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.

Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams

This thesis is a study of a rather new logic called dependence logic and its closure under classical negation, team logic. In this thesis, dependence logic is investigated from several aspects. Some rules are presented for quantifier swapping in dependence logic and team logic. Such rules are among the basic tools one must be familiar with in order to gain the required intuition for using the logic for practical purposes. The thesis compares Ehrenfeucht-Fraïssé (EF) games of first order logic and dependence logic and defines a third EF game that characterises a mixed case where first order formulas are measured in the formula rank of dependence logic. The thesis contains detailed proofs of several translations between dependence logic, team logic, second order logic and its existential fragment. Translations are useful for showing relationships between the expressive powers of logics. Also, by inspecting the form of the translated formulas, one can see how an aspect of one logic can be expressed in the other logic. The thesis makes preliminary investigations into proof theory of dependence logic. Attempts focus on finding a complete proof system for a modest yet nontrivial fragment of dependence logic. A key problem is identified and addressed in adapting a known proof system of classical propositional logic to become a proof system for the fragment, namely that the rule of contraction is needed but is unsound in its unrestricted form. A proof system is suggested for the fragment and its completeness conjectured. Finally, the thesis investigates the very foundation of dependence logic. An alternative semantics called 1-semantics is suggested for the syntax of dependence logic. There are several key differences between 1-semantics and other semantics of dependence logic. 1-semantics is derived from first order semantics by a natural type shift. Therefore 1-semantics reflects an established semantics in a coherent manner. Negation in 1-semantics is a semantic operation and satisfies the law of excluded middle. A translation is provided from unrestricted formulas of existential second order logic into 1-semantics. Also game theoretic semantics are considerd in the light of 1-semantics.

Kriitkko Einari J. Vehmas ja moderni taide

The doctoral dissertation Critic Einari J. Vehmas and Modern Art deals with one of the central figures of the Finnish art scene and his work as an art critic, art museum curator and cultural critic. The main body of research material consists of the writings of Einari J. Vehmas (1902 1980) from 1937 to the late 1960s. Vehmas wrote art reviews for magazines, and from the year 1945 he was a regular art critic for one of the major newspapers in Finland. Vehmas was heavily inclined towards French literature and visual arts. Marcel Proust and Charles Baudelaire influenced his views on the nature of art from the late 1920s onwards. Vehmas is commonly regarded as the most influential art critic of post-war Finland. His writings have been referred to and cited in numerous research papers on Finnish 20th-century art. A lesser known aspect of his work is his position as the deputy director of the Ateneum Art Museum, the Finnish national gallery. Through his art museum work, his opinions also shaped the canon of modern art considered particularly Finnish following the second world war. The main emphasis of the dissertation is on studying Vehmas s writings, but it also illustrates the diversity of his involvement in Finnish cultural life through biographical documents. The long chronological span of the dissertation emphasises how certain central themes accumulate in Vehmas s writings. The aim of the dissertation is also to show how strongly certain philosophical and theoretical concepts from the early 20th century, specifically Wassily Kandinsky s principle of inner necessity and Henri Bergson s epistemology highlighting intuition and instinct, continued to influence the Finnish art discourse even in the early 1960s, in part thanks to the writings of Vehmas. Throughout his production, Vehmas contemplated the state and future of modern art and humanity. Vehmas used a colourful, vitalistic rhetoric to emphasise the role of modern art as a building block of culture and humanity. At the same time, however, he was a cultural pessimist whose art views became infused with anxiety, a sense of loss, and a desire to turn his back on the world.

The Role of Abduction in Self-Similarity

Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.

Hur höra tyst kunskap? Utveckling av en metod för studier av tyst kunnande

Det tysta kunnandet utgör en stor del av kunskapsresursen både hos oss som individer och i arbetsorganisationerna. Trots att vi omger oss med böcker, manualer och databaser, som alla är exempel på explicit kunskap, så är det ”den rätta känslan”, erfarenheten och våra färdigheter som avgör om och hur vi klarar av våra uppgifter. Dessa begrepp är alla relaterade till den tysta dimensionen av kunskap. En dimension som traditionellt karaktäriserats som abstrakt, individuell, omedveten, praktisk, erfarenhetsbaserad och framför allt svår att uttrycka. Alla dessa är karaktärsdrag som ställt speciella krav inom kunskapsforskning och -ledning. Resultatet av detta är att både forskning och ledning av det tysta kunnandet har åsidosatts till förmån för forskning och ledning av explicit kunskap. Ett bidragande problem har varit bristen på lämpliga metoder för att ur ett företagsekonomiskt perspektiv studera och leda tyst kunnande. Ett annat problem har varit oklarhet i begreppet tyst kunskap. Detta har lett till brist på förståelse och/eller missförstånd. För att råda bot på svårigheten att uttrycka vårt tysta kunnande har människan utvecklat olika begrepp som i vår vardagskommunikation symboliserar tyst kunnande. Begrepp som intuition, människokännedom, förhandlingsförmåga och kultur används vanligt och med dem uttrycker vi den tysta dimensionen av kunnande. Dessa begrepp utgör även grunden för den intervjumetod som utvecklats för att empiriskt studera eller i ledningssyfte kartlägga tyst kunnande. Metoden använder dessa ”Epitet för Tyst Kunskap” (ETK) som bas för stimuluskort-intervjuer. Intervjuer som visat sig öka möjligheten att utforska och kartlägga tyst kunnande i organisationer oberoende av om man är forskare eller företagsledare.

Individuals' Responsibility in Corporations

I discuss role responsibly, individual responsibility and collective responsibility in corporate multinational setting. My case study is about minerals used in electronics that come from the Democratic Republic of Congo. What I try to show throughout the thesis is how many things need to be taken into consideration when we discuss the responsibility of individuals in corporations. No easy and simple answers are available. Instead, we must keep in mind the complexity of the situation at all times, judging cases on individual basis, emphasizing the importance of individual judgement and virtue, as well as the responsibility we all share as members of groups and the wider society. I begin by discussing the demands that are placed on us as employees. There is always a potential for a conflict between our different roles and also the wider demands placed on us. Role demands are usually much more specific than the wider question of how we should act as human beings. The terminology of roles can also be misleading as it can create illusions about our work selves being somehow radically separated from our everyday, true selves. The nature of collective decision-making and its implications for responsibility is important too. When discussing the moral responsibility of an employee in a corporate setting, one must take into account arguments from individual and collective responsibility, as well as role ethics. Individual responsibility is not a separate or competing notion from that of collective responsibility. Rather, the two are interlinked. Individuals' responsibilities in collective settings combine both individual responsibility and collective responsibility (which is different from aggregate individual responsibility). In the majority of cases, both will apply in various degrees. Some members might have individual responsibility in addition to the collective responsibility, while others just the collective responsibility. There are also times when no-one bears individual moral responsibility but the members are still responsible for the collective part. My intuition is that collective moral responsibility is strongly linked to the way the collective setting affects individual judgements and moulds the decisions, and how the individuals use the collective setting to further their own ends. Individuals remain the moral agents but responsibility is collective if the actions in question are collective in character. I also explore the impacts of bureaucratic ethic and its influence on the individual. Bureaucracies can compartmentalize work to such a degree that individual human action is reduced to mere behaviour. Responsibility is diffused and the people working in the bureaucracy can come to view their actions to be outside the normal human realm where they would be responsible for what they do. Language games and rules, anonymity, internal power struggles, and the fragmentation of information are just some of the reasons responsibility and morality can get blurry in big institutional settings. Throughout the thesis I defend the following theses: ● People act differently depending on their roles. This is necessary for our society to function, but the more specific role demands should always be kept in check by the wider requirements of being a good human being. ● Acts in corporations (and other large collectives) are not reducible to individual actions, and cannot be explained fully by the behaviour of individual employees. ● Individuals are responsible for the actions that they undertake in the collective as role occupiers and are very rarely off the hook. Hiding behind role demands is usually only an excuse and shows a lack of virtue. ● Individuals in roles can be responsible even when the collective is not. This depends on if the act they performed was corporate in nature or not. ● Bureaucratic structure affects individual thinking and is not always a healthy environment to work in. ● Individual members can share responsibility with the collective and our share of the collective responsibility is strongly linked to our relations. ● Corporations and other collectives can be responsible for harm even when no individual is at fault. The structure and the policies of the collective are crucial. ● Socialization plays an important role in our morality at both work and outside it. We are all responsible for the kind of moral context we create. ● When accepting a role or a position in a collective, we are attaching ourselves with the values of that collective. ● Ethical theories should put more emphasis on good judgement and decision-making instead of vague generalisations. My conclusion is that the individual person is always in the centre when it comes to responsibility, and not so easily off the hook as we sometimes think. What we do, and especially who we choose to associate ourselves with, does matter and we should be more careful when we choose who we work for. Individuals within corporations are responsible for choosing that the corporation they associate with is one that they can ascribe to morally, if not fully, then at least for the most part. Individuals are also inclusively responsible to a varying degree for the collective activities they contribute to, even in overdetermined contexts. We all are responsible for the kind of corporations we choose to support through our actions as consumers, investors and citizens.