The Versatility of Universality in Principia Mathematica

In this article, I examine the ramified-type theory set out in the first edition of Russell and Whitehead's Principia Mathematica. My starting point is the ‘no loss of generality’ problem: Russell, in the Introduction (Russell, B. and Whitehead, A. N. 1910. Principia Mathematica, Volume I, 1st ed., Cambridge: Cambridge University Press, pp. 53–54), says that one can account for all propositional functions using predicative variables only, that is, dismissing non-predicative variables. That claim is not self-evident at all, hence a problem. The purpose of this article is to clarify Russell's claim and to solve the ‘no loss of generality’ problem. I first remark that the hierarchy of propositional functions calls for a fine-grained conception of ramified types as propositional forms (‘ramif-types’). Then, comparing different important interpretations of Principia’s theory of types, I consider the question as to whether Principia allows for non-predicative propositional functions and variables thereof. I explain how the distinction between the formal system of the theory, on the one hand, and its realizations in different epistemic universes, on the other hand, makes it possible to give us a more satisfactory answer to that question than those given by previous commentators, and, as a consequence, to solve the ‘no loss of generality’ problem. The solution consists in a substitutional semantics for non-predicative variables and non-predicative complex terms, based on an epistemic understanding of the order component of ramified types. The rest of the article then develops that epistemic understanding, adding an original epistemic model theory to the formal system of types. This shows that the universality sought by Russell for logic does not preclude semantical considerations, contrary to what van Heijenoort and Hintikka have claimed.     

The Definability of the set of natural numbers in the 1925 Principia Mathematica

In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Gödel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered.     

Quantification Theory in *8 of Principia Mathematica and the Empty Domain

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain.     

尼采1885年初之后的遗稿编订

本文围绕《尼采考订版全集》第九系列对于尼采晚期遗稿的编订,分析了从福斯特—尼采版全集,历经Giorgio Colli与Mazzino Montinari的考订版(系列1-8),一直到最新晚期手稿编纂中编辑范式的转变(系列9)。特别在历史比较的视域下,介绍了以形态学原则还原尼采手稿的编辑方法、原则及其优点。     

康德遗著——遗世手稿、康德的工作方式和遗稿新编

康德的《遗著》包含着康德的从自然的理性形而上学向经验科学过渡的未完成的哲学计划,《康德全集》中原有的非批判的版本存在着诸多欠缺,因此新的版面采用发生学的结构分析,通过对康德的工作方式的考察,重现了康德的凌乱而又被密集书写的手稿上的文字产生的时间顺序和逻辑关系,从而最大限度地还原了康德对这一问题的整个思考过程。     

ITC Guidelines for Translating and Adapting Tests (Second Edition)

The second edition of the International Test Commission Guidelines for Translating and Adapting Tests was prepared between 2005 and 2015 to improve upon the first edition, and to respond to advances in testing technology and practices. The 18 guidelines are organized into six categories to facilitate their use: pre-condition (3), test development (5), confirmation (4), administration (2), scoring and interpretation (2), and documentation (2). For each guideline, an explanation is provided along with suggestions for practice. A checklist is provided to improve the implementation of the guidelines.     

The Westminster Dictionary of Theological Terms,Second Edition,Revised and Expanded

A collection of books, ephemera, and correspondence belonging to Lawrence Kaye Hyde located in the San Diego State University Library provides an intriguing glimpse into 19th- and 20th-century Western Esotericism. Hyde belonged to numerous metaphysical organizations and maintained a wide-ranging correspondence with religious thinkers around the world. By considering Hyde's unique esoteric library against the backdrop of current scholarship in Western Esoteric Studies, this article examines key concepts in the field (such as gnosis, concordance, and the cultic milieu) and assesses the collection's potential for supporting research in this emerging discipline.     

Comparison of the Vineland Adaptive Behavior Scales, Second Edition, and the Bayley Scales of Infant and Toddler Development, Third Edition

The Vineland Adaptive Behavior Scales, Second Edition (Vineland-II), and Bayley Scales of Infant and Toddler Development, Third Edition (Bayley-III) were administered to 65 children between the ages of 12 and 42 months referred for developmental delays. Standard scores and age equivalents were compared across instruments. Analyses showed no statistical difference between Vineland-II ABC standard scores and cognitive levels obtained from the Bayley-III. However, Vineland-II Communication and Motor domain standard scores were significantly higher than corresponding scores on the Bayley-III. In addition, age equivalent scores were significantly higher on the Vineland-II for the fine motor subdomain. Implications for early intervention are discussed.     

The Second Step of the B‐Deduction

This paper offers a new interpretation of Kant's puzzling claim that the B‐Deduction in the Critique of Pure Reason should be considered as having two main steps. Previous commentators have tended to agree in general on the first step as arguing for the necessity of the categories for possible experience, but disagree on what the second step is and whether Kant even needs a second step. I argue that the two parts of the B‐Deduction correspond to the two aspects of a priori cognition: necessity and universality. The bulk of the paper consists of support for the second step, the universality of the categories. I show that Kant's arguments in the second half of the B‐Deduction aim to define the scope of that universality for possible experience by considering the possibilities of divine intellectual intuition, of non‐human kinds of sensible intuition, and of apperception of the self. In these ways Kant delimits the boundaries of the applicability of the categories and excludes any other possible experience for human beings.