One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.

Richard Heck and John Burgess have shown that Frege’s Basic Law V is consistent with predicative comprehension and that the resulting theory interprets Robinson Arithmetic. There are also many other ways to keep Frege from being contradictory. This paper shows that Basic Law V is also consistent with positive comprehension and that the resulting theory also interprets Robinson Arithmetic. In addition, the theory of positive Frege provides a new understanding of Dummett’s “indefinitely extensible concepts.”

This paper compares Frege’s philosophy of mathematics with a naturalistic and nominalistic philosophy of mathematics developed in Ye (2010a, 2010b, 2010c, 2011), and it defends the latter against the former. The paper focuses on Frege’s account of the applicability of mathematics in the sciences and his conceptual realism. It argues that the naturalistic and nominalistic approach fares better than the Fregean approach in terms of its logical accuracy and clarity in explaining the applicability of mathematics in the sciences, its ability to reveal the real issues in explaining human epistemic and semantic access to objects, its prospect for resolving internal difficulties and developing into a full-fledged theory with rich details, as well its consistency with other areas of our scientific knowledge. Trivial criticisms such as “Frege is against naturalism here and therefore he is wrong” will be avoided as the paper tries to evaluate the two approaches on a neutral ground by focusing on meta-theoretical features such as accuracy, richness of detail, prospects for resolving internal issues, and consistency with other knowledge. The arguments in this paper apply not merely to Frege’s philosophy. They apply as well to all philosophies that accept a Fregean account of the applicability of mathematics or accept conceptual realism. Some of these philosophies profess to endorse naturalism.

Semantic relationism is a methodology proposed by Kit Fine for solving the antinomy of variables. Fine proposed the relational semantics for first-order logic, which can be used to solve Frege’s puzzle of names. In this paper, I generalize Frege’s puzzle to other linguistic expressions, including definite descriptions, predicates, quantifiers and modalities. I then apply Fine’s semantic relationistic approach to these puzzles.

Zhong 中 is a very important philosophical concept in early Confucianism. Both the received ancient Confucian classics and the newly discovered ancient bamboo manuscripts tell us that adhering to the principle of zhong was an important charge that had been transmitted and inherited by early ancient Chinese political leaders from generation to generation. Confucius and his followers adopted the concept of zhong and further developed it into a sophisticated doctrine, which is usually called zhongdao 中道 (the Way of zhong) or zhongyong 中庸. Being a polysemous word, zhong has several different but philosophically related meanings. However, for a long time, people usually understood zhong in the sense of only one of its meanings, and zhongdao or zhongyong has been commonly interpreted as “the doctrine of the mean.” My argument in this paper is that a synthetic interpretation, which includes all the semantic meanings of zhong is necessary in order to acquire a deep and well-rounded comprehension of the philosophical significance of the Way of zhong. The Way of zhong features a dialectal view of the relationship between heaven and human beings, mind and materials, subjective desire and the available objective conditions, self and others, centrality and diversity, and so on. The Way of zhong has become a widely applied philosophical methodology in Confucianism, as well as a political principle and a kind of personal moral merit in early Confucian doctrines. Today, it still has relevance in contemporary Chinese social and cultural contexts.

A general account of the Confucian self as either collectivist or relational requires careful examination. This article begins with the major textual resources of the Confucian tradition and then compares this idea of moral expansion with Deweyan ideas of the self and community. By parsing key Confucian terms that comprise the meaning of “being together” and “mutual association,” the author argues that Confucian selves and individuals are fundamentally contextually creative. By comparing the Confucian idea of family with the Deweyan notion of community, the author further supports his argument that the Confucian self is always co-creative with others. Despite the fact that Confucian ethics has long been considered either a kind of virtue ethics or a kind of role ethics, the author argues that Confucian ethics is better viewed as a kind of co-creative ethics, which stems from an ethical theory concerning the co-creative self and other.

This paper investigates Xunzi’s ideas on self and community. According to Xunzi, the origin of Confucian rituals lies in the need to nourish human desires. However, this nourishment is more than the simple satisfaction of desire. Rather, in the development of rituals, desires are evaluated and directed according to the overall good of a person in order that the person can actively pursue fulfilment and self-realization. If human beings are controlled by momentary desires, they live like beasts and cannot act as autonomous agents. Confucian rituals constitute a normative framework for human life and desires. Following Xunzi, this normative framework is based on a cultural and collective interpretation of our own nature. Through Confucian rituals a person can not only satisfy desires properly, but can also enjoy human relationships within the community. Most importantly, it is through these Confucian rituals that a person realizes himself as an agent who can control and direct his own life.

The onto-hermeneutic approach to bentiyong 本体用 championed by Cheng Chung-Ying 成中英 is a valuable addition to comparative philosophy. In his well-honed reading, bentiyong is described as the continuous, integrative substance at the base of things, which becomes known through an ongoing hermeneutic integration and interpretation of reality. However, his use of the English word “substance” to describe bentiyong is problematic, mainly because substance, being without properties and existing without change, cannot be read as part of a hermeneutic process. Luckily, there are resources within the Chinese philosophical tradition that can help in overcoming some of the difficulties in translation presented here. Namely, the way that Zhu Xi 朱熹 approaches ti-yong as a principle (li 理) provides a better and more fittingly discursive basis for expressing the onto-hermeneutic character of bentiyong intended by Cheng, and allows English translation of the term with a firm footing in mainstream Neo-Confucianism.

This essay attempts to compare Kant’s better man and the Confucian junzi in the Zhongyong, and argues that Kant’s idea of the better man, which expresses human self-improvement in ultimate freedom, is in fact a conception very similar to that of the Confucian junzi, which denotes an ideal human being in cheng. Kant attributes the lack of emphasis on self-improvement in Western culture to the Christian conception of grace, and demonstrates the possibility of self-improvement on the ground of ultimate freedom. We may call this treatment “the Confucian solution” in Kant’s thought. My intention is to explicate the conceptual commonality between the better man and the junzi and demonstrate the Confucian element in Kant’s religious thought.