Response to Stuart Kurtz and Ann Pederson

I respond herein to reviews of my recent book by Ann Pederson and Stuart Kurtz. With respect to Pederson's concerns, a constructive theology formulated from the ideas of communication theory need not necessarily neglect pressing historical issues of the poor and powerless. The potential for such relevance remains strong. This is true as well for the application of the system to particular myths and rituals. Also, while I speak positively of computers as instruments of disclosure and the theories upon with they are based as resources for theological construction, this should not be construed as an endorsement of just any application of information technology in a world that tends to distort all good things. With respect to Kurtz's concerns, while thermodynamics plays a role in discussions of the primordial chaos, notions from communication theory are far more central. Also, the use of the language of the theory for theology does not necessarily require theological relevance for all of Claude Shannon's technical conclusions. My uses of infinity are taken from traditional theology and analytic geometry rather than from pure mathematics, although fruitful development along those lines is entirely possible. Pederson and Kurtz are generous with both their praise and concerns. The praise will encourage me to further this project along lines provided by the concerns.     

Finitism,Divisibilty, and the Beginning of the Universe: Replies to Loke and Dumsday

Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.     

Finitism and Divisibility: A Reply to Puryear

Puryear (AJP, 2014) develops an objection against a prominent attempt to show that the universe must have a temporal beginning. Here I formulate a reply.     

Descartes and More on the infinity of the world

ABSTRACT

In this paper, I address the controversy between Henry More and René Descartes on the indefinite extension of the world. I provide a new reading of Descartes’ famous final answer of 15 April 1649. I read the entire debate in the terms of a disagreement concerning the epistemological status of the necessity of our judgement about the extension of the universe. Accordingly, the disagreement on the infinity of the world constitutes a case of a more general disagreement on the nature of the necessity of the theorems of Cartesian Physics. In particular, as concerns Descartes’ last reply, I argue that his assertion that a finite world is contradictory should be interpreted as a reply to More’s claim that the thesis of the infinity of the world, in so far as it cannot be grounded on the identity between matter and extension, does not express a logical necessity. Descartes’ assertion of the logical impossibility of a finite world, far from being, as it has always been read, a concession he made under the pressure of More’s objections, expresses the more radical element of the entire debate about the extension of the universe.     

老子之道的虚空特征与本体性之新探

"道"是老子哲学体系中的核心。"道"以"虚空"或"无"的形态存在,"虚空"或"无"是物质的潜在状态。"道"是混成之物,所以"道"是具有精妙的内部结构特性的,它是人类尚未完全认识的物质存在的高级形态。宇宙万物是"道"创生与演化的结果,而且在演化的过程中,"道"的作用是"无为而无不为"的。在研究宇宙的本体(或本源)问题上,没有其它的概念可以替代它、超越它。"道"是具有至上性的。     

Are there True Contradictions? A Critical Discussion of Graham Priest's, Beyond the limits of thought

The present article critically examines three aspects of Graham Priest's dialetheic analysis of very important kinds of limitations (the limit of what can be expressed, described, conceived, known, or the limit of some operation or other). First, it is shown that Priest's considerations focusing on Hegel's account of the infinite cannot be sustained, mainly because Priest seems to rely on a too restrictive notion of object. Second, we discuss Priest's treatment of the paradoxes in Cantorian set-theory. It is shown that Priest does not address the issue in full generality; rather, he relies on a reading of Cantor which implicitly attributes a very strong principle concerning quantification over arbitrary domains to Cantor. Third, the main piece of Priest's work, the so-called “inclosure schema”, is investigated. This schema is supposed to formalize the core of many well-known paradoxes. We claim, however, that formally the schema is not sound. This revised version was published online in August 2006 with corrections to the Cover Date.     

人是怎样与世界统一的——一个关于细胞信息跨膜传递特异性的假说

本文在讨论有限和无限的对立统一规律在抗原和抗体产生机制中的体现的基础上,提出关于细胞信息跨膜传递特异性机制的假说：第一信使可能由有限的基本单位构成,其信息的特异性可能通过有限的信息中介的组合来得以体现,效应部位也可能因具有特定的信息中介结合位点的组合而产生特异的细胞效应。本文最后为这一假说的证实提出展望。     

A dialogue on Zeno's paradox of Achilles and the tortoise

The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible divisibility.     

Book Reviews

Books reviewed:
John Lachs, In Love with Life: Reflections on the Joy of Living and Why We Hate To Die
Lou Marinoff, Plato not Prozac: Applying Philosophy to Everyday Problems
Victoria Davion and Clark Wolf (eds), The Idea of a Political Liberalism: Essays on Rawls     

What is “the ineffable” exactly?

“The ineffable” in Wittgenstein’s Tractatus Logico-Philosophicus is an essential term that has various interpretations. It could be divided into two types, namely, positive and negative, or real and fake. The negative or fake type can be clarified by logical analysis, while the positive or real type can be understood only through philosophical critique. Both the positive and negative types consist of infinity or absoluteness, but the infinity is subject to distinctions in meaning and logic. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2005, (8): 64–68