Graham Priest's Mathematical Analysis of the Concept of Emptiness†

In his article ‘The Structure of Emptiness’ (cf. Priest 2009 Priest, G. 2009. ‘The structure of emptiness’, Philosophy East and West, 59 (4), 467–80. doi: 10.1353/pew.0.0069[Crossref], [Web of Science ®] , [Google Scholar]) Graham Priest examines the concept of emptiness in the Mādhyamaka school of Nāgārjuna and his commentators Candrakī?rti and Tsongkhapa from a mathematical point of view. The approach attempted in this article does not involve any commitment to Priest's more controversial dialethic Mādhyamaka interpretation. The purpose of the present paper is to explain Priest's sketchy but very insightful interpretation of objects as non-well-founded sets in greater detail. Some problems concerning his idea to model the Mādhyamaka claim of the emptiness of emptiness by means of this kind of framework will be noted. Moreover, we will also discuss the possibility to represent the Mādhyamika's denial of the existence of irreducible constituents of empirical reality within a well-founded system of set theory. Finally, some slight mistakes in Priest's mathematical construction need to be pointed out.     

Are there limits to binaural additivity of loudness?

In recent years there has been notable interest in additive models of sensory integration. Binaural additivity has emerged as a main hypothesis in the loudness-scaling literature and has recently been asserted by authors using an axiomatic approach to psychophysics. Restrictions of the range of stimuli used in the majority of former experiments, and inherent weaknesses of the axiomatic study by Levelt, Riemersma, and Bunt (1972) are discussed as providing reasons for the present investigation. A limited binaural additivity (LBA) model is proposed that assumes contralateral binaural inhibition for interaural intensity differences that exceed a critical level. Experimental data are reported for 12 subjects in a loudness-matching task designed to test the axioms of cancellation and of commutativity, both necessary to the existence of strict binaural additivity. In a 2 X 2 design, frequencies of 200 Hz and 2 kHz were used, and mean intensity levels were 20 dB apart. Additivity was found violated in 33 out of 48 possible tests. The LBA model is shown to predict the systematic nonadditivity in the loudness judgments and to conform to results from other studies.     

Serendipity? Are there gender differences in the adoption of computers? A case study

In a study of the effect of learning styles of patent examiners on adoption of computers, there was an important serendipitous finding: women showed a greater propensity to adopt than did men. Moreover, within the sample of women covered in the study, adoption of the computer related to a preference for abstract thinking, scientific education, and effective use of training. No such relationships were found within the group of men. Women were more encouraging to others than men but less assertive in assisting others to learn how to use the computer, implying that the socialization of men and women affects their behavior. The data also suggest that there are important implications of these findings for programs intended to train men and women to use the computer. This paper speculates on the reasons for and implications of these findings.     

Are there degrees of belief?

John Maynard Keynes claimed that not all probabilities were comparable. Frank Ramsey argued that they were, and that Keynes's views to the contrary rested on a confusion of degree of entailment and degree of belief. We will argue that Keynes and Ramsey largely talked past each other, and yet that there are issues of great significance underlying their dispute. In particular, the simple principle of maximizing expected utility may be seen in a new light as one step of a rich and complex process.     

Are we pushing the limits of public health interventions for smoking cessation?

The phenomenon of smoking cessation that takes place outside formal programs, which serve a small proportion of smokers, is an important public health issue. Self-help strategies represent an approach to potentially cost-effective smoking intervention that can be conveniently used by large groups of smokers. In this issue of Health Psychology, Gritz, Berman, Bastani, and Wu (1992) demonstrate that the mailing of self-help smoking cessation materials to nonvolunteer women in a health maintenance organization, without any personal contact, produces little behavior change beyond what occurs in the environment without such distribution. This outcome is not surprising and does not illiminate the possibility of efficacious use of self-help materials with a nonvolunteer population. An essential question is: Could these materials have been distributed in such a way as to increase their use and eventual efficacy? Efforts to attract more smokers to use existing materials are an essential element of self-help strategies. An effective public health approach is a comprehensive one that successfully engages the individual and, through multiple channels in the community, provides reinforcement, supports, and norms for not smoking.     

Are there limits to scientists’ obligations to seek and engage dissenters?

Dissent is thought to play a valuable role in science, so that scientific communities ought to create opportunities for receiving critical feedback and take dissenting views seriously. There is concern, however, that some dissent does more harm than good. Dissent on climate change and evolutionary theory, for example, has confused the public, created doubt about existing consensus, derailed public policy, and forced scientists to devote resources to respond. Are there limits to the extent to which scientific communities have obligations to seek and engage dissenting views? We consider the two main criteria that have been offered for what constitutes “normatively appropriate dissent” or the sort of dissent that ought to have the opportunity to be heard and taken seriously. Many have argued that dissenters must (1) engage in uptake of criticism against their own views and (2) share some standards for theory appraisal. We argue these criteria ultimately are unsuccessful.     

Are True Scores and Construct Scores the Same? A critical examination of their substitutability and the implications for research results

Relations between constructs are estimated based on correlations between measures of constructs corrected for measurement error. This process assumes that the true scores on the measure are linearly related to construct scores, an assumption that may not hold. We examined the extent to which differences in distribution shape reduce the correlation between true scores on a measure and scores on the underlying construct they are intended to measure. We found, via a series of Monte Carlo simulations, that when the actual construct distribution is normal, nonnormal distributions of true scores caused this correlation to drop by an average of only .02 across 15 conditions. When both construct and true score distributions assumed different combinations of nonnormal distributions, the average correlation was reduced by .05 across 375 conditions. We conclude that theory‐based scales intended to measure constructs usually correlate highly with the constructs they are constructed to measure. We show that, as a result, in most cases true score correlations only modestly underestimate correlations between different constructs. However, in cases in which the two constructs are redundant, this underestimation can lead to the false conclusion that the constructs are ‘correlated but distinct constructs,’ resulting in construct proliferation.     

Are there two classes of classically-conditioned responses?

It is proposed that two response classes interact during classical conditioning: (1) a specific effect which directs responding towards or away from the CS, depending upon whether a positive or negative outcome is signaled, and (2) a general, emotional effect which interferes with responding. The interaction between these two response classes can account for the varied results obtained under CER and autoshaping procedures, and must be considered in any analysis which attempts to account for the complex nature of the conditioned response.     

Are there virtuous types? Finite mixture modeling of the VIA Inventory of Strengths

ABSTRACT

Philosophical and religious traditions often refer to ‘the virtuous person.’ This terminology usually carries with it the assumption that a class of individuals exists who have achieved a virtuous state. This study attempted to test that implication. The VIA Inventory of Strengths (VIA-IS) is intended as a comprehensive assessment of character strengths, which are conceptualized as markers of virtuous character. One prior study using taxometric methods found no evidence for the existence of such a category of individuals using VIA-IS scores. Subsequent literature has suggested the superiority of finite mixture modeling for identifying categorical structure. Latent profile analyses of 1–10 classes were conducted in a stratified sample of 10,000 adults. The results provided little evidence for class structure, and support thinking of virtue as something we must continuously pursue rather than a state that we achieve.     

Are Line Lengths Critical to the Discrimination of Axisymmetric Pairs of Figures from Disoriented Identical Pairs?

I examined whether the lack of a difference in line lengths made the discrimination of axisymmetric (Ax) pairs of figures from disoriented identical (Idr) pairs difficult. Three basic pair types were prepared: Idr, Ax, and nonidentical/nonaxisymmetric (Nd) pairs. To avoid confusion arising from structural differences, all pairs of figures were set to be mutually isomorphic. Two figures of a pair were controlled to have the same line lengths of respective figural components (Experiment 1) or the same lengths of individual line segments (Experiment 2) in experiments where participants decided if the figures were the same/different. Experiment 1 showed longer latencies for Ax pairs than for Nd pairs, indicating that these feature values alone did not cause difficulty in discrimination. Experiment 2 showed that only Nd pairs with all line segments having the same lengths for the two figures had the same latencies as Ax pairs. The sameness of individual line segments in simple pairs of figures made discrimination difficult.     

Are thought experiments “disturbing”? The case of armchair physics

Philosophical Studies - Proponents of the “negative program” in experimental philosophy have argued that judgements in philosophical cases, also known as case judgements, are unreliable...     

Are there Local Differences in Support for Violent Radicalization? A Study on College Students in the Province of Quebec,Canada

Support for violent radicalization (VR) is a multidimensional phenomenon determined by individual, social, and contextual variables. However, how local contexts influence the configurations of risk and protective factors leading to the process of VR remains an open question. In line with a socioecological framework, this study aims to investigate local differences in support for VR and its associated risk factors (i.e., immigrant status, social adversity, depression, and collective identity) among college students in Quebec, a Canadian province with a variety of social and political contexts (i.e., Francophone Montreal, Quebec City, rural/suburban areas, and Anglophone communities). A total of 1765 college students (71% women; 73% aged between 16 and 21 years) completed an online survey. Mixed-effects models were implemented to test local differences in support for VR and its risk factors. Results showed that the association between social adversity (i.e., discrimination and exposure to violence) and support for VR varied by local context. Specifically, social adversity was a risk factor across all contexts but Quebec City. Although prevention programs may target common determinants of support for VR, they need to be tailored according to local realities, and in particular the level of social diversity and the relative prevalence of mainstream radical discourses.