Paradoxes of happiness

To get happiness forget about it; then, with any luck, happiness will come as a by-product in pursuing meaningful activities and relationships. This adage is known as the paradox of happiness, but actually it contains a number of different paradoxes concerning aims, success, freedom, and attitudes. These paradoxes enhance our understanding of the complexity of happiness and its interaction with other values in good lives, that is, lives which are happy as well as morally decent, meaningful, and fulfilling. Yet, each paradox conveys a one-sided truth that needs to be balanced with others. Happiness, understood as subjective well-being, involves positively evaluating our lives and living with a sense of well-being. As such, it should not be confused with either pleasure or normative conceptions of “true” happiness.     

Minimalism and Paradoxes

This paper argues against minimalism about truth. It does so by way of acomparison of the theory of truth with the theory of sets, and considerationof where paradoxes may arise in each. The paper proceeds by asking twoseemingly unrelated questions. First, what is the theory of truth about?Answering this question shows that minimalism bears important similaritiesto naive set theory. Second, why is there no strengthened version ofRussell's paradox, as there is a strengthened Liar paradox? Answering thisquestion shows that like naive set theory, minimalism is unable to makeadequate progress in resolving the paradoxes, and must be replaced by adrastically different sort of theory. Such a theory, it is shown, must befundamentally non-minimalist.     

Antonyms and Paradoxes

Adjectives can be gradable or non-gradable and this aspect of their meaning is responsible for their different distribution and also for their classification into two different classes of antonyms. Non-gradable antonyms are called contradictories: they are neither true nor false together and exclude any middle term; gradable antonyms are called contraries: they are not simultaneously true, but may be simultaneously false. While with contraries a negative disjunction (neque...neque) can define an intermediate level, with contradictories it simply means that either term of the disjunction is excluded. There are however some Latin examples, such as neque vivus neque mortuus (`neither alive nor dead'), where the negation of a contradictory pair is used to convey a third, intermediate value. This third possibility is precisely what gives place to a paradox. Such an intermediate level can be defined also by terms like semivivus, semianimis (`half-dead'). Following Ducrot's theory on argumentation, such terms represent an argumentative attenuation, not with respect to life, rather with respect to death. With contradictories, in fact, the use of semi-, like the use of negation, gives the assertion of the opposite term as a result.     

Paradoxes in Aulus Gellius

The noctes Atticae of Aulus Gellius contain almost all the ancient paradoxes. Nevertheless, in comparison with his philosophical sources, the author shows a shift in the perspective of his approach. He analyses the `master argument' of Diodorus Chronus only from an ethical point of view and, among the seven paradoxes attributed to Eubulides of Milet, he quotes the `heap' as an absurdity (absurdum), the `horned one' and the `not-someone' as a trap (captio), the `liar' as a sophism (sophisma). Following the advice of Cynics, Gellius mistrusts deceptive manoeuvres, which highlight gaps in binary logic. At the same time, however, he is interested in argumentative structures, which lead one of two opponents on to victory. The extensive report of the quarrel between Protagoras and Evathlus, and many observations of Gellius on convertible forms of reasoning in literary texts fall within this rhetorical field.     

悖论的自指性与循环性

本文使用语义网分析悖论与自指性和循环性。主要结论是证明了有穷悖论都是自指的,同时其矛盾性必定基于循环性。我们还证明存在非自指但基于循环性的(无穷)悖论,比如亚布鲁悖论及其一般变形;又证明了存在自指但不基于循环性的(无穷)悖论,比如超穷赫兹伯格悖论和麦基悖论。这表明自指性与循环性对悖论而言是两个不同的概念。     

Paradoxes and Failures of Cut

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system—ST—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to.