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31.
Benjamin R. George 《Studia Logica》2006,84(3):425-449
The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several
known results for the case of finite characterizability are extended to infinite characterizability, and investigations of
the second-order theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about
the relationship between ordinal characterizability and ordinal arithmetic. The broader significance of cardinal characterizability
and the relationships between different notions of characterizability are also discussed.
AMS subject classification : 03B15 and 03C85
Presented by Melvin Fitting 相似文献
32.
采用数字大小判断任务,探讨正负数混合呈现对负数SNARC效应的影响。结果发现,负数单独呈现条件下,负数出现反转的SNARC效应;负数和无加号正数混合呈现,且只对负数作反应条件下,负数有反转SNARC效应;负数和有加号正数混合呈现,且只对负数作反应条件下,负数出现反转SNARC效应;负数和无加号正数混合呈现,并对正负数分别作反应的条件下,负数有反转SNARC效应出现,而正数出现SNARC效应。说明负数空间表征受其绝对值大小的影响,绝对值较小的负数(-1、-2)表征在心理数字线的左侧,绝对值较大的负数(-8、-9)表征在数字线的右侧,且不能延伸至心理数字线左侧。 相似文献
33.
We report a study that examines whether the presentation of irrelevant, ordinal information at central fixation interacts with the allocation of attention beyond fixation. Previous research has demonstrated that number perception influences the allocation of spatial attention, such that the presentation of a spatially nonpredictive number at fixation results in attention being allocated to the left when the central number is low (e.g., 1), and attention being allocated to the right when the central number is high (e.g., 9). Here, we examine whether this attentional SNARC effect (spatial numerical association of response codes) generalizes to other ordinal sequences: letters, days, and months. Though we replicate the attentional SNARC we find that this effect is number-specific, unless participants are required to process the cue in an order-relevant fashion. This discovery of number-specificity has important implications both for the functional separation between SNARC and attention-SNARC effects, as well as lending support to recent theories regarding the specificity of a shared neural architecture between numbers and visuospatial attention. 相似文献
34.
通过设置垂直维度上不同的情境,本研究采用“奇偶判断任务”探讨了情境对序数空间表征的影响。结果发现,只有序数的情况下,被试对小数的上键反应或下键反应、对大数的上键反应或下键反应都没有显著差异;在楼层情境下,被试对小数的下键反应更快,对大数的上键反应更快;在家谱情境下,被试对小数的上键反应更快,对大数的下键反应更快。以上结果表明,垂直维度上序数的空间表征受到情境的影响,这说明在垂直维度上数字的空间表征具有动态性,且受到具体和情境的调节。 相似文献
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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. 相似文献
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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。 相似文献
40.
《Quarterly journal of experimental psychology (2006)》2013,66(3):444-458
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. 相似文献