In this paper we investigate problems about densities ofe-generic,s-generic andp-generic degrees. We, in particular, show that allp-generic degrees are non-branching, which answers an open question by Jockusch who asked: whether alls-generic degrees are non-branching and refutes a conjecture of Ingrassia; the set of degrees containing r.e.p-generic sets is the same as the set of r.e. degrees containing an r.e. non-autoreducible set.

We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.

We prove that there is no sw-complete c.e. real, negatively answering a question in [6].

We investigate the initial segment complexity of random reals. Let K denote prefix-free Kolmogorov complexity. A natural measure of the relative randomness of two reals α and β is to compare complexity K and K. It is well-known that a real α is 1-random iff there is a constant c such that for all n, Kn−c. We ask the question, what else can be said about the initial segment complexity of random reals. Thus, we study the fine behaviour of K (...) for random α. Following work of Downey, Hirschfeldt and LaForte, we say that αK β iff there is a constant such that for all n, . We call the equivalence classes under this measure of relative randomness K-degrees. We give proofs that there is a random real α so that lim supn K−K=∞ where Ω is Chaitin's random real. One is based upon work of Solovay, and the other exploits a new idea. Further, based on this new idea, we prove there are uncountably many K-degrees of random reals by proving that μ=0. As a corollary to the proof we can prove there is no largest K-degree. Finally we prove that if n ≠ m then the initial segment complexities of the natural n- and m-random sets and Ω︀) are different. The techniques introduced in this paper have already found a number of other applications. (shrink)

We consider how to represent the measurable sets in an infinite measure space. We use sequences of simple measurable sets converging under metrics to represent general measurable sets. Then we study the computability of the measure and the set operators of measurable sets with respect to such representations.

We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable topological spaces (...) constructed. (shrink)

On definable filters in computably enumerable degrees.

In this paper, we will prove that the plus cupping degrees generate a definable ideal on c.e. degrees different from other ones known so far, thus answering a question asked by Li and Yang (Proceedings of the 7th and the 8th Asian Logic Conferences. World Scientific Press, Singapore, 2003).

Moderate pragmatic invariantism (MPI) is a proposal to explain why our intuitions about the truth-value of knowledge claims vary with stakes and salient error-possibilities. The basic idea is that this variation is due to a variation not in the propositions expressed (as epistemic contextualists would have it) but in the propositions conversationally implicated. I will argue that MPI is mistaken: I will distinguish two kinds of implicature, namely, additive and substitutional implicatures. I will then argue, first, that the proponent of (...) MPI cannot appeal to additive implicatures because they don’t affect truth-value intuitions in the required way. Second, I will argue that the proponent of MPI cannot appeal to substitutional implicatures either because, even though they may have the required effects on truth-value intuitions, they don’t feature in the relevant cases. It follows that MPI is mistaken because whether the proponent of MPI appeals to additive or substitutional implicatures, at least one of the claims that make up her view is false. Along the way, I will suggest principles about implicatures that should be relevant not only to MPI, but to pragmatic accounts of seemingly semantic intuitions in general. (shrink)

In "A Problem in Possible-World Semantics," David Kaplan presented a consistent and intelligible modal principle that cannot be validated by any possible world frame (in the terminology of modal logic, any neighborhood frame). However, Kaplan's problem is tempered by the fact that his principle is stated in a language with propositional quantification, so possible world semantics for the basic modal language without propositional quantifiers is not directly affected, and the fact that on careful inspection his principle does not target the (...) world part of possible world semantics—the atomicity of the algebra of propositions—but rather the idea of propositional quantification over a complete Boolean algebra of propositions. By contrast, in this paper we present a simple and intelligible modal principle, without propositional quantifiers, that cannot be validated by any possible world frame precisely because of their assumption of atomicity (i.e., the principle also cannot be validated by any atomic Boolean algebra expansion). It follows from a theorem of David Lewis that our logic is as simple as possible in terms of modal nesting depth (two). We prove the consistency of the logic using a generalization of possible world semantics known as possibility semantics. We also prove the completeness of the logic (and two other relevant logics) with respect to possibility semantics. Finally, we observe that the logic we identify naturally arises in the study of Peano Arithmetic. (shrink)

This article brings together two sets of data that are rarely discussed in concert; namely, disagreement and testimony data. I will argue that relativism yields a much more elegant account of these data than its major rival, contextualism. The basic idea will be that contextualists can account for disagreement data only by adopting principles that preclude a simple account of testimony data. I will conclude that, other things being equal, we should prefer relativism to contextualism. In making this comparative point, (...) I will also defend self-standing relativist accounts of disagreement and testimony data. (shrink)

Kennedy (Linguist Philos 30:1–45, 2007) forcefully proposes what is now a widely assumed semantics for absolute gradable adjectives. On this semantics, maximum standard adjectives like “straight” and “dry” ascribe a maximal degree of the underlying quantity. Meanwhile, minimum standard adjectives like “bent” and “wet” merely ascribe a non-zero, non-minimal degree of the underlying quantity. This theory clashes with the ordinary intuition that sentences like “The stick is straight” are frequently true while sentences like “The stick is bent” are frequently informative, (...) and fans of the indicated theory of absolute gradable adjectives appeal to loose talk in response. One goal of this paper is to show that all extant theories of loose talk are inconsistent with this response strategy. Another goal is to offer a revised version of Hoek’s (Philos Rev 127:151–196, 2018, in: Proceedings of the 22nd Amsterdam Colloquium, 2019) recent theory of loose talk that accommodates absolute gradable adjectives after all, while being defensible against a range of important concerns. (shrink)

This book shows how pressing issues in bioethics – e.g. the ownership of biological material and human cognitive enhancement – successfully can be discussed with in a virtue ethics framework. This is not intended as a complete or exegetic account of virtue ethics. Rather, the aim here is to discuss how some key ideas in Aristotle’s Nicomachean Ethics, when interpreted pragmatically, can be a productive way to approach some hot issues in bioethics. In spite of being a very promising theoretical (...) perspective virtue ethics has so far been underdeveloped both in bioethics and neuroethics and most discussions have been conducted in consequentialist and/or deontological terms. ​. (shrink)

In this paper we prove that any c. e. degree is splittable with an c. e. infimum over any lesser c. e. degree in the class of d-c. e. degrees.

Examines the impact of both Bertrand Russell and John Dewey's philosophical influences on Chinese intellectuals during their visit in the 1920s. Also features biographical information on Russell and Dewey, important speeches and correspondences between Russell, Dewey, and Chinese scholars, a list of Russell and Dewey's works, and the timelines of Russell and Dewey's visits to China.

1920年代，羅素首次訪華，這位西方知名哲學家與文人間的對話，最終成了中國文化沿革的見證。 本書深入探討羅素與中國文人的互動關係，在東西方思想對話的歷史語境中還原羅素，分析這位哲學家濃厚中國情結的前因後果，審視羅素與當時中國各界的互動，見證了中國文化發展的歷程。羅素藉由各種不同方式「對話」的 對象包括：梁啟超、蔡元培、章太炎、胡適、丁文江、魯迅、郭沫若、林語堂、徐志摩、梁實秋、趙元任、楊端六；孫中山、譚延闓、毛澤東、陳獨秀、李大釗、張太雷、瞿秋白、周恩來、張國燾、張申府；以及梁漱溟、張東蓀 、金岳霖、馮友蘭、李石岑、傅銅、張岱年、賀麟、洪謙、任華、沈有鼎、王浩、牟宗三、唐君毅、張君勱、徐復觀、方東美、殷海光等代表人物。.

EDITOR’S ABSTRACTThe popular Chinese portrayal of the victory of Confucianism, or in Chinese terms “dismiss the hundred schools of thought and revere only the Confucian arts,” has been challenged by some scholars in the past decades. Ding’s essay illustrates not only how it has been challenged but also how the catch phrase influences the scholarly discussion. As he indicates, recent Chinese studies that attempt to subvert the traditional theory share the same “flow.” They fail to note that the expression (...) “dismiss the hundred schools of thought and revere only the Confucian arts” has had very negative connotations since it was invoked by Yi Baisha 易白沙 to harshly denounce Confucianism for being responsible for the centuries-long Chinese autocracy. (shrink)

EDITOR’S ABSTRACTThis article argues that the early Laozi text underwent three stages: The first had section divisions on the basis of the meaning. The second stage was the formative period of the Laozi text influenced by cosmological numerology; the Silk Manuscript version A is its testimony. The third stage finalized the text through the canonization of the Classic by Emperor Jing; it is represented by the Peking University Han Bamboo Slips, Yan Zun, and Liu Xiang versions and became the received (...) edition. From the Han Bamboo Slips to the Liu Xiang version, the Laozi’s two parts and section numbering became increasingly balanced and symmetric. Ding urges scholars to pay attention to all these developments when studying the Laozi text. (shrink)