History of Logic

Ce volume couvre un domaine de recherche absolument nouveau : le champ qui s'étend de la logique à l'argumentation. Après une analyse rigoureuse des fondements de la logique mathématique, l'auteur montre l'importance de l'argumentation et des preuves argumentatives dans les affaires humaines. Il tente ensuite de fonder scientifiquement l'étude des argumentations et d'ouvrir de nouvelles voies dans le domaine jusqu'ici peu connu de la logique naturelle. Les pages qui sont dans ce volume consacrées à la logique naturelle sont d'une nouveauté (...) absolue, et valent comme un apport de premier ordre au débat actuel sur la crise de la Raison. J.B. Grize s'affirme dans ce volume comme le plus novateur des chercheurs suisses d'aujourd'hui.? Page de début Préface Bibliographie de Jean-Blaise Grize Présentation Introduction. Vers une logique naturelle 1. Portée et limites de la formalisation 2. Théorie et explication 3. Remarques sur les limitations des formalismes 4. Vers une logique du quotidien 5. Logique et sciences humaines 6. Vers une psycho-logique 7. Réflexions pour une recherche sur l'argumentation 8. Logique et adaptation. En hommage au professeur 9. La schématisation et ses problèmes 10. Logique et organisation du discours 11. Logique et argumentation 12. Schématisation, représentations et images 13. Logique du discours et institutions sociales 14. Quelques opérations de la logique naturelle 15. Pour aborder l'étude des structures du discoursquotidien Bibliographie des ouvrages cités Index des noms Page de fin. (shrink)

In recent decades, research in the square of opposition has increased. New interpretations, extensions, and generalizations have been suggested, both Aristotelian and non-Aristotelian ones. The paper attempts to compare different versions of the square of opposition. For this reason, we appeal to the wider categorical model-theoretic framework of the theory of institutions.

If an argument is valid, it is impossible for its premises to be true, and its conclusion false. But how should we understand these notions of truth and impossibility? Here, I present the answers given by John Buridan (ca. 1300-60), showing (i) how he understands truth in his anti-realist metaphysics, and (ii) how he understands modality in connection with causal powers. In short: if an argument exists and is valid, there does not exist a power capable of making the premises (...) true and, at the same time, making the conclusion false. (shrink)

Commentary on the Taḥrīr al-qawāʻid al-manṭiqīyah fī sharḥ al-Risālah al-Shamsīyah, a noted text book for religious schools.

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...) that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

[English in PhilArchive, unpublished]. Ruđer Bošković's (Rogerius Joseph Boscovich, 1711-1787) induction is described as a reasoning procedure that combines abductive, generalizing and deductive forms of inference. According to Bošković, the application of inductive reasoning extends beyond natural science. Bošković's critique of the use of the principle of sufficient reason is discussed, and constructive rules of Bošković's inductive logic are proposed from the standpoint of contemporary justification logic. To that end, justification logic could be extended with Bošković's typology of reasons. Hunter's (...) result (1965) is conceived as a confirmation that the inference from the constructive defectus rationis is a necessary component of Bošković's induction. - English version in _PhilArchive_. (shrink)

It is shown in what sense essential characteristics of formalism, which is normative for exact knowledge, can be found already in Aristotle. It is described how exactness and formalism are pre-conditioned by sensible intuition. The machine character (Turing machine) of a formalism is considered. The general concept of provability leads to an expanding and dynamic understanding of a formalism, with the final source of logical patterns in the "forms of life" (Wittgenstein).

The starting point of this paper is Andrej Ule’s book Osnovna filozofska vprašanja sodobne logike [Basic Philosophical Questions of Contemporary Logic] from 1982. Specifically, I focus on his assessment of Frege, Russell and Wittgenstein’s views on the ontological status of logic and its apriority. Ule claims that all three thinkers failed because they did not take into account the role a human being plays in this as the creator of language. In this assessment, I recognize the rejection of metaphysics and (...) the linguistic approach to philosophical issues that were characteristic of analytic philosophy in the past. I shortly describe this position and the role that the discussed authors played in its development. I conclude with my own assessment of the proposed views based on the contemporary, metaphysics-friendly position. (shrink)

This article outlines the history of logic in China from 1949 to 2019. Firstly, it presents a rough picture of Chinese logic before 1949 using broad brushstrokes. Secondly, it divides the whole process of development into two stages. In the first 30 years from 1949 to 1979, Chinese logic made some achievements, but also went along some detours, and its overall situation was unsatisfactory. In the latter 40 years from 1979 to 2019, due to Deng Xiaoping’s reform and opening up, (...) many Chinese logicians went abroad for academic visits or to study degrees in foreign universities or research institutes, gradually became familiar with and even integrated into the international mainstream of logic teaching and research, and ushered in the great flourishing of logic in China we see today. Finally, it draws four lessons from this process of development, as follows. 1) Let politics and academia live in peace, by respecting and adhering to the idea of academic freedom. 2) Academic advances cannot be achieved in isolation from the world, so we should fully embrace the international academic community, while insisting on our own independent thinking. 3) We should always adhere to the policy of “letting a hundred flowers blossom and a hundred schools of thought contend”, so that different academic viewpoints and tendencies can be improved and developed in their mutual collision. 4) We should culti- vate academic self-confidence, gradually make the change from pure follow-up learning to original work in some fields of logic. (shrink)

Synkategorematische Sprachzeichen bilden ein zentrales Thema der Logik, Sprachphilosophie, Linguistik und Grammatik von der Antike bis zur Gegenwart. Im Mittelalter verstand man unter "syncategoremata "Ausdrücke, denen eine besondere Bedeutung für die logische Analyse von Aussagen und Schlüssen zukommt. Zu den Synkategoremata zählte eine relativ eng begrenzte Gruppe von Wörtern wie etwa die distributiven Zeichen ("jeder", "kein"), die Exklusiva ("allein", "nur"), Konjunktionen wie "und", "oder" und "wenn", die Kopula "ist", aber auch einzelne Verben wie "anfangen" und "aufhören". Synkategoremata haben anders als (...) Kategoremata wie "Mensch", "Lebewesen "und "läuft" keine selbständige Bezeichnungsfunktion, sondern erhalten eine solche Funktion erst im Satzzusammenhang. In den im 13. Jhdt. verbreiteten und einflussreichen Traktaten dieses Genres werden Synkategoremata oft unter Rückgriff auf Sophismata, d.h. mehrdeutige, analysebedürftige Aussagen, behandelt. Im Mittelpunkt stehen neben Fragen zu ihrem Skopus (insbesondere bei quantifizierenden und in irgendeiner Form negierenden Zeichen) auch die der Abhängigkeit ihrer syntaktischen Funktion von ihrer Bezeichnungsfunktion. Die Traktate bieten Regeln zur Verwendung der einzelnen Synkategoremata und weisen dabei vielfältige Bezüge zur aristotelischen Logik, speziell der Fehlschlusslehre, sowie zu den genuin mittelalterlichen Lehren der Folgerungen und der Supposition der Termini auf. (shrink)

Are psychiatric disorders natural kinds? This question has received a lot of attention within present-day philosophy of psychiatry, where many authors debate the ontology and nature of mental disorders. Similarly, historians of psychiatry, dating back to Foucault, have debated whether psychiatric researchers conceived of mental disorders as natural kinds or not. However, historians of psychiatry have paid little to no attention to the influence of (a) theories within logic, and (b) theories within metaphysics on psychiatric accounts of proper method, and (...) on accounts of the nature and classification of mental disorders. Historically, however, logic and metaphysics have extensively shaped methods and interpretations of classifications in the natural sciences. This paper corrects this lacuna in the history of psychiatry, and demonstrates that theories within logic and metaphysics, articulated by Christian Wolff (1679-1754), have significantly shaped the conception of medical method and (psychiatric) nosology of the influential nosologist Boissier De Sauvages (1706-1767). After treating Sauvages, I discuss the method of the influential nosologist William Cullen (1710-1790), and demonstrate the continuity between the classificatory methods of Sauvages and Cullen. I show that both Sauvages and Cullen were essentialists concerning medical diseases in general and psychiatric disorders in particular, contributing to the history of conceptions of the ontology and nature of mental disorders. (shrink)

En The paradox of Addition and its dissolution (1969), Mario Bunge presenta algunos argumentos para mostrar que la Regla de Adición puede ocasionar paradojas o problemas semánticos. Posteriormente, Margáin (1972) y Robles (1976) mostraron que las afirmaciones de Bunge son insostenibles, al menos desde el punto de vista de la lógica clásica. Aunque estamos de acuerdo con las críticas de Margáin y Robles, no estamos de acuerdo en el diagnóstico del origen del problema y tampoco con la manera en la (...) que se proponen solucionarlo. En esta medida, en este texto mostraremos cómo la Regla de Adición sí trae problemas semánticos que pueden ser planteados desde diferentes perspectivas contemporáneas, como la extensionalidad del condicional, los principios proscriptivos y la validez conexiva. (shrink)

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of this term: (...) necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent. -/- . (shrink)

A sound historiographical account of the role of logic in the development of medieval philosophical and theological reflection requires a thorough examination of its historical roots and its theoretical implications. An apparent historiographical bias, due to the idea that only the development of contemporary formal logic enables a proper reconstruction of the whole history of logic, can be exposed by taking into account the case of the medieval discussions on the topics, starting from their late-antiquity legacy. An attentive inspection of (...) the successive stages of the gradual formalisation process of medieval topical logic brings to the fore significant theoretical aspects in the philosophy of logic, all too often left aside in common contemporary discussions. In particular, the distinction between topical maxims and topical differences, or principles according to and principles from which an inference is drawn, highlights the specific nature of a major part of medieval logic, that deals with meta-logical issues by means of higher-order logical resources. It is precisely this special character of medieval logic that proves to be of the highest significance in the discussion of the most subtle theological—and just as well philosophical—questions that engaged medieval authors, thus testifying to the essential role of logic in the overall development of medieval thought. (shrink)

"A Little More Logical" is the perfect guide for anyone looking to improve their critical thinking and logical reasoning skills. With chapters on everything from logic basics to fallacies of weak induction to moral reasoning, this book covers all the essential concepts you need to become a more logical thinker. You'll learn about influential figures in the field of logic, such as Rudolph Carnap, Betrrand Russell, and Ada Lovelace, and how to apply your newfound knowledge to real-world situations. Whether you're (...) looking to engage in debates with others, make better decisions in your personal and professional life, or simply want to improve your overall critical thinking skills, "A Little More Logical" has you covered. So why wait? Start learning and become a little more logical today! -/- "A Little More Logical" differs from typical logical textbooks in a number of ways. One key difference is its emphasis on engaging and relatable examples and case studies. Rather than simply presenting dry definitions and concepts, the book uses fables, stories, and real-world situations to illustrate key ideas and make them more relatable for readers. -/- Another unique aspect of "A Little More Logical" is its inclusion of "Minds that Mattered" sections, which highlight the contributions and insights of influential figures in the field of logic and critical thinking. These sections provide readers with a deeper understanding of the history and development of logical principles and offer valuable context for the concepts being discussed. -/- Additionally, "A Little More Logical" covers a wide range of topics beyond the basics of logic and argument evaluation. Chapters on moral reasoning, probability and inductive logic, scientific reasoning, conspiracy theories, statistical reasoning, and the history of formal logic offer a more comprehensive and well-rounded understanding of logic and critical thinking. -/- Overall, "A Little More Logical" stands out as a dynamic and engaging resource for anyone looking to improve their logical reasoning abilities. Its relatable examples, historical context, and broad coverage make it a valuable resource for anyone interested in mastering the principles of logic. -/- This is a free, Creative-Commons-licensed book. (shrink)

Susan Stebbing (1885–1943), the UK’s first female professor of philosophy, was a key figure in the development of analytic philosophy. Stebbing wrote the world’s first accessible book on the new polyadic logic and its philosophy. She made major contributions to the philosophy of science, metaphysics, philosophical logic, critical thinking, and applied philosophy. Nonetheless she has remained largely neglected by historians of analytic philosophy. This Element provides a thorough yet accessible overview of Stebbing’s positive, original contributions, including her solution to the (...) paradox of analysis, her account of the relation of sense-data to physical objects, and her anti-idealist interpretation of the new Einsteinian physics. Stebbing’s innovative work in these and other areas helped move analytic philosophy from its early phase to its middle period. (shrink)

André de Muralt has carried out a rigorous comparative analysis of phenomenological logic and scholastic logic of Thomist origin in order to elucidate whether Husserlian intentionality could be related to Thomist intentionality. This comparative analysis has brought to light that the Husserlian conception of logic responds to a dialectic structure which commits it to critical and metaphysical premises completely opposed to those of Thomist realism.

This work sheds light on the presence of Aristotelian elements in Augustine’s early works, which was more substantial than what it is usually believed. In fact, the young African rhetorician did not only know Aristotle’s Categoriae, which he read when he was a student in Carthage, but also other works by him, such as his De interpretatione, already translated into Latin at Augustine’s time, as well as Aristotelian-inspired works. That is the case of Themistius’s paraphrases of Aristotle’s Analytica and his (...) commentary on Aristotle’s Metaphysica, which Augustine knew well, especially with regard to book IV. Moreover, Augustine knew the De mundo by Apuleius, who perhaps was also the author of a Peri hermeneias, and who translated during the second century several Aristotelian-inspired works on various natural topics. Moreover, Augustine read the summaries of Plotinus’s Enneades, translated into Latin by Marius Victorinus, and Cicero’s Hortensius, which constitutes a commentary on Aristotle’s De interpretatione. (shrink)

In this paper, I examine Gilbert Ryle’s claim that ordinary competence with logical principles or rules is a kind of knowing how, where such knowledge is understood as a skill, a multi-track disposition. Ryle argues that his account of ordinary logical competence helps avoid Lewis Carroll’s famous regress argument (Carroll 1895), which suggests that elementary deductive reasoning might be impossible. Indeed, Carroll’s regress is the central motivation for Ryle’s account. I argue that this account is inadequate on two counts: it (...) cannot serve to articulate the way ordinary reasoners might exercise their knowledge in reasoning and it does not do much to help us avoid Carroll’s regress. I sketch an alternative view, still Rylean in spirit, that fares better on both counts. (shrink)

Traditionally, logic was viewed as a purely European tradition, founded in Ancient Greece by Aristotle and then developed in Catholic and Byzantine scholasticism as well as in Islamic and Judaic Ar...

This entirely new English translation of Buridan's classic treatment of logical consequence aims to make accessible to the modern reader the foremost treatment of the subject in the middle ages. The translation is accompanied by an introduction in which Buridan's ideas are set in their historical context and clearly explained.

Taftāzānī, Masʻūd ibn ʻUmar, 1322-1389?. Tahdhīb al-manṭiq wa-al-kalām.

Ibn Taymīyah, Aḥmad ibn ʻAbd al-Ḥalīm, 1263-1328. Naqḍ al-manṭiq; Islamic philosophy; logic.

Abraham Fraunce’s The Shepherds’ Logic (c. 1585) is one of the first English adaptations of Petrus Ramus’s Dialecticae libri duo (1556). Preserved in a manuscript also containing two shorter essays on Ramist dialectic, the work was later modified and enlarged for publication as The Lawyers’ Logic (1588). But Fraunce’s substantial and almost exclusive use of Edmund Spenser’s The Shepherds’ Calendar (1579) as the source for practical examples makes the manuscript treatise a unique document revealing the influence of the Ramist reform (...) of the arts of discourse on the new literary elite led by Philip Sidney and Gabriel Harvey. This is the first published critical edition of Fraunce’s early treatise and the two companion essays. It presents the texts in modernized spelling, traces their sources and contexts, and draws out their literary and philosophical implications. It also includes relevant excerpts from The Lawyers’ Logic, such as Fraunce’s quantitative-verse translation of Virgil’s Second Eclogue and its Ramist analysis, and a full catalogue of the quotations from Spenser’s Calendar. As a whole, this edition sees Fraunce’s pastoral logic as a first-hand testimony showing how scholarly training in the Renaissance arts of discourse enlightened the composition and interpretation of poetic texts. (shrink)