A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking.

---

Reality Testing and Testing Reality in Group TreatmentPart I: Reality and Reality Testing

This two-part contribution addresses reality, reality testing, and testing reality—how we think about and may technically approach these concepts. Part I provides a topic overview and focuses on reality testing. Part II (in an upcoming issue) focuses on testing reality and how it promotes emergence of new or previously inhibited forms of engagement.

Reality testing and testing reality represent two fundamental, reciprocal manifestations of the drive to know and of tasks of learning: approaching problems and solving them. While testing reality involves approaching reality without necessarily looking for or coming to definition or clarity, reality testing centers on a particular theme or object. It evolves towards organization and rationality, with a goal to define and solve problems—or to avoid them.

Engaging the group and supporting individuals in these two types of approaches to learning requires a well-defined therapeutic focus on process and purpose; at times, different tactics and techniques are appropriate.     

虚拟与虚拟实在

虚拟是这个时代的热门词,也是当下文化的关键词.在三亿多的网民中,很多人见面时的问候语从吃过没有变为魔兽了吗抑或摘菜了没有,网络虚拟生活已经成为国人乃至世人一种必不可少的生活方式.二十年前美国学者迈克海姆写过一本关于虚拟实在的书,大约十年前引入国内,引发了国内学者关于虚拟实在的研究和讨论.但由于当时国内的信息技术尚未普及,网民数量稀少,所以他的书和这场讨论未能引起社会轰动并深入持久下去.如今恰逢读网时代,我们重拾虚拟实在,重新探讨它的形而上以及与虚拟的区别与联系,因为它是我们在谈及当下文化时绝不能回避和忽略的问题.     

Reality Testing and Testing Reality in Group Treatment

This two-part contribution addresses concepts of “reality,” “reality testing,” and “testing reality,” as they apply to group treatment. Part I provided topic overview and focused on reality testing. Part II focuses on testing reality and how it promotes emergence of new or previously inhibited forms of engagement.

Whereas reality testing centers on a particular theme or object, with a goal to define and solve problems, testing reality involves approaching targets of interest without necessarily looking for or coming to definition or clarity. It is wide open, spontaneous, and unbounded, and may take the individual and group into realms that are uncomfortable and even unwanted. Engaging the group and supporting individuals in these two approaches to learning requires a well-defined therapeutic focus on process and purpose; at times, different tactics and techniques are called for.     

Reality monitoring and the media

The study of reality monitoring is concerned with the factors and processes that influence the veridicality of memories and knowledge, and the reasonableness of beliefs. In thinking about the mass media and reality monitoring, there are intriguing and challenging issues at multiple levels of analysis. At the individual level, we can ask how the media influence individuals' memories, knowledge and beliefs, and what determines whether individuals are able to identify and mitigate or benefit from the media's effects. At the institutional level, we can ask about the factors that determine the veridicality of the information presented, for example, the institutional procedures and criteria used for assessing and controlling the quality of the products produced. At the inter‐institutional level we can consider the role that the media play in monitoring the products and actions of other institutions (e.g. government) and, in turn, how other institutions monitor the media. Interaction across these levels is also important, for example, how does individuals' trust in, or cynicism about, the media's institutional reality monitoring mechanisms affect how individuals process the media and, in turn, how the media engages in intra‐ and inter‐institutional reality monitoring. The media are interesting not only as an important source of individuals' cognitions and emotions, but for the key role the media play in a critical web of social/cultural reality monitoring mechanisms. Copyright © 2007 John Wiley & Sons, Ltd.     

神话·梦想·现实--神舟六号载人航天飞行的随想

当神州共庆神舟载人航天飞行圆满成功之际,当千年古老的神话变为现实之际,远古缔造飞天神话的先民、先贤,终于盼到了飞天梦想的实现。千年追梦,千年追仙,千年夙愿的道教界人士更是心潮澎湃,欢欣鼓舞。无须座谈,无须号召,一切都是自发和情不自禁地表达:神舟六号的成功,是我国经济实力、科学实力乃至综合国力日益强大的象征,是我们伟大祖国日益繁荣昌盛的标志,是中华民族巍然屹立世界民族之林的宣言。古老的华夏,五千年的民族,创造和演绎了无数美好的神话:妇幼皆知的嫦娥奔月;优美翱游天际的飞天;“御风而行”的列子;“乘云气御飞龙而游于六合…     

Temporal Language and Temporal Reality

It has recently been argued that the new B-theory of time argues invalidly from the claim that tensed sentences have tenseless truth-conditions to the conclusion that temporal reality is tenseless. But while early B-theorists may have relied on some such inference, new B-theorists do not. Giving tenseless truth-conditions for tensed sentences is not intended to prove that temporal reality is tenseless. Rather it is intended to undermine the A-theorist's move from claims about the irreducibility of tensed language to the conclusion that temporal reality must be tensed. I examine how A-theorists have used facts about language in attempting to establish their conclusions about the nature of temporal reality. I take the recent work of William Lane Craig, and argue that he moves illicitly from facts about temporal language to his conclusion that temporal reality is tensed.     

Reality and Existence in Anselm

It is a premise of a widely endorsed putative refutation of Anselm's ontological argument that 'exists' is not a predicate. This Note argues that although 'exists' has the superficial grammatical appearance of a predicate in the Proslogion , Anselm does not in fact rely on the premise that 'exists' is a logical predicate (or that existing is a property) in his putative proof. It follows that even if some argument for the conclusion that 'exists' is not a predicate is sound, that argument is not a refutation of Anselm's argument.     

Categories and Levels of Reality

The discussion of the relation of levels of reality to categories is important because categories have often been interpreted as constituting levels of reality. This article explores whether this view is correct, and argues it is not. Categories as such should not be understood to constitute levels of reality, although particular categories may. The article begins with a discussion of levels of reality and then turns to specific questions about categories and how they are related to these levels.     

Veiled Reality and Structural Realism

Abstract

The noted philosopher of science, Bernard d'Espagnat, tries to mediate between objective reality and empirical reality via the notion of veiled reality: namely, while the laws proper to things in themselves are unknown, their existence and interrelated activity can be inferred from observation and analysis of human experience. The author claims that Whiteheadian creativity offers a better candidate for the notion of veiled reality because it is a transcendent activity, not a transcendent actuality. Likewise, a revision of the Whiteheadian category of society as a structured field of activity for its constituent actual entities indirectly confirms Henri Poincaré's notion of structural realism.     

Theism and Mathematics

The author investigates the connection between God and mathematics, and argues (1) that the “unreasonable effectiveness of mathematics” makes much better sense from the perspective of theism than from that of naturalism, (2) that the accessibility (to us human beings) of advanced mathematics is much more likely given theism than given naturalism, (3) that the existence of sets, numbers, functions and the like fits in much better with theism than with naturalism, and (4) that the alleged epistemological obstacles to knowledge of mathematics offered by the abstract character of numbers, sets, etc., disappear from the point of view of theism.