In Zettel, Wittgenstein considered a modified version of Cantor’s diagonal argument. According to Wittgenstein, Cantor’s number, different with other numbers, is defined based on a countable set. If Cantor’s number belongs to the countable set, the definition of Cantor’s number become incomplete. Therefore, Cantor’s number is not a number at all in this context. We can see some examples in the form of recursive functions. The definition "f(a)=f(a)" can not decide anything about the value of f(a). The definiton is incomplete. (...) The definition of "f(a)=1+f(a)" can not decide anything about the value of f(a) too. The definiton is incomplete.<br><br>According to Wittgenstein, the contradiction, in Cantor's proof, originates from the hidden presumption that the definition of Cantor’s number is complete. The contradiction shows that the definition of Cantor’s number is incomplete. <br><br>According to Wittgenstein’s analysis, Cantor’s diagonal argument is invalid. But different with Intuitionistic analysis, Wittgenstein did not reject other parts of classical mathematics. Wittgenstein did not reject definitions using self-reference, but showed that this kind of definitions is incomplete.<br><br>Based on Thomson’s diagonal lemma, there is a close relation between a majority of paradoxes and Cantor’s diagonal argument. Therefore, Wittgenstein’s analysis on Cantor’s diagonal argument can be applied to provide a unified solution to paradoxes. (shrink)

The grue paradox, also called the new riddle of induction, posed a great challenge to the common understanding about induction. This paper shows that there is a close relation between the grue paradox and the problem of conditionals. This paper presents a general form of the grue predicate. Based on the general form, this paper argues that this kind of predicates can not be used for induction and prediction.

According to some pessimists, trusting moral testimony is an action in which the agent does not think about moral questions by herself, and thus it is unacceptable. I argue for optimism by giving some reasons to display moral agents are still depending upon their own in many cases of moral testimony. Specifically, I argue that testimony is a form of social cooperation: the division of epistemic labor. My strategy is as follows: First, I give a principle to show when an (...) agent could reasonably trust moral testimony. Specifically, an agent could reasonably accept the testimony, when she can reasonably expect she would make the same or similar judgment with the testifier. Second, I show how moral testimony could work as a form of social cooperation. Given the principle of the same judgment, it is reasonable for the agent to form a moral belief and act with moral testimony. And it provides us higher efficiency in moral knowledge and shows respect for each moral agent. After that, I provide explanations for the problem of moral disagreement and moral understanding with such a principle for moral testimony. Finally, I respond to some possible objections and give some clarifications of my argument. (shrink)

Relational egalitarians claim that a situation is just only if everyone it involves relates to one another as equals. It implies that relational egalitarians believe the ideal of “living as equals” (for short) is desirable, and furthermore, necessary for justice. In this paper, I distinguish three accounts of the desirability of the ideal: the instrumental value account, the non‐instrumental value account, and the non‐consequentialist account. I argue that the former two accounts cannot provide satisfying reasons for being a relational egalitarian. (...) Instead, the ideal of “living as equals” ought to be understood as fundamentally a moral requirement in a non‐consequentialist sense. In addition, a pluralist (though fundamentally non‐consequentialist) approach is welcome. (shrink)

Presentism usually holds that only present entities exist. In contrast to presentism, eternalism holds that past, present, and future entities all exist. According to some philosophers, presentism is intuitively incompatible with time travel. In this paper, I defend the compatibility between presentism and time travel by arguing for a plausible account of causation in the presentist framework. To achieve my goal, I respond to an objection to presentist time travel that is based on the nonexistence of the past: the Causation (...) Objection. According to the Causation Objection, causal relations between objects at different times are necessary for time travel, but these are impossible for presentists. I evaluate a possible reply based on a non-relational account of causation and show that this reply is not satisfying. Subsequently, I put forward a fact-based account of causal relation. I argue that presentists could accept facts instead of events as causal relata, thus establishing causal relations. As all facts about the past, the present, and the future exist in the present, we could explain how backward causation works and describe the discrepancy between personal time and external time in presentist time travel; in this way, I argue, we could vindicate the compatibility between presentism and time travel. (shrink)

The problem of Free Will is an important topic in religion, philosophy and neuroscience. We will introduce a new model of free will: free choice under constraints. Under outer and inner constraints, human still have the ability of free choice. Outer constrains include physical rules, environment and so on. Inner constrains include customs, desires, habits, preferences and so on. Given a specific context, human have the ability of deciding Yes/No on a specific preference. The free choices are caused, but not (...) determined, by the outer and inner constraints. In addition, the free choices will refashion the inner constraints. Preferences are gradually formed by human, thus they may be gradually de-formed by human. Human can keep the positive preferences, while de-form the negative preferences. When we de-form the negative preferences, we have the chance to pursue another new possibility. So are scientists. They can keep the positive aspects of the known theory, while eliminate the negative aspects. When they eliminate the negative aspects of old conceptual schema, they have the chance to pursue another new conceptual schema. (shrink)

I present an affirmation of nothingness in the humor of Zhuang Zi 莊子. This essay begins with two images that present a playful transgression of perspectives: the butterfly dream and the discussion over the Hao river. I dwell on these transgressions to highlight the challenge for each to question one’s perspectives and to shift its grounding from epistemic to aesthetic value. Such a sensitivity suggests a mindfulness of the transformation of things 物化. This reinforces reality’s ephemerality, and I, following (...) David Chai, point what lies behind this as the non-being of nothingness 無無. The centrality of the Dao 道 qua nothingness is mirrored by a Daoist who becomes sensitive to the transformation of things and who ultimately undercomes reality, i.e., decenters oneself. This type of existence is what it means to be zhenuinly 真 pretending, which Zhuang Zi does, manifested by the humor in his work. (shrink)

I consider the intertextuality between Chinese and Western thought by exploring how images, metaphors, and ideas from the texts associated with Zhuangzi and Laozi were appropriated in early twentieth-century German philosophy. This interest in “Lao-Zhuang Daoism” encompasses a diverse range of thinkers including Buber and Heidegger. I examine how the problematization of utility, usefulness, and “purposiveness” in Zhuangzi and Laozi becomes a key point for their German philosophical reception; how it is the poetic character of the Zhuangzi that hints (...) at an appropriate response to the crisis and loss of meaning that characterizes technological modernity and its instrumental technological rationality; that is, how the “poetic” and “spiritual” world perceived in Lao-Zhuang thought became part of Buber's and Heidegger's critical encounter and confrontation with technological modernity; and how their concern with Zhuangzi does not signify a return to a dogmatic religiosity or otherworldly mysticism; it anticipates a this-worldly spiritual or poetic way of dwelling immanently within the world. (shrink)

The thorny problem, which we are confronted with in translating the term of “Sein”(Being) from western Philosophy into Chinese, highlights the ambiguity, paradoxy and vagueness of the issue of Sein from a specific viewpoint. Although there is no exact equivalent in Chinese for the word of “Sein”, we use several different words to express the meanings consisted in the issue of “Sein”. By comparison we may find that what is discussed by Zhuang Zi using the terms of “Shi” and (...) “Fei” are just in a considerable degree the same issue discussed by Heidegger using the terms of “Sein” and “Dasein”. However, they gave different opinions to the issue, which show their divergence in their philosophic thinking. (shrink)