69 found
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  1. Recent Work in Epistemic Logic.Wolfgang Lenzen - 1978 - Acta Philosophica Fennica 30:1-219.
  2.  14
    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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  3.  14
    What Follows From the Impossible: Everything or Nothing?Wolfgang Lenzen - forthcoming - History and Philosophy of Logic:1-23.
    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 ar...
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  4.  43
    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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  5.  50
    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. Glauben, Wissen Und Wahrscheinlichkeit. Systeme Der Epistemischen Logik.Wolfgang Lenzen - 1985 - Erkenntnis 23 (1):97-112.
     
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  7.  25
    Leibniz's Logic.Wolfgang Lenzen - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier. pp. 3--1.
  8.  30
    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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  9.  7
    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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  10. Leibniz: Logic.Wolfgang Lenzen - 2014 - Internet Encyclopedia of Philosophy.
    Leibniz: Logic The revolutionary ideas of Gottfried Wilhelm Leibniz (1646-1716) on logic were developed by him between 1670 and 1690. The ideas can be divided into four areas: the Syllogism, the Universal Calculus, Propositional Logic, and Modal Logic. These revolutionary ideas remained hidden in the Archive of the Royal Library in Hanover until 1903 when the French mathematician […].
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  11. 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.  31
    Epistemic Logic.Wolfgang Lenzen - 2004 - In M. Sintonen, J. Wolenski & I. Niiniluoto (eds.), Handbook of Epistemology. Kluwer Academic Publishers. 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. 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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  15. Leibniz and the Calculus Ratiocinator.Wolfgang Lenzen - 2018 - In Sven Hansson (ed.), Technology and Mathematics. Springer Verlag.
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  16. "Unbestimmte Begriffe" bei Leibniz.Wolfgang Lenzen - 1984 - Studia Leibnitiana 16:1.
    In many of his logical writings, G. W. Leibniz makes use of two kinds of symbols : while A, B, C, . . . stand for certain determinate or definite concepts, X, Y, Z, . . . are referred to as "indefinite concepts". We investigate the various rôles played by these variables and show i) that their most important function consists in serving as quantifiers ; ii) that Leibniz's elliptic representation of the quantifiers by means of two sorts of „indefinite (...)
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  17. Das System der Leibnizschen Logik.Wolfgang Lenzen - 1992 - Studia Leibnitiana 24 (1):112-116.
  18.  10
    How to Square Knowledge and Belief.Wolfgang Lenzen - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 305--311.
  19. Theorien der Bestätigung Wissenschaftlicher Hypothesen.Wolfgang Lenzen - 1974
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  20.  10
    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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  21.  26
    On the Representation of Classificatory Value Structures.Wolfgang Lenzen - 1983 - Theory and Decision 15 (4):349-369.
  22.  16
    On Some Substitution Instances of R1 and L1.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19:159.
  23.  6
    Leibniz's Calculus of Strict Implication.Wolfgang Lenzen - 1987 - In Jan T. J. Srzednicki (ed.), Initiatives in Logic. M. Nijhoff. pp. 1--35.
  24.  12
    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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  25.  91
    On Leibniz's Essay 'Mathesis Rationis'.Wolfgang Lenzen - 1990 - Topoi 9 (1):29-59.
  26. 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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  27. 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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  28. Die Paradoxie der überraschenden Übung: Logische, epistemologische und pragmatische Aspekte.Wolfgang Lenzen - 1976 - Logique Et Analyse 19 (74):267-284.
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  29.  17
    Searles verpatzte Lösung des Freiheitsproblems.Wolfgang Lenzen - 2005 - Facta Philosophica 7 (1):35-68.
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  30.  17
    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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  31.  11
    A Rare Accident.Wolfgang Lenzen - 1978 - Notre Dame Journal of Formal Logic 19 (2):249-250.
  32. Alles nur Illusionen? - Philosophische (In-)Konsequenzen der Neurobiologie.Wolfgang Lenzen - 2005 - Facta Philosophica 7 (2):189-229.
  33.  13
    Principia Calculi Rationalis.Gottfried Wilhelm Leibniz & Wolfgang Lenzen - 2019 - The Leibniz Review 29:51-57.
  34.  93
    Leibniz on Privative and Primitive Terms.Wolfgang Lenzen - 1991 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 6 (1-2):83-96.
    We first present an edition of the manuscript LH VII, B 2, 39 in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of privative, and of primitive terms.This formalism involves a symbolic treatment of conceptual quantification which differs quite considerably from Leibniz’s “standard” theory of “indefinite concepts” as developed, e.g., in the “General Inquirles” In the subsequent commentary we give an interpretation and a critical evaluation of Leibniz’s symbolic apparatus. It turns out that the (...)
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  35. Mathesis Rationis Festschrift Für Heinrich Schepers.Albert Heinekamp, Heinrich Schepers, Martin Schneider & Wolfgang Lenzen - 1990
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  36. Abtreibung, Intersubjektiver Nutzenvergleich und der Wert des Lebens.Wolfgang Lenzen - 1995 - Ethik Und Sozialwissenschaften 6 (2):200.
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  37. Über Rainer Enskats 'Wahrheit und Entdeckung'.Wolfgang Lenzen - 1990 - Allgemeine Zeitschrift für Philosophie 15 (3):87.
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  38. Frege und Leibniz.Wolfgang Lenzen - 1995 - In Ingolf Max (ed.), Logik und Mathematik. de Gruyter. pp. 82-92.
  39. GW Leibniz Die Grundlagen des logischen Kalkuls.Wolfgang Lenzen - 2003 - History and Philosophy of Logic 24 (2):141-162.
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  40. Hans Ineichen: Einstellungssätze.Wolfgang Lenzen - 1989 - Philosophische Rundschau 36:41.
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  41. On the Origin of the Utilitarian Maximization Requirement.Wolfgang Lenzen - 2003 - History of Philosophy & Logical Analysis 6 (1):151-165.
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  42.  2
    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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  43. On the Origin of the Utilitarian Maximization Requirement.Wolfgang Lenzen - 2003 - History of Philosophy & Logical Analysis 6.
    Since the total utility of an action A, U, is taken as the decisive criterion for the moral quality of A in the sense that A1 is morally better than A2 iff U > U, utilitarian ethics usually requires that we should always chose that action A* by which the total utility is maximized. This requirement, however, is fundamentally mistaken since it entails that any morally good action A1 is forbidden as long as there exists another alternative A2 which is (...)
     
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  44.  27
    Ockham’s Calculus of Strict Implication.Wolfgang Lenzen - 2015 - Logica Universalis 9 (2):181-191.
    In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.
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  45.  26
    Das Töten von Tieren und von Föten.Wolfgang Lenzen - 1990 - Analyse & Kritik 12 (2):190-205.
    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 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.  21
    Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4.Wolfgang Lenzen - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (7-9):131-143.
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  47.  21
    Belief and Probability.Wolfgang Lenzen - 1979 - Grazer Philosophische Studien 9 (1):199-207.
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  48.  23
    Zum Problem des Fundamentalismus aus der Perspektive der epistemischen Logik.Wolfgang Lenzen - 1984 - Grazer Philosophische Studien 22 (1):13-25.
    Aus epistemisch-logischer Sicht reduziert sich das Fundamentalismusproblem auf die Fragen, ob die Bedingung "a's Glaube, daß p, ist fundiert" notwendig bzw. — im Verband mit "p ist wahr" und "a ist davon überzeugt, daß p " — auch hinreichend dafür ist, daß a weiß, daß p. Drei Explikationsversuche der Fundiertheitsbedingung werden untersucht: während die ersten beiden, mit den üblichen epistemischen Termen 'wissen' und 'überzeugt sein' formulierten Varianten scheitern, erweist sich die dritte Definition mittels des Terms 'evident sein' als erfolgversprechend, sofern (...)
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  49.  33
    Ploucquet’s “Refutation” of the Traditional Square of Opposition.Wolfgang Lenzen - 2008 - Logica Universalis 2 (1):43-58.
    . In the 18th century, Gottfried Ploucquet developed a new syllogistic logic where the categorical forms are interpreted as set-theoretical identities, or diversities, between the full extension, or a non-empty part of the extension, of the subject and the predicate. With the help of two operators ‘O’ (for “Omne”) and ‘Q’ (for “Quoddam”), the UA and PA are represented as ‘O(S) – Q(P)’ and ‘Q(S) – Q(P)’, respectively, while UN and PN take the form ‘O(S) > O(P)’ and ‘Q(S) > (...)
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  50. Damasios Theorie der Emotionen.Wolfgang Lenzen - 2004 - Facta Philosophica 6 (2):269-309.
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