The Ideal of Harmony in Ancient Chinese and Greek Philosophy

This article offers a study of the early formation and development of the ideal of harmony in ancient Chinese philosophy and ancient Greek philosophy. It shows that, unlike the Pythagorean notion of harmony, which is primarily based on a linear progressive model with a pre-set order, the ancient Chinese concept of harmony is best understood as a comprehensive process of harmonization. It encompasses spatial as well as temporal dimensions, metaphysical as well as moral and aesthetical dimensions. It is a fundamentally open notion in the sense that it does not aim to conform to any pre-set order. This broader, richer, and more liberal understanding of harmony has had a profound influence on Chinese culture as whole in its long history.     

The Epsilon Calculus and Herbrand Complexity

Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator e _x . Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.     

动机的概率意义——概率归并定理与Monty Hall问题的非贝叶斯解

本文探讨Monty Hall问题认知困惑的形成因素。通过对该问题数学结构的分析,导出一个与该问题的解密切相关的定理——概率归并定理;并依据该定理给出了Monty Hall问题的一种更直观的数学解。     

An impossibility theorem for verisimilitude

In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements of Unanimity, Independence of irrelevant alternatives and Non-dictatorship at the level of sentence variables. By giving a formal account of the incompatibility of the considerations of content and likeness, our impossibility result makes it possible to systematize the discussion about verisimilitude, and to understand it in more general terms.     

Genetic Influence Helps Explain Variation in Human Fertility: Evidence From Recent Behavioral and Molecular Genetic Studies

To search for genetic influence on human fertility differentials appears inconsistent with past empirical research and prior interpretations of Fisher's fundamental theorem of natural selection. We discuss Fisher's theorem and give reasons why genetic influences may indeed account for individual differences in human fertility. We review recent empirical studies showing genetic influence on variance in fertility outcomes and precursors to fertility. Further, some of the genetic variance underlying fertility outcomes overlaps with that underlying fertility precursors. Findings from different cultures, different times, different levels of data, and both behavioral and molecular genetic designs lead to the same conclusion: Fertility differentials are genetically influenced, and at least part of the influence derives from behavioral precursors that are under volitional control, which are themselves genetically mediated.     

The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective

It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

Interval estimation for the intraclass correlation in dirichlet-multinomial data

When the underlying distribution is discrete with a limited number of categories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of large sample theory, this paper develops an asymptotic closed-form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category. This paper employs Monte Carlo simulation to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleading. We find that when the number of classes is 20, the interval estimator proposed here can generally perform reasonably well in a variety of situations. This paper further notes that the proposed interval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to account for this case, as well as a discussion on the relationship between the intraclass correlation and a kappa-type measure defined here and on the limitation of the corresponding kappa-type estimator are given.The authors wish to thank the Editor, the Associate Editor, and the three referees for many valuable comments and suggestions to improve the clarity of this paper. The works for the first, the third, and the fourth authors were partially supported by grant #R01AR43025-01 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases.