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.

Lähteiden lumoamat : Henry Biaudet, Liisi Karttunen ja suomalainen historiantutkimus Roomassa 1900-luvun alussa

Enchanted by Sources. Henry Biaudet, Liisi Karttunen and Finnish Historical Research in Rome in the Early Twentieth Century This study traces the scholarly endeavours of Henry Biaudet (1870 1915) and Liisi Karttunen (1880 1957) and "La mission historique finlandaise à Rome" which they founded in 1909. They are forgotten in Finnish historiography, but remain internationally renowned for their contribution to the nunciature studies. By investigating their historical work on the Counter- Reformation era, their roles in the scientific communities of Helsinki and Rome as well as the intersection of politics and science in their scholarly practices the study explores the nature of historical research in general at the turn of the twentieth century. The work covers fields such as historiography, university history and the political use of history. Methodologically the research is based on the analysis and contextualization of published and unpublished sources (e.g. correspondences, university records, scholarly publications and reviews in academic journals). Henry Biaudet criticized the previous research on the Nordic Counter-Reformation for its narrow national scope and sources. He sought out a new approach, including the use of sources in archives all over Europe and the inclusion of the Catholic viewpoint. Accordingly, Biaudet and Karttunen searched for records in archives in Southern Europe. Their unorthodox interpretations were denounced in Finland since the picture they gave of late sixteenth-century Sweden was too different from the national narrative. Moreover, Finnish national identity was firmly rooted in Protestantism, and questioning the benevolence of the Reformation and its main actors was considered as an attack not only against historical truth but also national values. The comparison between Biaudet s and Karttunen s arguments and the accepted narrative in Finland shows how traditional interpretations of the Nordic Reformation were influenced by the Lutheran ethos and European anticlerical rhetoric. Historians have recently paid substantial attention to the political use of history, usually focusing on politicized constructions of the national past. This study shows how research that met the criteria of modern historiography also served political purposes. Conducting research in an international community of historians and publishing ambitious scholarly studies that interested an international audience were ways to create a positive image of Finland abroad. These were not uniquely Finnish ideas but rather ideas shared by the international community of historians in Rome. In this context, scientific pursuits were given a clear political meaning. This enhances our understanding of nineteenth-century historiography being firmly rooted between science and politics.