论“后天八卦”中的数理内涵──兼论《禹贡》和《太玄》对称三进制

"先天八卦"中具有数理内涵,同样,"后天八卦"中亦具有数理内涵。前者呈二进制形态,后者则为三进制形态。《系辞》曰:"太极生两仪,两仪生四象,四象生八卦。"其实,四象生八卦有两种不同的逻辑法则,这两种不同的逻辑法则导致二进制八卦与三进制八卦。而且"后天八卦"与五行具有内在的关联,因此,"后天八卦"中的数理内涵比"先天八卦"中的数理内涵更显丰富。     

逻辑基础问题(中)

运用本文第一部分新建立起来的方法论,我在本文第二部分为逻辑构造了一个基础。我的出发点是逻辑在人类知识中所执行的任务。为了完成这一任务,逻辑必须满足强大的正确性要求,由此,它必须既建基于人类心灵之中也建基于世界之中。但是逻辑又不能建基于世界的任何事物之中;它必须建基于世界的某一方面,这个方面强大到足以支撑关于逻辑后承(逻辑地从什么得出什么)的断言。我对这个问题的解决办法是把逻辑建基于一种特别强的法则类型即"形式"法则之中。我证明,由于这些法则的特别强大的"不变性"程度这个特征,它们足够强大到为逻辑提供基础,然后我解释了逻辑是如何建基于这样的法则之中的。这个基础包含着形式性的一个标准以及基于这个标准而为逻辑常项提出的一个标准——逻辑常项是逻辑真和逻辑后承的"引擎"。     

完备的八卦演绎系统简论

先天八卦次序图中的横向爻符结构与数学上Rademacher函数具有一一对应的关系。已经证明,Rademacher函数系是不完备的标准直交系,而仅是Walsh函数系的一个真子集,后者才是完备标准直交系。换言之,先天八卦次序图是不完备的。如何建立一个数学上完备的八卦演绎系统,是本文所要尝试去解决的。借助于八卦完成的组合设计中的SBIBD（7,4,2）设计,促成了对一个完备的八卦系统的构造设计。     

先天《易》范式预测与决策方法探究——以金融投资为例

本文借用先天<易>特别是"先天六十四卦方圆图"的符号体系,并通过对其六爻内涵与排列顺序作出新的定义,采用演绎逻辑方法和辨证逻辑方法,揭示了周期性变化是事物发展的结构特征."爻"的性质(阴或阳),根据"笛卡尔坐标周期分析法"--单因素周期分析法,由模糊数学之"隶属度"决定.综合分析所得"卦象"及其在"六十四卦方圆图"中之位置,是预测和决策的理论依据.以金融投资为例,展示了先天<易>范式预测与决策方法之可操作性.     

重构道德法则的先验演绎——对康德伦理学两次演绎的考察

在《道德形而上学的奠基》与《实践理性批判》中,康德伦理学有两次不同的先验演绎。在《道德形而上学的奠基》,这一先验演绎是康德论证"一项定言命令式如何可能"的关键环节。而在《实践理性批判》,康德否定了先验演绎的必要性与可能性,并将其归咎于我们无法对自由理念作出理论阐明。然而,作为道德法则的先验演绎的替代方案,《实践理性批判》的"理性事实"并不令人信服。本文将考察两版演绎问题,进一步重构一个新的先验演绎,它将以《道德形而上学的奠基》的演绎为基础,通过"目的王国"概念联结道德法则与理性存在者;《实践理性批判》的"敬重情感"可以为这一新的演绎提供情感意义上的动机。这将形成一个《道德形而上学的奠基》与《实践理性批判》互补的解释,目的是通过构建新的道德法则的先验演绎,尝试阐明康德的道德法则如何可以运用于现实的人。     

"象思维"视野下的"易道"

"易道"的根本在于,观物取象,并进而在象的流动与转化中洞察出卦象,由卦象以尽意."象思维"的本质在于"非实体性",而这种非实体性使<周易>的象思维具有"原发创生"性,并且表现出与西方实体性的概念思维本质不同.从原发创生的视角观之,历史上和今天关于卦爻之象数与卦爻辞哪个根本的问题,可以归结为原发创生的"筑象"过程."原发创生",就是无极而太极之生,是"无中生有"和"有中见无"之生.     

论汉宋易学太极说与茶山太极体系的建构

茶山从易学文本出发,通过反思、批评以前易学家的观点与思想,详细地论述了太极演化与《周易》卦象符号(消息卦与衍卦)及大衍筮法的关系,提出太极是"阴阳之胚胎万物之初""《周易》推移之法全俟太极造化""揲蓍之法,必又象之"十二消息卦推移的观点。从自然界的太极演化,推演出八卦、消息推移、从消息推移推演出揲蓍之法,阐明了《周易》卦象符号与大衍筮法的客观依据,建构了以太极为核心的易学哲学逻辑体系。其价值表现在理性批判精神、创新的观点和易学逻辑体系建构。虽然其许多论证不乏牵强,结论也未必完全符合易学文本,然而,茶山太极观,以其理性的批判精神、独特的易学见解和较为严密的易学体系,丝毫不逊色于中国同时期的易学家,不失为东亚易学史上的璀璨明珠。     

"预测大师"为什么不去预测彩票

著名的预测大师S先生说:“《周易》是我国的预测学、信息科学的起源和基础。《周易》中阴阳八卦符号和六十四卦的卦象、爻象,不仅是宇宙间万物万事的密码标志,而且是一个储存量很大的信息库。可以说,是一部既简单又无形的万能预测器。” “八卦具有独特种奇的超前预测、超前反映的功能。它既能上测天下测地,又能中测人事;     

定律的逻辑概率一定为0吗?

波普尔曾论证"定律的逻辑概率为0"这一论题,以反对基于贝叶斯定理的归纳逻辑。他对该论题的证明本质上有三个:(a)独立性论证;(b)反杰弗里斯论证;(c)维度论证。本文将论证他的这三个论证均不成立。(a)论证的错误在于假定Uij的独立性;(b)论证错误地使用了古德曼类似物;(c)论证中则断定了与概率演算不一致的命题。总的来看,他的错误或许来自于对逻辑和认识论逻辑的混淆。     

《周易》卦爻起源新解

《周易》八卦与卦爻是怎样产生的?各家之说均未能就八卦与之所象征的事物之间的内在联系和表述性意义作出逻辑关系缜密的合理解释。其实,阴阳概念的产生与阳光的向背有关。中国古人受太阳光线的启发,创造出了卦爻符号。代表太阳光线的符号为"—",代表没有太阳光线的符号为"--"。由三个卦爻组成的八卦卦象与所代表的事物之间存在着生动形象的内在联系。阳爻符号"—"是一条线,是奇数,阴爻符号"--"是两条短线,是偶数,这或许就是奇数为阳、偶数为阴这一说法的最原始起源。     

The Eight Trigrams of the Chinese I Ching and the Eight Primary Emotions

Durkheim and Mauss, in Primitive Classification , concluded that the emotions play a causal role in the history of dual symbolic classification systems, but could not test this intuitive speculation because they saw a classification of the emotions as impossible. In this paper a portion of Plutchik's psychoevolutionary model of the primary emotions are assumed to be valid and are then investigated through analysis of one of their three case studies of primitive classification, that of classification in ancient China, where their emphasis was on the eight "trigrams" or "powers" that they saw arranged in a "divinatory compass." The trigrams are three-line components of the "hexagrams," the six-line figures that are interpreted as master signs in I Ching divination rituals. Using Plutchik's psychoevolutionary classification of the emotions as a basis of comparison, especially his model of the primary emotions as adaptive reactions to the positive and negative experiences of four existential problems – identity, temporality/reproduction, hierarchy, and territoriality – it is found that both trigrams and primary emotions exist as four pairs of opposites. The eight trigrams and eight primary emotions similarly can be seen as adaptive reactions to the four basic problems of life. Through structural analysis, correspondences between the trigrams and the primary emotions are developed, the result being that the primary emotions are structurally isomorphic and very close in first meanings to the primary attributes of the trigrams. Implications of this isomorphism of structure for the development of a social psychology of the emotions are discussed.     

Squares in Fork Arrow Logic

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares.     

《易纬》八卦卦气思想初探

<易纬>的<乾凿度>和<通卦验>分别记载了两种八卦卦气思想,虽然都是关于八卦于一年中用事的学说,但二者在具体内容、卦序、所属易学流派等方面有所不同.本文即对这些方面作了初步探索.     

论文王卦位的形成及其与《易经》的关系

文王卦位是以中国原有的时空观念为基础,适应占筮需要形成的.最迟在西周之时,先后形成了四时与四方相配的时空统一观念,以及五行顺次相生观念.文王卦位的安排,首先是将四时与四方相配延展为八个时段与八方一一相配,然后据八卦的卦象、卦德排定其时位与方位,理解时位是理解卦位的关键.在卦位的安排中,很可能已考虑到五行的循环相生.这种卦位说形成于古经<周易>成书前,<易经>在观象系辞中利用了这种卦位说.     

On Fork Arrow Logic and its Expressive Power

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order correspondence language, so both can express the same input–output behavior of processes.     

Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤ω

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers p, p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (Kremer, 1997). It is shown that if the Kripke structures are restricted to trees of at height and width at most , the resulting logics are decidable. This provides a partial answer to a question by Kremer. The result also transfers to modal S4 and some Gödel–Dummett logics with quantifiers over propositions.     

Dynamic Topological Completeness for

Dynamic topological logic (DTL) combines topological and temporalmodalities to express asymptotic properties of dynamic systemson topological spaces. A dynamic topological model is a tripleX ,f , V , where X is a topological space, f : X X a continuousfunction and V a truth valuation assigning subsets of X to propositionalvariables. Valid formulas are those that are true in every model,independently of X or f. A natural problem that arises is toidentify the logics obtained on familiar spaces, such as . It [9] it was shown that any satisfiable formulacould be satisfied in some for n large enough, but the question of how the logic varieswith n remained open. In this paper we prove that any fragment of DTL that is completefor locally finite Kripke frames is complete for . This includes DTL; it also includes some largerfragments, such as DTL₁, where "henceforth" may not appear inthe scope of a topological operator. We show that satisfiabilityof any formula of our language in a locally finite Kripke frameimplies satisfiability in by constructing continuous, open maps from the plane intoarbitrary locally finite Kripke frames, which give us a typeof bisimulation. We also show that the results cannot be extendedto arbitrary formulas of DTL by exhibiting a formula which isvalid in but not in arbitrarytopological spaces.     

《周易》对《林兰香》叙事艺术的影响

《林兰香》是一部优秀的世情小说,它的叙事艺术有独特的风格,它模仿《易经》,采用了以“数”谋篇布局的叙事方法．《林兰香》八卷六十四回,六十四是《易经》卦数之总．《林兰香》叙事以八回作为一个单元,每八回有一个相对完整的故事或主题．这个故事或主题又往往孕育着与之不合谐乃至对立的因素．《林兰香》“倚数”结撰,其谋篇布局之法,体现了作者对人生命运的思考,在艺术上则形成了“循环往复”之美．