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.

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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.     

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.     

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.     

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.     

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.     

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.     

Levels of Reality

Philosophers and non‐philosophers have been attracted to the idea that the world incorporates levels of being: higher‐level items – ordinary objects, artifacts, human beings – depend on, but are not in any sense reducible to, items at lower levels. I argue that the motivation for levels stems from an implicit acceptance of a Picture Theory of language according to which we can ‘read off’ features of the world from ways we describe the world. Abandonment of the Picture Theory opens the way to a ‘no levels’ conception of reality, a conception that honors anti‐reductionist sentiments and preserves the status of the special sciences without the ontological baggage.     

Reality as Trauma

Trauma is usually understood as reaction to an exceptional disorganizing event. Instead, it can be recognized as the underlying fabric of everyday experience, entailing reality’s fundamental unpredictability, constant change, and the inevitable erosions wrought by sickness, aging, and death. This paper draws on Ferenczi’s psychoanalytic thinking to develop this view of reality as trauma, and to suggest a shift in interpersonal self-regard as central to psychoanalytic change.