Xiong Shili on the Nature,the Mind and the Origin of Badness as Evidenced in Ming Xin Pian 明心篇 (Explaining the Mind )

The question of the origin of badness is a core problematic in New Confucian philosopher Xiong Shili’s 熊十力 (1885–1968) Ming Xin Pian明心篇 (Explaining the Mind; 1959), a work representative of his thought towards the end of his life. In this essay, I examine how Xiong uses the concepts of the nature (xing 性) and the mind (xin 心) to explain the origin of moral badness. Xiong asserts that the Buddhists never concerned themselves with the problem of the origin of ignorance and delusion, afflictions that in turn lead to suffering and wrongdoing. Xiong sets out to redress what he claims the Buddhists had failed to do. I argue that the conceptual structure of both Xiong Shili’s and Zhu Xi’s 朱熹 (1130–1200) theoretical approaches to this problem are isomorphic. The isomorphism is significant because it suggests that Xiong consciously drew on Zhu Xi and/or the Buddhist models that Zhu in turn drew on. I provide evidence to show that even as late as 1959, and despite his increasingly entrenched criticisms of Buddhism, Xiong continued to draw on key concepts and models drawn from Buddhist philosophy of mind.     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

On Modal Logics of Partial Recursive Functions

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established. Presented by Melvin Fitting     

Lambda Calculus and Intuitionistic Linear Logic

The introduction of Linear Logic extends the Curry-Howard Isomorphism to intensional aspects of the typed functional programming. In particular, every formula of Linear Logic tells whether the term it is a type for, can be either erased/duplicated or not, during a computation. So, Linear Logic can be seen as a model of a computational environment with an explicit control about the management of resources.This paper introduces a typed functional language ! and a categorical model for it.The terms of ! encode a version of natural deduction for Intuitionistic Linear Logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. Correspondingly, the terms of ! are built out of two disjoint sets of variables. Moreover, the -abstractions of ! bind variables and patterns. The use of two different kinds of variables and the patterns allow a very compact definition of the one-step operational semantics of !, unlike all other extensions of Curry-Howard Isomorphism to Intuitionistic Linear Logic. The language ! is Church-Rosser and enjoys both Strong Normalizability and Subject Reduction.The categorical model induces operational equivalences like, for example, a set of extensional equivalences.The paper presents also an untyped version of ! and a type assignment for it, using formulas of Linear Logic as types. The type assignment inherits from ! all the good computational properties and enjoys also the Principal-Type Property.     

Are Line Lengths Critical to the Discrimination of Axisymmetric Pairs of Figures from Disoriented Identical Pairs?

I examined whether the lack of a difference in line lengths made the discrimination of axisymmetric (Ax) pairs of figures from disoriented identical (Idr) pairs difficult. Three basic pair types were prepared: Idr, Ax, and nonidentical/nonaxisymmetric (Nd) pairs. To avoid confusion arising from structural differences, all pairs of figures were set to be mutually isomorphic. Two figures of a pair were controlled to have the same line lengths of respective figural components (Experiment 1) or the same lengths of individual line segments (Experiment 2) in experiments where participants decided if the figures were the same/different. Experiment 1 showed longer latencies for Ax pairs than for Nd pairs, indicating that these feature values alone did not cause difficulty in discrimination. Experiment 2 showed that only Nd pairs with all line segments having the same lengths for the two figures had the same latencies as Ax pairs. The sameness of individual line segments in simple pairs of figures made discrimination difficult.     

Li Zehou and Moritz Schlick on the Roots of Beauty

Beginning from the Enlightenment view that beauty or art is ＂useless,＂ the attempts to explain how aesthetic experience and judgment are possible presented by Moritz Schlick and Li Zehou are examined, compared and contrasted. The paper treats three main subjects, the anthropological origins of beauty, the origins of aesthetic judgments and the problem of the purpose or function of beauty or aesthetic experience. In the first--the historical-causal roots of beauty--the problem discussed is how to account for aesthetics in light of the practical needs and pursuits of human beings. For Schlick, the problem is couched in terms of how aesthetic experience can be made consistent with natural selection. The second main subject-the philosophical roots of beauty-is a discussion of the origin in the sense of justification of aesthetic judgments. And the third examines the problem of assigning some purpose to aesthetic feelings and attitudes. An apparent contrast is made, and perhaps resolved, between the respective views of Schlick and Li.     

Narrow Structuralism: Paving a Middle Path Between Cummins and Millikan

Millikan [2000] has levelled a number of persuasive criticisms against Cummins's [1996] theory of mental representation. In this paper, I pave a middle path in the debate between Cummins [2000] and Millikan [2000] to answer two questions. (1) How are representations applied to targets? (2) How is the content of a representation determined? The result is a new theory of mental representation, which I call narrow structuralism.