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.

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.

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.

Growing Flowers in the Frost: Civic Activity, Citizenship and Gender in Russia

This study analyzes civic activity, citizenship and their gendered manifestations in contemporary Russia. It is based on a case study conducted in the city of Tver , located in the vicinity of Moscow, during 2001-2005. The data consists of interviews with civic activists and municipal and regional authorities; observations of civic organizations; and a quantitative survey conducted among local civic groups. The theoretical and methodological framework of the study draws upon a micro perspective on organization, discourse analysis, gender and citizenship theories and Pierre Bourdieu s theory of fields and capital. This study develops theoretical understanding of the characteristics and logic of civic organization in Russia. It shows that social class centrally structures the field of civic activity. Organizations can be seen as a vehicle of the educated class to advocate their interests, help themselves and seek both social and individual-level change. The study also argues that civic organizations founded during the post-Soviet era are often an institutionalized form of informal social networks. Networks, which were a central element of everyday interaction in Soviet society, are a resource and often the only resource available that can be made use of in contemporary organizational activities. The study argues that gender operates as a key structuring principle in the Russian socio-political community. Civic activity is often discursively associated with femininity and institutional politics with masculinity. Women tend to participate more than men in civic organizations, while men dominate the formal political domain. The study shows that civic organizations are important loci of communality. This communality, however, differs from the communality envisioned in the communitarian and social capital debates in the West. It is selective communality , as it is restricted to the members of the organizations and does not create generalized reciprocity and trust. Civic organizations tend to build upon and reproduce the traditional Russian organizational form of circles , kruzhki. Along with the analysis of civic activities, the study also examines the redefinition of the role and functions of the state. The authorities interviewed in this study understand civic organizations as serving those goals and interests determined by the authorities, instead of viewing them as sites of citizens self-organization around interests and problems citizens themselves deem important, or as a counterforce to the state. By contrast, civic activists understand the core of organizational activity to be advocacy of their interests and rights, tackling social problems, the pursuit of wider social change and self-help. Co-operation between authorities and organizations tends to be personified and based upon unequal, hierarchical patron-client arrangements, which inhibits the development of democratic governance. The study will be published in Routledge Contemporary Russia and Eastern Europe Series later this year.

Group Beliefs : Studies on the Nature and Logic of Collective Doxastic Attitudes

This thesis studies the nature and logic of collective doxastic attitudes, or what is referred to in ordinary language as "group beliefs". Beliefs and other intentional attitudes are attributed to groups and collections of people, and such attributions are used to explain and predict the actions of groups. The thesis develops an understanding of group beliefs as voluntarily adopted views or acceptances rather than as ordinary beliefs. Such an understanding can provide new answers to questions concerning collective knowledge and justification of group beliefs, and it allows developing modal logics with collective doxastic and epistemic notions. The thesis consists of six articles. The first three articles are philosophical studies concerned with the nature of group beliefs. The last three articles are logical studies that aim at developing proof-theoretical calculi for reasoning about collective doxastic attitudes.

Exploring Customer Value Formation: A Customer Dominant Logic Perspective

This paper extends current discussions about value creation and proposes a customer dominant value perspective. A customer-dominant marketing logic positions the customer in the center, rather than the service provider/producer or the interaction or the system. The focus is shifted from the company´s service processes involving the customer, to the customer´s multi-contextual value formation, involving the company. It is argued that value is not always an active process of creation; instead value is embedded and formed in the highly dynamic and multi-contextual reality and life of the customer. This leads to a need to look beyond the current line of visibility where visible customer-company interactions are focused to the invisible and mental life of the customer. From this follows a need to extend the temporal scope, from exchange and use even further to accumulated experiences in the customer´s life. The aim of this paper is to explore value formation from a customer dominant logic perspective. This is done in three steps: first, value formation is contrasted to earlier views on the company’s role in value creation by using a broad ontologically driven framework discussing what, how, when, where and who. Next, implications of the proposed characteristics of value formation compared to earlier approaches are put forward. Finally, some tentative suggestions of how this perspective would affect marketing in service companies are presented. As value formation in a CDL perspective has a different focus and scope than earlier views on value it leads to posing questions about the customer that reveals earlier hidden aspects of the role of a service for the customer. This insight might be used in service development and innovation.

Rethinking Service Companies’ Business Logic: Do We Need a Customer-Dominant Logic as a Guideline?

Purpose –This paper explores and expands the roles of customers and companies in creating value by introducing a new a customer-based approach to service. The customer’s logic is examined as being the foundation of a customer-based marketing and business logic. Design/methodology/approach – The authors argue that both goods-dominant logics and service-dominant logics are provider-dominant. Contrasting the customer-dominant logic with provider-dominant logics, the paper examines the creation of service value from the perspectives of value-in-use, the customer’s own context, and the customer’s experience of service. Findings –Moving from a provider-dominant logic to a customer-dominant logic uncovered five major challenges to service marketers: Company involvement, company control in co-creation, visibility of value creation, locus of customer experience, and character of customer experience. Research limitations/implications – The paper is exploratory. It presents and discusses a conceptual model and suggests implications for research and practice. Practical implications –Awareness of the mechanisms of customer logic will provide businesses with new perspectives on the role of the company in their customer’s lives. We propose that understanding the customer’s logic should represent the starting-point for the marketer’s business logic. Originality/value – The paper increases the understanding of how the customer’s logic underpins the customer-dominant business logic. By exploring consequences of applying a customer-dominant logic, we suggest further directions for theoretical and empirical research.

Re-Conceptualizing Value-Creation From Industrial Business Logic to Service Business Logic

There is an urgent interest in marketing to move away from neo-classical value definitions suggesting that value creation is a process of exchanging goods for money. In the present paper, value creation is conceptualized as an integration of two distinct, yet closely coupled processes. First, actors co-create what this paper calls an underlying basis of value. This is done by interactively re-configuring resources. By relating and combining resources, activity sets, and risks across actor boundaries in novel ways actors create joint productivity gains – a concept very similar to density (Normann, 2001). Second, actors engage in a process of signification and evaluation. Signification implies co-constructing the meaning and worth of joint productivity gains co-created through interactive resource re-configuration, as well as sharing those gains through a pricing mechanism as value to involved actors. The conceptual framework highlights an all-important dynamics associated with ´value creation´ and ´value´ - a dynamics the paper claims has eluded past marketing research. The paper argues that the framework presented here is appropriate for the interactive service perspective, where value and value creation are not objectively given, but depend on the power of involved actors´ socially constructed frames to mobilize resources across actor boundaries in ways that ´enhance system well-being´ (Vargo et al., 2008). The paper contributes to research on Service Logic, Service-Dominant Logic, and Service Science.

Towards Service Logic: The Unique Contribution of Value Co-Creation

The underpinning logic of value co-creation in service logic is analysed. It is observed that three of the ten foundational premises of the so-called service-dominant logic are problematic and do not support an understanding of value-co-creation and creation that is meaningful for theoretical development and decision making in business and marketing practice. Without a thorough understanding of the interaction concept, the locus and nature of value co-creation cannot be identified. Based on the analysis in the present article it is observed that a unique contribution of a service perspective on business (service logic) is not that customers always are co-creators of value, but that under certain circumstances the service provider gets opportunities to co-create value together with its customers. Finally, the three problematic premises are reformulated accordingly.

What Can A Service Logic Offer Marketing Theory

The goods-dominated marketing model has major shortcomings as a guiding marketing theory. Its marketing mix approach is mainly geared towards buying and does not include consumption as an integral part of marketing theory. Although it is during the process of consuming goods and services that value is generated for customers and the foundation for repeat purchasing and customer relationships are laid, this process is left outside the scope of marketing. The focus in service marketing is not on a product but on interactions in service encounters. Consumption has become an integral part of a holistic marketing model. Other than standardized goods-based value propositions can be better understood when taking a servicebased approach. It is concluded that marketing based on a goods logic is but a special case of marketing based on a service logic and applicable only in certain contexts with standardized products.