逻辑哲学聚焦逻辑研究中萌生的哲学问题,是对逻辑对象、逻辑性质以及逻辑学研究范围的哲学反思.格拉纳达大学(University of Granada)哲学系逻辑与科学哲学教授玛丽亚·荷西·芙拉波莉2023年出版的《命题优先性:一种实用主义的逻辑哲学》(以下简称《命题优先性》)探索了一条将当代逻辑复归人类主体实践性的逻辑哲学研究新路径.
We study definable J-sets for definable groups and compare them with weakly generic sets. We show that the property whether J-sets coincide with weakly generic sets is invariant on enough saturated models and hence a model-theoretical property. We have a positive answer for superstable commutative groups and some easy examples in pCF. We also give an example for noncoincidence.
本文构建了非正规时态逻辑C2t的矢列演算GC2t.运用高野道夫(M.Takana)的语义方法证明了 GC2t的子公式性质,进而证明了 GC2t的有穷模型性和可判定性.另外,本文还证明了 GC2t的插值性质.
在其一生的哲学研究和教学生涯中,康德对逻辑给予了特别的关注.他所关注的逻辑首先是沃尔夫学派的逻辑,进而是亚里士多德所建立的传统逻辑.康德对亚里士多德逻辑做出了极高的评价,认为它"已经结束了并且完成了".但是,这并非就意味着康德对这样的逻辑就无法做出任何实质性的贡献了.实际上,康德对传统逻辑进行了系统的整理和改造,澄清了逻辑的许多基本概念,特别是他对逻辑的本性做出了深入的思考.在思考逻辑的本性问题过程中,他对逻辑与世界内的对象的关系问题给出了极为深刻的回答.他回答中的一些内容可以说颇为现代,与维特根斯坦的相关观点在某种程度上不谋而合.
传统词项逻辑试图接纳亚里士多德逻辑不认可的负词项,但这使得传统词项逻辑成为了一个不一致的理论,原因是负词项的引入与传统的周延理论存在冲突.取消负词项的合法地位可以直接消解不一致性,但会极大缩小词项逻辑的表达与推理能力.因此,对周延理论进行怎样的修改才能使词项逻辑恢复一致并判定出全部有效三段论,是词项逻辑面临的一大难题.传统逻辑学家对该难题进行了一定的探索,但并没有产生一个公认可行的解决方案.现代逻辑学家对该难题的研究存在两种路径:一是在保留周延性传统内涵的基础上修改命题中词项周延性的四条规定,二是修改或删除周延性传统内涵以保留命题中词项周延性的四条规定.其中第二种路径可以与现代逻辑的研究成果相结合并进一步判定出接纳负词项的全部有效三段论,体现了词项逻辑中周延理论最前沿的发展趋势.解决该难题有助于完善逻辑学的理论,促进词项逻辑的进一步发展.
决策论哲学中的一个重要问题是如何在规范层面上理解经典决策论.即使作为形式工具,自创始之初它就被认为符合人类理性选择的某些基本原则,被用来说明和预测选择行动.这一决策论的心智主义解释预设理论元素具有心理实存对应物.当代对心智主义预设的质疑认为,它误解了决策论的形式理论.同时,决策论的规范维度也受到行为经济学等实证研究的挑战.然而,通过进一步分析决策论的规范性刻画问题,本文辩护一种从规范层面刻画经典决策论的立场,旨在表明规范性决策论是评估选择合意性的一种"逻辑".
论证型式刻画了既非演绎也非归纳的所谓第三类论证即假定性论证的推论结构.以非形式逻辑学家沃尔顿、布莱尔、汉森为代表的肯定派主张型式具有规范性,平托则对这一主流看法表示反对.通过对肯定派与否定派相关论述的批判性考察,本文厘清了"论证型式的规范性"论题的内涵,提出型式的规范性包含证明力与约束力双重维度;其次,讨论了批判性问题在评估假定性论证时的显性运用和隐性运用,揭示了肯定派论述中的不一致与概念混淆,在平托的基础上进一步论证了型式没有证明力,没有推论性联系上的好坏之分,假定性论证不能仅凭所例示的型式而区分出好坏;最后,考察了型式与论证提出者、接受者在对话中的行为之间的关系,修正了肯定派的某些提法,认为型式能够引导论证参与者根据对话类型的目标与规则进行话步交换并对实际对话进行评估,但这种约束是间接的、有限度的.
This paper introduces diagrams in projective geometry as valid proving tools.Al-though diagrams are used to support the understanding of proofs in projective geometry,they are not considered as proofs themselves.We will show that diagrams can be transformed in cut-free proofs with elementary expense and vice versa.This means,that diagrams are a valid and complete proof tool,however diagrams may be non-elementarily more complex than usual proofs using lemmata(cuts).As an interesting consequence of these analyses we will demon-strate,that diagrams are not constructive in the logical sense.
The contemporary"proof mining"paradigm has its historical roots in Georg Kreisel's program of"unwinding of proofs".In this paper we elaborate on the tremendous influence Kreisel's ideas have had and still have on this applied reorientation of proof theory and discuss some logical aspects of"proof mining".
An event is modally real in one world if it occurs either in the world or in one of its possible worlds;accordingly,an event is modally nonreal in one world if it does not occur in the world or in any one of its possible worlds.We call a place where all modally nonreal events of a world occur or exist as a modally black hole.This paper presents logical systems for modally real events and modally nonreal events,proves their soundness,and establishes their completeness.
A famous result,due to Kreisel and Lévy(1968),characterizes the uniform reflec-tion principle for Peano arithmetic,RFN(PA),in terms of the transfinite induction principle TI(ε0),namely induction up the ordinal ε0,which is the first ordinal α such that ωα=α.In this article we prove a generalization of this result germane to large swathes of set theories.These set theories T are of the following kind.They comprise Kripke-Platek set theory,KP,but their additional axioms are required to be of restricted syntactic complexity,that is,there exists a fixed n such that they are all of Πn form.A typical example is KP+Powerset+Ξ1-Separation+Ξ2-Collection with Ξ1,Ξ2 ? Πn for some n.The characterization of T+RFN(T)will be given in terms of an induction principle TI(εΩ+1),allowing induction up to the first class ordinal α such that Ωα=α,where Ω stands for the class of all(set)ordinals.The definition of the class ordering εΩ+1 is akin to that of the ordinal representation system for ε0 used in proof theory,whereby the role of the ordinal ω is now played by the entire class of ordinals.The proof that RFN(T)entails TI(εΩ+1)overT is fairly standard in that is uses techniques essentially developed by Gentzen.The converse entailment,though,is the hard part.In the case of PA,Kreisel and Lévy used the no-counterexample interpretation in a formalization due to Tait(1965).The idea of using a cut elimination procedure instead is owed to Kreisel and was implemented by Schwichtenberg(1977).Technically,it shows that the cut elimination procedure for infinite derivations can be engineered via a primitive recursive function for a natural(albeit quite subtle)coding of infinite derivations,which allow for delay inferences(called improper applications of the w-rule),where the premisses are the same as the conclusion.A mathematically rigorous and detailed account of how to work with such codes poses a considerable challenge.In this article we shall be avoiding codes for infinite derivations entirely by utilizing a detour through a fragment of Constructive Zermelo-Fraenkel set theory,CZF,in which general inductively defined classes can be handled without any problems.The exposition of this technical move in a set-theoretic context,which parallels the one by Buchholz(1997)for arithmetic,is quite interesting in its own right.In general,the restriction on the complexity of the axioms of T that do not belong to KP is necessary.For instance,the above characterization does not extend to ZF.Indeed,ZF proves TI(εΩ+1).Naturally,other ordinal representation systems come to mind,for instance,Γ0,which was used by Feferman and Schütte to characterize the strength of autonomous progressions of theories.It would be interesting to figure out what kind of reflection principle corresponds to the induction principle for the class version of Γ0,i.e.,ΓΩ+1.
Current research on causes of deep disagreement with respect to cultural con-stituents sees a tension between the collectivist indistinguishability and the highly individualist idiosyncrasy of cultural knowledge.The tension in its settlement calls for a new way,which takes both epistemic statuses of culture into consideration.This paper answers this call and at-tempts to build a new way by drawing insights from post-Gricean Relevance Theory.It argues that,in looking for the cultural factors that contribute to deep disagreement,we should neither merely look to the cultural knowledge indistinguishably held by the speech participants,nor re-strict our attention to the idiosyncratic knowledge of each individual.Rather,we ought to take stock of cultural manifest knowledge,in the statuses of cultural manifestness,which designates the cultural competence of individual participants.
Metaphor is pervasive in everyday life, and it is not only a form of rhetoric but also a crucial cognitive mechanism. Based on the ad hoc concept and the principle of relevance, relevance theory（RT） explains the inference process and the conditions limiting linguistic metaphor comprehension, but formalizing its analysis remains a formidable challenge. The Iterated Best Response（IBR） model of game-theoretic pragmatics arises as an efficient model capable of addressing the issue. The model focuses on analyzing communicative contexts and encompasses shared information, signal strategy, rational selection, utility, and probabilistic belief. Its solution concept adopts an internal viewpoint to illustrate how communicators achieve equilibrium（the correct understanding of an expression）. Consequently, the IBR model can provide a comprehensive method for formalizing the inference process and its RT-explained constraint conditions. Within the framework of the IBR model, this article examines the process of interaction between the various elements of metaphor usage in order to demonstrate how the process of using metaphors can be formalized effectively.
Finding and defending new axioms for set theory is an important topic in the philosophy of set theory, and the large cardinal axiom is one of the alternatives for new axioms.There are currently two main types of justifications for large cardinal axioms: the extrinsic justifications and the intrinsic justifications. The extrinsic justifications, from the point of view of richness and utility in mathematical practice, do not satisfy the realists.The realists wish to provide some justifications based on the nature of the concept of the set, i.e., to provide intrinsic justifications for large cardinals. I discuss a view of logic from the realism perspective and why we should defend intrinsic justifications for large cardinals under this view, and give examples of how it is possible to justify large cardinals under the realism perspective.
Stance detection aims at detecting the position tendency of a text with respect to the views expressed on a specific topic. This paper adopts current prompt-based learning techniques in the field of natural language processing and proposes novel design methods among the two main engineering approaches for prompt learning（template engineering and expression engineering）: the masked position-oriented manual template MPOT and the semantic similarity-weighted expression SSWV. Accordingly, the paper proposes a prompt-based stance detection model P-RoBERTa MPOT+SSWV ,and compares it with the automatic template method P-tuning. The model achieves excellent accuracy on the NLPCC Chinese microblog stance detection dataset and the online textual argument corpus of Sun Yat-sen University. The experiments in this paper show that the P-RoBERTa MPOT+SSWV model outperforms the model using the pre-training +fine-tuning approach under small sample learning conditions. The paper shows that the prompt learning-based model design approach is useful for text stance detection tasks and achieves very impressive performance even under small sample learning conditions.
One part of Frege’s logicism is to reduce the theory of real numbers to logic. In Basic Laws of Arithmetic, real numbers are intended to be defined as the ratios of quantities in a domain of quantities, which is a class belonging to a positive class. Although the system established in the work is inconsistent, the theory of real numbers presentend therein can be reconstructed in a consistent way. Kutschera chose to reconstruct it in the set-theoretic setting and proved that both a Fregean domain of quantities and the set of Fregean real numbers are dense, continuous and ordered abelian groups with Archimedean property. On the basis of his work, it is further shown in the paper that they are also Dedekind-continuous, Archimedean ordered fields.
Arguments from gradualism are a type of arguments common to meet in everyday life, yet have not received specific discussion. Instead, with almost the same form,sorites paradox and sorites slippery slope arguments have received much more concerns and studies. Although sorites paradox and sorites slippery slope arguments were traditionally considered to be fallacies, we could avoid obtaining absurd or inacceptable results if we restrict the length of inference in those arguments. In other words, unlike sorites paradox or sorites slippery slope arguments, not all arguments from gradualism will obtain inacceptable results. Then, when will arguments from gradualism obtain acceptable results, so belong to good arguments, and when will they obtain inacceptable results, so belong to bad arguments? D. Walton thought that if a sorites slippery slope argument moved from the controlled zone, through the gray zone, and finally into the uncontrolled zone, it would reach inacceptable results. However, how could we precisely define and recognize the crucial gray zone? To answer those questions, this article will use probability theory and fuzzy set to quantitatively characterize the inference procedure of arguments from gradualism, sorites paradox and sorites slippery slope arguments, and reveal some connections and differences among those three types of arguments.
In 1929 Wittgenstein returned to Cambridge and immediately wrote a number of philosophical notes that clearly marked the beginnings of a transition in his thinking.We can get some clues to describe his transition from the only published paper “Some Remarks on Logical Form”, Philosophical Remark sorted out from manuscripts of the same period and the conversations between Wittgenstein and Vienna Circle recorded by Waismann. One of the clues is his reflection on the color exclusion problem made him change his views on the elementary propositions. And then he renounced the use of truthfunctional apparatus to reveal an underlying general form of propositions. At this stage of his thinking, he did not abandon all basic ideas of Tractatus Logico-Philosophicus at once, but tried to modify his account by introducing a new approach to allow for the possibility of elementary propositions that are incompatible with on another, which finally forced him to acknowledge the existence of elementary propositions which are “incomplete pictures”. This paper attempts to review the process of the transition at Wittgenstein’s own words.
Philosophers believe that a language must conform to the composition principle in order to be mastered. In order to prove this conclusion, linguist James Higginbotham carefully examine the question of whether natural language quantitative conditional sentences conform to compositionality. James Higginbotham thought that the quantified conditionals of natural language must satisfy two presuppositions in order to conform to compositionality: The antecedent being counterfactually irrelevant to the consequent?satisfying the law of Conditional Excluded Middle. But these two conditions have no sound basis, thus the question of whether quantified conditional sentences conform to the principle of compositionality is a real problem. However, Higginbotham’s argument,despite its merits, contains errors. This paper will correct Higginbotham’s argument, and argue that natural language conditional sentences are full of ambiguity and ambiguity,and must be paraphrased to make them conform to compositionality. Under certain conditions, natural language conditional sentences can be compounded, because the semantics are determined before the grammar.
Intuitively, different kinds of propositions have different ways of being true. Truth pluralists often unpack this intuitive idea in terms of truth properties. So, metaphysically speaking, the core thesis of truth pluralism is that there are different truth properties.Intuitively, compounds are true in some way different from atomics. To avoid postulating specific truth properties for compounds, Douglas Edwards proposes to construe the ways compounds are true as truth conditions, and then to appeal to the separability thesis to block the introduction of truth properties from the statements of truth conditions. I will argue that Edwards’ s strategy can be applied to atomics as well, and so strengthens the double-counting objection to truth pluralism, which urges us to accept truth monism rather than truth pluralism.
