68 found
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  1.  47
    Rewriting the History of Connexive Logic.Wolfgang Lenzen - 2022 - Journal of Philosophical Logic 51 (3):525-553.
    The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...)
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  2. (1 other version)Recent work in epistemic logic.Wolfgang Lenzen - 1978 - Acta Philosophica Fennica 30:1-219.
  3.  53
    A Critical Examination of the Historical Origins of Connexive Logic.Wolfgang Lenzen - 2019 - History and Philosophy of Logic 41 (1):16-35.
    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 (...)
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  4.  64
    What Follows from the Impossible: Everything or Nothing? (An Interpretation of the ‘Avranches Text’ and the Ars Meliduna).Wolfgang Lenzen - 2021 - History and Philosophy of Logic 43 (4):309-331.
    One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...)
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  5.  39
    Epistemologische betrachtungen zu [S4, S5].Wolfgang Lenzen - 1979 - Erkenntnis 14 (1):33-56.
    The numerous modal systems between S4 and S5 are investigated from an epistemological point of view by interpreting necessity either as knowledge or as (strong) belief. It is shown that-granted some assumptions about epistemic logic for which the author has argued elsewhere-the system S4.4 may be interpreted as the logic of true belief, while S4.3.2 and S4.2 may be taken to represent epistemic logic systems for individuals who accept the scheme knowledge = true belief only for certain special instances. There (...)
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  6.  16
    Buridan on ‘Ex impossibili quodlibet’, ‘Ex contradictione quodlibet’, and ‘Ex falso quodlibet’.Wolfgang Lenzen - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Buridan endorsed the principles that any impossible, and a fortiori any self-contradictory, proposition entails each proposition. These principles are usually referred to as ‘Ex impossibili quodlibet’ (EIQ) and ‘Ex contradictione quodlibet’ (ECQ). Buridan further considered the instance ECCQ according to which any proposition follows from the conjunction of two contradictory propositions. Buridan showed how ECCQ can be proven by means the usual laws of conjunction and disjunction. Furthermore, he discovered that EIQ can be derived from ECCQ by means of the (...)
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  7.  69
    Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«.Wolfgang Lenzen - 2017 - Logica Universalis 11 (1):85-104.
    The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from (...)
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  8.  39
    (1 other version)Leibniz's logic.Wolfgang Lenzen - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the history of logic. Boston: Elsevier. pp. 3--1.
  9.  47
    Leibniz’s Logic and the “Cube of Opposition”.Wolfgang Lenzen - 2016 - Logica Universalis 10 (2-3):171-189.
    After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz. Within Leibniz’s algebra of concepts, the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as ‘S contains P’ and ‘S contains Not-P’, ‘S doesn’t contain P’ and ‘S doesn’t contain Not-P’, respectively. Next we consider Leibniz’s version of the so-called Quantification of (...)
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  10. Glauben, Wissen Und Wahrscheinlichkeit. Systeme Der Epistemischen Logik.Wolfgang Lenzen - 1985 - Erkenntnis 23 (1):97-112.
     
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  11. (1 other version)Leibniz und die Boolesche Algebra.Wolfgang Lenzen - 1984 - Studia Leibnitiana 16:187.
    It is well known that in his logical writings Leibniz typically disregarded the operation of disjunction, confining himself to the theory of conjunction ajid negation. Now, while this fact has been interpreted by Couturat and others as indicating a serious incompleteness of the Leibnizian calculus, it is shown in this paper that actually Leibniz's conjunction-negation logic, with 'est Ens', i. e. 'is possible' as an additional logical operator, is provably equivalent to Boolean algebra. Moreover, already in the Generales Inquisitiones of (...)
     
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  12.  43
    Epistemic logic.Wolfgang Lenzen - 2004 - In Ilkka Niiniluoto, Matti Sintonen & Jan Woleński (eds.), Handbook of Epistemology. Dordrecht: Kluwer Academic. pp. 963--983.
  13. Zur extensionalen und "intensionalen" Interpretation der Leibnizschen Logik.Wolfgang Lenzen - 1983 - Studia Leibnitiana 15:129.
    Against the prevailing opinion expressed, e.g., by L. Couturat it is argued that the so-called „intensional“ point of view which Leibniz mostly preferred to the nowadays usual extensional interpretation is neither „confuse et vague“ nor may it be made responsible for the alleged „échec final de son système“ . We present a precise definition of an „intensional“ semantics which reflects the Leibnizian ideas and which may be proven to be equivalent to standard extensional semantics.
     
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  14.  19
    How to Square Knowledge and Belief.Wolfgang Lenzen - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 305--311.
  15. Non est non est est non. Zu Leibnizens Theorie der Negation.Wolfgang Lenzen - 1986 - Studia Leibnitiana 18 (1):1-37.
    Leibniz's development of a "calculus universalis" stands and falls with his theory of negation. During the entire period of the elaboration of the algebra of concepts, L1, Leibniz had to struggle hard to grasp the difference between propositional and conceptual negation. Within the framework of syllogistic, this difference seems to disappear because 'Omne A non B' may be taken to be equivalent to ‘Omne A est non-B’. Within the "universal calculus", however, the informal quantifier expression 'omne' is to be dropped. (...)
     
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  16. (1 other version)Das System der Leibnizschen Logik.Wolfgang Lenzen - 1992 - Studia Leibnitiana 24 (1):112-116.
  17.  24
    Kilwardby's 55th Lesson.Wolfgang Lenzen - forthcoming - Logic and Logical Philosophy:1.
    In “Lectio 55” of his Notule libri Priorum, Robert Kilwardby discussed various objections that had been raised against Aristotle’s Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, ∼p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (∼p → p) would be “absurd”. (...)
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  18.  19
    Leibniz's calculus of strict implication.Wolfgang Lenzen - 1987 - In Jan T. J. Srzednicki (ed.), Initiatives in logic. Boston: M. Nijhoff. pp. 1--35.
  19.  5
    Theorien der Bestätigung wissenschaftlicher Hypothesen.Wolfgang Lenzen - 1974
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  20. Leibniz and the Calculus Ratiocinator.Wolfgang Lenzen - 2018 - In Sven Ove Hansson (ed.), Technology and Mathematics: Philosophical and Historical Investigations. Cham, Switzerland: Springer Verlag.
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  21.  8
    Abelard: Logic.Wolfgang Lenzen - 2024 - Internet Encyclopedia of Philosophy.
    Abelard: Logic This article describes and reconstructs Peter Abelard’s logic of the twelfth century. Much of what he regarded as logic is now classified as ontology or philosophical semantics. The article concentrates on his treatment of the relation of consequence. Abelard’s most important logical innovations consist of two points: The distinction between two kinds of … Continue reading Abelard: Logic →.
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  22.  15
    S4:1:4 = s4:1:2 and s4:021 = s4:04.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19 (July):465-466.
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  23.  29
    On some substitution instances of R1 and L1.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19:159.
  24.  36
    On the representation of classificatory value structures.Wolfgang Lenzen - 1983 - Theory and Decision 15 (4):349-369.
  25.  34
    S4.1.4=S4.1.2 and S4.021=S4.04.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19 (3):465-466.
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  26.  5
    Buridan’s Theory of Consequences.Wolfgang Lenzen - forthcoming - History and Philosophy of Logic:1-25.
    Buridan endorses the basic idea that q follows from p iff it is impossible that p is true but q is false. Since he also accepts the law that, if p is impossible, the conjunction (p ∧ q) must be impossible, he comes to regard the principle ‘Ex impossibili quodlibet’ (EIQ) as basically correct. However, his logic is based on a ‘nominalist’ view according to which propositions are tokens of spoken, written or thought language existing in space of time, and (...)
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  27.  22
    Possibility and Necessity in the Time of Peter Abelard by Irene Binini.Wolfgang Lenzen - 2023 - Journal of the History of Philosophy 61 (2):327-329.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Possibility and Necessity in the Time of Peter Abelard by Irene BininiWolfgang LenzenIrene Binini. Possibility and Necessity in the Time of Peter Abelard. Investigating Medieval Philosophy Series. Leiden: Brill, 2021. Pp. xii + 326. Hardback, $166.00.This book is an impressive work written by a young Italian scholar who received her PhD only five years ago in Pisa. It is divided into three parts. Part 1 gives a survey (...)
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  28.  32
    Searles verpatzte Lösung des Freiheitsproblems.Wolfgang Lenzen - 2005 - Facta Philosophica 7 (1):35-68.
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  29. Auf der Suche nach dem verlorenen »Selbst« — Thomas Metzinger und die »letzte Kränkung« der Menschheit.Wolfgang Lenzen - 2006 - Facta Philosophica 8 (1-2):161-192.
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  30. On Leibniz's Essay 'Mathesis Rationis'.Wolfgang Lenzen - 1990 - Topoi 9 (1):29-59.
  31.  18
    Damasios Theorie der Emotionen.Wolfgang Lenzen - 2004 - Facta Philosophica 6 (2):269-309.
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  32.  11
    Guilielmi Pacidii Non plus ultra, oder: Eine Rekonstruktion des Leibnizschen Plus-Minus-Kalküls.Wolfgang Lenzen - 2000 - History of Philosophy & Logical Analysis 3 (1):71-118.
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  33.  16
    A rare accident.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19 (2):249-250.
  34. Die Paradoxie der überraschenden Übung: Logische, epistemologische und pragmatische Aspekte.Wolfgang Lenzen - 1976 - Logique Et Analyse 19 (74):267-284.
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  35. Alles nur Illusionen? - Philosophische (In-)Konsequenzen der Neurobiologie.Wolfgang Lenzen - 2005 - Facta Philosophica 7 (2):189-229.
  36.  14
    Über Rainer Enskats,Wahrheit und Entdeckung'.Wolfgang Lenzen - 1990 - Allgemeine Zeitschrift für Philosophie 15 (3):87-92.
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  37.  16
    Mathesis rationis: Festschrift für Heinrich Schepers.Albert Heinekamp, Heinrich Schepers, Martin Schneider & Wolfgang Lenzen - 1990
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  38.  29
    Principia Calculi rationalis.Gottfried Wilhelm Leibniz & Wolfgang Lenzen - 2019 - The Leibniz Review 29:51-57.
  39. Abtreibung, Intersubjektiver Nutzenvergleich und der Wert des Lebens.Wolfgang Lenzen - 1995 - Ethik Und Sozialwissenschaften 6 (2):200.
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  40.  35
    Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4.Wolfgang Lenzen - 1980 - Mathematical Logic Quarterly 26 (7-9):131-143.
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  41.  14
    What is (or at least appears to be) wrong with intuitionistic logic?Wolfgang Lenzen - 1991 - In Georg Schurz (ed.), Advances in Scientific Philosophy. pp. 173-186.
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  42.  45
    Doxastic logic and the Burge-Buridan-paradox.Wolfgang Lenzen - 1981 - Philosophical Studies 39 (1):43 - 49.
  43.  40
    Der “logische calcul herrn prof. Ploucquets”.Wolfgang Lenzen - 2008 - Archiv für Geschichte der Philosophie 90 (1):74-114.
    In several works published between 1759 and 1782, Gottfried Ploucquet developed a logical system which deviates from traditional syllogistics in several respects. The most important features – which are critically examined in this paper – comprise.
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  44.  7
    Das System der Leibnizschen Logik.Wolfgang Lenzen - 1990 - New York: Walter de Gruyter.
  45.  41
    Das Töten von Tieren und von Föten.Wolfgang Lenzen - 1990 - Analyse & Kritik 12 (2):190-204.
    Singer’s ‘Practical Ethics’ is based on a form of utilitarianism which takes into account the interests of a living being if and only if it displays a minimum of rationality and (self-)consciousness. Accordingly aborting a human fetus in an early stage of development is held to be morally acceptable, whereas killing chicken, pigs, and cattle for mere culinary pleasure is not. Singer's view on abortion are refuted because they only consider the actual properties of the fetus but ignore the quality (...)
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  46.  19
    Die Verwirrungen des Skeptizismus.Wolfgang Lenzen - 1982 - Grazer Philosophische Studien 18 (1):123-135.
    Ausgehend von Descartes' Meditationen werden die Standard-Argumente für den — auf den Bereich empirischer Propositionen beschränkten — Skeptizismus untersucht. Der Versuch einer empirischen Begründung nach dem Schema "Wir haben uns alle schon einmal geirrt, also sollten wir es für möglich halten, daß wir uns immer irren" erweist sich dabei als zirkulär; der alternative, apriorische Begründungsversuch der Art "Es ist stets (logisch) möglich, daß wir uns irren, also wissen wir nichts mit absoluter Sicherheit" beruht dagegen auf einer Verwechslung der Begriffe logischer (...)
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  47.  11
    Das weite Spektrum der Analytischen Philosophie: Festschrift für Franz von Kutschera.Wolfgang Lenzen (ed.) - 1997 - New York: De Gruyter.
  48.  39
    Ex nihilo nihil fit.Wolfgang Lenzen - 2019 - The Leibniz Review 29:59-81.
    In the essay “Principia Calculi rationalis” Leibniz attempts to prove the theory of the syllogism within his own logic of concepts. This task would be quite easy if one made unrestricted use of the fundamental laws discovered by Leibniz, e.g., in the “General Inquiries” of 1686. In the essays of August 1690, Leibniz had developed some similar proofs which, however, he considered as unsatisfactory because they presupposed the unproven law of contraposition: “If concept A contains concept B, then conversely Non-B (...)
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  49.  16
    Frege und Leibniz.Wolfgang Lenzen - 1995 - In Ingolf Max (ed.), Logik und Mathematik. de Gruyter. pp. 82-92.
  50. GW Leibniz Die Grundlagen des logischen Kalkuls.Wolfgang Lenzen - 2003 - History and Philosophy of Logic 24 (2):141-162.
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