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.

Radiation effects in supported nanoparticles

Nanotechnology applications are entering the market in increasing numbers, nanoparticles being among the main classes of materials used. Particles can be used, e.g., for catalysing chemical reactions, such as is done in car exhaust catalysts today. They can also modify the optical and electronic properties of materials or be used as building blocks for thin film coatings on a variety of surfaces. To develop materials for specific applications, an intricate control of the particle properties, structure, size and shape is required. All these depend on a multitude of factors from methods of synthesis and deposition to post-processing. This thesis addresses the control of nanoparticle structure by low-energy cluster beam deposition and post-synthesis ion irradiation. Cluster deposition in high vacuum offers a method for obtaining precisely controlled cluster-assembled materials with minimal contamination. Due to the clusters small size, however, the cluster-surface interaction may drastically change the cluster properties on deposition. In this thesis, the deposition process of metal and alloy clusters on metallic surfaces is modelled using molecular dynamics simulations, and the mechanisms influencing cluster structure are identified. Two mechanisms, mechanical melting upon deposition and thermally activated dislocation motion, are shown to determine whether a deposited cluster will align epitaxially with its support. The semiconductor industry has used ion irradiation as a tool to modify material properties for decades. Irradiation can be used for doping, patterning surfaces, and inducing chemical ordering in alloys, just to give a few examples. The irradiation response of nanoparticles has, however, remained an almost uncharted territory. Although irradiation effects in nanoparticles embedded inside solid matrices have been studied, almost no work has been done on supported particles. In this thesis, the response of supported nanoparticles is studied systematically for heavy and light ion irradiation. The processes leading to damage production are identified and models are developed for both types of irradiation. In recent experiments, helium irradiation has been shown to induce a phase transformation from multiply twinned to single-crystalline nanoparticles in bimetallic alloys, but the nature of the transition has remained unknown. The alloys for which the effect has been observed are CuAu and FePt. It is shown in this thesis that transient amorphization leads to the observed transition and that while CuAu and FePt do not amorphize upon irradiation in bulk or as thin films, they readily do so as nanoparticles. This is the first time such an effect is demonstrated with supported particles, not embedded in a matrix where mixing is always an issue. An understanding of the above physical processes is essential, if nanoparticles are to be used in applications in an optimal way. This thesis clarifies the mechanisms which control particle morphology, and paves way for the synthesis of nanostructured materials tailored for specific applications.

Tonically Active Kainate Receptors (tKARs) : A Novel Mechanism Regulating Neuronal Function in the Brain

Fast excitatory transmission between neurons in the central nervous system is mainly mediated by L-glutamate acting on ligand gated (ionotropic) receptors. These are further categorized according to their pharmacological properties to AMPA (2-amino-3-(5-methyl-3-oxo-1,2- oxazol-4-yl)propanoic acid), NMDA (N-Methyl-D-aspartic acid) and kainate (KAR) subclasses. In the rat and the mouse hippocampus, development of glutamatergic transmission is most dynamic during the first postnatal weeks. This coincides with the declining developmental expression of the GluK1 subunit-containing KARs. However, the function of KARs during early development of the brain is poorly understood. The present study reveals novel types of tonically active KARs (hereafter referred to as tKARs) which play a central role in functional development of the hippocampal CA3-CA1 network. The study shows for the first time how concomitant pre- and postsynaptic KAR function contributes to development of CA3-CA1 circuitry by regulating transmitter release and interneuron excitability. Moreover, the tKAR-dependent regulation of transmitter release provides a novel mechanism for silencing and unsilencing early synapses and thus shaping the early synaptic connectivity. The role of GluK1-containing KARs was studied in area CA3 of the neonatal hippocampus. The data demonstrate that presynaptic KARs in excitatory synapses to both pyramidal cells and interneurons are tonically activated by ambient glutamate and that they regulate glutamate release differentially, depending on target cell type. At synapses to pyramidal cells these tKARs inhibit glutamate release in a G-protein dependent manner but in contrast, at synapses to interneurons, tKARs facilitate glutamate release. On the network level these mechanisms act together upregulating activity of GABAergic microcircuits and promoting endogenous hippocampal network oscillations. By virtue of this, tKARs are likely to have an instrumental role in the functional development of the hippocampal circuitry. The next step was to investigate the role of GluK1 -containing receptors in the regulation of interneuron excitability. The spontaneous firing of interneurons in the CA3 stratum lucidum is markedly decreased during development. The shift involves tKARs that inhibit medium-duration afterhyperpolarization (mAHP) in these neurons during the first postnatal week. This promotes burst spiking of interneurons and thereby increases GABAergic activity in the network synergistically with the tKAR-mediated facilitation of their excitatory drive. During development the amplitude of evoked medium afterhyperpolarizing current (ImAHP) is dramatically increased due to decoupling tKAR activation and ImAHP modulation. These changes take place at the same time when the endogeneous network oscillations disappear. These tKAR-driven mechanisms in the CA3 area regulate both GABAergic and glutamatergic transmission and thus gate the feedforward excitatory drive to the area CA1. Here presynaptic tKARs to CA1 pyramidal cells suppress glutamate release and enable strong facilitation in response to high-frequency input. Therefore, CA1 synapses are finely tuned to high-frequency transmission; an activity pattern that is common in neonatal CA3-CA1 circuitry both in vivo and in vitro. The tKAR-regulated release probability acts as a novel presynaptic silencing mechanism that can be unsilenced in response to Hebbian activity. The present results shed new light on the mechanisms modulating the early network activity that paves the way for oscillations lying behind cognitive tasks such as learning and memory. Kainate receptor antagonists are already being developed for therapeutic use for instance against pain and migraine. Because of these modulatory actions, tKARs also represent an attractive candidate for therapeutic treatment of developmentally related complications such as learning disabilities.