This article is a lecture note I wrote for my philosophy of mathematics course. Its main task is to explain the main ideas of Gupta's acceptable model proposed in his paper [J. Philos. Logic 11(1), 1–60, 1982]. I aim to provide detailed information on a result established by Gupta. On the one hand, I hope this explanation can be helpful for those who are learning Gupta's acceptable model, and on the other hand, I also hope to provide a guide for (...) beginners to interpret literature. (shrink)

We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the same condition. In this paper, we outline some results and questions around the degrees of paradoxicality and summarize recent progress.

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...) that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (J Philos Logic 34(2):155–192, 2005), and the dependence digraph by Beringer and Schindler (Reference graphs and semantic paradox, 2015. https://www.academia.edu/19234872/reference_graphs_and_semantic_paradox). Unlike the usual discussion about self-reference of paradoxes centering around Yablo’s paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb’s dependence relation. They are called ‘locally finite paradoxes’, satisfying that any sentence in (...) these paradoxes can depend on finitely many sentences. I prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the ‘circularity dependence’ of paradoxes, which was introduced by Hsiung (Logic J IGPL 22(1):24–38, 2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König’s infinity lemma. In contrast, this paper also shows that Yablo’s paradox and its ∀∃\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\forall \exists $$\end{document}-unwinding variant are non-self-referential, and neither McGee’s paradox nor the ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-cycle liar has circularity dependence. (shrink)

According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for any finitely many numbers greater than 1, (...) if any of them is not divisible by any other, we can construct a Boolean paradox whose primary revision periods are just these numbers. Consequently, the degrees of Boolean paradoxes form an unbounded dense lattice. The area of Boolean paradoxes is proved to be rich in mathematical structures and properties. (shrink)

According to the revision theory of truth, the binary sequences generated by the paradoxical sentences in revision sequence are always unstable. In this paper, we work backwards, trying to reconstruct the paradoxical sentences from some of their binary sequences. We give a general procedure of constructing paradoxes with specific binary sequences through some typical examples. Particularly, we construct what Herzberger called “unstable statements with unpredictably complicated variations in truth value.” Besides, we also construct those paradoxes with infinitely many finite primary (...) periods but without any infinite primary period, those with an infinite critical point but without any finite primary period, and so on. This is the first formal appearance of these paradoxes. Our construction demonstrates that the binary sequences generated by a paradoxical sentence are something like genes from which we can even rebuild the original sentence itself. (shrink)

It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: (...) his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition. (shrink)

A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in (...) and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain's card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness. (shrink)

The unwinding that Cook, 767–774 2004) proposed is a simple but powerful method of generating new paradoxes from known ones. This paper extends Cook’s unwinding to a larger class of paradoxes and studies further the basic properties of the unwinding. The unwinding we study is a procedure, by which when inputting a Boolean modal net together with a definable digraph, we get a set of sentences in which we have a ‘counterpart’ for each sentence of the Boolean modal net and (...) each point of the digraph. What is more, whenever a sentence of the Boolean modal net says another sentence is necessary, then the counterpart of the first sentence at a point correspondingly says the counterparts of the second one at all accessible points of that point are all true. The output of the procedure is called ‘the unwinding of a Boolean modal net on a definable digraph’. We prove that the unwinding procedure preserves paradoxicality: a Boolean modal net is paradoxical on a definable digraph, iff the unwinding of it on this digraph is also paradoxical. Besides, the dependence digraph for the unwinding of a Boolean modal net on a definable digraph is proved to be isomorphic to the unwinding of the dependence digraph for the Boolean modal net on the previous definable digraph. So the unwinding of a Boolean modal net on a digraph is self-referential, iff the Boolean modal net is self-referential and the digraph is cyclic. Thus, on the one hand, the unwinding of any Boolean modal net on an acyclic digraph is non-self-referential. In particular, the unwinding of any Boolean modal net on \ is non-self-referential. On the other hand, if a Boolean modal net is paradoxical on a locally finite digraph, the unwinding of it on that digraph must be self-referential. Hence, starting from a Boolean modal paradox, the unwinding can output a non-self-referential paradox only if the digraph is not locally finite. (shrink)

Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...) iff this frame contains at least an infinite walk which has an arbitrarily large depth. We thus get that $\lambda^n$ has a degree of paradoxicality no more than $\lambda^m$ iff the multiplicity of 2 in the (unique) prime factorisation of $n$ is no more than that in the prime factorisation of $m$; and all tranfinite $\lambda^\alpha$ has the same degree of paradoxcality but has a higher degree of paradoxicality than any $\lambda^n$. (shrink)

Cook regards Sorenson’s so-called ‘the no-no paradox’ as only a kind of ‘meta-paradox’ or ‘quasi-paradox’ because the symmetry principle that Sorenson imposes on the paradox is meta-theoretic. He rebuilds this paradox at the object-language level by replacing the symmetry principle with some ‘background principles governing the truth predicate’. He thus argues that the no-no paradox is a ‘new type of paradox’ in that its paradoxicality depends on these principles. This paper shows that any theory is inconsistent with the T-schema instances (...) for the no-no sentences, plus the T-schema instance for a Curry sentence associated with the symmetry of the no-no sentences. It turns out that the no-no paradox still depends on the problematic instances of the T-schema in a way that the liar paradox does. What distinguishes the no-no paradox is the T-schema instance for the above Curry sentence, which encodes Sorensen’s symmetry principle at the object-language level. (shrink)

This paper aims to explore the relationship between the necessity predicate and the truth predicate by comparing two possible-world interpretations. The first interpretation, proposed by Halbach et al. (J Philos Log 32(2):179–223, 2003), is for the necessity predicate, and the second, proposed by Hsiung (Stud Log 91(2):239–271, 2009), is for the truth predicate. To achieve this goal, we examine the connections and differences between paradoxical sentences that involve either the necessity predicate or the truth predicate. A primary connection is (...) established through two translations that change only one of the predicates to the other while keeping everything else unchanged. We prove that in bijective frames, a set of sentences that contains one of the two semantic predicates has the same paradoxicality as the corresponding set of sentences that contains the other predicate obtained through translation. However, there are substantial differences as well. First, the necessity predicate and the truth predicate, under the two interpretations, cannot be defined by each other. Moreover, for sentences that involve only the truth predicate, their paradoxicality is preserved under the homomorphisms of frames. For sentences containing the necessity predicate, their paradoxicality is preserved under bounded morphisms, but none of these sentences can have their paradoxicality preserved under the extension of frames. Finally, we also show that paradoxical sentences involving the necessity predicate and those involving the truth predicate differ significantly in terms of mirror symmetry, circularity dependence, and frame compactness. (shrink)

In various theories of truth, people have set forth many definitions to clarify in what sense a set of sentences is paradoxical. But what, exactly, is _a_ paradox per se? It has not yet been realized that there is a gap between ‘being paradoxical’ and ‘being a paradox’. This paper proposes that a paradox is a minimally paradoxical set meeting some closure property. Along this line of thought, we give five tentative definitions based upon the folk notion of paradoxicality implied (...) in Tarski’s undefinability theorem of truth and the dependence relation proposed by Leitgeb (J Philos Log 34(2):155–192, 2005). A definition of ‘being a paradox’ is acceptable if its extension must be sufficiently comprehensive to include all known paradoxes on the one hand, and its standard must also be high enough to exclude those that are evidently not paradoxes on the other hand. It turns out that only the last attempt is acceptable: a set of sentences is a paradox if it is paradoxical and self-dependent, and at the same time, it and any of its paradoxical and self-dependent subsets bisimulate each other. In this way, we articulate in what sense a set of sentences is a paradox, and so establish a connection between the notion of a paradox and the notion of paradoxicality. (shrink)

By introducing the intensional mappings and their properties, we establish a new semantical approach of characterizing intermediate logics. First prove that this new approach provides a general method of characterizing and comparing logics without changing the semantical interpretation of implication connective. Then show that it is adequate to characterize all Kripke_complete intermediate logics by showing that each of these logics is sound and complete with respect to its (unique) ‘weakest characterization property’ of intensional mappings. In particular, we show that classical (...) logic has the weakest characterization property , which is the strongest among all possible weakest characterization properties of intermediate logics. Finally, it follows from this result that a translation is an embedding of classical logic into intuitionistic logic, iff. its semantical counterpart has the property. (shrink)

This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘_m_-cycle unwinding’ of the original Boolean system for any positive integer _m_. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the _m_-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of a Boolean paradox, this (...) paradox and its _m_-cycle unwinding have the same primary periods. In this way, we can produce an indirectly self-referential Boolean paradox with the same periodic characteristics as a known Boolean paradox. (shrink)

Chinese culture is a lively and active organism. If we are to get to the real image of Chinese culture, we should take as a starting point the first passage of the Chung-yung [Doctrine of the Mean], which expounds its basic principles: "That which Heaven has decreed is called Nature, to follow that Nature is called tao [way] and to cultivate the tao is called instruction." This passage uses three phrases and one breath; these three phrases have a unified nature (...) which cannot be separated and which constitute one long sentence. Because of this, the words as a whole lead people to think of a richly vital and great tree which has the will of Heaven as its roots, human nature as its shoots, the tao as its trunk, and cultural instruction as its branches, leaves, and blossoms. As for the fruit, in terms of the individual, it is the achievement of a completely beautiful character, and in terms of the masses of the people, it is the ordering of the country and the pacification of the realm, the progression from the era of peace under the ancient kings to the age of the Grand Unity [ta-t'ung]. (shrink)

Pathological morphogenesis on leaves of Fraxinus ornus (ash) and Solanum lycopersicum (tomato) under the influence of mites (Aceria fraxinivora and Eriophyes cladophthirus respectively) leads to a range of structures whose morphology and development cannot be reduced to the classical categories of plant morphology, but present a heterogeneous continuum which links fundamental structural categories. These findings support the pyramid model of plant construction.

Negative workplace gossip generates social undermining and great side effects to employees. But, the damage of negative gossip is mainly aimed at the employee who perceived being targeted. The purpose of this study is to develop a conceptual model in which perceived negative workplace gossip influences employees’ in-role behavior and organizational citizenship behavior differentially by changing employees’ self-concept (organizational based self-esteem and perceived insider status). 336 employees from 7 Chinese companies were investigated for empirical analysis on proposed hypotheses, and results (...) show that: (1) Perceived negative workplace gossip adversely influences employees’ IRB and OCB. (2) Self-concept (OBSE and PIS) plays a mediating role in the relationship between perceived negative workplace gossip and employees’ behaviors (IRB and OCB); (3) Employees’ hostile attribution bias moderates the relationship between perceived negative workplace gossip and self-concept (OBSE and PIS); and also moderates the mediating effect of self-concept (OBSE and PIS) on the relationship between perceived negative workplace gossip and employees’ behaviors (IRB and OCB). Thus, our findings provide deeper insights into the potential harmful effects of gossip. In addition, we help to explain the underlying mechanism and boundary condition of these effects. (shrink)

The online edition supplements this index with hyperlinks as well as including internal hyperlinks to related entries in the text, CrossRef citations, and links ...

In this paper, I focus on the representations of Black women in contrast to Black men found within Frantz Fanon’s philosophical work Black Skin, White Masks. I propose that while Fanon’s racial dialectical work is very significant, he often lacks acknowledgement of the multidimensionality of the Black woman’s lived experience specifically. Drawing on the theory of intersectionality, coined by Kimberlé Crenshaw, I argue that Fanon does not recognize the different layers of oppression operating in Black women’s lives to the degree (...) that he fails to include them within his framework of both liberation and resistance from racial oppression. (shrink)

This Is A New Release Of The Original 1898 Edition.

本书从关于人性的基本理论出发,对中国的社会、家庭、人的种种现象提出了一系列问题,并提出了解决这些问题的思路和方法。.

Tu Wei-ming is the foremost exponent of Confucian thought in the United States today. Over the last two decades he has been developing a creative scholarly interpretation of Confucian humanism as a living tradition. The result is a work of interpretive brilliance that revitalizes Confucian thought, making it a legitimate concern of contemporary philosophical reflections.

本书是关于新意识形态批评的论文集,本书要论述的意图是:以理论与社会生活的密切关系而言,中国文论家可以创造出自己的“本位话语”,其具体问题集中为两个,即文化转型中的当代中国的精神建构和建立文学理论的本位 话语。.

Although previous studies focus on the role of women in the boardroom and corporate response to natural disasters, none evaluate how women directors influence corporate philanthropic disaster response (CPDR). This study collects data on the philanthropic responses of privately owned Chinese firms to the Wenchuan earthquake of May 12, 2008, and the Yushu earthquake of April 14, 2010. We find that when at least three women serve on a board of directors (BOD), their companies’ responses to natural disasters are more (...) significant. Age diversity among women on BODs as well as good corporate profitability (e.g., high earnings per share) positively moderates the relationship between women on BODs and CPDR. (shrink)

The study analyzes the influential factors of consumers’ willingness to purchase gray-market smartphones by considering the model of novelty seeking, status consumption, integrity, and perceived risk. Attitude toward counterfeit is used as mediation in the model. The causalities in the model of problematic willingness of consumer to purchase gray-market smartphones are hypothesized. A total sample of 350 respondents with 238 effective samples is collected by interviewing with questionnaires at the service counters of telecommunications operators. Structure equation modeling (SEM) is adopted (...) in the analysis. Consumers’ attitude toward counterfeit goods is found to be positively related to the willingness of consumers to purchase gray-market smartphones, but perceived risk is negatively related to consumers’ willingness to purchase. As for personality constructs, integrity and status consumption are found to be negatively related to consumers’ attitude toward counterfeit goods, but novelty seeking is positively related to the attitude. Further, managerial implications for branded smartphone manufacturers and telecommunications regulators are provided by the research. (shrink)

The high turnover of nurses has become a global problem. Several studies have proposed that nurses' perceptions of the ethical climate of their organization are related to higher job satisfaction and organizational commitment, and thus lead to lower turnover. However, there is limited empirical evidence supporting a relationship between different types of ethical climate within organizations and facets of job satisfaction. Furthermore, no published studies have investigated the impact of different types of ethical climate on the three components of organizational (...) commitment. This study attempts to explore the different types of ethical climate that exist in hospitals, and the degree of job satisfaction and organizational commitment of nurses in Taiwan. It uses path analysis to understand which types of ethical climate influence different facets of job satisfaction. The study also examines the impact of different types of ethical climate and facets of job satisfaction on the three components of organizational commitment. Questionnaires were distributed to 352 nurses. The relationships among variables were assessed by factor analysis, reliability, descriptive statistics, correlations, and regression. The important conclusion is that hospitals can increase job satisfaction and organizational commitment by influencing an organization's ethical climate. Hospital administrators can foster within organizations the climate types of caring, independent, and rules climate that increase satisfaction, while preventing organizations from developing the type of instrumental climate that decreases it. (shrink)