Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first (...) theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...) concrete example of the C*-algebra M n (ℂ) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ℘(M n (ℂ)) of projections in M n (ℂ) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice $\mathcal{O}(\Sigma_{n})$ of functions from the poset $\mathcal{C}(M_{n}(\mathbb{C}))$ of all unital commutative C*-subalgebras C of M n (ℂ) to ℘(M n (ℂ)). The lattice $\mathcal{O}(\Sigma_{n})$ is essentially the (pointfree) topology of the quantum phase space Σ n , and as such defines a Heyting algebra. Each element of $\mathcal{O}(\Sigma_{n})$ corresponds to a “Bohrified” proposition, in the sense that to each classical context $C\in\mathcal{C}(M_{n}(\mathbb{C}))$ it associates a yes-no question (i.e. an element of the Boolean lattice ℘(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann. (shrink)

OBJECTIVES: Early-emerging, temperamental differences in fear-related traits may be a heritable vulnerability factor for anxiety disorders. Previous research indicates that the serotonin transporter promoter region polymorphism is a candidate gene for such traits. METHODS: Associations between 5-HTTLPR genotype and indices of fearful child temperament, derived from maternal report and standardized laboratory observations, were examined in a community sample of 95 preschool-aged children. RESULTS: Children with one or more long alleles of the 5-HTTLPR gene were rated as significantly more nervous during (...) standardized laboratory tasks than children who were homozygous for the short alleles. Children homozygous for the short alleles were also rated as significantly shyer, by maternal report, than those with at least one copy of the long allele of the 5-HTTLPR gene. CONCLUSIONS: This study extends the literature linking the short alleles of the serotonin transporter promoter region polymorphism to fear and anxiety-related traits in early childhood and adulthood, and is one of very few studies to examine the molecular genetics of preschoolers' temperament using multiple measures of traits in a normative sample. (shrink)

REALISM AND IDEALISM 1. THE CONFLICTING ELEMENTS OF THE ONTOLOGICAL QUESTION No matter what direction philosophical speculation may take, no matter how it ...

This chapter contains sections titled: A Timeline of Medieval Logicians A Guide to the Literature.