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.

Genomic approach to organ-specific growth control

Growth is a fundamental aspect of life cycle of all organisms. Body size varies highly in most animal groups, such as mammals. Moreover, growth of a multicellular organism is not uniform enlargement of size, but different body parts and organs grow to their characteristic sizes at different times. Currently very little is known about the molecular mechanisms governing this organ-specific growth. The genome sequencing projects have provided complete genomic DNA sequences of several species over the past decade. The amount of genomic sequence information, including sequence variants within species, is constantly increasing. Based on the universal genetic code, we can make sense of this sequence information as far as it codes proteins. However, less is known about the molecular mechanisms that control expression of genes, and about the variations in gene expression that underlie many pathological states in humans. This is caused in part by lack of information about the second genetic code that consists of the binding specificities of transcription factors and the combinatorial code by which transcription factor binding sites are assembled to form tissue-specific and/or ligand-regulated enhancer elements. This thesis presents a high-throughput assay for identification of transcription factor binding specificities, which were then used to measure the DNA binding profiles of transcription factors involved in growth control. We developed ‘enhancer element locator’, a computational tool, which can be used to predict functional enhancer elements. A genome-wide prediction of human and mouse enhancer elements generated a large database of enhancer elements. This database can be used to identify target genes of signaling pathways, and to predict activated transcription factors based on changes in gene expression. Predictions validated in transgenic mouse embryos revealed the presence of multiple tissue-specific enhancers in mouse c- and N-Myc genes, which has implications to organ specific growth control and tumor type specificity of oncogenes. Furthermore, we were able to locate a variation in a single nucleotide, which carries a susceptibility to colorectal cancer, to an enhancer element and propose a mechanism by which this SNP might be involved in generation of colorectal cancer.