A New Semantics for Systems of Logic of Essence

The purpose of the present paper is to provide a way of understanding systems of logic of essence by introducing a new semantic framework for them. Three central results are achieved: first, the now standard Fitting semantics for the propositional logic of evidence is adapted in order to provide a new, simplified semantics for the propositional logic of essence; secondly, we show how it is possible to construe the concept of necessary truth explicitly by using the concept of essential truth; finally, Fitting semantics is adapted in order to present a simplified semantics for the quantified logic of essence.     

Rumfitt on the logic of set theory

According to a famous argument by Dummett, the concept of set is indefinitely extensible, and the logic appropriate for reasoning about the instances of any such concept is intuitionistic, not classical. But Dummett's argument is widely regarded as obscure. This note explains how the final chapter of Rumfitt's important new book advances our understanding of Dummett's argument, but it also points out some problems and unanswered questions. Finally, Rumfitt's reconstruction of Dummett's argument is contrasted with my own preferred alternative.     

On Bolzano's Concept of a Sum

Alongside his groundbreaking work in logic, Bernard Bolzano (1781–1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.     

Dialektik Und Formalisierung

Dialectics and Formalization. In an appendix to his article Can the concept of dialectic be made clear? (JGPS 27: 131–165) the author critically examined an attempt by D. Wandschneider of reconstructing Hegelian dialectical logic by displaying antinomic structures. The main steps of this reconstruction were formalized within the framework of second order predicate logic. In his reply (JGPS 27: 347–352) Wandschneider argues that formalization is the wrong way of interpreting and judging his reconstruction project on the ground that the understanding of predication is already presupposed by predicate logic and, therefore, cannot be formalized. In the present contribution it is shown that Wandschneider's criticism is based on a fundamentally mistaken conception of formalization and formal logic and that the problems posed by his project remain completely unresolved.     

Completeness: from Gödel to Henkin

This paper focuses on the evolution of the notion of completeness in contemporary logic. We discuss the differences between the notions of completeness of a theory, the completeness of a calculus, and the completeness of a logic in the light of Gödel's and Tarski's crucial contributions.We place special emphasis on understanding the differences in how these concepts were used then and now, as well as on the role they play in logic. Nevertheless, we can still observe a certain ambiguity in the use of the close notions of completeness of a calculus and completeness of a logic. We analyze the state of the art under which Gödel's proof of completeness was developed, particularly when dealing with the decision problem for first-order logic. We believe that Gödel had to face the following dilemma: either semantics is decidable, in which case the completeness of the logic is trivial or, completeness is a critical property but in this case it cannot be obtained as a corollary of a previous decidability result. As far as first-order logic is concerned, our thesis is that the contemporary understanding of completeness of a calculus was born as a generalization of the concept of completeness of a theory. The last part of this study is devoted to Henkin's work concerning the generalization of his completeness proof to any logic from his initial work in type theory.     

Nothing More or Less than Logic: General Logic, Transcendental Philosophy, and Kant's Repudiation of Fichte's Wissenschaftslehre

In this paper I lay the foundations for an understanding of one of Fichte's most neglected and least understood texts: the late lecture course on Transcendental Logic. I situate this work in the context of Fichte's lifelong struggle with the problem of understanding the relation between logic and philosophy – a problem that I show to figure centrally both in Fichte's own revolutionary thinking and in his response to Kant's notorious denunciation of the Wissenschaftslehre. By attending to this context we can understand Fichte's philosophical ambitions in the late lectures: a critique of particular doctrines of general logic; a critique of the conception of thought presupposed both by the traditional logic and by Kant himself; and a new conception of the relation between logic and the philosophical theory of experience. This revised version was published online in June 2006 with corrections to the Cover Date.     

Essay Review

The incompleteness and artificiality of the ‘traditional logic’ of the textbooks is reflected in the way that syllogisms are commonly enumerated. The number said to be valid varies, but all the numbers given are of a kind that logicians should find irritating. Even the apparent harmony of what is almost invariably said to be the total number of syllogisms, 256, turns out to be illusory. In the following, it is shown that the concept of a distribution-value, which is related to the traditional theory of distribution, and the familiar concept of quantity together suffice to produce a far better way of enumerating syllogisms and a more complete understanding of the systematic features of syllogistic logic.     

The Open-Endedness of the Set Concept and the Semantics of Set Theory

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory.     

Gay Marriage and the Paradox of Existence

Helping students or workshop participants radically expand their critical-thinking horizons beyond conventional dualistic bounds on the subject of gay marriage is difficult. The paradoxical logic of Nagarjuna's tetralemma is one means to do so. They learn not only this new investigative tool and deepen their understanding of the perspectives surrounding gay marriage, but have to examine the degree to which they limit their own capacity to think.     

Naturalizing logic: Errors of reasoning vindicated: Logic reapproaches cognitive science

A complete revision of mainstream logic is an urgent task to be achieved. This revision will be able to bring logic into a creative rapprochement with cognitive science. This can be achieved by trying to do for logic what over forty years ago Quine and others attempted for epistemology. It is necessary to propose a “naturalization” of the logic of human inference. This paper deals with an examination of how the naturalization process might go, together with some indication of what might be achieved by it. To assist the reader in understanding the naturalization of logic I will take advantage of my own research on the concept of abduction, which vindicates the positive cognitive value of the fallacy of the affirming the consequent thanks to the so-called EC-model (Eco-Cognitive model), and of the recent book Errors of Reasoning: Naturalizing the Logic of Inference (2013) [86], by John Woods. While this paper certainly aims at promoting the research program on the naturalization of logic, it also further advocates the placement of abduction in the research programmes of logic, and stresses to what extent our contemporary philosophical and logical tradition is indebted towards Charles Sanders Peirce, a thinker often praised for his productivity but whose quality and importance are too often overlooked.     

A logic LU for understanding

Understanding a proposition for an intelligent agent is an important epistemic concept. We first discuss intuitively general logic characteristics of understanding, and give a language and a semantics containing understanding as a modal operator. Secondly, we develop the system LU for the operator, give some results of its proof theory, and then we prove the frame soundness and frame completeness of LU.     

墨家逻辑推理模式的新解释

墨家是先秦诸多学派之一,墨家逻辑也是中国古代本土逻辑思想的典范之一。墨子及其后学创立了中国思想史上第一个＂以名举实,以辞舒意,以说出故＂的墨家逻辑体系,成为中国古代逻辑思想发展的优秀代表。墨家逻辑的主要推理模式包括：＂辟＂、＂侔＂、＂援＂、＂推＂等。墨家逻辑思想的研究开启了中国逻辑思想研究的先河,墨家逻辑思想研究是中国逻辑思想研究的核心内容之一。国际逻辑学界对作为非印—欧语言系统的中国逻辑的关注,显示了中国逻辑独立存在的价值。今天的中国逻辑思想研究处于现代逻辑发展与中国现代文化发展的交汇点上,需要我们从逻辑和中国文化的角度来研究中国逻辑思想。用逻辑的一般特性来分析墨家逻辑,依据工具性、形式性和有效性这三个方面,是解释墨家逻辑的一个新角度。     

干预训练对儿童掌握遗传知识的作用

引入干预训练法探讨儿童的遗传概念的发展开辟了儿童朴素生物学认知领域研究的新方向。文章从干预内容（关于遗传的事实性知识与概念重组）和形式（讲授与同伴互动）两个方面报告了近些年有关干预训练影响儿童对遗传知识掌握的研究进展,并从不同干预内容和形式以及被试年龄选取的适当性三个方面,深入分析了以往各种干预方法效果差异的原因,最后提出未来的研究应致力于改进干预训练内容、探索儿童遗传概念获得的最佳时期和发展的快速期,强化儿童遗传认知的研究与幼儿生物科学启蒙教育之间的联系     

Truth Values and Proof Theory

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.     

The Logic of Pragmatic Truth

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.     

皮亚杰晚年的“新理论”及其思考

皮亚杰的经典认知发展理论堪称典范,但也并非尽如人意,以致20世纪60、70年代其理论经常遭受抨击。文章以对皮亚杰经典理论的批评和质疑为起点,重点介绍皮亚杰在生命的最后阶段所进行的理论建设,并试图对皮亚杰的新理论做出初步评价。作者认为,皮亚杰晚年的新理论建立在对应性、态射、范畴、转换等新的概念体系之上,并将发展视为从心理内态射到心理间态射,再到超态射的演变过程。由此,新理论强调了“水平”概念和“意义逻辑”,弱化了早期的“阶段”概念和“命题逻辑”。     

Kant on the Logical Origin of Concepts

In his lectures on general logic Kant maintains that the generality of a representation (the form of a concept) arises from the logical acts of comparison, reflection and abstraction. These acts are commonly understood to be identical with the acts that generate reflected schemata. I argue that this is mistaken, and that the generality of concepts, as products of the understanding, should be distinguished from the classificatory generality of schemata, which are products of the imagination. A Kantian concept does not provide mere criteria for noting sameness and difference in things, but instead reflects the inner nature of things. Its form consists in the self‐consciousness of a capacity to judge (i.e. the Concept is the ‘I think’).     

Using Syllogistics to Teach Metalogic

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object‐theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics.     

Webers Idealtypus Als Methode Zur Bestimmung Des Begriffsinhaltes Theoretischer Begriffe in Den Kulturwissenschaften

Weber's Ideal Type as a Method of Forming the Content of Theoretical Concepts in Social Sciences}. Max Weber introduced the ideal type as the specific method of concept formation in social sciences. But the ideal type is not established in social research. Instead, authors in philosophy of science until today try to reconstruct and interpret what Weber said about ideal types as well as what might be their importance in Weber's social theory. The thesis of the following paper is that the difficulties in understanding Weber's ideal types are linked with Weber's intensional logic of concept formation. The thesis is defended in three steps. The first step deals with Weber's understanding of what is a scientific question in cultural sciences. Secondly Weber's critical arguments against positivism, hegelianism and historism are worked out. Thirdly, Weber's method of concept formation is reconstructed.