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This paper proves a precisification of Hume’s Law—the thesis that one cannot get an ought from an is—as an instance of a more general theorem which establishes several other philosophically interesting, though less controversial, barriers to logical consequence.

Advances in Philosophical Logic

The article is devoted to the study of the status of intensionality in the exact contexts of logical and mathematical theories. The emergence of intensionality in logical and mathematical discourse leads to significant obstacles in its formalization due to the appearance of indirect contexts, the uncertainty of its indication in the theoretical apparatus, as well as the presence of various kinds of difficult-to-account semantic distinctions. The refusal to consider intensionality in logic is connected with Bertrand Russell’s criticism of Alexius Meinong’s intensionality ontology, and with Willard Van Orman Quine’s criticism of the concept of meaning and quantification of modalities. It is shown that this criticism is based on a preference for the theory of indication over the theory of meaning, in terms of the distinction “Bedeutung” and “Sinn” introduced by Gottlob Frege. The extensionality thesis is explicated; by analogy with it the intensionality thesis is constructed. It is shown that complete parallelism is not possible here, and therefore we should proceed from finding cases of extensionality violation. Since the construction of formal logical systems is to a certain extent connected with the programs of the foundations of mathematics, the complex interweaving of philosophical and purely technical questions makes the question of the role of intensionality in mathematics quite confusing. However, there is one clue here: programs in the foundations of mathematics have given rise to metamathematics, which, although it stands alone, is considered a branch of mathematics. It is not by chance that, judging by the problems arising in connection with intensionality, there is a growing suspicion that intensionality can play a significant role in metamathematics. As for the question of the sense in which metamathematics results can be considered mathematical, in terms of the presence of intensional contexts in both disciplines, it is a matter of taste: for example, the autonomy of mathematical knowledge as a result of the desire of mathematicians to eliminate the influence of philosophy that took place in the case of David Hilbert may be worth considering in the context of mathematics. Thus, the rather vague concept of intensionality receives various explications in different contexts, whether it is philosophical logic or metamathematics. In any case, the detection of context intensionality is always associated with a clear narrowing of the research area. It is obvious that the creation of a more general theory of intensionality is possible within a more general framework, in which logic and mathematics must be combined. In this respect, we can hope for the resumption of a logical project, which would be a purely logical consideration made of the natural and the mathematical.

In this article I argue that Hegel and Saussure both discovered a new mode of theorization that I propose to call ‘structural explication’. This is distinct from the generally dominant ‘linear’ mode of theorization—i.e., causal and quasi-causal explanations. I also argue that the standard criticisms usually directed against Hegel and Saussure stem from a failure to appreciate the nature of structural explication. For example, both Hegel and Saussure argue that—in some deep sense—form can generate content. But this must be comprehended in a strictly non-linear way. A linear interpretation of such arguments will lead to absurdities. I propose to call such deep generative structures (with a nod to Kant) the ‘necessary structures of possibility’. By comparing Hegel's thoughts on the science of a philosophical logic and Saussure's thoughts on the science of a general linguistics it is possible to discern a deep ‘scientific’ affinity. Furthermore, I argue that the structural level cannot be accounted for in any linear way. On the contrary, the linear explanation is fundamentally dependent on a structural explication of the genesis of the basic terms it assumes as ‘given’. A possible reason for the pervasiveness of the linear explanation (besides, perhaps, the success of causality-oriented natural sciences) is that discursive language is linear and our lived experience in time is linear. Thus, a structural explication will inherently appear less intuitive, and maybe also less ‘satisfying’, than a linear explanation. Finally, I also bring the distinction between the linear and the structural to bear on Robert Brandom's normative pragmatist reading of Hegel's ‘semantic holism’.

We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing (Journal of Philosophical Logic, 47(2), 259–279, 2018).

Das Buch untersucht die logischen Grundsatzfragen und Elemente, die dem Heideggerschen Werk zugrundeliegen. Zentrale Vorlesungen und Texte werden anhand des Begriffes des Streites als logische Reflexionen Heideggers exploriert, um so einen bisher wenig untersuchten Aspekt des Heideggerschen Denkens herauszustellen. Dabei wird eine Brücke geschlagen vom Spätwerk zum Frühwerk, letzteres also aus der später entfalteten Komplexität heraus interpretiert. Drei elementare Streitrelationen werden dabei als ineinandergreifend gedacht: der formale Streit als zugrundeliegende Form, der existenziale Streit, welcher den retroaktiven Zeitaspekt des Streites fokussiert und der geschichtliche Streit, welcher den Ereignisbegriff des Spätwerks klärt. The books research is focused on the logical foundations and elements of Heideggers work. Major texts and several of the lecture courses are interpreted by utilizing the concept of strife to research this under-explored aspect of Heideggerian thought. Central to this is a reading of Heidegger orienting itself on the later texts as an interpretative key to the earlier works. This leads to the formulation of three interlocked concepts of strife. The formal structure of strife itself, the existential strife which focuses a retroactive concept of time and the historical strife. The latter offers an interpretation of the concept of the event which is central to Heideggers later works.

In a recent paper, Negri and Pavlović (Studia Logica 1–35, 2020) have formulated a decidable sequent calculus for the logic of agency, specifically for a deliberative see-to-it-that modality, or dstit. In that paper the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (Facing the future: agents and choices in our indeterminist world. Oxford University Press, Oxford, 2001). And while the influence of the latter book on the study of logics of agency cannot be overstated, we note that this is not the only axiomatization of that modality available. In fact, an earlier (and arguably purer) one was offered in Xu (J Philosophical Logic 27(5):505–552, 1998). In this article we fill this lacuna by proving that this alternative axiomatization is likewise readily derivable in the system of Negri and Pavlović (Studia Logica 1–35, 2020).

In the chapter on quantum logic in Volume 6 of Handbook of Philosophical Logic, Dalla Chiara and Giuntini make an interesting observation that there is a unified relational semantics underlying both the \(\{ {\lnot }, {\wedge } \}\)-fragment of intuitionistic logic and ortho-logic. In this paper, we contribute to a systematic investigation of this relational semantics by providing an axiomatization of its logic.

El presente trabajo analizará el concepto de verdad en el evangelio de San Juan. El análisis se basa en los texto donde la palabra griega "Ἀλήθεια" es usada. Basándonos en su etimología iremos explorando lo que Juan nos quiere decir en cada texto del evangelio. Este artículo no pretende ser exhaustivo desde el punto de vista filosófico-teológico, sólo pretende comentar y extraer una concepción coherente de la verdad en el evangelio de San Juan., This paper makes an analysis of the concept of truth in St John Gospel. This analysis is made on the selected texts where instances of the Greek word "Ἀλήθεια" appears. By using its etymology, we will explore what St John says about the truth in each passage. This paper is not exhaustive from the philosophical-theologic point of view, its aim is to comment and extract a coherent conception of the truth in the Gospel of St John.

Following Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

This article examines J. S. Mill's philosophical logic as the basis for his political philosophy. In particular, it explores how he understands the logical mechanism of political discourse in his work A System of Logic and how this understanding supports his defense of freedom of thought and discussion in his On Liberty (chapter 2). While it is well known in the scholarly literature that Mill draws on Socratic dialectic to develop his view of political discourse, this article investigates in detail the logic behind the Socratic dialectic, thereby identifying the historical significance of Mill's defense of liberty of discussion.

There is an apparent dilemma for hierarchical accounts of propositions, raised by Bruno Whittle (Journal of Philosophical Logic, 46, 215–231, 2017): either such accounts do not offer adequate treatment of connectives and quantifiers, or they eviscerate the logic. I discuss what a plausible hierarchical conception of propositions might amount to, and show that on that conception, Whittle’s dilemma is not compelling. Thus, there are good reasons why proponents of hierarchical accounts of propositions (such as Russell, Church, or Kaplan) did not see the difficulty Whittle raises.

Backwards-looking operators Saarinen, E. [1979. “Backwards-Looking Operators in Tense Logic and in Natural Language.” In Essays on Mathematical and Philosophical Logic, edited by J. Hintikka, I. Ni...

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature (see, e.g. Mares, Studia Logica 51(1), 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71(1), 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are (Fine, Journal of Philosophical Logic 17(1), 27–59, 1988; Mares, Studia Logica 51(1), 1–20, 1992), both of which are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic.

This biocentric reading of Francis Cabrel’s “La Corrida” from the lens of Michel Onfray’s philosophy explores their emotional plea for the abolition of bullfighting in Southern France. For both the acclaimed songwriter and the maverick philosopher, there is no valid moral or philosophical justification for the continued existence of this cultural practice. Albeit in very different artistic mediums, Cabrel and Onfray generate equally persuasive dystopian visions of the carnage that transpires in the arena. Both artists cogently deconstruct the pervasive cultural and philosophical logic often used by supporters of this controversial blood sport urging global society to take action. In line with a growing body of empirical evidence, Cabrel and Onfray present the bull as a highly sentient being that suffers a slow and agonizing death in the arena. Debunking the unfounded notion that the behavior of non-human agents is purely mechanistic in nature, Cabrel and Onfray implore us to reexamine ubiquitous simulacra...

Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed sometimes, in both everyday discourse and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences., Comment: 19 pages

Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded by an aura of scepticism that has kept most philosophers away. In this paper I suggest we shouldn’t give up all hope. First, I introduce the reader to these issues. Second, I discuss the conditions a good notion of reference in arithmetic must satisfy. Accordingly, I then introduce adequate notions of reference for the language of first-order arithmetic, which I show to be fruitful for addressing the aforementioned issues in metamathematics.

Alfred Tarski’s refinement of an account of truth into a formal system that turns on the acceptance of Convention-T has had a lasting impact on philosophical logic, especially work concerning truth, meaning, and other semantic notions. In a series of studies completed from the 1930s to the 1960s, Arne Naess collected and analysed intuitive responses from non-philosophers to questions concerning truth, synonymy, certainty, and probability. Among the formulations of truth studied by Naess were practical variants of expressions of the form “p’ is true if and only if p’. This paper calls attention to a series of experimental results Naess overlooked in his original study. These data collectively suggest that acceptance of expressions of the form “p’ is true if and only if p’ varies according to what kind of statement p is.

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language (using truth functional connectives and quantifiers). This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given.

Built in 1991, the theoretical framework of Boltanski and Thevenot has often been considered as heteronomous, unconcerned about current sociological issues or at worst useless to understand those phenomena it aspires to. Nevertheless, it still remains an effective tool to understand how things, human beings, (inter)actions get organized. By means of the construction of a new “city” (a main political and philosophical logic), this text defends this postulate. He demonstrates that the grammar of justification allows to analyze current problems and federate environmental claims and actions undertaken too often outside the box.

International audience; The paper discusses graded extensions of the cube of opposition, a structure that naturally emerges from the square of opposition in philosophical logic. These extensions of the cube of opposition agree with possibility theory and its four set functions. This extended cube then provides a synthetic and unified view of possibility theory. This is an opportunity to revisit basic notions of possibility theory, in particular regarding the handling of fuzzy events. It turns out that in possibility theory, two extensions of the four basic set functions to fuzzy events exist, which are needed for serving different purposes. The expressions of these extensions involve many-valued conjunction and implication operators that are related either via semi-duality or via residuation.

In this chapter, I present my methodology—Possible Worlds Theory—which I argue is the most suitable methodology with which to analyse counterfactual historical fiction. I begin by explaining the theory in detail. For this purpose, I trace the development of Possible Worlds Theory from its foundation in philosophical logic to its application in narratology. The chapter will suggest ways in which Possible Worlds Theory is highly relevant for the analysis of counterfactual historical fiction, but also indicate that it requires modification and supplementation for it to be entirely successful.

In the literature of Chinese philosophical logic, there are at least four representative interpretations and analyses of the logical and philosophical thinking in the Gongsun Longzi. These four different interpretations are: Hu Shih’s 胡適 “description-theoretical interpretation,” Fung Yu-lan’s 馮友蘭 “Platonic realistic interpretation,” Janusz Chmielewski’s “set-theoretical interpretation,” and Chad Hansen’s “nominalistic interpretation” which is based on his mass-noun hypothesis. In this chapter, I will demonstrate that all these interpretations are not in accordance with the text and also not coherent and comprehensive in interpretation. Moreover, I will use the first-order predicate logic to analyse the logical structure of the philosophical thinking in the text, especially in the Discourse on White-Horse, and explain its philosophical implication.

The Categories took root with the Arab philosopher Abu Ishaq Yaqoub al-Kindi as one of the most important logical, philosophical and linguistic investigations. And before al-Farabi’s works the understanding of the Categories, the basis for the acquisition of logical and philosophical knowledge was not completed. Abu Nasr Al-Farabi, who was a student of Bishr Matta bin Yunus, and took the making of logic from Yuhanna Ibn Haylan, was the first to develop the science of Aristotelian logic in its comprehensive and detailed form. Al-Farabi became the first teacher for those who wanted to stand on the truth of Aristotelian logic, and to understand the meaning of Categories, and how they are the firsts established for all sciences The text of al-Farabi was the mayor in Ibn Baja’s philosophy in Andalusia. The main goal and purpose of this study is to try understanding the Categories in the thought of Abu Nasr al-Farabi, by arranging the al-Farabi texts that dealt with this topic, in an attempt to reveal his understanding of the Categories, and to try to answer the question of what is the purpose of the Categories. He made of logic a race that includes three types, the first is linguistic logic, the second is philosophical logic, and the third is intellectual logic, making the strength of the soul the bearer of this logic, this power which is the utterance and from which the name of logic is derived. Since the goal of philosophy is to reach the final perfection, and to reach the truth, which is the ultimate happiness, and proof was the conductor of truth and certainty, according to Al-Farabi, the Categories were the bearer of this perfection by force, as the proof material was twice, the first being the material for proof in terms of words, and in the second the material for proof in terms of meanings, and the last being the purpose. Key words: philosophy, logic, categories, intelligibles, sayings, Aristotle, al-Farabi.

This short note reviews briefly the history of logic in the last 100 years or so, discussing the rise of “classical” logic, and then of non-classical logic. The role of logic in contemporary departments of mathematics, computer science, and philosophy is then discussed. A few final words address the question of where logic might be going.

The opinions and suggestions in this article are addressed to young academicians carrying out their studies in the field of philosophical logic in relation to philosophy. This target group contains especially academicians working in the field of traditional logic taught in theology faculties as well as academicians who have studied in philosophy departments and who are interested in contemporary logic and the philosophy of logic in Turkey. Logic is the term given for the discipline which aims to establish the place – in other words the playground – where almost all the issues and problems concerning humanity are discussed and expressed in a healthy as possible manner. Logic is the field in which the fundamental rules guide all parties in the debate in their search for the truth. Moreover, many of the topics covered are those touching the grounds of logic. In this respect, the extent to which logic is unbiased or neutral in relation to the different philosophical positions adopted in all these issues is open to discussion. Taking this background into consideration, the article aims to make some suggestions to logicians in philosophy and theology.

Perhaps it is not overly pedantic to say that one will find Wittgenstein’s Tractatus Logico-Philosophicus very difficult even if one first understands Russell’s philosophical logic. But the question remains as to whether the work is intended in alliance with Russell’s research program for a scientific method in philosophy or splits from that program. This paper endeavors to answer the question by revealing new evidence that Wittgenstein held his Doctrine of Showing in 1913 and that it was a demand he imposed in criticizing Russell’s multiple relation theory of judgment.

This paper focuses on two interrelated issues about the prospects for research projects in experimental philosophical logic. The first issue is about the role that logic plays in such projects; the second involves the role that experimental results from the cognitive sciences play in them. I argue that some notion of logic plays a crucial role in these research projects, and, in turn, the results of these projects might inform substantive debates in the philosophy of logic.

This thesis can be ideally placed at the intersection of three research topics: conditional logics, proof theory and neighbourhood semantics. The family of logics under scope stems from the works of Stalnaker and Lewis, and extends classical propositional logic by means of a two-place modal operator, which expresses a fine-grained notion of conditionality. The semantics of these logics is modularly defined in terms of neighbourhood models. The research aim is to investigate the proof theory of conditional logics, by defining sequent calculi for them. The proof systems introduced are extensions of Gentzen’s sequent calculus; they are either labelled, defined by enriching the language, or internal, which add structural connectives to the sequents. Moreover, the calculi are standard: they are composed of a finite number of rules, each displaying a fixed number of premisses. The thesis is organized in six chapters. Chapters 1 contains an axiomatic and semantic overview of conditional logics, while Chapter 2 is a short introduction to proof theory. The original contributions to the subject are presented in chapters 3 – 6. Chapter 3 introduces labelled calculi based on neighbourhood models for preferential conditional logics, and Chapter 4 presents different internal proof systems covering counterfactual logics, a subfamily of preferential logics. Chapter 5 analyses the relationship between proof systems by presenting a mapping between a labelled and an internal calculus. Finally, the proof-theoretic methods developed for conditional logics are applied in chapter 6 to the multi-agent epistemic logic. Tämä väitöskirja sijoittuu ideaalisesti kolmen tutkimusaiheen risteykseen: konditionaalien logiikka, todistusteoria, ja ympäristösemantiikka. Katettujen logiikoiden perhe periytyy Stalnakein ja Lewisin töistä ja laajentaa klassillista lauselogiikkaa kaksipaikkaisen modaalioperaattorin kautta. Se ilmaisee hienojakoisen konditionaalisuuden käsitteen. Näiden logiikoiden semantiikka määritellään modulaarisesti ympäristösemantiikan termein. Tutkimuksen tavoitteena on selvittää konditionaalien logiikan todistusteoriaa määrittelemällä niille sekvenssikalkyyleita. Esitellyt todistussysteemit ovat Gentzenin sekvenssikalkyylin laajennuksia; ne ovat joko merkeillä varustettuja, joihin päädytään kielen rikastuksella, tai sisäisiä, joihin päädytään lisäämällä sekvensseihin rakenteellisia konnektiiveja. Nämä laajennukset ovat myös standardikalkyyleja: ne muodostuvat äärellisestä määrästä sääntöjä, joissa jokaisessa on kiinteä määrä premissejä. Väitöskirja muodostuu kuudesta kappaleesta. Kappale 1 sisältää aksiomattisen ja semanttisen katsauksen konditionaalien logiikkaan, ja kappale 2 on taas lyhyt johdatus todistusteoriaan. Uudet tutkimuspanokset aiheeseen on esitetty kappaleissa 3-6. Kappale 3 esittää ns. merkityt sekvenssikalkyylit joiden perustana on preferentiaalisten konditionaalien logiikan ympäristömallit, kappale 4 esittää erilaisia sisäisiä todistussysteemejä jotka kattavat kontrafaktuaalien logiikat, jotka ovat preferentiaalisten logiikoiden alaperhe. Kappale 5 analysoi eri todistussysteemien välisiä suhteita merkkikalkyyylien ja sisäisten kalkyylien välisen kuvauksen kautta. Kuudennessa ja viimeisessä kappaleessa sovelletaan konditionaalien logiikalle kehitettyjä todistusteoreettisia metodeja useamman agentin episteemiseen logiikkaan. La thèse se place à l’intersection de trois sujets de recherche : logiques conditionnelles, théorie de la démonstration et sémantique de voisinage. La famille de logiques conditionnelles considérées provient dès ouvrages de Stalnaker et Lewis. Elle est une extension de la logique classique propositionnelle avec un opérateur modal à deux places, qui exprime une notion affinée de conditionnalité. La sémantique de ces logiques est définie en termes de modèles de voisinage. Le but de la recherche est d'étudier la théorie de la démonstration des logiques conditionnelles, en précisant leur calculs des sequents. Les calculs définis sont des extensions du calcul des sequents de Gentzen ; ils sont étiquetés, c’est à dire définis en enrichissant le langage, ou internes, qui rajoutent des connecteurs structurels aux sequents. La thèse est organisée en six chapitres. Le chapitre 1 présente les axiomes et la sémantique des logiques conditionnelles et le chapitre 2 introduit la théorie de la démonstration. Les contributions originelles au sujet sont traitées dans les chapitres 3 – 6. Le chapitre 3 introduit des calculs de sequents étiquetés basés sur la sémantique de voisinage pour les logiques conditionnelles préférentielles. Le chapitre 4 présente différents systèmes internes de calcul pour les logiques counterfactuelles, une sous-famille des logiques préférentielles. Le chapitre 5 analyse la relation parmi les systèmes de preuve en présentant les deux côtés d’une traduction entre un calcul étiqueté et un calcul interne. Finalement, au chapitre 6, les méthodes de la théorie de la démonstration conditionnelle sont appliquées à une logique épistémique multi-agente.