Paradoxes in Double Extension Set Theories

Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs.     

On the need for negative local item dependence

While negative local item dependence (LID) has been discussed in numerous articles, its occurrence and effects often go unrecognized. This is due in part to confusion over what unidimensional latent trait is being utilized in evaluating the LID of multidimensional testing data. This article addresses this confusion by using an appropriately chosen latent variable to condition on. It then provides a proof that negative LID must occur when unidimensional ability estimates (such as number right score) are obtained from data which follow a very general class of multidimensional item response theory models. The importance of specifying what unidimensional latent trait is used, and its effect on the sign of the LIDs are shown to have implications in regard to a variety of foundational theoretical arguments, to the simulation of LID data sets, and to the use of testlet scoring for removing LID.This paper is based in part on a chapter in the first author's doctoral dissertation, written at the University of Illinois at Urbana-Champaign under the supervision of William Stout. Part of this research has been presented at the annual meeting of the National Council on Measurement in Education, San Diego, California, April 14–16, 1998.The research of the first author was partially supported by a Harold Gulliksen Psychometric fellowship through Educational Testing Service and by a Research and Productive Scholarship award from the University of South Carolina.     

The Moral Contours of Empathy

Morally contoured empathy is a form of reasonable partiality essential to the healthy care of dependents. It is critical as an epistemic aid in determining proper moral responsiveness; it is also, within certain richly normative roles and relationships, itself a crucial constitutive mode of moral connection. Yet the achievement of empathy is no easy feat. Patterns of incuriosity imperil connection, impeding empathic engagement; inappropriate empathic engagement, on the other hand, can result in self-effacement. Impartial moral principles and constraints offer at best meager protection against these perils, and hence serve poorly in securing morally contoured empathy. More nuanced and practical guidance should be sought in normatively substantive conceptions of our roles and relationships and their defining moral stakes. These, joined with more abstract moral tools, can facilitate rich, narratively textured interpretations of moralitys demands. While the content of our normative conceptions must be continually debated, engaging in this debate is vital to the achievement of proper empathy, and thus to effective, respectful, morally healthy care of dependents.This paper was originally presented at the conference on Reasonable Partiality at the Vrije Universiteit, Amsterdam, October 22–24, 2003. I wish to thank all those present for stimulating discussion. Special thanks go to Bert Musschenga, who organized the conference, and who has provided insightful feedback on this paper. Warm thanks as well to Brenda Almond and Bernie Rollin for lively exchanges on the issues addressed here and to Nancy Sherman for sharing with me an ongoing fascination with, and her own fantastic work on, empathy. Comments from an anonymous reviewer for the journal were challenging and helpful. Finally, I wish to express gratitude beyond normal bounds to Maggie Little both for her generosity, keen insight, and artful intervention at key points in this essays evolution and for her ground-breaking work on deontic pluralism that deeply influences the position I frame here.     

The Rôle of Language In Belief Revision

Analytical tools that give precision to the concept of "independence of syntax" are developed in the form of a series of substitutivity principles. These principles are applied in a study of the rôle of language in belief revision theory. It is shown that sets of sentences can be used in models of belief revision to convey more information than what is conveyed by the combined propositional contents of the respective sets. It is argued that it would be unwise to programmatically restrain the use of sets of sentences to that of representing propositional contents. Instead, the expressive power of language should be used as fully as possible. Therefore, syntax-independence should not be seen as a criterion of adequacy for language-based models of information-processing, but rather as a property that emerges from some but not all the idealization processes through which such models are constructed.     

The adoption of innovation in collective action organizations

This study used a quantitative/qualitative methodology to explore how collective action organizations (CAOs) remain open to organizational change and innovation. It examined the adoption of inclusion—a recent innovation in the field of disabilities—by local chapters of The Arc Michigan (a disabilities CAO). We found considerable variability in the adoption of inclusion by local Arc chapters. This variability was significantly related to the ecology surrounding these chapters. Local Arc chapters that had adopted an inclusion philosophy had significantly different internal and external environments from those that had not adopted inclusion. Our qualitative findings make it clear, however, that innovative Arc chapters were not the passive recipients of these internal and external influences. These chapters were proactive players in defining and shaping the nature of their internal and external environments. Strategies that were related to a chapter's ability to remain open to innovation included (a) a change orientation, (b) a conscious philosophy or vision, (c) a proactive strategy for achieving chapter goals and overcoming barriers to change, (d) the creation of a supportive organizational network, and (e) avoidance of resource dependencies that required them to engage in activities that were inconsistent with the innovation. These findings provide a framework by which CAOs can maintain an openness to innovation and remain on the forefront of social change.     

Paradoxical decrease of imitation performance with age in children

Imitation development was studied in a cross-sectional design involving 174 primary-school children (aged 6–10), focusing on the effect of actions' complexity and error analysis to infer the underlying cognitive processes. Participants had to imitate the model's actions as if they were in front of a mirror (‘specularly’). Complexity varied across three levels: movements of a single limb; arm and leg of the same body side; or arm and leg of opposite body sides. While the overall error rate decreased with age, this was not true of all error categories. The rate of ‘side’ errors (using a limb of the wrong body side) paradoxically increased with age (from 9 years). However, with increasing age, the error rate also became less sensitive to the complexity of the action. This pattern is consistent with the hypothesis that older children have the working memory (WM) resources and the body knowledge necessary to imitate ‘anatomically’, which leads to additional side errors. Younger children might be paradoxically free from such interference because their WM and/or body knowledge are insufficient for anatomical imitation. Yet, their limited WM resources would prevent them from successfully managing the conflict between spatial codes involved in complex actions (e.g. moving the left arm and the right leg). We also found evidence that action side and content might be stored in separate short-term memory (STM) systems: increasing the number of sides to be encoded only affected side retrieval, but not content retrieval; symmetrically, increasing the content (number of movements) of the action only affected content retrieval, but not side retrieval. In conclusion, results suggest that anatomical imitation might interfere with specular imitation at age 9 and that STM storages for side and content of actions are separate.     

Significance tests to determine the direction of effects in linear regression models

Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non‐normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one‐sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice.     

Intrinsic Causation in Humean Supervenience

The paper investigates whether causation is extrinsic in Humean Supervenience (HS) in the sense that being caused by is an intrinsic relation between token causes and effects. The underlying goal is to test whether causality is extrinsic for Humeans and intrinsic for anti‐Humeans in this sense. I argue that causation is typically extrinsic in HS, but it is intrinsic to event pairs that collectively exhaust almost the whole of history. 1     

Double Reference Points: the Effects of Social and Financial Reference Points on Decisions Under Risk

The existing literature is inconsistent about how social comparison affects risk attitudes. We propose a framework where the total utility is composed of the social and financial utilities. The financial utility is consistent with prospect theory (i.e., an S‐shaped utility function with a financial reference point), whereas the social utility is affected by both social and financial reference points. Therefore, social risk attitudes are determined by interaction between gains/losses in both social and financial contexts. On the basis of safety‐first principle, we propose that when experiencing financial gains, individuals tend to seek upside potential and take social risks (i.e., a convex social utility function). In contrast, when facing financial losses, people would be more risk seeking in social gains but more risk averse in social losses to maximize security (i.e., an inverse S‐shaped utility function). We also propose that the relative importance of financial and social utilities depends on the saliency of the reference points and size of stakes. Studies 1 and 2 showed that individuals were risk seeking in both social gains and losses with social reference points alone. Studies 3 and 4 demonstrated that when both financial and social reference points were salient, participants were risk averse in both social gains and losses when facing financial gains, but risk seeking in social gains and risk averse in social losses when facing financial losses. The hypotheses derived from the theoretical framework were in general supported by our experiments. Copyright © 2015 John Wiley & Sons, Ltd.     

Representationalism,perceptual distortion and the limits of phenomenal concepts

This paper replies to objections from perceptual distortion (blur, perspective, double vision, etc.) against the representationalist thesis that the phenomenal characters of experiences supervene on their intentional contents. It has been argued that some pairs of distorted and undistorted experiences share contents without sharing phenomenal characters, which is incompatible with the supervenience thesis. In reply, I suggest that such cases are not counterexamples to the representationalist thesis because the contents of distorted experiences are always impoverished in some way compared to those of normal experiences. This can be shown by considering limit cases of perceptual distortion, for example, maximally blurry experiences, which manifestly lack details present in clear experiences. I argue that since there is no reasonable way to draw the line between distorted experiences that have degraded content and distorted experiences that do not, we should allow that an increase in distortion is always accompanied by a degradation in content. I also discuss the prospects for a positive account of the contents specific to distorted experiences. I argue that the prospects for such an account are dim, but that this is due to limitations of our phenomenal concepts, not to the falsity of the representationalist thesis.