The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

No-Proposition View of Vagueness

Peer reviewed

No-Proposition View of Vagueness

Peer reviewed

Benthic foraminifera of the Red Sea

The distribution of living (Rose Bengal-stained), dead and fossil benthic foraminifera was investigated in six short cores (multicores, 30-32 cm total length) recovered from the central Red Sea. The ecological preferences as well as the relationship between the live and dead/fossil assemblages (preserved down-core) were examined. The sites, located along a W-E profile and between the depth of 366 and 1782 m, extend from the center of the oxygen minimum zone (OMZ, ~200-650 m), through its margin at ~600 m, and down to the well-aerated deep-water environment. Live (Rose-Bengal stained) and coexisting dead foraminifera were studied in the upper 5 cm of each of the sites, and the fossil record was studied down to ~32 cm. Q-mode Principal Component Analysis was used and four distinct foraminiferal fossil assemblages were determined. These assemblages follow different water mass properties. In the center of the OMZ, where the organic carbon content is highest and the oxygen concentration is lowest (<=0.5 ml O2/l), the Bolivina persiensis-Bulimina marginata-Discorbinella rhodiensis assemblage dominates. The slightly more aerated and lower organic-carbon-content seafloor, at the margin of the OMZ, is characterized by the Neouvigerina porrecta-Gyroidinoides cf. G. soldanii assemblage. The transitional environment, between 900-1200 m, with its well-aerated and oligotrophic seafloor, is dominated by the Neouvigerina ampullacea-Cibicides mabahethi assemblage. The deeper water (>1500 m), characterized by the most oxygenated and oligotrophic seafloor conditions, is associated with the Astrononion sp. A-Hanzawaia sp. A assemblage. Throughout the Red Sea extremely high values of temperature and salinity are constant below ~200 m depth, but the flux of organic matter to the sea floor varies considerably with bathymetry and appears to be the main controlling factor governing the distribution pattern of the benthic foraminifera. Comparison between live and the dead/fossil assemblages reveals a large difference between the two. Processes that may control this difference include species-specific high turnover rates, and preferential predation and loss of fragile taxa (either by chemical or microbial processes). Significant variations in the degree of loss of the organic-cemented agglutinants were observed down core. This group is preserved down to 5-10 cm at the shallow OMZ sites and down to greater depths at well-aerated and oligotrophic sites. The lower rate of disintegration of these forms, in the deeper locations of the Red Sea, may be related to low microbial activity. This results in the preservation of increasing numbers of organic-cemented shells down-core.