Set Theory and its Place in the Foundations of Mathematics:a new look at an old question

This paper reviews the claims of several main-stream candidates to be the foundations of mathematics, including set theory. The review concludes that at this level of mathematical knowledge it would be very unreasonable to settle with any one of these foundations and that the only reasonable choice is a pluralist one

Inconsistent boundaries

Research on this paper was supported by a grant from the Marsden Fund, Royal Society of New Zealand.Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected (Varzi in Noûs 31:26–58, 1997). In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty parts, in delivering a balanced and bounded metaphysics of naive space.PostprintPeer reviewe

Impossible worlds

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources

Mereotopological Connection

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified—the strength of the connection and its multiplicity

The genetic study of three population microisolates in South Tyrol (MICROS): study design and epidemiological perspectives

<p>Abstract</p> <p>Background</p> <p>There is increasing evidence of the important role that small, isolated populations could play in finding genes involved in the etiology of diseases. For historical and political reasons, South Tyrol, the northern most Italian region, includes several villages of small dimensions which remained isolated over the centuries.</p> <p>Methods</p> <p>The MICROS study is a population-based survey on three small, isolated villages, characterized by: old settlement; small number of founders; high endogamy rates; slow/null population expansion. During the stage-1 (2002/03) genealogical data, screening questionnaires, clinical measurements, blood and urine samples, and DNA were collected for 1175 adult volunteers. Stage-2, concerning trait diagnoses, linkage analysis and association studies, is ongoing. The selection of the traits is being driven by expert clinicians. Preliminary, descriptive statistics were obtained. Power simulations for finding linkage on a quantitative trait locus (QTL) were undertaken.</p> <p>Results</p> <p>Starting from participants, genealogies were reconstructed for 50,037 subjects, going back to the early 1600s. Within the last five generations, subjects were clustered in one pedigree of 7049 subjects plus 178 smaller pedigrees (3 to 85 subjects each). A significant probability of familial clustering was assessed for many traits, especially among the cardiovascular, neurological and respiratory traits. Simulations showed that the MICROS pedigree has a substantial power to detect a LOD score ≥ 3 when the QTL specific heritability is ≥ 20%.</p> <p>Conclusion</p> <p>The MICROS study is an extensive, ongoing, two-stage survey aimed at characterizing the genetic epidemiology of Mendelian and complex diseases. Our approach, involving different scientific disciplines, is an advantageous strategy to define and to study population isolates. The isolation of the Alpine populations, together with the extensive data collected so far, make the MICROS study a powerful resource for the study of diseases in many fields of medicine. Recent successes and simulation studies give us confidence that our pedigrees can be valuable both in finding new candidates loci and to confirm existing candidate genes.</p

A Century of Inference: 1837-1936

Constructivism, Judgement and Meanin