SCNU Center for Logic and Analytic Philosophy

Abstract:

  This 70-year retrospective of the Chinese work on philosophy of logic is presented mainly in terms of the notion of the “philosophy of logic”, the notion of logic and the social-cultural role of logic. It generally involves three kinds of questions, namely, how to distinguish philosophical logic from the philosophy of logic, what the nature and scope of logic is from Chinese scholars’ point of view, and why the social-cultural role of logic is underscored in the Chinese context. Finally, some of the prospects for the future studies of philosophy of logic in China are indicated.

摘 要：绿蓝悖论是现代归纳逻辑研究的一个重大事件，它直接挑战了归纳的逻辑基础，迫使人们重新思考现代归纳逻辑的发展方向的问题。近年来，归纳逻辑的研究出现了两种截然不同的研究取向。而在某种意义上，它们都是对绿蓝悖论的最新回应。一方面，以诺顿为代表的实质归纳理论主张彻底摒弃归纳的形式化规则，认为应当把归纳推理研究的重心集中到经验事实中来。另一方面，一个鲜明的对比是，帕里斯所建构的纯粹归纳逻辑体系进一步发挥了卡尔纳普的形式归纳思想，明确地把归纳当作数理逻辑的一个分支来研究。这两种不同的归纳理论是否可以共存？

摘 要：熊明（2020）把初等元胞自动机与自指语句结合起来进行研究，建立起二者在演化过程方面的紧密关联。沿此路径，本文主要考虑一类称为总和型的二维冯诺依曼型元胞自动机，给出其自指语句表达形式。并且通过利用自指语句的性质，寻找元胞自动机相对应的不动点，将其与自指悖论相联系。同时，通过分析其演化过程的（不）稳定性特征，进行了相应的分类。

摘 要：作为说谎者悖论的推广,n-跳跃说谎者悖论是这样一种悖论,其中的语句在关系框架中每隔n个点真值都发生改变。利用布尔悖论的语义封闭性等特性,证明当n大于1时,n-跳跃说谎者悖论不可能通过布尔悖论来进行表达。同时,对任意的n,给出构造一类布尔悖论的方法,使得它们在比n-跳跃说谎者悖论规定稍弱的意义下,满足所谓的弱n-跳跃说谎者悖论的规定。这部分地解决了n-跳跃说谎者悖论的可定义性问题。

摘要：作为多元主义真理论的主要代表,功能主义真理论主张真是一种功能性质,能够被不同论域的低阶性质显现。因此,真既是"一"又是"多"。低阶性质与真之间是反对称的显现关系,前者显现后者,后者内在于前者。可以看出,显现是功能主义真理论的重要概念,显现关系是真之"一"与"多"之间的桥梁;然而,显现关系也遭到了质疑。 

Abstract：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 (not necessarily meeting Cook’s background principles) 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.

Link to the official publication.

Abstract: We use the truth predicate to replace the proof predicate in the Solovay functions. What we obtain is the Solovay–liar functions, a mixture of the Solovay function and the liar paradox. The Solovay–liar functions are defined on frames. We provide a sufficient and necessary condition of frames for deciding whether a Solovay–liar function leads to a paradox. Besides, we prove that all possible paradoxes generated from the Solovay–liar functions are a weakening of a paradox including the liar paradox in the sense that they have lower degrees of paradoxicality than the latter. Among such paradoxes, some are so radically different from all the known paradoxes that they cannot be characterized by the definitional equivalences in the same way as the known paradoxes are usually characterized. We also study other similar functions obtained by mixing Solovay functions with other paradoxes.

Link to the official publication.

摘要：所有已知的悖论语句在修正过程的有穷阶段上都出现周期性的循环样式。对此，赫兹伯格设想了一种在修正过程中“越来越慢地交错真假”的语句：“它们在连续的两个阶段为真，然后在随后的连续三个阶段为假，进而又在随后的连续四个阶段为真，以此类推。”本文基于一种构造有穷悖论的方法，借助无穷命题逻辑语言，构造出赫兹伯格语句——它们本质上是一种无穷悖论。此法从特定修正过程出发，逆向构造出具有特定复杂度的悖论。这种构造扩展了当前真理论中的悖论语句的范围，为悖论的研究提出了新的课题。

Link to the official publication

Logic in Asia: Studia Logica Library. Springer, Singapore. Online-first: https://doi.org/10.1007/978-981-15-7134-3_2.

Abstract：The sentences that Solovay constructed in his famous theorem on arithmetical completeness of Gödel-Löb provability logic are all undecidable. We use Solovay’s method to construct paradoxes, which bear to the Solovay’s sentences much the same relation as the liar paradox bears to the Gödel sentence. The main idea is to use the truth predicate instead of the provability predicate in the formalisation of the Solovay function. A typical example of such paradoxes may be seen as obtained from two ordinary paradoxes by damaging symmetry of the `baptising’ biconditionals. We prove that this paradox is a proper weakening of the latter two in the sense that the former has a strictly lower degree of paradoxicality than the latter two. Solovay’s method provides a new approach to finding various kinds of paradoxes.

Link to the official publication

Abstract：The unwinding that Cook (J. Symbol. Log. 69(3), 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 ⟨ℕ,<⟩ 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.

Link to the official publication