A new definition of well-behaved discrimination functions

A discrimination function shows the probability or degree with which stimuli are discriminated from each other when presented in pairs. In a previous publication [Kujala, J.V., & Dzhafarov, E.N. (2008). On minima of discrimination functions. Journal of Mathematical Psychology, 52, 116–127] we introduced a condition under which the conformity of a discrimination function with the law of Regular Minimality (which says, essentially, that “being least discriminable from” is a symmetric relation) implies the constancy of the function’s minima (i.e., the same level of discriminability of every stimulus from the stimulus least discriminable from it). This condition, referred to as “well-behavedness,” turns out to be unnecessarily restrictive. In this note we give a significantly more general definition of well-behavedness, applicable to all Hausdorff arc-connected stimulus spaces. The definition employs the notion of the smallest transitively and topologically closed extension of a relation. We provide a transfinite-recursive construction for this notion and illustrate it by examples.     

周敦颐的《太极图说》、《易》象数及西方有关学说

本文从《易》象数的角度来解释周敦颐的《太极图说》与《通书》,认为这种象数的“二对生”的区别性特征是周氏学说的内在发动结构,由此而提出一些很不同于流行的“宇宙论加上伦理学”的解释模式的思路。在一些被长久争论的问题上,比如“太极与无极的关系”、“太极与两仪的关系”、“诚与太极的关系”、“中与太极和诚的关系”,都提出了新的看法。在这新的理解方式中,周敦颐的《太极图说》就不止是程朱陆王的一个含糊的先导,而是融合了儒道释的思想精华,而又有着自己独特的思想原发力与中和的精微境界的划时代的哲理学说,其蕴义(比如超出理气二分的原本发生论)并未被后来的理学家们穷尽。本文最后将周敦颐的思想与西方的毕达哥拉斯及莱布尼兹的学说进行对比,一方面揭示“象数”在伟大的哲理传统中的关键作用,另一方面又表明中西两大传统之间存在的深刻差异在结构上的原因。     

Philosophers ought to develop,theorize about,and use philosophically relevant AI

The transformative power of artificial intelligence (AI) is coming to philosophy—the only question is the degree to which philosophers will harness it. This paper argues that the application of AI tools to philosophy could have an impact on the field comparable to the advent of writing, and that it is likely that philosophical progress will significantly increase as a consequence of AI. The role of philosophers in this story is not merely to use AI but also to help develop it and theorize about it. In fact, the paper argues that philosophers have a prima facie obligation to spend significant effort in doing so, at least insofar as they should spend effort philosophizing.     

What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables?

Abstract

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a large number of variables (p). A large p can cause T_ml, the most widely used likelihood ratio statistic, to depart drastically from the assumed chi-square distribution even with normally distributed data and a relatively large sample size N. A key element affecting this behavior of T_ml is its mean bias. The focus of this article is to determine the cause of the bias. To this end, empirical means of T_ml via Monte Carlo simulation are used to obtain the empirical bias. The most effective predictors of the mean bias are subsequently identified and their predictive utility examined. The results are further used to predict type I errors of T_ml. The article also illustrates how to use the obtained results to determine the required sample size for T_ml to behave reasonably well. A real data example is presented to show the effect of the mean bias on model inference as well as how to correct the bias in practice.     

Protecting Against Low‐Probability Disasters: The Role of Worry

We carry out a large monetary stakes insurance experiment with very small probabilities of losses and ambiguous as well as exact probabilities. Many individuals do not want to pay anything for insurance whether the probabilities are given exactly or are ambiguous. Many others, however, are willing to pay surprisingly large amounts. With ambiguity, the percentage of those paying nothing is smaller and the willingness to pay (WTP) of the other individuals larger than with exact probabilities. Comparing elasticities with ambiguity, we find that worry is much more important than subjective probability in determining WTP for insurance. Furthermore, when the ambiguous loss probability is increased by a factor of 1000, it has almost no effect on WTP. Copyright © 2011 John Wiley & Sons, Ltd.     

The SNARC effect in the processing of second-language number words: Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

The Language of Creativity: Evidence from Humans and Large Language Models

Recent developments in computerized scoring via semantic distance have provided automated assessments of verbal creativity. Here, we extend past work, applying computational linguistic approaches to characterize salient features of creative text. We hypothesize that, in addition to semantic diversity, the degree to which a story includes perceptual details, thus transporting the reader to another time and place, would be predictive of creativity. Additionally, we explore the use of generative language models to supplement human data collection and examine the extent to which machine-generated stories can mimic human creativity. We collect 600 short stories from human participants and GPT-3, subsequently randomized and assessed on their creative quality. Results indicate that the presence of perceptual details, in conjunction with semantic diversity, is highly predictive of creativity. These results were replicated in an independent sample of stories (n = 120) generated by GPT-4. We do not observe a significant difference between human and AI-generated stories in terms of creativity ratings, and we also observe positive correlations between human and AI assessments of creativity. Implications and future directions are discussed.     

The revelation of the negative side of a mental number line depends on list context: Evidence from a sign priming paradigm

Two parity judgement experiments examined how the activation of spatial-numerical associations of a single, centrally presented digit, reflected by the Spatial-Numerical Association Response Codes (SNARC) effect, is modulated by a preceding + (plus) or ? (minus) prime. The centrally presented prime prior to a digit presentation presumably triggers its positive or negative attributes. When the plus- and minus-primed trials were blocked, the left-small/right-large SNARC effects occurred regardless of prime type. When the plus- and minus-primed trials were randomly intermixed, this left-small/right-large SNARC effect occurred for plus-primed digits, but was reversed for minus-primed digits. The implications of this finding for context-dependent SNARC effects are discussed.     

Numerical comparison of two-digit numbers: How differences at encoding can involve differences in processing

The study of two-digit numbers processing has recently gathered a growing interest. Here, we examine whether differences at encoding of two-digit oral verbal numerals induce differences in the type of processing involved. Twenty-four participants were submitted to a comparison task to 55. Differences at encoding were introduced by the use of dichotic listening and synchronous (synchronous condition) or asynchronous presentation (tens-first and units-first conditions) of the two-digit numerals' components. Our results showed that differences at the encoding stage of two-digit numerals involve: (1) different comparison processes (tens-first and units-first conditions: parallel comparison; synchronous condition: parallel and holistic comparison); and (2) differences in the weight of the tens- and units-effects. Therefore, attentional mechanisms determining at the encoding stage how much attention is paid to the two-digit numerals' components might account for the different types of processing found with two-digit numbers.