Real Analysis in Paraconsistent Logic

This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.     

Eternalism and Propositional Multitasking: in defence of the Operator Argument

It is widely held that propositions perform a plethora of theoretical roles. They are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, the referents of ??that??-clauses, and the primary bearers of truth. This assumption is often combined with the claim that propositions have their truth-values eternally. Following Kaplan??s and Lewis??s Operator Argument, I argue that the compositional semantic values of sentences do not correspond to eternal propositions. Therefore, we cannot hold on to both assumptions at the same time: either we regard the non-eternal entities that realize the compositional role of propositions as fulfilling the remaining theoretical roles, or we abandon the assumption that there is a unique realizer. The Operator Argument has recently come under attack, mainly for its intensional assumptions. However, rejecting these assumptions is not a sufficient defense of eternal propositions as compositional semantic values of sentences. Firstly, we can give a generalized version of the Operator Argument that seems independent of the contested assumptions. Secondly, the extensional alternative to the intensional framework does not allow us to retain eternal propositions as unique semantic values either.     

Design and its discontents

The design argument was rebutted by David Hume. He argued that the world and its contents (such as organisms) were not analogous to human artifacts. Hume further suggested that there were equally plausible alternatives to design to explain the organized complexity of the cosmos, such as random processes in multiple universes, or that matter could have inherent properties to self-organize, absent any external crafting. William Paley, writing after Hume, argued that the functional complexity of living beings, however, defied naturalistic explanations. In effect he dared anyone to come up with an alternative to his inference to design, and hence a designer, outside of nature. Charles Darwin explained the apparent design of functional complexity by his theory of natural selection. Asa Gray, however, in essays as well as in correspondence with Darwin argued that natural selection allowed for a type of ‘evolutionary teleology’ in which design at most could be considered the result of universal principles. F.E. Hicks updated Hume by specifically objecting to the use of design arguments by Paley. Hicks argued that the apparent design seen in nature reflected order at a deep level in nature. The design argument was briefly revived by Lawrence Henderson early in the twentieth century but he ultimately concluded that design and teleology were not necessarily mutually entailing and he retracted his design argument in favor of one that he termed ‘natural teleology’. The current claims of ‘intelligent design’ have the same logical problems that have beset previous design arguments. If design is divorced from teleology and its discontents put behind us, then there is a possibility that the latter can have a place in the development of theories to explain the phenomena of emergent complexity.     

Predicting school achievement from cognitive and non-cognitive variables in a Chinese sample of elementary school children

The present study had two aims: First, to investigate the joint and specific roles of working memory (WM) and intelligence as predictors of school achievement. And second, to replicate and extend earlier findings (Spinath, Spinath, Harlaar, & Plomin, 2006) on the incremental validity of non-cognitive over cognitive abilities in the prediction of school achievement. The present sample consisted of N = 179 Chinese primary school children in the fourth grade. All measures including working memory (WM), intelligence and motivational items were assessed in class. Teachers provided test scores for the domains of Chinese and Math. We found that WM was a good predictor of school achievement and comparable in predictive power to intelligence. Together, cognitive ability including both WM and intelligence explained 17.8% and 36.4% of the variance in children's Chinese and Math scores, respectively. The relative importance of WM and intelligence varied with school domains with greater predictive power of WM for Math while intelligence explained a greater proportion of the variance in Chinese although the magnitude of this difference was only moderate. Domain-specific motivational constructs contributed only marginally to the prediction of school achievement for both Chinese and Math.     

Verisimilitude and Belief Revision. With a Focus on the Relevant Element Account

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.     

Rating Scales as Predictors—The Old Question of Scale Level and Some Answers

Rating scales as predictors in regression models are typically treated as metrically scaled variables or, alternatively, are coded in dummy variables. The first approach implies a scale level that is not justified, the latter approach results in a large number of parameters to be estimated. Therefore, when rating scales are dummy-coded, applications are often restricted to the use of a few predictors. The penalization approach advocated here takes the scale level serious by using only the ordering of categories but is shown to work in the high dimensional case. We consider the proper modeling of rating scales as predictors and selection procedures by using penalization methods that are tailored to ordinal predictors. In addition to the selection of predictors, the clustering of categories is investigated. Existing methodology is extended to the wider class of generalized linear models. Moreover, higher order differences that allow shrinkage towards a polynomial as well as monotonicity constraints and alternative penalties are introduced. The proposed penalization approaches are illustrated by use of the Motivational States Questionnaire.     

Completeness and Correspondence in Chellas–Segerberg Semantics

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.     

A Longitudinal Examination of Overgeneral Memory and Psychopathology in Children Following Recent Trauma Exposure

This study represents the first longitudinal examination of the trajectory of overgeneral memory (OGM) in children and how this relates to psychopathology immediately after trauma exposure. We recruited fifty 7‐ to 17‐year‐olds who had experienced an accidental injury that resulted in hospital admission. Assessment of psychological symptoms, OGM and cognitive processes proposed to drive OGM was completed at three points over a 6‐month period post‐trauma. We found that OGM was not related to depressive symptoms and that time since trauma exposure moderated the relationship between post‐traumatic stress disorder symptoms and OGM. Although no relationship was found in the first 3 months following trauma, OGM was protective against post‐traumatic stress disorder symptoms at 6 months post‐trauma. Despite models of OGM (e.g. Williams et al., 2007 ) emphasising the role of rumination and executive control in explaining OGM, we found no evidence that they were related to OGM. Copyright © 2014 John Wiley & Sons, Ltd.