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Arabic logicians in the thirteenth century discussed a set of arguments raised by the theologian Fakhr al-Dīn al-Rāzī (d. 1210) that in some respects closely resembles Carroll's paradox. Roughly, the paradox states that we can never reach a conclusion from a set of premises without incurring an infinite regress. The present article presents and discusses Rāzī's formulation of the problem with syllogistic deduction, his own solutions to the problem, and the contributions of Afḍal al-Dīn al-Khūnajī (d. 1248) and Najm al-Dīn al-Kātibī (d. 1276). It is argued that the proposed solutions developed by these authors are best understood as tending in the direction of Gilbert Ryle's distinction between knowing-that and knowing-how. [ABSTRACT FROM AUTHOR]

We present how the theory of reasoning developed by Tadeusz Czeżowski, a Polish logician and a member of the Lvov-Warsaw School (LWS) can be applied to the mediaeval texts which interpret the Bible, which we collectively call as Biblical exegesis (BE). In the first part of the paper, we characterise Czeżowski's theory of reasoning with some modifications based on remarks of Kazimierz Ajdukiewicz. On these grounds, we discuss the nature of reasoning and its different types, as well as the problem of textual representation of reasoning. In the second part, we describe the analytical nature of some BE at the end of twelfth century and in the thirteenth century by referring to the examples of Stephen Langton, Robert Grosseteste, Bonaventure, Albert the Great and Thomas Aquinas. We argue that they represented an analytical approach in BE, characterised by advanced use of logic and specific methods, including reasoning reconstruction and logical analysis. In the third part, we present selected examples to show how Czeżowski's framework helps in identifying various types of reasoning. We indicate some universal problems with the textual representation of reasoning found in the BE of the authors in question. Lastly, we point out how Czeżowski's framework enables the understanding of phenomena such as 'Special Biblical Inference'. Thanks to this experiment, we can see how a framework as advanced as that offered by LWS representatives can be put to the test using mediaeval Biblical commentaries, yielding interesting results. [ABSTRACT FROM AUTHOR]

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position was shared by Twardowski's students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. [ABSTRACT FROM AUTHOR]

This paper argues that being there, actually existing, is a notion that cannot be explicated by formal logicians, cannot be defined in terms of conscious perception, and cannot be satisfactorily explained using the theories of mathematics or natural science. So, must we turn to theology to make up for the deficiencies of the methods so far canvassed? The paper concludes by considering the Thomistic identification of God with existence itself, but argues that it would be a mistake to suppose that the mystery of actual existence is thereby dispelled. [ABSTRACT FROM AUTHOR]

This article is about the evolution of logic and the inclusion of fallacies as active components in argumentation and debate. It emphasizes the need to develop a logical theory of the use of fallacies and legitimize them as part of modern reasoning. Additionally, it mentions the existence of different research communities in logic, each with different approaches and perspectives. The text also mentions the need to counteract fallacies in reasoning, especially in the context of media and social networks. Furthermore, it highlights the importance of developing a new logic that integrates fallacies and mentions advances in big data and theories of universal distortions as factors that allow for this next step. [Extracted from the article]

Following Avicenna, many Muslim philosophers and logicians have identified 'intellectual universal' (kullī ʿaqlī) with the very mental concept dependent on the mind. Apart from the controversies about Platonic Forms, they argue that they cannot be the very universals in logic. Accordingly, Mullā Ṣadrā's commentators have interpreted their view on intellectual universal in the Avicennian framework. In this interpretation, Mullā Ṣadrā has embraced Avicenna's explanation about mind-dependent universal concepts; however, he has modified some details of the issue as per his theory of the primacy of existence and Plato's theory of Forms. Having explained Sabzawārī and Ṭabāṭabā'ī's interpretation of Mullā Ṣadrā's view in his article, the author goes to propose a different interpretation according to which intellectual universals are identical with Platonic Forms, rather than the mind-dependent universal concepts. This Platonic interpretation is supported by three sets of evidences from Mullā Ṣadrā's own texts. It also shows how Mullā Ṣadrā has answered Avicenna's objection about the use of Platonic universal in logic. [ABSTRACT FROM AUTHOR]

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naive truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence non-classical theorists do not seem entitled to those results. In this paper we analyse these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity, and that once the ambiguity is removed there are no reasons to think that non-classical logicians are not entitled to their recapture results. [ABSTRACT FROM AUTHOR]

The logical rule of contraposition as applied to a particular affirmative proposition (I-contraposition), despite its rejection in the medieval Latin logic, had a different history in the medieval Arabic logic, varying from common acknowledgement to total dismissal (it was accepted by Avicenna and by all of his followers in the eleventh and twelfth centuries and rejected by all of Arabic logicians in the late thirteenth century onwards). This paper is a narrative of the fate of I-contraposition in the early Arabic logic. I will study Avicenna's, al-Suhrawardī's, al-Rāzī's, al-Kashshī's, and al-Khūnajī's views on this rule. Although Avicenna explicitly acknowledged I-contraposition in a brief note, and in an apparently Meinongian language, the other four figures found I-contraposition problematic and listed some counterexamples to it. Nonetheless, they all attempted to justify Avicenna's acceptance of the rule by restricting its application conditions. These efforts led to interesting syntactic and semantic analyses but gathered little attention from later medieval logicians. Finally, in the middle Arabic logic, the revised versions of I-contraposition were also declared invalid. [ABSTRACT FROM AUTHOR]

Kajiyama has argued that the basis for the concept of jāti (false rejoinder) as described in the Nyāyasūtra is the concept xiang ying (相応) as found in the Fangbian xin lun (方便心論). Kajiyama has also shown that the sophistic arguments called xiang ying are very similar to the prasaṅga arguments of Nāgārjuna, the founder of the Madhyamaka school. It thus seems worthwhile to investigate how later Mādhyamika philosophers treated the concept of jāti that originally appeared as the result of the Nyāyasūtra's criticism of the concept xiang ying and was later accepted by Buddhist logicians such as Dignāga. This paper shows that there were two entirely opposite Mādhyamika positions regarding the concept of jāti. In order to demonstrate this difference, this paper examines in detail statements about jātis that appear in various treatises, especially two works by Bhāviveka and three works by Candrakīrti. As the result, it becomes clear that the differences in the two positions correspond essentially to the differences in how Dignāgaʼs logic was evaluated by the so-called Svātantrika and Prāsaṅgika within the Madhyamaka school. [ABSTRACT FROM AUTHOR]

The aim of this article is to present some of the fundamental aspects of Heinrich Scholz's life and work to an international audience, providing archival sources and key publications about him. My intention is also to present sources – mainly letters – in an English translation for the first time. First, I discuss the autobiographical note that Scholz wrote around 1948; second, I provide a concise account of his intellectual trajectory; and third, I focus on some of the defining moral episodes in his personal life, which form the majority of this article. Successively, I deal with his role during the Nazi regime, his contacts with Polish and Dutch logicians (using unpublished correspondences), and several personal crises, which had a huge impact on his life and work. [ABSTRACT FROM AUTHOR]

Logical anti‐exceptionalism is the view that logic is not special, it is continuous with science. This continuity is typically understood in terms of the use of the abductive method in logical theory choice, with logical knowledge resulting from our choice of the theory best accounting for the data. In this paper, we argue for two related claims: (i) that this understanding of the continuity between logic and science faces considerable challenges; and (ii) that such challenges may be avoided by elaborating the continuity of logic with science in terms of the "logic‐as‐models" approach. More specifically, we defend that logical theories should be seen in the lights of the "models‐as‐epistemic‐tools" approach, an approach to the nature of models in empirical science more closely connected with current scientific practice. The result is a version of logical anti‐exceptionalism opening new perspectives for the philosophical understanding of logic. [ABSTRACT FROM AUTHOR]

In one of his papers, Moti Mizrahi argues that arguments from an expert opinion are weak arguments. His thesis may seem controversial due to the consensus on this topic in the field of informal logic. I argue that its controversy is framework-dependent, and if translated into a different framework, it appears to be a correct, however trivial, claim. I will use a framework based on Douglas Walton's argumentation scheme theory and his conception of examination dialogue to demonstrate that it is so. It appears that Mizrahi's idiosyncratic framework provides an excessively restrictive conception of an argument from expert opinion than Walton's scheme does. There is no quarrel between both frameworks, as they yield analogous, almost identical, outcomes of argument evaluation. The actual and crucial disagreement is on the topic of argument classification. Mizrahi's conception of arguments from an expert opinion imposes exact conditions that such argument must fulfil: an expert's opinion o truth-value must be unknown; o must be unsupported by any evidence; an expert's peers neither accept o nor reject it. These exclude, by definition, every possible strong, in Walton's terms, variant of such an argument. Therefore, if rephrased with the notions of the examination dialogue framework, Mizrahi's thesis sounds as follows: weak arguments from expert opinion are weak arguments. [ABSTRACT FROM AUTHOR]

A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is D No D is A Whenever H is Z then Some J is not A The present paper will be devoted to discussions of the validity of mixed conditional-categorical syllogisms of this form, and purported counterexamples, from Avicenna (d. 1037) to Urmawī (d. 1283). One major problem that was discussed, related to modern discussions of the context-sensitivity of counterfactual conditionals, is that if the antecedent of the conditional premise is incompatible with the categorical premise, then there is no guarantee that the latter will combine syllogistically with the consequent of the conditional premise. Plausible formalizations of the argument reinforce the misgivings expressed by some thirteenth-century Arabic logicians. [ABSTRACT FROM AUTHOR]

In his Formal Logic, Arthur N. Prior (1914–1969) declared that Jan Łukasiewicz's logical notation is 'unquestionably the best logical symbolism for most purposes'. Whether he had a substantive, and not only practical, reason for this notational preference is unclear. Through an investigation of his philosophical outlook towards the nature of logic and representation in general, and the nature of logical 'operators' in particular, this paper suggests that there might be a substantive argument for this declaration. This argument is premised on Prior's own metaphysical view that an adequate notation must represent the functional nature of these operators. [ABSTRACT FROM AUTHOR]

In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form. [ABSTRACT FROM AUTHOR]

This paper aims to reassess a notion in the works of the later Husserl that is both historically important and philosophically insightful, but remains understudied, namely, that of type. In opposition to a standard reading which treats Husserl's type presentations as pre-conceptual habits, this paper argues that these representations are a specific kind of concept. More precisely, it shows that Husserl's account of type presentations is akin to the contemporary prototype theory of concepts. This is historically important, since the predecessor of the prototype theory is usually said to be Wittgenstein. From a philosophical standpoint, the paper shows that Husserl has an innovative account of the connection between type concepts and their extension. Contrary to the standard view of extensions as sets and thus sharp entities, Husserl develops a correlationalist theory of concepts, according to which, for the specific characteristics in the structure of a concept, there are corresponding characteristics in the arrangement of its members, and vice versa. According to this theory, while sharp concepts lead to sharp extensions, vague concepts such as (proto)type concepts lead to vague extensions. The paper presents this understanding of Husserl in detail and explains its philosophical significance. [ABSTRACT FROM AUTHOR]

Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as 'classical recapture'. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The goal of the paper is to address this problem. First, I discuss a number of different ways to characterize the idea of classical recapture and I examine how far it can be pushed. Secondly, I argue that a palatable form of classical recapture is given by the thought that classical logic can be retained for statements that are grounded (in Kripke's sense). To substantiate this view I provide a formal fixed‐point semantics for a language containing a predicate standing for the concept of groundedness and I address a couple of objections that have been deployed against the claim that classical recapture can aid the non‐classical logician's cause. [ABSTRACT FROM AUTHOR]

The logical analysis of Nāgārjuna's (c. 200 CE) catuṣkoṭi (tetralemma or four-corners) has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners' formalization typically appears as: A, Not A (¬A), Both (A &¬A), and Neither (¬[A∨¬A]). The pulse of the controversy is the repetition of negations (¬) in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa (nominal or implicative negation) and prasajya-pratiṣedha (verbal or non-implicative negation). This paper builds off Westerhoff's account and presents some subtleties of Nāgārjuna's use of these negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna's use of na (not) and a(n)- (non-) within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. [ABSTRACT FROM AUTHOR]

Peirce’s triadic logic has been under discussion since its discovery in the 1960s by Fisch and Turquette. The experiments with matrices of three-valued logic are recorded in a few pages of unpublished manuscripts dated 1909, a decade before similar systems have been developed by logicians. The purposes of Peirce’s work on such logic, as well as semantical aspects of his system, are disputable. In the most extensive work about it, Turquette suggested that the matrices are related in dual pairs of axiomatic Hilbert-style systems. In this paper, we present a simple tableau proof for a fragment of Peirce three-valued logic, called P3, based on similar approaches in many-valued literature. We demonstrated that this proof is sound and complete. Besides that, taking the false as the only undesignated value and adding non-classical negations to the calculus, we can explore paraconsistent and paracompleteness theories into P3. [ABSTRACT FROM AUTHOR]

It is quite common among historians of Arabic logic to attribute MS Aḥmad iii, no. 3401, entitled Al-manṭiq al-kabīr (Major [book on] logic), to Fakhr al-Dīn Rāzī. This view is expressed explicitly and forcefully by Franziska Knobel (2015) and Turgut Akyüz and Elmin Aliyev (2020). In this paper, we try to refute this attribution through textual analysis, thereby exposing new evidence to the contrary. We show that the text has several references to Fakhr al-Dīn Rāzī himself as well as to some later logicians such as Rāzī's pupil Zayn al-Dīn Kashshī and the latter's successor Afḍal al-Dīn Khūnajī. We also show that contrary to some contemporary historians, all references to 'kitābunā al-kabīr' ('our major book') in Rāzī's Sharḥ Al-ishārāt do not refer to Al-manṭiq al-kabīr, but to Al-mabāhith al-mashriqiyya. [ABSTRACT FROM AUTHOR]

Verbal root and verbal ending are most important aspects of the analysis of verbal cognition i.e. sentence meaning. All the languages of the world possess fine collection of expressive words. These words are generally categorized into nouns and verbs depending upon their functional aspects. But the question is - what makes these words expressive or what makes them potential? This question leads me to conduct the research on the origin of the words. I found root as the centre of my research problem. Such a question is nicely dealt with by ancient Sanskrit grammarians, Logicians and Mīmāṁsakas.

We examine a contribution L. Susan Stebbing made to the understanding of critical thinking and its relation to formal logic. Stebbing took expertise in formal logic to authorise logical intervention in public debate, specifically in assessing of the validity of everyday reasoning. She held, however, that formal logic is purely the study of logical form. Given the problems of ascertaining logical form in any particular instance, and that logical form does not always track informal validity, it is difficult to see how she could justify her belief in logical interventionism. Her answer to this problem is the contribution we explore here. It involves the view that although the logician's expertise is not sufficient to assess arguments made in everyday contexts on its own, it nevertheless plays a unique role in giving systematicity and direction to the critique of such arguments, in particular, in public debate. [ABSTRACT FROM AUTHOR]

In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant logic was shown by Kosta Do en in 1992. By that time the material on relevant logic was well known; however, there is more of interest in Orlov's paper than this: his remarks on intuitionism, the motivation for his construction, and its wider implications. This paper explains and reflects on these matters. [ABSTRACT FROM AUTHOR]

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During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about 'symbolical logic'. The letters to the editor shed interesting light on the early reception of MacColl's contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of the development of British algebraic logic in the confusing intermediary period between the 1870s and 1890s. [ABSTRACT FROM AUTHOR]

Logicians (i.e. "Al-Mutakalimoun") utilized various arguments to justify their exegesis position of the Quran text that is different from traditional ancestral scholars. Some of these arguments were regarding cases of belief, especially God's attributes. This particular argument was based on rejecting the explicit direct meaning when reading the text, claiming that the apparent manifestation is not intended. This led them to manipulate the text to support their interpretation, using what they termed "delegation". The present paper investigates Ibn Taymiya's approach to Quran and Prophet Muhammad's sayings in relation to Logicians' argument concerning the direct text meaning and its real purpose. The method utilized is primarily deductive and analytical. The work reveals the necessity of reading and adopting Quran texts, as they are in relation to Almighty God, without using similitude. The ultimate guide for that is to achieve the appropriate understanding of the Holy Quran and Prophet Muhammad's traditions. [ABSTRACT FROM AUTHOR]

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition 'if B is not great, B itself is great [...] is impossible'. Similarly, Boethius maintained that two implications of the type 'If p then r' and 'If p then not-r' are incompatible. Furthermore, Chrysippus proclaimed a conditional to be 'sound when the contradictory of its consequent is incompatible with its antecedent', a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to 'normal' conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle's and Boethius' theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don't give rise to any non-classical system of genuinely connexive logic. [ABSTRACT FROM AUTHOR]

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert. [ABSTRACT FROM AUTHOR]

In this paper I will attempt to explain why the controversy surrounding the alleged refutation of Mechanism by Gödel's theorem is continuing even after its unanimous refutation by logicians. I will argue that the philosophical point its proponents want to establish is a necessary gap between the intended meaning and its formulation. Such a gap is the main tenet of philosophical hermeneutics. While Gödel's theorem does not disprove Mechanism, it is nevertheless an important illustration of the hermeneutic principle. The ongoing misunderstanding is therefore based in a distinction between a metalogical illustration of a crucial feature of human understanding, and a logically precise, but wrong claim. The main reason for the confusion is the fact that in order to make the claim logically precise, it must be transformed in a way which destroys its informal value. Part of this transformation is a clear distinction between the Turing Machine as a mathematical object and a machine as a physical device. [ABSTRACT FROM AUTHOR]

This is a paper for a special issue of Semiotic Studies devoted to Stanislaw Krajewski's paper (2020). This paper gives some supplementary notes to Krajewski's (2020) on the Anti-Mechanist Arguments based on Gödel's incompleteness theorem. In Section 3, we give some additional explanations to Section 4-6 in Krajewski's (2020) and classify some misunderstandings of Gödel's incompleteness theorem related to Anti- Mechanist Arguments. In Section 4 and 5, we give a more detailed discussion of Gödel's Disjunctive Thesis, Gödel's Undemonstrability of Consistency Thesis and the definability of natural numbers as in Section 7-8 in Krajewski's (2020), describing how recent advances bear on these issues. [ABSTRACT FROM AUTHOR]

Georg Kreisel (1972) suggested various ways out of the Gödel incompleteness theorems. His remarks on ways out were somewhat parenthetical, and suggestive. He did not develop them in subsequent papers. One aim of this paper is not to develop those remarks, but to show how the basic idea that they express can be used to reason about the Lucas-Penrose-Putnam arguments that human minds are not (entirely) finitary computational machines. Another aim is to show how one of Putnam's two anti-functionalist arguments (that use the Gödel incompleteness theorems) avoids the logical error in the Lucas-Penrose arguments, extends those arguments, but succumbs to an absurdity. A third aim is to provide a categorization of the Lucas-Penrose-Putnam anti-functionalist arguments. [ABSTRACT FROM AUTHOR]

We show that the name "Lucas-Penrose thesis" encompasses several different theses. All these theses refer to extremely vague concepts, and so are either practically meaningless, or obviously false. The arguments for the various theses, in turn, are based on confusions with regard to the meaning(s) of these vague notions, and on unjustified hidden assumptions concerning them. All these observations are true also for all interesting versions of the much weaker (and by far more widely accepted) thesis known as "Gödel disjunction". Our main conclusions are that pure mathematical theorems cannot decide alone any question which is not purely mathematical, and that an argument that cannot be fully formalized cannot be taken as a mathematical proof. [ABSTRACT FROM AUTHOR]

Many medieval philosophers and logicians regarded modal logic as a model for epistemic, normative and optative concepts on the basis of their apparent similarities to modal concepts. These interpretations of modal logic led to critical studies of the applicability of modal principles to deontic concepts. Some philosophers presented apparent counterexamples to the deontic interpretation of the Consequence Principle, according to which the consequences of what is obligatory (or permitted) are also obligatory (permitted). These examples are variants of Lennart Åqvist's paradox of the Good Samaritan. In this article it is argued that the examples involve a confusion between the compounded and the divided senses of deontic propositions, and are not genuine counterexamples to the Consequence Principle. If the concept of knowledge is analysed as epistemically satisfactory belief, the paradox of epistemic obligation can be solved in a similar way. [ABSTRACT FROM AUTHOR]

Aristotle gave seven arguments for the law of non-contradiction. The first one is against a special case of dialetheism, the view that only some contradictions are true, and other six arguments are mostly against trivialism, the view that everything and consequently every contraction is true. Aristotle never argued that dialetheism entails trivialism. Unlike Aristotle, Avicenna, in his defense of LNC, not only considers trivialism and argues against it, but also argues that dialetheism entails trivialism. The argument that dialetheism entails trivialism is called explosion. It is usually known that the first argument for explosion is given by the twelfth century logician William of Soissons. In this paper, we will meet Avicenna's different argument for explosion and then I will demonstrate that this argument is a non-sequitur. [ABSTRACT FROM AUTHOR]

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode (as opposed to displayed mode). Moreover, procedures are not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. [ABSTRACT FROM AUTHOR]

We present a proof-theoretical analysis of the theory of definite descriptions which emerges from Frege's approach and was formally developed by Kalish and Montague. This theory of definite descriptions is based on the assumption that all descriptions are treated as genuine terms. In particular, a special object is chosen as a designatum for all descriptions which fail to designate a unique object. Kalish and Montague provided a semantical treatment of such theory as well as complete axiomatic and natural deduction formalization. In the paper we provide a sequent calculus formalization of this logic and prove cut elimination theorem in the constructive manner. [ABSTRACT FROM AUTHOR]

The rule of contraposition has been investigated thoroughly by Arabic logicians. In this paper, we study the work done by Fārābā and Avicenna, the fathers of Arabic logic. Fārābā studied contraposition of universal affirmatives, discussed its four forms, and discovered a relation between one form and the conversion of negative universals. Although Fārābā and logicians before him have used contraposition only for conditionals, as well as for indefinite and universal affirmative categorical propositions, Avicenna generalized the rule to all the four Aristotelian quantified categorical propositions. However, many of his ideas on contraposition were opposed by his 12th and 13th century followers, which are to be investigated later. [ABSTRACT FROM AUTHOR]

Abstract We explore the formation of Logic as an academic discipline and community in Russia before the revolution of 1917. In particular, we look at the various communication strategies that emerged within this community and its relations with the wider international scientific community. Interaction with Mathematics, which was undergoing its own "foundational revolution," played a major role in the transition from archaic syllogistic to modern formal logic. We make extensive use of original sources, many of which have not been reprinted since their first publication. [ABSTRACT FROM AUTHOR]

The article generalizes the standard threshold models of diffusion in social networks by introducing the notion of recalcitrant agents, i.e. agents that are fully resistant to the diffusion process. The focus of the article is on capturing a ternary influence relation between groups of agents: agents in one group can indirectly influence agents in another group in spite of the agents in the third group being recalcitrant. The main technical result is a sound and complete axiomatization of this relation. [ABSTRACT FROM AUTHOR]

Marketers have yet to adopt a standard repertoire of techniques with which they can critically evaluate argument-centered works. Certain analytical techniques of the logician are proposed for evaluating such works. The authors provide an example to illustrate the use and value of these techniques. [ABSTRACT FROM AUTHOR]

In a recent paper, Wigglesworth claims that syntactic criteria of theoretical equivalence are not appropriate for settling questions of equivalence between logical theories, since such criteria judge classical and intuitionistic logic to be equivalent; he concludes that logicians should use semantic criteria instead. However, this is an artefact of the particular syntactic criterion chosen, which is an implausible criterion of theoretical equivalence (even in the non-logical case). Correspondingly, there is nothing to suggest that a more plausible syntactic criterion should not be used to settle questions of equivalence between different logical theories; such a criterion (which may already be found in the literature) is exhibited and shown to judge classical and intuitionistic logic to be inequivalent. [ABSTRACT FROM AUTHOR]

This article addresses the deduction problem of a formula from a countable theory in the first-order Gödel logic. We generalise the well-known hyperresolution principle for deduction in Gödel logic. Our approach is based on translation of a formula to an equivalent satisfiable finite order clausal theory, consisting of order clauses. We introduce a notion of quantified atom: a formula a is a quantified atom if a = Qx, p(t0, ..., tn), where Q is a quantifier (∀, ∃), p(t0, ..., tn) is an atom, and x is a variable occurring in p(t0, ..., tn); for all i ≤ n, either ti = x or x does not occur in ti. Then an order clause is a finite set of order literals of the form ϵ1 ⋄ ϵ 2, where ϵi is either an atom, or a truth constant (0, 1), or a quantified atom, and ⋄ is either a connective ≖, equality, or ≺ strict order. ≖ and ≺ are interpreted by the equality and standard strict linear order on [0, 1], respectively. On the basis of the hyperresolution principle, a calculus operating over order clausal theories is devised. The calculus is proved to be refutation sound and complete for the countable case. As an interesting consequence, we get an affirmative solution to the open problem of recursive enumerability of unsatisfiable formulae in Gödel logic. [ABSTRACT FROM AUTHOR]

Derrida, for reasons which he never made clear publicly, published his mémoire for the diplôme d'études supérieures only in 1990, some thirty-five years after it had been written. Had it been published much earlier, some of the dispiritingly ill-informed remarks about his work might have been avoided. The mémoire, entitled The Problem of Genesis in Husserl's Philosophy, reveals that he is, when required, perfectly able to write a standard thesis in straightforward French. And that, in particular, he is aware of the work of the great logician Gottlob Frege in its relation to Husserl. [ABSTRACT FROM AUTHOR]