We define $\Psi $ -autoreducible sets given an autoreduction procedure $\Psi $. Then, we show that for any $\Psi $, a measurable class of $\Psi $ -autoreducible sets has measure zero. Using this, we show that classes of cototal, uniformly introenumerable, introenumerable, and hyper-cototal enumeration degrees all have measure zero. By analyzing the arithmetical complexity of the classes of cototal sets and cototal enumeration degrees, we show that weakly 2-random sets cannot be cototal and weakly 3-random sets cannot be of (...) cototal enumeration degree. Then, we see that this result is optimal by showing that there exists a 1-random cototal set and a 2-random set of cototal enumeration degree. For uniformly introenumerable degrees and introenumerable degrees, we utilize $\Psi $ -autoreducibility again to show the optimal result that no weakly 3-random sets can have introenumerable enumeration degree. We also show that no 1-random set can be introenumerable. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...) enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

The topic of time is central to Levinas's philosophy. By examining aspects of the Biblical stories of Abraham and Moses compared with Greek myths, mainly that of Cronos devouring his children, this paper aims to show that Levinas's view of time, though certainly indebted to the Greek (i.e. philosophical) tradition, contains traces of Biblical experiences. Moreover, Levinas's interpretation of time will serve as a concrete demonstration of the way the Jewish experience enables Levinas to express his criticism of the philosophical-Greek (...) tradition. (shrink)

We would like to thank an anonymous referee for his helpful comments on a previous version of this paper.

Difference is a category of relationship lying between identity and non-identity, and equality and inequality. This concept is both the Confucian reflection of the real relationship between things in the world and the value ideal of Confucianism. The Confucian idea of difference, embodied in the view of human relationships, of world, and of nature, seeks to build a rational order based on difference, so as to reach a harmonious, united and ideal state. Confucians in the past dynasties continually interpreted difference (...) and raised it to the level of ontology, enriching the system of Confucianism. (shrink)

Understanding a proposition for an intelligent agent is an important epistemic concept. We first discuss intuitively general logic characteristics of understanding, and give a language and a semantics containing understanding as a modal operator. Secondly, we develop the system LU for the operator, give some results of its proof theory, and then we prove the frame soundness and frame completeness of LU.

We construct a Hilbert style system RPL for the notion of plausibility measure introduced by Halpern J, and we prove the soundness and completeness with respect to a neighborhood style semantics. Using the language of RPL, we demonstrate that it can define well-studied notions of necessity, conditionals and propositional identity.

When speaking of pre-Qin Dynasty theories on human nature, past scholars divided Confucius, Mencius and Xunzi into three categories, and they tended to divide the theories into moral categories of good and evil. The discovery of bamboo and silk sheets from this period, however, has offered some valuable literature, providing a historical opportunity for the thorough research of pre-Qin Dynasty theories on human nature. Based on the information on the recently excavated bamboo and silk sheets, especially the essay titled “Xing (...) Zi Ming Chu” on bamboo sheets unearthed in Guodian, this essay examines pre-Qin Dynasty theories on human nature from a new perspective. In doing so, it looks forward to a breakthrough in academic patterns of thought which typically defined pre-Qin Dynasty theories on human nature as good or evil, and thus a closer look at the original appearance of pre-Qin Dynasty theories on human nature as a whole. (shrink)

Confucianism defined benevolence with “feelings” and “love.” “Feelings” in Confucianism can be mainly divided into three categories: feelings in general, love for one’s relatives, and compassion. The seven kinds of feeling in which people respond to things can be summarized as “likes and dislikes.” The mind responds to things through feelings; based on the mind of benevolence and righteousness or feelings of compassion, the expression of feelings can conform to the principle of the mean and reach the integration of self (...) and others, and of self and external things. The “relations between the seven kinds of feelings and the Four Commencements,” however, was not developed into a theoretical idea in Confucianism. After Confucius, the relationship between the universality of natural sympathies and the gradation of love for relatives gradually became an important subject in Confucian ideas of benevolence and love. By “refuting Yang Zhu and Mozi,” Mencius systematically expounded on this issue. Love had two ends: self-love and natural sympathies, between which existed the love for relatives. These two ends were not the two extremes of Yang’s self-interest and Mozi’s universal love. Love for relatives not only implied a gradation, but also contained universality and transcendence that came from self-love. Love for relatives, natural sympathies and self-love had a kind of tension and connectivity between two dynamic ends. The Confucian idea of benevolence and love hence demonstrated differences and interconnectivity. An accurate understanding of such “feelings” and “love” is important for us to grasp Confucian thoughts on benevolence and its realization. (shrink)

One of the major divergences between dynamical systems theory and symbolism lies in their views on the role of representation in cognition. From the perspective of development, the cognitive development could be divided into three levels: sensorimotor, imagery representation and linguistic representation. It is claimed that representation is not a sufficient condition though it is necessary for cognition. However, it does not mean that the authors agree with the notion of strong coupling in dynamicism that completely rejects representation.