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.

Kutsu kuuliaisuuteen : James I. Packerin liittonomistinen raamattukäsitys

This dissertation examines James I. Packer s view of the Bible as the book of God s revelation. However, this study could not be complete without discussion of his background ideas about God, man and the foundations of theology. The research method used in this dissertation is systematic analysis. I analyse key theological concepts in the data, such as inerrancy, God s word and the covenant of grace, and examine Packer s concepts primarily in the context of the reformed tradition that he represents. Although the dissertation presents the philosophical premises of Packer s thought, the focus is on an analysis of theological concepts. Packer claims to approach theological issues broadly and to reject legalism. However, he also considers Calvinist thinking to be best suited to theological work and emphasises the central role of law in his view of the Bible. My dissertation pays particular attention to the status of law in Packer s theology and especially in the covenant of grace. The dissertation shows that the fundamental theological structure of Packer s view of the Bible is based on Puritan covenant theology, which consists of the temporally successive covenant of works and covenant of grace. Covenant theology stresses the connection and friendship between God and man. Man s highest goal according to the Westminster Confession of Faith (1647) is to glorify the triune God and to rejoice in him for all eternity. After the fall of man, this friendship between God and man can only take place in the covenant of grace. For Packer, the covenant of grace encompasses not only the time of the Gospel, but also the time of the law before the Gospel. Consequently, the covenant of grace incorporates in its very essence the demand of obedience to God s law. Covenant theology forms the foundation for both his view of the Bible and his idea that a believer lives in a covenant of grace, the key aspects of which are God s commandments and man s works. Law and the Gospel are not considered fundamental opposites in the covenant of grace, unlike in justification. In the covenant of grace, man has become God s friend who obeys the law as the law of Christ in a way which differs from Luther s view of obedience to the faith . For Packer, covenant theology is a Puritan instrument to link predestination and sanctification. Works committed in obedience show that the believer belongs to the covenant of grace and will be among the saved. Although voluntary obedience to God s commandments is not a direct instrument to achieve salvation, it is a pivotal sign of predestination. God calls the predestined to salvation with an effectual calling, the reliable message of the Bible. In sanctification, God guides a believer living in the context of covenantal nomism. In that sense, the Bible is above all an instrument of law guided by reason. In man s obedience, God completes man s nature and restores the imago Dei in man.