Pure Land Buddhism ascribes to Amida some of the roles ascribed to God by Whitehead. The failure of Whiteheadians to clarify how God can play these roles also leaves doubtful the claim of Pure Land Buddhism. On the other hand, Whitehead’s emphasis on perpetual perishing reinforces the original Buddhist teaching of impermanence and together they provide the basic insight for authentic life.
We associate with any game G another game, which is a variant of it, and which we call . Winning strategies for have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over , and vice versa. Through we can express in algorithmic form, as a recursive winning strategy, many common proofs of non-constructive Mathematics, namely exactly the theorems of the (...) sub-classical logic Limit Computable Mathematics , Hayashi and Nakata ). (shrink)
This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle and positive responsiveness (...) are equivalent. By applying these results, we obtain a new characterization of the method of majority decision. (shrink)
The Trends in International Mathematics and Science Study found that even though children from all East Asian countries outperformed American children, American students reported higher self-evaluation of their math and science abilities than did students from East Asian countries such as China, Korea, and Japan (Mullis, Martin, Gonzalez, & Chrostowski, 2004). Such cross-cultural differences in self-appraisal ﬁt the stereotype of the modest East Asian and contribute to the received view that East Asians have less positive self-concepts than Americans. This view (...) was summarized recently by Heine, Lehman, Markus, and Kitayama (1999) as follows: ‘‘The need for positive self-regard, as it is currently conceptualized, is not a universal, but rather is rooted in significant aspects of North American culture’’ (p. 766; but cf. Sedikides, Gaertner, & Vevea. (shrink)
This paper aims to reexamine the axiom of the independence of irrelevant alternatives in the theory of social choice. A generalized notion of independence is introduced to clarify an informational requirement of binary independence which is usually imposed in the Arrovian framework. We characterize the implication of binary independence.
In [Ono 1987] H. Ono put the question about axiomatizing the intermediate predicate logicLFin characterized by the class of all finite Kripke frames. It was established in [ Skvortsov 1988] thatLFin is not recursively axiomatizable. One can easily show that for any finite posetM, the predicate logic characterized byM is recursively axiomatizable, and its axiomatization can be constructed effectively fromM. Namely, the set of formulas belonging to this logic is recursively enumerable, since it is embeddable in the two-sorted classical predicate (...) calculusCPC 2. Thus the logicLFin is II 2 0 -arithmetical.Here we give a more explicit II 2 0 -description ofLFin: it is presented as the intersection of a denumerable sequence of finitely axiomatizable Kripke-complete logics. Namely, we give an axiomatization of the logicLB n P m + characterized by the class of all posets of the finite height m and the finite branching n. A finite axiomatization of the predicate logicLP m + characterized by the class of all posets of the height m is known from [Yokota 1989]. We prove thatLB n P m + =,B n being the propositional axiom of the branching n. (shrink)
This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.
A syntactically optional constituent in a sentence can be deleted if it is recoverable from the preceding context. This does not mean, however, that all such constituents are deletable. This paper hypothesizes that there is a pecking order of deletion, which dictates that deletion should proceed from less important to more important information. Evidence is drawn from English, Russian and Japanese in support of this hypothesis. Interaction of this constraint with various syntactic rules in each individual language is examined, and (...) it it hypothesized that unacceptability does not result when the above peeking order of deletion principle is violated due to the structural pressure of the language. Further discourse deletion data from Russian and Japanese are introduced, and principles that control them are formulated and justified. (shrink)