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.

Test of the Clustering Hypothesis in the Helsinki Exchanges

This paper investigates the clustering pattern in the Finnish stock market. Using trading volume and time as factors capturing the clustering pattern in the market, the Keim and Madhavan (1996) and the Engle and Russell (1998) model provide the framework for the analysis. The descriptive and the parametric analysis provide evidences that an important determinant of the famous U-shape pattern in the market is the rate of information arrivals as measured by large trading volumes and durations at the market open and close. Precisely, 1) the larger the trading volume, the greater the impact on prices both in the short and the long run, thus prices will differ across quantities. 2) Large trading volume is a non-linear function of price changes in the long run. 3) Arrival times are positively autocorrelated, indicating a clustering pattern and 4) Information arrivals as approximated by durations are negatively related to trading flow.

An Empirical Study of the Mixture of Time and Movements in Prices

This paper investigates the persistent pattern in the Helsinki Exchanges. The persistent pattern is analyzed using a time and a price approach. It is hypothesized that arrival times are related to movements in prices. Thus, the arrival times are defined as durations and formulated as an Autoregressive Conditional Duration (ACD) model as in Engle and Russell (1998). The prices are defined as price changes and formulated as a GARCH process including duration measures. The research question follows from market microstructure predictions about price intensities defined as time between price changes. The microstructure theory states that long transaction durations might be associated with both no news and bad news. Accordingly, short durations would be related to high volatility and long durations to low volatility. As a result, the spread will tend to be larger under intensive moments. The main findings of this study are 1) arrival times are positively autocorrelated and 2) long durations are associated with low volatility in the market.

Kymmenen koirarodun perinnöllinen monimuotoisuus

Tämän tutkimuksen tavoitteena oli selvittää koirarotujen sisäistä ja välistä perinnöllistä muuntelua ja populaatioiden rakenteita. Tutkimuksessa käytettiin Finnzymes Oy:ltä saatua koirien mikrosatelliittimerkkeihin perustuvaa genotyypitysaineistoa. Lopullisessa aineistossa oli 395 koiraa kymmenestä keskenään varsin erilaisesta rodusta. Koirien määrä rotua kohti vaihteli 31:stä 53:een. Tutkimuksessa käytettiin 18 mikrosatelliittilokusta. Alleelirikkaus vaihteli mikrosatelliittilokuksissa välillä 2,0 – 9,9. Kaikkein muuntelevin lokus oli AHT137 ja vähiten muunteleva AHTk211. Jackrussellinterrierin alleelirikkaus oli yli kaikkien lokusten tarkasteltuna suurinta ja cavalier kingcharlesinspanielin pienintä. Eniten Hardy-Weinbergin tasapainosta poikkeavia mikrosatelliittilokuksia oli schipperke- rodulla. Coton de tulearin, saksanpaimenkoiran ja suomenlapinkoiran kaikki mikrosatelliittilokukset olivat Hardy-Weinbergin tasapainossa. Cavalier kingcharlesinspanielin havaittu heterotsygotia-aste oli matalin kaikkien lokusten yli tarkasteltuna (0,50) ja suomenlapinkoiran korkein (0,73). Ainoat tilastollisesti merkitsevät FIS-arvot olivat schipperken lokuksessa INU030 (0,39) ja kaikkien lokusten yli tarkasteltuna (0,11). Eniten populaatioiden välisiin eroihin perustuvaa muuntelua oli cavalier kingcharlesinspanielin ja pitkäkarvaisen collien välillä (FST = 0,34) ja vähiten chihuahuan ja coton de tulearin välillä (FST = 0,07). Koko aineistossa noin 17,7 % populaatioiden välisestä geneettisestä muuntelusta johtui populaatioiden välisistä eroista. Rodut ovat tulosten perusteella selvästi erillisiä populaatioita. Coton de tulearin alleeliparit olivat selvästi eniten kytkentäepätasapainossa keskenään (94) ja tiibetinspanielin vähiten (15). Pitkäkarvaisen collien tehollinen populaatiokoko oli pienin (35) ja chihuahuan suurin (86). U seiden populaatiogeneettisten tunnuslukujen perusteella nousivat esiin cavalier kingcharlesinspanieli, pitkäkarvainen collie ja schipperke perinnöllisen muuntelun vähäisyyden perusteella ja chihuahua, jackrussellinterrieri ja suomenlapinkoira keskimääräistä suuremman perinnöllisen muuntelun perusteella. Selityksiä geneettisen monimuotoisuuden vaihteluun näillä roduilla löytyy rotujen historiasta.

Microsite occupancy and spatial structure of regeneration in three late-successional Norway spruce forests in northern Europe

A comparison of microsite occupancy and the spatial structure of regeneration in three areas of late-successional Norway spruce dominated forest. Pallas-Ylläs is understood to have been influenced only by small-scale disturbance; Dvina-Pinega has had sporadic larger-scale disturbances; Kazkim has been affected by fire. All spruce and birch trees with diameter at breast height (DBH) ?10 cm were mapped in five stands on 40 m x 400 m transects, and those with DBH < 10 cm on 2 or 4 m x 400 m subplots. Microsite type was inventoried at 1m intervals along the centre line and for each tree with DBH < 10 cm. At all study areas small seedlings (h < 0.3 m, DBH < 10 cm) preferentially occupied disturbed microsites. In contrast, spruce saplings (h ? 1.3 m, DBH <10 cm) at all study areas showed less, or no, preference. At Pallas-Ylläs spruce seedlings (h < 1.3 m, DBH < 10 cm) and saplings (h ? 1.3 m, DBH < 10 cm) exhibited spatial correlation at scales from 32-52 m. At Dvina-Pinega saplings of both spruce and birch exhibited spatial correlation at scales from 32-81 m. At Kazkim spatial correlation of seedlings and saplings of both species was exhibited over variable distances. No spatial cross-correlation was found between overstorey basal area (DBH ? 10 cm) and regeneration (h ? 1.3 m, DBH < 10 cm) at any study area. The results confirm the importance of disturbed microsites for seedling establishment, but suggest that undisturbed microsites may sometimes be more advantageous for long-term tree survival. The regeneration gap concept may not be useful in describing the regeneration dynamics of late-successional boreal forests.

Cost and effectiveness of legal mandates for the practice of forestry on private land.

XVIII IUFRO World Congress, Ljubljana 1986.