Conceptual engineering for mathematical concepts

In this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory.     

Not quite neo-sentimentalism

The view that some evaluative concepts are identical to some affective concepts naturally falls out of neo-sentimentalism, but it is unstable. This paper argues for a view of evaluative concepts that is neo-sentimentalist in spirit but which eschews the identity claim. If we adopt a Peacockean view of concepts, then we should think of some evaluative concepts as having possession conditions that are affective in some way. I argue that the best version of this thought claims that possessing those concepts requires being rationally compelled to form evaluative beliefs in response to certain emotions.     

Attributes of God: Conceptual Foundations of a Foundational Belief

Anthropomorphism, or the attribution of human properties to nonhuman entities, is often posited as an explanation for the origin and nature of God concepts, but it remains unclear which human properties we tend to attribute to God and under what conditions. In three studies, participants decided whether two types of human properties—psychological (mind‐dependent) properties and physiological (body‐dependent) properties—could or could not be attributed to God. In Study 1 (n = 1,525), participants made significantly more psychological attributions than physiological attributions, and the frequency of those attributions was correlated both with participants’ religiosity and with their attribution of abstract, theological properties. In Study 2 (n = 99) and Study 3 (n = 138), participants not only showed the same preference for psychological properties but were also significantly faster, more consistent, and more confident when attributing psychological properties to God than when attributing physiological properties. And when denying properties to God, they showed the reverse pattern—that is, they were slower, less consistent, and less confident when denying psychological properties than when denying physiological properties. These patterns were observed both in a predominantly Christian population (Study 2) and a predominantly Hindu population (Study 3). Overall, we argue that God is conceptualized not as a person in general but as an agent in particular, attributed a mind by default but attributed a body only upon further consideration.     

Cultural conceptions of a bereavement-related illness in a South African indigenous community

This study explored cultural conceptions of a bereavement-related illness among elderly (aged 34–85yrs) Northern Sotho-speaking people in Limpopo province. The participants (n = 14, females = 50%, mean age = 59 years, SD: 13.7 years) were purposively selected and interviewed using in-depth interviews. Data were analysed using Hycner’s adapted phenomenological method. Three themes emerged from the analysis: debilitating and life-threatening symptoms of the illness; aetiology explained by ritual taboo violations; and management of the illness through ritual cleansing. The cleansing process incorporates the administration of traditional herbs. The findings suggest bereavement-related illness in an African cultural community to be explained by their cultural concept of distress understandings.     

Auditory spatial concepts in blind football experts

ObjectivesWe compared the spatial concepts given to sounds' directions by blind football players with both blind non-athletes and sighted individuals.MethodParticipants verbally described the directions of sounds around them by using predefined spatial concept labels, under two blocked conditions: 1) facing front, 2) pointing with the hand towards the stimulus.ResultsBlind football players categorized the directions more precisely (i.e., they used simple labels for describing the cardinal directions and combined labels for the intermediate ones) than the other groups, and their categorization was less sensitive to the response conditions than blind non-athletes. Sighted participants' categorization was similar to previous studies, in which the front and back regions were generally more precisely described than the sides, where simple labels were often used for describing directions around the absolute left and right.ConclusionsThe differences in conceptual categorization of sound directions are a) in sighted individuals, influenced by the representation of the visual space b) in blind individuals, influenced by the level of expertise in action and locomotion based on non-visual information, which can be increased by auditive stimulation provided by blind football training.     

3~5岁幼儿权力概念多重隐喻的认知发展

为考察3~5岁幼儿“权力”概念的大小、垂直空间和重量多重隐喻的认知发展进程, 研究采用了将权力人物和无权力人物图片放置大圆形或小圆形、垂直空间的上方框或下方框和不平衡跷跷板重端或轻端的图片迫选任务。通过3个实验及综合分析发现：3岁幼儿尚不具备权力隐喻理解能力; 4岁是幼儿权力隐喻理解能力的重要发展时期, 具备正极权力概念的隐喻理解能力, 建立起有权力为“大、高、重”的多重隐喻联结; 5岁幼儿的权力隐喻理解能力进一步增强, 已具备较完整的多重隐喻理解能力, 建立起有权力为“大、高、重”、无权力为“小、下、轻”的多重隐喻联结。3~5岁幼儿“权力”概念的大小、垂直空间和重量多重隐喻理解能力同步发展, 不受隐喻靶域习得时间早晚的影响。系列研究表明, 学龄前幼儿的权力隐喻理解能力发展趋势符合隐喻一致性理论, 隐喻表征的产生并非“有或无”的模式, 而是“渐进”呈现发展。     

On the Question, “What is Law?”

Res Publica - Re-framing discussion of the question, “What is law?“ in terms of the contexts in which the whole question makes sense allows us to see that jurisprudence is about...     

Choosing among natural stimuli

Pigeons worked on concurrent variable-interval, variable-interval schedules with the alternatives signaled by slides either containing trees or not. The schedules were designed to hold both overall and relative rates of reinforcement within narrowly constrained limits, and slides were quasi-randomly ordered each day. Responding to the two alternatives was well described by the generalized matching equation with substantial undermatching. Using an adaptation of the matching law, we estimated that the subjects were correctly classifying 82% to 95% of exemplars. The matching performance transferred to new exemplars of trees and nontrees with only slight generalization decrement. The pigeons appeared to be discriminating among exemplars even when the alternatives provided equal rates of reinforcement and the average relative performances were close to 50%.     

Concept learning by monkeys with video picture images and a touch screen.

Two rhesus monkeys were trained in a same/different task to discriminate digitized computer-stored picture stimuli. The pictures were digitized from 35-mm slides and presented in pairs on a computer monitor. The monkeys were required to touch the pictures and then make a choice response to indicate whether the pictures were identical or nonidentical. The response areas and stimuli were located to the sides of the picture stimuli. Responses were defined and monitored by an infrared matrix touch screen. After learning the same/different task, both monkeys showed performance accuracy with novel picture stimuli similar to that with training picture stimuli. This accurate novel-picture transfer indicates that a same/different concept had been learned, a concept similar to the one they had previously demonstrated in a different apparatus with rear-projected slide stimuli and a response lever.     

Adult's failures on euclidean and projective spatial tasks: Implications for characterizing spatial cognition

In their initial study of the development of children's spatial concepts, Piaget and Inhelder (1956) designed the “water-level” and “plumb-line” tasks to assess children's Euclidean abilities to perceive and represent horizontals and verticals. Surprisingly, subsequent research has shown that many adults perform badly on these tasks designed for children. Here we studied whether adults (N=160) would also have difficulty on a shadow projection task developed to assess theoretically related projective spatial concepts. The data showed that some adults had difficulty on the shadow task, whether tested by a drawing or by a selection task, and whether scored with respect to qualitative shape or metric accuracy. Performance was significantly worse on complex than simple forms, and when sex differences emerged, they favored males. As hypothesized, the best predictor of shadow performance was performance on the Euclidean tasks. Scores on the Embedded Figures Test and participant sex accounted for small (but significant) additional variance on shadow performance. Implications for theories of spatial development and for modeling individual differences in spatial cognition are discussed.