Is the History of our Universe Finite?

Modern cosmology indicates that our universe has a finite age. However, it is not understood whether the initial state before the Big Bang is finite in history or not. In this article, I show by simple arguments that the initial state must be finite in history if it is real. If the initial state is not real, a special transition is needed to specify the beginning of the real time. Moreover, if our universe is just one of the many universes, it can be shown that the history of the universe generator must also be finite.     

Validation of a reflective practice rubric for evaluating the complexity of teacher candidate digital and written reflections

This study was conducted to validate the effectiveness of a previously published rubric for evaluating the reflective characteristics contained within reflective artifacts. The goal of the study was to test the validity of the rubric when evaluating written reflection and digital artifacts of teacher candidates. The theory of reflection is discussed, and the process of eliciting higher levels of reflection through various modalities from written prompts. Secondly, this study describes the process participants followed while learning to use the rubric, the methods of evaluating artifacts using the rubric, and the results the study produced. The rubric proved to be an effective tool when determining the level of reflection, a teacher candidate demonstrated. Lastly, this article discusses limitations of the rubric, as well as suggestions for further research regarding teaching reflective practices, and how to refine one’s own reflective skills to achieve a level of deep reflection on/for action.     

An analysis of autobiographical tools in written reflection: implications for teaching critical thinking and goal-setting

This paper analyzes the results of an 18 month study of a variety of participants involved in written reflection on their learning, both in classes at two universities in the Southern US or in voluntary focus groups. The purpose of the study was to analyze the effects of including autobiographical tools in written reflection. Participants used three tools from the genre of autobiography as they reflected on their learning inside either course content, internship experiences, experiential learning, or goal-setting. Over 500 samples were gathered, offering a large data set for analysis of what kinds of best practice produce quality reflective writing. Through analysis of the data and student surveys and interviews, results show increased attention to critical thinking and metacognition; expressed flexibility, adaptability, and ability to handle ambiguity; and value in connection to others/empathy-building as a result of incorporating autobiographical tools in reflective prompts. The study indicated that reflections using the same autobiographical tool over the course of several sessions seemed to produce deeper levels of reflection and more engagement with the autobiographical tool. Of the three autobiographical tools used in the study, the tool that seemed most helpful to participants was reflection as storytelling that revealed aspects of the self.     

Outwitting the rational mind: How effortful thinking influences price cognition

Prior research presents mixed findings on how people's degrees of effortful thinking influence their reliance on heuristics and biases. Although the tenets of dual process theory would argue that effortful thinking should attenuate people's reliance on heuristics, a number of contemporary findings suggest otherwise: Effortful thinking may, in fact, enhance biased processing of information in certain instances. This research shows how, in the context of pricing, people's degrees of effortful thinking can amplify their inclination towards biased processing of price information. In five studies (n = 1,339), we find that effortful thinking induces a greater preference for nine‐ending (vs. zero‐ending) prices, and the effect is mainly driven by people's greater propensity for argument‐based decision making. Such predilection to nine‐endings attenuates with lower cognitive effort in processing price information. Moreover, when locus of deliberation shifts from price to quality, consumers' preference for nine‐ending priced options is subdued.     

The Burden of Proof and Its Role in Argumentation

The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the latter case, it is not necessarily important whether that degree of belief exceeds a particular threshold (e.g., ‘reasonable doubt’). We explore the consequences of this distinction for the role that the “burden of proof” has played in argumentation and in theories of fallacy.     

Closed systems,explanations, and the cosmological argument

Examples involving infinite suspended chains or infinite trains are sometimes used to defend perceived weaknesses in traditional cosmological arguments. In this article, we distinguish two versions of the cosmological argument, suggest that such examples can only be relevant if it is one specific type of cosmological argument that is being considered, and then criticize the use of such examples in this particular type of cosmological argument. Our criticism revolves around a discussion of what it means to call a system closed, and what it means to call an explanation complete. Our analysis makes no suppositions about the nature of the infinite, and is therefore independent of many of the issues around which contemporary discussions of the cosmological argument have tended to revolve.     

Weighing evils: the C. S. Lewis approach

It is often argued that the great quantity of evil in our world makes God’s existence less likely than a lesser quantity would, and this, presumably, because the probability that some evils are gratuitous increases as the overall quantity of evil increases. Often, an additive approach to quantifying evil is employed in such arguments. In this paper, we examine C. S. Lewis’ objection to the additive approach, arguing that although he is correct to reject this approach, there is a sense in which he underestimates the quantity of pain. However, the quantity of pain in that sense does not significantly increase the probability that some pain is gratuitous. Therefore, the quantitative argument likely fails.     

More than One Flaw: Reply to Millican

Millican (Mind 113(451):437–476, 2004) claims to have detected ‘the one fatal flaw in Anselm’s ontological argument.’ I argue that there is more than one important flaw in the position defended in Millican (Mind 113(451):437–476, 2004). First, Millican’s reconstruction of Anselm’s argument does serious violence to the original text. Second, Millican’s generalised objection fails to diagnose any flaw in a vast range of ontological arguments. Third, there are independent reasons for thinking that Millican’s generalised objection is unpersuasive.     

What Are Degrees of Belief?

Probabilism is committed to two theses:

父母-儿童共同活动中的互动与儿童的数学学习

本研究运用结构性观察方法对两组4岁儿童与父母在四种活动中的互动进行了分析与比较。一组儿童为书面数符号测查高分者,二组儿童为书面数符号测查低分者。85对父母一儿童对子参加了4个各有15分钟的共同活动,阅读、数学题、纸和积木,并完成一个微型问卷。结果表明,在这些活动中包含了多种数学知识学习和多种以父母为主导的互动策略;两组对子之间在数学事件频次上无差异,但一组父母更多地运用了一些积极策略,二组父母更多地运用了一些消极策略;二组中有更多儿童对互动表现出消极回应和注意力问题。两个组的父母在家中与儿童一起进行诸如阅读和做数学题的共同活动的频次与质量上表现出差异。