De Finetti, Countable Additivity, Consistency and Coherence

Many people believe that there is a Dutch Book argument establishingthat the principle of countable additivity is a condition ofcoherence. De Finetti himself did not, but for reasons thatare at first sight perplexing. I show that he rejected countableadditivity, and hence the Dutch Book argument for it, becausecountable additivity conflicted with intuitive principles aboutthe scope of authentic consistency constraints. These he oftenclaimed were logical in nature, but he never attempted to relatethis idea to deductive logic and its own concept of consistency.This I do, showing that at one level the definitions of deductiveand probabilistic consistency are identical, differing onlyin the nature of the constraints imposed. In the probabilisticcase I believe that R.T. Cox's ‘scale-free’ axiomsfor subjective probability are the most suitable candidates.

1 Introduction

2 Coherence and Consistency

3 The InfiniteFair Lottery

4 The Puzzle Resolved—But Replaced by Another

5 Countable Additivity, Conglomerability and Dutch Books

6The Probability Axioms and Cox's Theorem

7 Truth and Probability

8 Conclusion: ‘Logical Omniscience’

     

The Last Mathematician from Hilbert's Gottingen: Saunders Mac Lane as Philosopher of Mathematics

While Saunders Mac Lane studied for his D.Phil in Göttingen,he heard David Hilbert's weekly lectures on philosophy, talkedphilosophy with Hermann Weyl, and studied it with Moritz Geiger.Their philosophies and Emmy Noether's algebra all influencedhis conception of category theory, which has become the workingstructure theory of mathematics. His practice has constantlyaffirmed that a proper large-scale organization for mathematicsis the most efficient path to valuable specific results—whilehe sees that the question of which results are valuable hasan ineliminable philosophic aspect. His philosophy relies onthe ideas of truth and existence he studied in Göttingen.His career is a case study relating naturalism in philosophyof mathematics to philosophy as it naturally arises in mathematics.

1. Introduction
2. Structures and Morphisms
3. Varieties of Structuralism
4. Göttingen
5. Logic: Mac Lane's Dissertation
6. Emmy Noether
7. Natural Transformations
8. Grothendieck: Toposes and Universes
9. Lawvere and Foundations
10. Truth and Existence
11. Naturalism
12. Austere Forms of Beauty

     

Grade repetition and psychological referrals in relation to child behavior checklist scores for students in elementary school

A sample of 738 students from grades 1 to 5 who were exhibiting behavior problems were nominated by teachers and subsequently assessed for behavioral disturbance using the Teacher's Report Form (TRF) of the Child Behavior Checklist. The data were analyzed to assess the accuracy of the TRF in discriminating disturbed and nondisturbed students, the internal consistency of the instrument, and its validity against measures of school functioning in terms of grade repetition and referral for special services support.     

Tour de France Champions born or made: where do we take the genetics of performance?

ABSTRACT

Cyclists in the Tour de France are endurance specialists. Twin and family studies have shown that approximately 50% of the variance in a number of performance-related phenotypes (whether measured at baseline, i.e., natural talent, or in response to training) including those important to cycling can be explained by genetic variation. Research into the specific genetic variants that are responsible has identified over 200 genes containing common genetic variants involved in the genetic predisposition to physical performance. However, typically these explain only a small portion of the variance, perhaps 1–2% and collectively they rarely explain anything approaching the 50% of the variance identified in the twin and family studies. Thus, there is a gap in our understanding of the relationship between heritability and performance. This gap may be bridged by investigation of rare variants or epigenetic variation or by altering study designs through increased collaborations to pool existing cohorts together. Initial findings from such efforts show promising results. This mini-review will touch on the genetics and epigenetics of sporting performance, how they relate to cyclists in the Tour de France and where best future efforts may be directed as well as discuss some preliminary research findings.     

Vocational education and development: key issues, with special reference to the Arab world

Despite the considerable capacity of most Arab governments to invest in education for development, relatively little has been achieved in the vocational and technical sector. Yet, as is well known, it is the production of good quality technicians that is crucial to sustainable industrial development at a national level. In this paper we attempt an analysis of the situation — to identify key issues that need to be addressed if progress is to be made. Two broad problems underlie the contemporary crisis: aspects of Arabic culture that tend to constrain wider involvement in vocational and technical employment, and the low status of technical education in the Western model of education bequeathed to these nations by the legacy of colonialism. Some recommendations are made to assist the resolution of the problem.     

Social engagement and regional theatre: patterns of theatre attendance

This paper assesses the degree to which a typical regional theatre engages with society. It uses postcodes from theatre booking data and compares the socioecenomic profiles of these postcodes with postcodes from which no theatregoers are drawn. A re-working of recent theories of class provides a conceptual context, whilst discriminant analysis is used to identify the socioecenomic factors of postcodes associated with theatre and non-theatre attendance. Education factors were the principal determinants of attendance, with occupational categories being important, but lower socioecenomic groups were less likely to engage with theatre. However, social engagement and factors determining attendance varied by type of show: comedy, drama, family and Shakespearian productions.