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.

Locality and order-invariant logics

Malli on logiikassa käytetty abstraktio monille matemaattisille objekteille. Esimerkiksi verkot, ryhmät ja metriset avaruudet ovat malleja. Äärellisten mallien teoria on logiikan osa-alue, jossa tarkastellaan logiikkojen, formaalien kielten, ilmaisuvoimaa malleissa, joiden alkioiden lukumäärä on äärellinen. Rajoittuminen äärellisiin malleihin mahdollistaa tulosten soveltamisen teoreettisessa tietojenkäsittelytieteessä, jonka näkökulmasta logiikan kaavoja voidaan ajatella ohjelmina ja äärellisiä malleja niiden syötteinä. Lokaalisuus tarkoittaa logiikan kyvyttömyyttä erottaa toisistaan malleja, joiden paikalliset piirteet vastaavat toisiaan. Väitöskirjassa tarkastellaan useita lokaalisuuden muotoja ja niiden säilymistä logiikkoja yhdistellessä. Kehitettyjä työkaluja apuna käyttäen osoitetaan, että Gaifman- ja Hanf-lokaalisuudeksi kutsuttujen varianttien välissä on lokaalisuuskäsitteiden hierarkia, jonka eri tasot voidaan erottaa toisistaan kasvavaa dimensiota olevissa hiloissa. Toisaalta osoitetaan, että lokaalisuuskäsitteet eivät eroa toisistaan, kun rajoitutaan tarkastelemaan äärellisiä puita. Järjestysinvariantit logiikat ovat kieliä, joissa on käytössä sisäänrakennettu järjestysrelaatio, mutta sitä on käytettävä siten, etteivät kaavojen ilmaisemat asiat riipu valitusta järjestyksestä. Määritelmää voi motivoida tietojenkäsittelyn näkökulmasta: vaikka ohjelman syötteen tietojen järjestyksellä ei olisi odotetun tuloksen kannalta merkitystä, on syöte tietokoneen muistissa aina jossakin järjestyksessä, jota ohjelma voi laskennassaan hyödyntää. Väitöskirjassa tutkitaan minkälaisia lokaalisuuden muotoja järjestysinvariantit ensimmäisen kertaluvun predikaattilogiikan laajennukset yksipaikkaisilla kvanttoreilla voivat toteuttaa. Tuloksia sovelletaan tarkastelemalla, milloin sisäänrakennettu järjestys lisää logiikan ilmaisuvoimaa äärellisissä puissa.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Marketing and the Logic of Service: Value Facilitation, Value Creation and Co-creation, and Their Marketing Implications

The discussion of a service-dominant logic has made the findings of decades of service marketing research a topic of interest for marketing at large. Some fundamental aspects of the logic such as value creation and its marketing implications are more complex than they have been treated as so far and need to be further developed to serve marketing theory and practice well. Following the analysis in the present article it is argued that although customers are co-producers in service processes, according to the value-in-use notion adopted in the contemporary marketing and management literature they are fundamentally the creators of value for themselves. Furthermore, it is concluded that although by providing goods and services as input resources into customers’ consumption and value-generating processes firms are fundamentally value facilitators, interactions with customers that exist or can be created enable firms to engage themselves with their customers’ processes and thereby they become co-creators of value with their customers. As marketing implications it is observed that 1) the goal of marketing is to support customers’ value creation, 2) following a service logic and due to the existence of interactions where the firm’s and the customer’s processes merge into an integrated joint value creation process, the firm is not restricted to making value propositions only, but can directly and actively influence the customer’s value fulfilment as well and extend its marketing process to include activities during customer-firm interactions, and 3) although all goods and services are consumed as service, customers’ purchasing decisions can be expected to be dependant of whether they have the skills and interest to use a resource, such as a good, as service or want to buy extended market offerings including process-related elements. Finally, the analysis concludes with five service logic theses.

Making Sense of Value and Value Co-Creation in Service Logic

In order to further develop the logic of service, value creation, value co-creation and value have to be formally and rigorously defined, so that the nature, content and locus of value and the roles of service providers and customers in value creation can be unambiguously assessed. In the present article, following the underpinning logic of value-in-use, it is demonstrated that in order to achieve this, value creation is best defined as the customer’s creation of value-in-use. The analysis shows that the firm’s and customer’s processes and activities can be divided into a provider sphere, closed for the customer, and a customer sphere, closed for the firm. Value creation occurs in the customer sphere, whereas firms in the provider sphere facilitate value creation by producing resources and processes which represent potential value or expected value-in use for their customers. By getting access to the closed customer sphere, firms can create a joint value sphere and engage in customers’ value creation as co-creators of value with them. This approach establishes a theoretically sound foundation for understanding value creation in service logic, and enables meaningful managerial implications, for example as to what is required for co-creation of value, and also further theoretical elaborations.

Empire, Tourism, Nostalgia: Joseph Brodsky and Travel Writing

Joseph Brodsky, one of the most influential Russian intellectuals of the late Soviet period, was born in Leningrad in 1940, emigrated to the United States in 1972, received the Nobel Prize for Literature in 1987, and died in New York City in 1996. Brodsky was one of the leading public figures of Soviet emigration in the Cold War period, and his role as a model for the constructing of Russian cultural identities in the last years of the Soviet Union was, and still is, extremely important. One of Joseph Brodsky’s great contributions to Russian culture of the latter half of the twentieth century is the wide geographical scope of his poetic and prose works. Brodsky was not a travel writer, but he was a traveling writer who wrote a considerable number of poems and essays which relate to his trips and travels in the Soviet empire and outside it. Travel writing offered for Brodsky a discursive space for negotiating his own transculturation, while it also offered him a discursive space for making powerful statements about displacement, culture, history and geography, time and space—all major themes of his poetry. In this study of Joseph Brodsky’s travel writing I focus on his travel texts in poetry and prose, which relate to his post-1972 trips to Mexico, Brazil, Turkey, and Venice. Questions of empire, tourism, and nostalgia are foregrounded in one way or another in Brodsky’s travel writing performed in emigration. I explore these concepts through the study of tropes, strategies of identity construction, and the politics of representation. The theoretical premises of my work draw on the literary and cultural criticism which has evolved around the study of travel and travel writing in recent years. These approaches have gained much from the scholarly experience provided by postcolonial critique. Shifting the focus away from the concept of exile, the traditional framework for scholarly discussions of Brodsky’s works, I propose to review Brodsky’s travel poetry and prose as a response not only to his exilic condition but to the postmodern and postcolonial landscape, which initially shaped the writing of these texts. Discussing Brodsky’s travel writing in this context offers previously unexplored perspectives for analyzing the geopolitical, philosophical, and linguistic premises of his poetic imagination. By situating Brodsky’s travel writing in the geopolitical landscape of postcolonial postmodernity, I attempt to show how Brodsky’s engagement with his contemporary cultural practices in the West was incorporated into his Russian-language travel poetry and prose and how this engagement thus contributed to these texts’ status as exceptional and unique literary events within late Soviet Russian cultural practices.

Problems of Proto-Slavic Historical Nominal Morphology : On the Basis of Old Church Slavic

In this study I offer a diachronic solution for a number of difficult inflectional endings in Old Church Slavic nominal declensions. In this context I address the perhaps most disputed and the most important question of the Slavic nominal inflectional morphology: whether there was in Proto-Slavic an Auslautgesetz (ALG), a law of final syllables, that narrowed the Proto-Indo-European vowel */o/ to */u/ in closed word-final syllables. In addition, the work contains an exhaustive morphological classification of the nouns and adjectives that occur in canonical Old Church Slavic. I argue that Proto-Indo-European */o/ became Proto-Slavic */u/ before word-final */s/ and */N/. This conclusion is based on the impossibility of finding credible analogical (as opposed to phonological) explanations for the forms supporting the ALG hypothesis, and on the survival of the neuter gender in Slavic. It is not likely that the */o/-stem nominative singular ending */-u/ was borrowed from the accusative singular, because the latter would have been the only paradigmatic form with the stem vowel */-u-/. It is equally unlikely that the ending */-u/ was borrowed from the */u/-stems, because the latter constituted a moribund class. The usually stated motivation for such an analogical borrowing, i.e. a need to prevent the merger of */o/-stem masculines with neuters of the same class, is not tenable. Extra-Slavic, as well as intra-Slavic evidence suggests that phonologically-triggered mergers between two semantically opaque genders do not tend to be prevented, but rather that such mergers lead to the loss of the gender opposition in question. On the other hand, if */-os/ had not become */-us/, most nouns and, most importantly, all adjectives and pronouns would have lost the formal distinction between masculines and neuters. This would have necessarily resulted in the loss of the neuter gender. A new explanation is given for the most apparent piece of evidence against the ALG hypothesis, the nominative-accusative singular of the */es/-stem neuters, e.g. nebo 'sky'. I argue that it arose in late Proto-Slavic dialects, replacing regular nebe, under the influence of the */o/- and */yo/-stems where a correlation had emerged between a hard root-final consonant and the termination -o, on the one hand, and a soft root-final consonant and the termination -e, on the other.

Principy sintaksicheskoj idiomatizacii

The book consists of an Introduction and four articles published both in Finland and abroad, written in English or Russian. They present the studies of eight Finnish and Russian idiomatic constructions that appear in the following examples: Ikkuna rikki — Окно сломано, lit.: ‘the window broken’, Äiti täällä — Мама здесь, lit.: ‘mother here’, Kaikki myymälöihin! — Все в магазин, lit.: ‘all to the shops’, Пить так пить! ≈ ‘When I drink, I drink (a lot)!’, etc. The aim of the studies is to reconstruct the origins and to trace the development of the above-mentioned constructions up to their modern usages. To this end, the constructions are investigated both from historical and from comparative perspectives. Finally, the case studies provide a possibility to develop more general bases of development of these 'ungrammatical' items. By attempting to answer the question why such constructions develop even though they destroy the harmonious structure of а language, some principles of idiomatization are postulated in the Conclusion.

A cross-linguistic study of lexical iconicity and its manifestation in bird names

Abstract This dissertation is a cross-linguistic study of lexical iconicity. The study is based on a genealogically stratified sample of 237 languages. The aim is to contribute with an empirical study to the growing dialogue focusing on different forms of lexical iconicity. The conceptual framework of the present study is based on an analysis of types and means of lexical iconicity in the sample languages. Archaeological and cultural evidence are used to tie lexical iconicity to its context. Phenomena related to lexical iconicity are studied both cross-linguistically and language-specifically. The cognitive difference between imitation and symbolism is essential. Lexical iconicity is not only about the iconic relationship between form and referents, but also about how certain iconic properties may become conventional, means used to create sound symbolism. All the sample languages show some evidence of lexical iconicity, demonstrating that it is a universal feature. Nine comparisons of onomatopoeic verbs and nouns, with samples varying between six and 141 languages, show that typologically highly different languages use similar means for creating words based on sound imitation. Two cross-linguistic comparisons of bird names demonstrate that a vast majority of the Eurasian names of the common cuckoo and the world-wide names of crow and raven of the 141 genera are onomatopoeic.

Talking About Time in Russian and Finnish

In this study I look at what people want to express when they talk about time in Russian and Finnish, and why they use the means they use. The material consists of expressions of time: 1087 from Russian and 1141 from Finnish. They have been collected from dictionaries, usage guides, corpora, and the Internet. An expression means here an idiomatic set of words in a preset form, a collocation or construction. They are studied as lexical entities, without a context, and analysed and categorized according to various features. The theoretical background for the study includes two completely different approaches. Functional Syntax is used in order to find out what general meanings the speaker wishes to convey when talking about time and how these meanings are expressed in specific languages. Conceptual metaphor theory is used for explaining why the expressions are as they are, i.e. what kind of conceptual metaphors (transfers from one conceptual domain to another) they include. The study has resulted in a grammatically glossed list of time expressions in Russian and Finnish, a list of 56 general meanings involved in these time expressions and an account of the means (constructions) that these languages have for expressing the general meanings defined. It also includes an analysis of conceptual metaphors behind the expressions. The general meanings involved turned out to revolve around expressing duration, point in time, period of time, frequency, sequence, passing of time, suitable time and the right time, life as time, limitedness of time, and some other notions having less obvious semantic relations to the others. Conceptual metaphor analysis of the material has shown that time is conceptualized in Russian and Finnish according to the metaphors Time Is Space (Time Is Container, Time Has Direction, Time Is Cycle, and the Time Line Metaphor), Time Is Resource (and its submapping Time Is Substance), Time Is Actor; and some characteristics are added to these conceptualizations with the help of the secondary metaphors Time Is Nature and Time Is Life. The limits between different conceptual metaphors and the connections these metaphors have with one another are looked at with the help of the theory of conceptual integration (the blending theory) and its schemas. The results of the study show that although Russian and Finnish are typologically different, they are very similar both in the needs of expression their speakers have concerning time, and in the conceptualizations behind expressing time. This study introduces both theoretical and methodological novelties in the nature of material used, in developing empirical methodology for conceptual metaphor studies, in the exactness of defining the limits of different conceptual metaphors, and in seeking unity among the different facets of time. Keywords: time, metaphor, time expression, idiom, conceptual metaphor theory, functional syntax, blending theory

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.