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.

Effect of waiting time on health outcomes and service utilization : A prospective randomized study on patients admitted to hospital for hip or knee replacement

Although the principle of equal access to medically justified treatment has been promoted by official health policies in many Western health care systems, practices do not completely meet policy targets. Waiting times for elective surgery vary between patient groups and regions, and growing problems in the availability of services threaten equal access to treatment. Waiting times have come to the attention of decision-makers, and several policy initiatives have been introduced to ensure the availability of care within a reasonable time. In Finland, for example, the treatment guarantee came into force in 2005. However, no consensus exists on optimal waiting time for different patient groups. The purpose of this multi-centre randomized controlled trial was to analyse health-related quality of life, pain and physical function in total hip or knee replacement patients during the waiting time and to evaluate whether the waiting time is associated with patients health outcomes at admission. This study also assessed whether the length of waiting time is associated with social and health services utilization in patients awaiting total hip or knee replacement. In addition, patients health-related quality of life was compared with that of the general population. Consecutive patients with a need for a primary total hip or knee replacement due to osteoarthritis were placed on the waiting list between August 2002 and November 2003. Patients were randomly assigned to a short waiting time (maximum 3 months) or a non-fixed waiting time (waiting time not fixed in advance, instead the patient followed the hospitals routine practice). Patients health-related quality of life was measured upon being placed on the waiting list and again at hospital admission using the generic 15D instrument. Pain and physical function were evaluated using the self-report Harris Hip Score for hip patients and a scale modified from the Knee Society Clinical Rating System for knee patients. Utilization measures were the use of home health care, rehabilitation and social services, physician visits and inpatient care. Health and social services use was low in both waiting time groups. The most common services used while waiting were rehabilitation services and informal care, including unpaid care provided by relatives, neighbours and volunteers. Although patients suffered from clear restrictions in usual activities and physical functioning, they seemed primarily to lean on informal care and personal networks instead of professional care. While longer waiting time did not result in poorer health-related quality of life at admission and use of services during the waiting time was similar to that at the time of placement on the list, there is likely to be higher costs of waiting by people who wait longer simply because they are using services for a longer period. In economic terms, this would represent a negative impact of waiting. Only a few reports have been published of the health-related quality of life of patients awaiting total hip or knee replacement. These findings demonstrate that, in addition to physical dimensions of health, patients suffered from restrictions in psychological well-being such as depression, distress and reduced vitality. This raises the question of how to support patients who suffer from psychological distress during the waiting time and how to develop strategies to improve patients initiatives to reduce symptoms and the burden of waiting. Key words: waiting time, total hip replacement, total knee replacement, health-related quality of life, randomized controlled trial, outcome assessment, social service, utilization of health services