Cut-Elimination and Quantification in Canonical Systems

Canonical Propositional Gentzen-type systems are systems which in addition to the standard axioms and structural rules have only pure logical rules with the sub-formula property, in which exactly one occurrence of a connective is introduced in the conclusion, and no other occurrence of any connective is mentioned anywhere else. In this paper we considerably generalize the notion of a “canonical system” to first-order languages and beyond. We extend the Propositional coherence criterion for the non-triviality of such systems to rules with unary quantifiers and show that it remains constructive. Then we provide semantics for such canonical systems using 2-valued non-deterministic matrices extended to languages with quantifiers, and prove that the following properties are equivalent for a canonical system G: (1) G admits Cut-Elimination, (2) G is coherent, and (3) G has a characteristic 2-valued non-deterministic matrix.     

Into the brain: where philosophy should go from here

The maturation of the cognitive neurosciences will throw light on many central philosophical issues. Among them: semantic theory, perception, learning, social and moral knowledge, and practical reasoning and decision making. As contemporary medicine cannot do without the achievements of modern biology, philosophy would be pitiful if it disregarded the achievements of brain research.     

KANT ON RELIGION AND SCIENCE: INDEPENDENCE OR INTEGRATION?

Abstract. Immanuel Kant's theoretical knowledge and practical knowledge tempt conclusion that natural science and religion are two independent discourses of a dualistic system. To be sure, knowledge is anchored in two kinds of causality. Theoretical knowledge is governed by physical causality. Practical knowledge is concerned with the human capacity to initiate a sequence of events that nature could not accomplish on its own—although in conformity with, not independent of, natural causality. Furthermore, the two realms presuppose a common totality of order not of humanity's creation. Without these presuppositions, we could not experience the world as we do, and it would never occur to us to engage in a scientific investigation of the natural world. Hence, we should first exhaust our attempts at explanation on the basis of physical causality before turning to the aid of teleology. The anomalous becomes an occasion to seek a physical law not yet known whereas the miraculous hinders search for a natural law. However, higher than knowledge of “what is” is our capacity to discern “what should be.” This is an inclusive moral capacity that establishes what it means to be human and unites all moral agents in an invisible kingdom of ends that constitutes a moral culture in the physical world uniting religion and science.     

DNA研究的历史带给我们的启示

自然科学发展日新月异。墨守成规的传统思维模式常常是羁绊研究工作停滞不前的主要障碍。通过纵观DNA双螺旋结构的研究历程,认识到实事求是的态度是确立正确研究方向的基础,而全方位、多视角、多学科交叉的开放性思维模式给科学研究带来了更宽阔的途径。     

广博·新颖·实用——读郭秀艳著《实验心理学》有感

郭秀艳著《实验心理学》于2004年由人民教育出版社出版。笔者认为该著作具有广博、新颖、实用的特色,是实验心理学中的一部力作,值得心理学专业的研究生仔细研读。     

Dialectics and practical wisdom

Dialectics is essentially the method or logos in which categories of forms are combined to explain things. Dialectics was developed because reason faces difficulties in grasping the sensible world. Practical wisdom is knowledge about some things or certain person or persons because of its variable objects. But it is not entirely specific or only about a particular thing and without universality in any sense. As one kind of dialectics, it combines various elements to accord with the right logos, similar to the way in which various forms are combined in theory. Therefore practical wisdom as a combination or polymerization of elements can be regarded as another kind of logic, namely practical logic or dialectics. __________ Translated from Zhexue Dongtai 哲学动态 (Philosophical Trends), 2005 (4) by Xie Yongkang     

Language, moral order and political praxis

The paper argues that the debate between objectivist criticism and postmodern critique represents a fracturing of the modes of mundane social and linguistic practice. The two together miss the open-textured character of language-in-use and the reflexive properties of situated human practice. Both difference and agreement are grounded in the multiplicity of criteria that are a feature of the logical grammar of language, and therefore of everyday praxis, including that of critique. To escape the duality of foundationalism on the one hand, and radical relativism on the other, attention to the praxiological details of human action and reasoning is needed. The paper draws on Wittgensteinian philosophy and ethnomethodological studies of reasoning to make its case.     

Sizing Things Up: Colloquial Reflection as Practical Wisdom

This essay reintroduces Rhetoric as the principle art for giving emphasis and importance to contested matters; in other words, for making things matter. In a speculative reading of the Aristotelian rhetorical tradition, Aristotle's interpretations of magnitude, contengency and practical wisdom are critically examined from both an aesthetic and an ethical-political point of view. The concluding discussion attempts to apply these same concepts to a growing dilemma in the present age. The dilemma is that monumental changes in scale have all but eroded the prospects for engaged encounters with contemporary contingency. It remains the challenge of rhetorical practice to reframe actions and events so that they and we may hold some hope for an engaged civic life.