Wittgenstein and the Real Numbers

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A real number, as an ‘extension’, is a homeless fiction; ‘homeless’ in that it neither is supported by anything nor supports anything. The picture of a real number as an ‘extension’ is not supported by actual practice in calculus; calculus has nothing to do with ‘extensions’. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being ‘existential axiomatics’. And in real analysis, as existential axiomatics, a point on the real line need not be an ‘extension’.     

Inversion domain boundary in a ZnO film

Transmission electron microscopy has been used to investigate the (1100) and (1103) inversion domain boundaries in a ZnO film prepared by molecular beam epitaxy. The inversion domain was revealed by dark-field images and confirmed by convergent-beam electron diffraction. Interacting with a (0002) stacking fault, the inversion domain boundary in the (1100) plane alters its orientation from the [0001] direction and climbs on the (1103) plane to release the strain energy. These features are characterized and analysed by high-resolution electron microscopy and the geometric phase method. The findings are significant for understanding the formation and propagation of inverse domain boundaries in epitaxial ZnO films.     

Misorientation characteristics of penetrating morphologies at the growth front of abnormally growing grains in aluminum alloy

The initial stage of abnormal grain growth of the aluminum alloy 5052 has been investigated using electron back-scattered diffraction to analyze the characteristic of misorientations of the penetrating morphology at the growth front. Among the 84 penetrating morphologies examined, none of the penetrated grain boundaries has low angles or coincidence site lattice (CSL) relations, whereas 66 penetrating grain boundaries have low angles or CSL relations. These results strongly suggest that the penetrating morphologies should result from triple-junction wetting.     

Thermal effects on infiltration of a solubility-sensitive volume-memory liquid

As the ion density at a solid–liquid interface changes, the interfacial tension varies accordingly, which can lead to a large energy density output, particularly when amplified by the high specific surface area of a nanoporous material. This concept is validated by the results of a controlled-temperature infiltration experiment on a hydrophobic zeolite immersed in a saturated aqueous solution of sodium acetate. As the temperature changes, the sodium acetate concentration varies significantly, which in turn causes a variation in infiltration pressure. Since the infiltration and defiltration are reversible, under the working pressure, this system exhibits a volume memory characteristic, with a non-monotonic temperature–volume relationship.     

Potential mapping of ZnO by off-axis electron holography

Off-axis electron holography has been used to map the electric potential derived from the spontaneous polarity in a ZnO film. A wedge-shaped ZnO film, in which the holograms and the object wave were reconstructed, was used. To interpret the phase image correctly, the reconstructed amplitude image was used to obtain information on the thickness, which was then applied to eliminate the thickness effect on the phase shift. The electric potential distribution was characterized and the polarity of the ZnO film determined.     

Accelerating heterogeneous nucleation to increase hardness and electrical conductivity by deformation prior to ageing for Cu-4 at.% Ti alloy

ABSTRACT

Deformation bands, especially shear bands were intentionally formed in supersaturated Cu-4 at.% Ti alloy by groove-rolling with 75% area reduction. Cold deformation prior to the ageing process changed the precipitation behaviour of the alloy. The deformed structure with shear bands was maintained, without showing recovery and recrystallisation, even after prolonged ageing at 450°C for more than one day. The thermally stable shear bands act as nucleation initiation sites and prevent the expansion of discontinuous cellular precipitates. The hardness reached a value of 305?Hv and an electrical conductivity of 15% IACS (IACS?=?International Annealed Copper Standard. 100% IACS is defined as the conductivity corresponding to a volume resistivity at 20°C of 17.241?nΩ), compared to 283?Hv and 13% IACS for conventional solid-solutioned and peak-hardened alloy. In addition, the ageing time to reach the highest hardness was shortened from 720 to 180?min at 450°C.     

医患关系紧张的心理成因探究——以急诊患者家属为例

随着经济社会的发展,医患关系日益成为人们关注的焦点.本文以急诊患者家属为例,从心理方面来探讨医患关系,分析医患关系紧张的原因:利益冲突、心理应激和缺乏沟通等;提出拉近医患关系的见解:医方要注重对患者家属的心理疏导与心理治疗,加强沟通,不断提高自身的能力素质.     

信任的心理结构

采用字词联想法对信任概念的心理结构进行了研究。聚类分析的结果表明,信任的心理结构包括认知评价、心理状态、互动行为、个性特征、行为规则和人员共六个方面。进一步分析表明,信任具有明显的利益期待和责任分享特征。     

Generalist genes and cognitive abilities in Chinese twins

This study considered how far nonverbal cognitive, language and reading abilities are affected by common genetic influences in a sample of 312 typically developing Chinese twin pairs aged from 3 to 11 years. Children were individually given tasks of Chinese word reading, receptive vocabulary, phonological memory, tone awareness, syllable and rhyme awareness, rapid automatized naming, morphological awareness and orthographic skills, and Raven's Colored Progressive Matrices. Factor analyses on the verbal tasks adjusted for age indicated two factors: Language as the first factor and Reading as the second factor. Univariate genetic analyses indicated that genetic influences were substantial for nonverbal cognitive ability and moderate for language and reading. Multivariate genetic analyses showed that nonverbal cognitive ability, language and reading were influenced by shared genetic origins, although there were specific genetic influences on verbal skills that were distinct from those on nonverbal cognitive ability. This study extends the Generalist Genes Hypothesis to Chinese language and reading skills, suggesting that the general effects of genes could be universal across languages.     

‘Serving Two Masters’: Protestant Churches in Korea and Money

Materialism or religio-economic entrepreneurship has been a primary impetus for the explosive growth of Protestant churches in Korea, especially since the 1960s, when rapid industrialisation began to propel Korean society into tremendous economic prosperity. However, since the early 1990s, there has been stagnation, even decline. The primary aim of this article is to identify the most pressing problems facing the Korean Protestant churches and show how these problems have begun to render them less vibrant and possibly to bring about decline in their membership. More specifically, the article identifies how materialism, having deeply penetrated Korean Christianity, led it first to grow and then decline; thus robbing it of its requisite or intrinsic organisational characteristics – being the light and salt of the world.