alla : Pohjoisen tutkimus ja Ruotsin tiedeseurojen suhteet Ranskaan 1700-luvulla

In the eighteenth century, the birth of scientific societies in Europe created a new framework for scientific cooperation. Through a new contextualist study of the contacts between the first scientific societies in Sweden and the most important science academy in Europe at the time, l Académie des Sciences in Paris, this dissertation aims to shed light on the role taken by the Swedish learned men in the new networks. It seeks to show that the academy model was related to a new idea of specialisation in science. In the course of the eighteenth century, it is argued, the study of the northern phenomena and regions offered the Swedes an important field of speciality with regard to their foreign colleagues. Although historical studies have often underlined the economic, practical undertone of eighteenth-century Swedish science, participation in fashionable scientific pursuits had also become an important scene for representation. However, the views prevailing in Europe tied civilisation and learning closely to the sunnier, southern climates, which had lead to the difficulty of portraying Sweden as a learned country. The image of the scientific North, as well as the Swedish strategies to polish the image of the North as a place for science, are analysed as seen from France. While sixteenth-century historians had preferred to put down the effects of the cold and claim a similarity of northern conditions to the others, the scientific exchange between Swedish and French researchers shows a new tendency to underline the difference of the North and its harsh climate. An explanation is sought by analysing how information about northern phenomena was used in France. In the European academies, new empirical methods had lead to a need for direct observations on different phenomena and circumstances. Rather than curiosities or objects for exoticism, the eighteenth-century depictions of the northern periphery tell about an emerging interest in the most extreme, and often most telling, examples of the workings of the invariable laws of nature. Whereas the idea of accumulating knowledge through cooperation was most manifest in joint astronomical projects, the idea of gathering and comparing data from differing places of observation appears also in other fields, from experimental philosophy to natural studies or medicine. The effects of these developments are studied and explained in connection to the Montesquieuan climate theories and the emerging pre-romantic ideas of man and society.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

Death, Destruction and Commemoration : Tracing ritual activities in Finnish Late Iron Age cemeteries (AD 550-1150)

The thesis is connected with death, memory and ancestor commemoration during the Merovingian Period, the Viking Age and the beginning of the Crusade Period (AD 550-1150) in Finland. During this time, cremation was the dominant burial rite. It was not until the end of the Viking Age that inhumation became more common but both cremations and inhumations are performed even at the same sites throughout the time. Three different burial types 1) cremation cemeteries below level ground, 2) inhumation burials and 3) water burials are discussed in five articles. I consider these burial forms from three different viewpoints; collectivity-individuality, visibility-invisibility and cremation-inhumation. The thesis also discusses the topics of memory, memorialisation and monument re-use, which have been neglected subjects in Finnish archaeology until now. Both cremation cemeteries below level ground and inhumation burials have been re-used during their time of usage, and on most occasions are situated in a landscape that is overlaid by other monuments as well. The main questions of the thesis are: What kinds of ritual behaviour can we detect in the burials during the period (AD 550-1150)? How did people perceive the moraine hills that functioned as burial places? What kind of re-use can be detected in the Iron Age cemeteries? Why have ancient sites and artefacts been re-used? This thesis shows that it is possible to claim that both artefact and site re-use is a much more widespread phenomenon than has previously been thought in Finnish archaeology. It is also a conscious and deliberate behaviour that can be related to an ancestor cult and commemoration of the dead. The funerary rituals during this time period show great variation and complex, both regionally and nationally. Not only have the dead been buried using elaborate rituals, they have also been mourned and commemorated in intricate ways that proves that death was not an end product, but the start of something new.

Literacy teaching and learning in a digital world: Challenges of a new era

Teachers the world over are aware of the range of new challenges that arise from this new era. One challenge is the role of digital technologies in literacy learning. Despite its reputation for being engaging, digital technologies do not always enhance learning outcomes. Whilst the concerns vary across time and place, the core issue of what is a highly sought after literacy learning outcome in this new era warrants consideration. This paper introduces Kalantzis and Cope’s (2005) theorisation of eight knowledge processes for literacy learning. They claim that experiencing the known, conceptualising by naming, analysing functionally and applying appropriately, whilst necessary, are not on their own sufficient for the development of high level literacy practices. It is their contention that students must also be able to experience the new, conceptualise by theorising, analyse creatively and apply critically. This theorisation forms an auditing framework for considering the outcomes of different uptakes of digital technologies in a Social Studies and a Science unit.

Writing Otherwise than Seeing : Writing and Exteriority in Maurice Blanchot

Maurice Blanchot (1907-2003), the French writer and novelist, is one of the most important figures in post-war French literature and philosophy. The main intention of this study is to figure out his position and originality in the field of phenomenology. Since this thesis concentrates on the notion of vision in Blanchot s work, its primary context is the post-war discussion of the relation between seeing and thinking in France, and particularly the discussion of the conditions of non-violent vision and language. The focus will be on the philosophical conversation between Blanchot and his contemporary philosophers. The central premise is the following: Blanchot relates the criticism of vision to the criticism of the representative model of language. In this thesis, Blanchot s definition of literary language as the refusal to reveal anything is read as a reference pointing in two directions. First, to Hegel s idea of naming as negativity which reveals Being incrementally to man, and second, to Heidegger s idea of poetry as the simultaneity of revealing and withdrawal; the aim is to prove that eventually Blanchot opposes both Hegel s idea of naming as a gradual revelation of the totality of being and Heidegger s conception of poetry as a way of revealing the truth of Being. My other central hypothesis is that for Blanchot, the criticism of the privilege of vision is always related to the problematic of the exteriority. The principal intention is to trace how Blanchot s idea of language as infinity and exteriority challenges both the Hegelian idea of naming as conceptualizing things and Heidegger s concept of language as a way to truth (as aletheia). The intention is to show how Blanchot, with his concepts of fascination, resemblance and image, both affirms and challenges the central points of Heidegger s thinking on language. Blanchot s originality in, and contribution to, the discussion about the violence of vision and language is found in his answer to the question of how to approach the other by avoiding the worst violence . I claim that by criticizing the idea of language as naming both in Hegel and Heidegger, Blanchot generates an account of language which, since it neither negates nor creates Being, is beyond the metaphysical opposition between Being and non-Being.

Energy-dependence of nitrate reductase induction in Candida-Utilis

The requirement of a suitable energy source during the induced synthesis of nitrate reductase in Image was investigated. The levels of nitrate reductase induced were shown to be energy-dependent, and to vary in response to the type of carbon source provided. Glycerol, fructose, ethanol, glucose, and sucrose served as efficient energy sources. Growth rate of the yeast and the induced level of nitrate reductase were dependent on the ratio of carbon to nitrogen in the induction medium, and ratio of 2 being optimal. Induction of nitrate reductase was inhibited by uncouplers, 2,4-dinitrophenol (DNP), dicumarol and carbonyl cyanide Candida-Utilis -trifluoromethoxy phenyl hydrazone (CCCP), and by cyanide and azide, indicating an absolute energy-dependency. The facilitation of induction of a high level of nitrate reductase by exogenously added ATP as sole source of energy confirmed the obligate requirement of ATP for the synthesis of nitrate reductase in Candida-Utilis.

Certainty or Faith? Arendt's and Merleau-Ponty's Critique of Cartesian Foundationalism

Epistemological foundationalism has for centuries attempted to unify all scientific inquiry into the context of one grand science, the first philosophy. One of the most important tasks of this tradition has been to ground all knowledge on absolutely certain foundations. In this master s thesis I ask the following question: To what extent and under what conditions is it possible to achieve absolute certainty in the sense of the attempts of Cartesian foundationalism? By examining how the 20th century philosophers, Edmund Husserl (1859-1938), Hannah Arendt (1906-1975) and Maurice Merleau-Ponty (1908-1961) interpret the epistemological methodology of René Descartes, I claim that the Cartesian achievement of absolute certainty rests on the implicit presupposition of an epistemologically prior form of faith in the world and trust (pistis) in other conscious beings. I show that knowledge is possible only within the context of a common world that is inhabited by several conscious beings that share a common linguistic system. This threefold element is shown to be the bedrock condition for any kind of philosophical inquiry. The main literature sources for this thesis are The Life of the Mind by Hannah Arendt, Le Visible et l invisible by Maurice Merleau-Ponty, Meditationes de Prima Philosophiae by René Descartes and Erfahrung und Urteil by Edmund Husserl.

Infinitiivi ja sen infiniittisyys : Tutkimus suomen kielen itsenäisistä A-infinitiivikonstruktioista

"Infinitive and its infinity" advocates an approach to infinitives that differs from most previous descriptions in several ways. Infinitives are generally considered to be an illustrative example of an inherently subordinated verb category. This is due to the fact that they are morphologically reduced and are allegedly not able to function as the only predicate of an independent clause. While former descriptions have thus treated infinitives as a linguistic category heavily dependent on the finite verb, my claim is that Finnish A-infinitives (e.g. juosta to run , olla to be ) can be used as independent grammatical units: they need not be either dependent or subordinated, but can have an equal status with finite constructions. In other words, they can be conceptually and interactionally non-dependent. Theoretically, the main objective of the thesis is to discover the nature of non-finite conceptualization and the ways in which it is utilized in everyday interactions. This is accomplished by contrasting finite and non-finite conceptualization with respect to the morphosyntactic marking of person, tense and modality. I argue that the morphologically reduced nature of infinitives can be used as an interactional resource. Independent A-infinitive constructions designate verbal processes that profile no participants, lack any connection with time, and present states of affairs as intensional, structural spaces. Consequently, they provide the interactants with a conceptual alternative in contrast to finite predications that are in Finnish always grammatically anchored to time, modality and person. The deictically unanchored character of A-infinitive constructions makes them highly affective and reflexive in nature. I discuss my findings primarily in the light of Cognitive Grammar. I have drawn insight from various other fields, too: among the theories that are touched upon are interactional linguistics, functional-typological linguistics, and studies on the poetic and metapragmatic use of language. The study is based on empirical data interpreted in qualitative terms. Analyses are based on 980 examples coming mainly from written language. Some 20 examples of spoken data are analyzed as well. In sum, the thesis presents a critical statement towards the finite-verb centred outlook on language and shows that analyzing non-finite elements as such reveals new aspects of grammar and interaction. This is to acknowledge the fact that infinitives, albeit prototypically participating in the coding of dependent events, can also be used outside of the context of the finite verb. Such a view poses several new research questions, as a linguistic category generally seen to code dependent, less prominent states of affairs , now is viewed on as possessing a full cognitive and pragmatic potential.

A measure of logical complexity of programs

The research in software science has so far been concentrated on three measures of program complexity: (a) software effort; (b) cyclomatic complexity; and (c) program knots. In this paper we propose a measure of the logical complexity of programs in terms of the variable dependency of sequence of computations, inductive effort in writing loops and complexity of data structures. The proposed complexity mensure is described with the aid of a graph which exhibits diagrammatically the dependence of a computation at a node upon the computation of other (earlier) nodes. Complexity measures of several example programs have been computed and the related issues have been discussed. The paper also describes the role played by data structures in deciding the program complexity.

The Statutory Defence(s) of 'peer professional opinion'

In the wake of the GFC and with ever increasing consumer-protection-related laws, clients are more aware of their rights and your obligations as a professional valuer. They also are more likely to take legal action if, as a result of their reliance on a valuation, they suffer a financial loss. In some Australian jurisdictions, in response to a claim of negligence, the professional valuer may be able to raise a professional practice defence under civil liability legislation. This article considers the nature of this statutory defence, what is required to rely upon it and in which jurisdictions it applies.

Recruitment dynamics of invasive species in rainforest habitats following Cyclone Larry

In tropical forests, natural disturbance creates opportunities for species to claim previously utilized space and resources and is considered an important mechanism in the maintenance of species diversity. However, ecologists have long recognized that disturbance also promotes exotic plant invasions. Cyclones cause extensive defoliation, loss of major branches and multiple tree falls, resulting in a significantly more open canopy and increased light and heat levels in the understorey. The widespread and massive disturbance caused by cyclones provides ideal conditions for rapid recruitment and spread of invasive species. The ecological roles of invasive species in rainforest habitats following such a severe disturbance are poorly understood. Severe category 4 Cyclone Larry crossed the North Queensland coast in March 2006 causing massive disturbance to rainforest habitats from Tully to Cairns and west to the Atherton Tablelands. We established 10 plots in an area extensively damaged by this cyclone near El Arish in North Queensland. On each plot nine 2 × 2 m quadrats were established with three quadrats per plot in each of the following treatments: (i) complete debris removal down to the soil layer, (ii) removal of coarse woody debris only, and (iii) uncleared. We monitored recruitment, growth and mortality of all native and invasive species in the 90 quadrats every 3 months since the cyclone. Here we present the recruitment dynamics of invasive species across the study area in relation to the level of disturbance, the type of quadrat treatment, and the diversity and abundance of the native recruiting flora over the first 12 months post-cyclone. Our results suggest that invasive species will mostly comprise a transient component of the flora in the early stages of the successional response. However, some species may have longer-term effects on the successional trajectory of the rainforest and future forest composition and structure.

Split-Freedom And Mvd-Intersection - A New Characterization Of Multivalued Dependencies Having Conflict-Free Covers

Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [2,12,15,16]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a confiict-free cover. In [8] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of “split-free” sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of “intersection” of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial-time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorthms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs,thereby showing that they are interesting in their own right.

The Freudian unconscious in the context of the cognitive orientation

For decades psychoanalysis was the discipline studying the unconscious, and other branches of study lacked competence to take a stand on the issues concerning the unconscious. From 1980s onwards intense study of the unconscious has been taken place in the scope of cognitive orientation. Thus, nowadays it is talked about both pyschoanalytic and cognitive unconscious. The aim of this thesis is to integrate psychoanalytic and cognitive views. When the "Freudian" conception of the unconscious is considered, there are four entangled issues: 1) what is the unconscious like, 2) how does the unconsciuos give rise to psychic disorders 3) why and how certain contents are missing from consciousness (repression of contents), 4) the emergence of those contents (becoming conscious of the repressed). The conventional psychoanalytic answer to the first question - and "the cornerstone of psychoanalysis" - is "the unconscious is mental". The issues 2)-4) depend radically on the answer given to the 1): "psychoanalytic" conceptualizations on them rest on the "cornerstone". That ground was challended in study I: it was argued that it has never been clear what does it mean that the unconscious is mental. Thus, it was stated that in the current state of art psychoanalysis should drop out the ephitet "mental" before the term unconscious. That claim creates a pressure to reappraise the convential "psychoanalytic" answers to the other questions, and that reappraisal was the aim of studies II and III. In study II the question 2) is approached in terms of implicit knowledge. Study III focuses on mechanisms, which determine which contents appear in the scope of consciousness, and also cause missing of contents from there (the questions 3) and 4)). In the core of study III there are distinctions concerning the processess occuring in the levels of the brain, consciousness, self-consciousness, and narrative self-consciousness. Studies I-III set "psychoanalytic" topics in the frames of cognitive view. The picture emerging from those studies is not especially useful for a clinican (psychotherapist). Studies IV and V focused that issue. Study IV is a rather serious critique toward neuropsychoanalysis. In it it was claimed that repressive functions of conscious states are in the core of clinical psychoanalysis, and functions in general cannot be reduced to neurophysiological terminology. Thus, the limits of neuropsychoanalysis are more strict than it has been realized: crucial clinical issues remain outside its scope. In study V it was focused on the confusing state of things that although unconscious fantasies do not exist, the idea on them has been an important conceptual tool for clinicans. When put in a larger context, the aim of study V is similar to that of study IV: to determine the relation between psychotherapists' and neuroscientists' terminologies. Studies III, IV and V apply the philosopher Daniel Dennett's model on different levels of explanation.