History of Logic from Aristotle to Gödel

by Raul Corazzon | e-mail: rc@ontology.co

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Leibniz on Logic, Language and Semiotics. Annotated bibliography (Second Part: L - Z)

BIBLIOGRAPHY

  1. Lenders, Winfried. 1971. Die Analytische Begriffs- Und Urteilstheorie Von G.W. Leibniz Und Chr. Wolff. Hildesheim: Georg Olms.

  2. Lenzen, Wolfgang. 1983. "Leibniz Und Die Entwicklung Der Modernen Logik." In Leibniz, Werk Und Wirkung. Iv. Internationaler Leibniz-Kongress (Hannover, 14 - 19 November 1983), 418-425. Hannover: Gottfried Wilhelm Leibniz Gesellschaft.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 15-22

  3. ———. 1983. "Zur 'Extensionalen' Und 'Intensionalen' Interpretation Der Leibnizschen Logik." Studia Leibnitiana no. 15:129-148.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 23-46.

    "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" (Couturat, La logique de Leibniz, 387). 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."

  4. ———. 1984. "'Unbestimmte Begriffe' Bei Leibniz." Studia Leibnitiana no. 16:1-26.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 99-131.

    "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 roles played by these variables and show: I) that their most important function consists in serving as (hidden) quantifiers; II) that Leibniz's elliptic representation of the quantifiers (both universal and existential) by means of two sorts of "indefinite concepts" leads to certain difficulties; III) that despite these problems Leibniz anticipated the most fundamental logical principles for the quantifiers and may thus be viewed as a forerunner of modern predicate logic."

  5. ———. 1984. "Leibniz Und Die Boolesche Algebra." Studia Leibnitiana no. 16:187-203.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 47-64.

    "It is well known that in his logical writings Leibniz typically disregarded the operation of (conceptual) disjunction, confining himself to the theory of conjunction and 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 (although definable) logical operator, is provably equivalent (or isomorphic) to Boolean algebra. Moreover, already in the "Generales inquisitiones" of 1686 Leibniz had established all basic principles that are necessary for a complete axiomatization of "Boolean" (or better: Leibnizian) algebra. In this sense Leibniz should be acknowledged as the true inventor of the algebra of sets."

  6. ———. 1986. "'Non Est' Non Est 'Est Non'. Zu Leibnizens Theorie Der Negation." Studia Leibnitiana no. 18:1-37.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 133-179.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. "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 (scholastic) 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. Accordingly, 'a non est b' expresses only the propositional negation of (the U A) 'a est b' and is hence logically weaker than (the U N) 'a est non-b'. Besides Leibniz's cardinal error of confusing propositional and conceptual negation the following issues are dealth with in this paper: "aristotelian" vs "scholastic syllogistic; metalinguistic theory of the truth-predicate; individual-concepts vs concepts in general."

  7. ———. 1987. "Leibniz's Calculus of Strict Implication." In Initiatives in Logic, edited by Srzednicki, Jan, 1-35. Dordrecht: Reidel.

    Translated in German and revised in: W. Lenzen - Calculus Universalis (2004) pp. 281-308.

  8. ———. 1988. "Zur Einbettung Der Syllogistik in Leibnizens 'Allgemeinen Kalkül'." Studia Leibnitiana.Sonderheft no. 15:38-71.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 181-216.

  9. ———. 1989. "Mögliche Individuen Und Mögliche Welten. Eine Begriffslogische Axiomatisierung Der Leibnizschen Ontologie." In Leibniz. Tradition Und Aktualität. V. Internationaler Leibniz-Kongress (Hannover, 14-19 November 1988), 464-470. Hannover: Gottfried Wilhelm Leibniz Gesellschaft.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 325-330.

  10. ———. 1989. "Concepts Vs. Predicates. Leibniz's Challenge to Modern Logic." In The Leibniz Renaissance. International Workshop, Firenze, 2-5 Giugno 1986, 153-172. Firenze: Olschki.

  11. ———. 1989. "Arithmetical Vs. 'Real' Addition. A Case Study of the Relation between Logic, Mathematics, and Metaphysics in Leibniz." In Leibnizian Inquiries. A Group of Essays, edited by Rescher, Nicholas, 149-157. Lanham: University Press of America.

  12. ———. 1989. "Arithmetizismus, Oder Wie Man Die Mengenlehre Aus Dem Kleinen Einmaleins Ableitet." In Traditionen Und Perspektiven Der Analytischen Philosophie. Festschrift Für Rudolf Haller, edited by Wolfgang, Gombocz, Rutte, Heiner and Sauer, Werner, 462-473. Wien: Hölder-Pichler-Tempsky.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 217-227.

  13. ———. 1990. Das System Der Leibnizschen Logik. Berlin: de Gruyter.

    Inhalt: Vorwort VII; Danksagung XIII; Leseanweisung XV-XVI; 1. Syllogisti 1; 2. Die Algebra der Begriffe 28; 3. Quantorenlogik 84; 4. Syllogistik im allgemeinen Kalkül 122; 5. Satzlogik 159; 6. Metaphysik 178; Verzeichnis der Formeln 213; Verzeichnis dr Zitate 225; Sachverzeichnis 231-235.

  14. ———. 1990. "Precis of the History of Logic from the Point of View of the Leibnizian Calculus." In Estudios De Historia De La Lógica. Actas Del Ii Simposio De Historia De La Lógica, Universidad De Navarra, Pamplona, 25-27 De Mayo De 1987, edited by Angelelli, Ignacio and D'Ors, Angel, 13-38. Pamplona: Ediciones Eunate.

  15. ———. 1990. "On Leibniz's Essay 'Mathesis Rationis' (Critical Edition and Commentary)." Topoi no. 9:29-59.

  16. ———. 1991. "Leibniz on Privative and Primitive Terms." Theoria.Revista de Teoria, Historia y Fundamentos de la Ciencia no. 6:83-96.

    "We first present an edition of the manuscript LH VII, B2 39, in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of private, 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 Inquiries".In the subsequent commentary, we give an interpretation and a critical evaluation of Leibniz's symbolic apparatus. It turns out that the definition of privative terms and primitive terms lead to certain inconsistencies which, however, can be avoided by slight modifications."

  17. ———. 1991. "Leibniz on Ens and Existence." In Existence and Explanation. Essays Presented in Honor of Karel Lambert, edited by Lambert, Karel, Spohn, Wolfgang, Fraassen, Bas C.van and Skyrms, Bryan, 59-75. Dordrecht: Kluwer.

    Translated in German as: 'Ens' und 'existens' bei Leibniz in: W. Lenzen - Calculus Universalis (2004) pp. 75-98

  18. ———. 1995. "Frege Und Leibniz." In Logik Und Mathematik. Frege-Kolloquium Jena 1993, edited by Ingolf, Max and Stelzner, Werner, 82-92. Berlin: de Gruyter.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 65-74.

    "In the essay "Booles rechnende Logik und die Begriffsschrift" of 1880 and in the posthumously published paper "Ueber den Zweck der Begriffsschrift" Gottlob Frege had briefly discussed the main elements of Leibniz's logic. By way of comparison with Boole's logic, Frege came to interpret Leibniz's expressions ens' and non ens' as equivalent to Boole's 1' (= universe of discourse) and 0' (= empty domain), respectively. This interpretation is not fully warranted, however. A closer examination of Leibniz's formal representation of the categorical forms in terms of ens' and non ens' reveals that A est ens' does not mean that (the extension of) concept A is equal to 1. Instead it only says that (the extension of) A in nonempty or--from an "intensional" point of view--that concept A is self-consistent."

  19. ———. 2000. "Wenn 0=1, Dann Ist Die, 'Reine Inhaltslogik' Unmöglich. Bemerkungen Zu Liskes Kritik Der Leibnizschen Begriffstheorie." Studia Leibnitiana no. 32:105-116.

    "In a 1994 paper entitled Ist eine reine Inhaltslogik möglich?, M. Liske attempted to show that Leibniz's theory of intensional concepts suffers from a serious inadequacy. Liske begins by defining the intension of a concept in two slightly different ways. Broadly conceived, Int(A) is the set of all concepts B which are contained in A, while in a narrow sense, Int(A) consists of all such B other than A itself."

  20. ———. 2000. "Guilielmi Pacidii Non Plus Ultra, Oder: Eine Rekonstruktion Des Leibnizschen Plus-Minus-Kalküls." Logical Analysis and History of Philosophy no. 3:71-118.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 229-279.

    "In the first part of this paper a short review of the recently published 4th volume of Series 6 (Philosophical Writings) of the Akademie-Ausgabe of Leibniz's Sämtliche Schriften und Briefe is given. This 3,000-page volume was edited by the Leibniz-Forschungsstelle in Münster, Germany. It contains unsurpassable, text-critical versions of more than 500 pieces which Leibniz composed between 1677 and 1690. One major topic dealt with in these essays is "Scientia Generalis, Characteristica, Calculus Universalis". Here we find in particular various fragments of a logical calculus that Leibniz developed around 1687. The main part of this paper presents a detailed reconstruction of this so-called "plus-minus-calculus" which, by way of its somewhat unorthodox operators of "addition" and "subtraction", inclusion and identity, "communication", "commune" and "nothing", provides an interesting alternative to the Boolean algebra of sets."

  21. ———. 2001. "Zur Logik Alethischer Und Deontischer Modalitäten Bei Leibniz." In Zwischen Traditioneller Und Moderner Logik. Nichtklassische Ansätze, edited by Stelzner, Werner and Stöckler, Manfred, 335-351. Paderborn: Mentis.

    Reprinted in revised form in: W. Lenzen - Calculus Universalis (2004) pp. 309-324.

  22. ———. 2003. "Grundfragen Des Logischen Kalküls. Eine Art Rezension Von F. Schupp (Hrg.), G. W. Leibniz, Die Grundlagen Des Logischen Kalküls." History and Philosophy of Logic no. 24:141-162.

  23. ———. 2004. Calculus Universalis. Studien Zur Logik Von G. W. Leibniz. Paderborn: Mentis Verlag.

    Inhaltverzeichnis: Vorwort 5; 1. Leibniz und die (Entwicklung der) moderne(n) Logik 15; 2 Zur extensionalen und "intensionalen" Interpretation der Leibnizschen Logik 23; 3. Leibniz und die Boolesche Algebra 47; 4 Frege und Leibniz 65; 5 'Ens' und 'existens' bei Leibniz 75; 6. "Unbestimmte Begriffe" bei Leibniz 99; 7 'Non est' non est 'est non' - Zu Leibniz' Theorie der Negation 133; 8. Zur Einbettung der Syllogistik in Leibniz' "Allgemeinen Kalkül" 181; 9. Arithmetizismus, oder: Wie Leibniz die Mengenlehre aus dem kleinen Einmaleins ableitet 217; 10. Guilielmi Pacidii Non plus ultra 229; 11. Leibni' Kalkül der strikten Implikation 281; 12. Zur Logik alethischer und deontischer Modalitäten bei Leibniz 309; 13. Mögliche Individuen und mögliche Welten - Eine begrifflogische Reknstruktionen von Leibniz' Ontologie 325; 14. Leibniz' ontologischer Gottesbeweis und das Problems de unmöglichen Dinge 331; 15 Anhänge 343; Literaturverzeichnis 367; Personenverzeichnis 373; Sachverzeichnis 376-380.

    "This book is a collection of essays published by the author in the long run of 1 about 20 years and is centered on the reconstruction of Leibniz's logical calculi. All the essays have been revised for the present edition and some of them constituted the background for Lenzen's first monograph on Leibniz's logic (Das System der Leibnizschen Logik, Berlin-New York, De Gruyter, 1990). A feature common to all these essays is the vindication of the relevance and originality of Leibniz's logical achievements. Lenzen manifests strong dissatisfaction with the evaluations of Leibniz's logic previously offered by interpreters like Louis Couturat, Clarence I. Lewis, Karl Dürr, William and Martha Kneale, and states that till now Leibniz's results in the field of logic have been widely underestimated (p. 22).

    The book contains a careful and detailed examination of almost all Leibniz's papers on the logical calculus and it is based on the knowledge of a wide range of texts unknown (or only partially known) to previous interpreters. Lenzen's acquaintance with the entire corpus of Leibniz's logical texts (including a number of relevant manuscripts) is impressive. Some chapters of the book in particular contain very solid and useful logical analyses. Chapter 7, for instance, includes the most profound account of Leibniz's theory of negation I ever read. Chapter 8 presents in a very clear way Leibniz's attempt to reduce traditional syllogistic to a calculus based on logical inclusion between terms. Chapter 14 is devoted to Leibniz's a priori proof of the existence of God and presents the first edition of an important manuscript on the proof. On chapters 3 and 5 a series of convincing reasons are given to argue that Leibniz's concept of ens does not have to be considered a constant in the logical calculus. In brief: this work discusses a wide range of topics in such a clear and learned way that it will surely become a reference book for scholars interested in the study of Leibniz's logical papers in the forthcoming years."

    From the Review of the book by Massimo Mugnai - The Leibniz Review - vol. 15, 2005, pp. 169-181

  24. ———. 2004. "Leibniz's Logic." In The Rise of Modern Logic: From Leibniz to Frege, edited by Gabbay, Dov and Woods, John, 1-83. Amsterdam: Elsevier.

    Handbook of the History of Logic: Vol. 3.

  25. ———. 2004. "Logical Criteria for Individual (Concepts)." In Individuals, Minds and Bodies: Themes from Leibniz, edited by Carrara, Massimiliano, Nunziante, Antonio-Maria and Tomasi, Gabriele, 87-107. Stuttgart: Steiner.

    Studia Leibnitiana. Sonderhefte 32

  26. ———. 2005. "Leibniz on Alethic and Deontic Modal Logic." In Leibniz Et Les Puissances Du Langage, edited by Berlioz, Dominique and Nef, Frédéric, 341-362. Paris: Vrin.

  27. Levey, Samuel. 2002. "Leibniz and the Sorites." Leibniz Review no. 12:25-49.

  28. Lewis, Clarence Irving. 1918. A Survey of Symbolic Logic. Berkeley: University of California Press.

    See Chapter I. The development of symbolic logic pp. 1-117. (On Leibniz pp. 5-18 and Appendix. Two fragments from Leibniz pp. 373-388).

    Reprinted New York, Dover Publishing 1960, with the omission of chapter V and VI.

  29. Madouas, Sébastien. 1999. "L'adam Vague Et La Constitution Des Mondes Possibles: Une Pensée Modale De L'individu." In L'actualité De Leibniz: Les Deux Labyrinthes, edited by Berlioz, Dominique and Nef, Frédéric, 363-388. Stuttgart: Franz Steiner.

  30. Marchlewitz, Ingrid, and Heinekamp, Albert, eds. 1990. Leibniz' Auseinandersetzung Mit Vorgängern Und Zeitgenossen. 27 ed.

    Studia Leibnitiana. Sonderheft.

  31. Martin, Gottfried. 1964. Leibniz: Logic and Metaphysics. Manchester: Manchester University Press.

    German edition: Leibniz. Logik und Metaphysik - Berlin, de Gruyter 1967; reprint: New York, Garland, 1985

  32. Mates, Benson. 1968. "Leibniz on Possible Worlds." In Logic, Methodology, and Philosophy of Science Iii., edited by Rootselaar, Bob van and Staal, Johan Frederik, 507-529. Amsterdam: North-Holland.

    Reprinted in: Harry Frankfurt (ed.) - Leibniz. A collection of critical essays - New York, Doubleday, 1972, pp. 335-364 and in: Roger Woolhouse (ed.) - Gottfried Wilhelm Leibniz. Metaphysics and its foundations - Gottfried Wilhelm Leibniz. Critical assessments - Vol. I - New York, Routledge, 1994, pp. 208-229.

  33. ———. 1979. "The Lingua Philosophica." Studia Leibnitiana.Sonderheft no. 8:59-66.

  34. McCadden, Carlos. 2001. "Leibniz's Principle of Contradiction Is Not What Aristotle Called the Most Certain of All Principles." Aletheia.An International Journal of Philosophy:469-485.

    "The object of this article is to show that the principle of contradiction in Leibniz is not the same principle that Aristotle called "the most certain of all principles". The five parts of this study are as follows: the first part shows the importance of the problem; the second is an exposé of Aristotle's thought on "the most certain of all principles." The third part treats of the principle of contradiction according to Leibniz; the fourth compares the thought of the two philosophers and draws some conclusions about the ramifications of their differences; the fifth part is a summary."

  35. Mertz, Donald. 1980. "Leibniz's Monadic Treatment of Relations." Auslegung no. 7:256-269.

    "Continuing in the line of Ishiguro and Hintikka, this paper explicates further the form of Leibniz's brief logical/syntactical program for relations, and this is then contrasted with his metaphysical/semantical treatment of them. The analysis shows a similar though not identical treatment of relations under both programs. The similarity lies in Leibniz's treating multi-term relations as one-term, monadic predicates with all other term-places being either instantiated, or bound by existential quantifiers, depending upon the program. Both programs require Leibniz to introduce a new non-truth-functional, yet "relational" connective between propositions."

  36. Mondadori, Fabrizio. 1975. "Leibniz and the Doctrine of Inter-World Identity." Studia Leibnitiana no. 7:22-57.

    Reprinted in: R. Woolhouse (ed.) - Gottfried Wilhelm Leibniz. Critical Assessments, Volume 1 - New York, Routledge, 1994, pp. 256-289

  37. ———. 2003. "Leibniz on Compossibility: Some Scholastic Sources." In The Medieval Heritage in Early Modern Metaphysics and Modal Theory, 1400-1700, edited by Friedman, Russell L. and Nielsen, Luge O., 309-338. Dordrecht: Kluwer.

  38. Moriconi, Enrico, and Offenberger, Niels. 1984. "Zur Frage Der Iv Syllogistischen Figur in Der Dissertatio De Arte Combinatoria: Eine Jugendsunde Leibnizens?" Studia Leibnitiana no. 16:212-216.

    "This paper is a discussion of Leibniz's juvenile thesis according to which "quarta figura aeque bona est ac ipsa prima; imo si modo, non praedicationis, ut vulgo solent, sed subjectionis, ut aristoteles, eam enunciemus, ex IV fiet I et contra" (Dissertatio de Arte Combinatoria, 25). The authors maintain that that thesis is syllogistically untenable, since the reduction device Leibniz suggested does not change the logical function of termini, but introduces a difference only from a grammatical point of view."

  39. Mugnai, Massimo. 1973. "Bertrand Russell E Il Problema Delle Relazioni in Leibniz." Rivista di Filosofia no. 64:356-362.

  40. ———. 1976. Astrazione E Realtà. Saggio Su Leibniz. Milano: Feltrinelli.

  41. ———. 1978. "Bemerkungen Zu Leibniz' Theorie Der Relationen." Studia Leibnitiana no. 10:2-21.

    "Many of the problems traditionally related to the interpretation of Leibniz' theory of relations may be seen in a better light considering essentially two factors: 1) the different plans (ontological, metaphysical, psychological and logical-linguistic) implied by Leibniz reflections on the subject; 2) the reference to scholastic and late-scholastic texts read or consulted by Leibniz. Relations for Leibniz are, from a metaphysical point of view, denominations only seemingly external, they are in reality "denominationes intrinsecae", and are founded on the general connection of all things. From a psychological point of view they are abstract entities that our mind builds by resemblance. From an ontological point of view they are individual accidents inherent to the substances. From a logical-linguistic point of view they are abstract structures that connect the one to the other at least two subjects. The propositions in which they appear, as for example the proposition "Paris loves Helen" are transformed by Leibniz in equivalent propositions joined by operators, which in medieval logic were known as "termini reduplicantes" (terms which define mostly intensional contexts)."

  42. ———. 1979. "Contesti Intensionali E Termini Reduplicativi Nella Grammatica Rationalis Di Leibniz." Rivista di Filosofia no. 70:32-44.

  43. ———. 1990. "A Systematical Approach to Leibniz's Theory of Relations and Relational Sentences." Topoi no. 9:61-81.

  44. ———. 1992. Leibniz's Theory of Relations. Stuttgart: Franz Steiner.

  45. Nef, Frédéric. 1999. "La Philosophie Modale De Leibniz Est-Elle Cohérente?: Essai Sur Des Problèmes D'interprétation De Notions Modales Leibniziennes À Propos Du Mythe De Sextus Et De L'oracle De Kégila." In L'actualité De Leibniz: Les Deux Labyrinthes, edited by Berlioz, Dominique and Nef, Frédéric, 277-305. Stuttgart: Franz Steiner.

  46. ———. 2000. Leibniz Et Le Langage. Paris: Presses Universitaires de France.

  47. ———. 2005. "Accidents Et Relations Individuelles Che Leibniz. Analyse Linguistique Et Formes Logiques." In Leibniz Et Les Puissances Du Langage, edited by Berlioz, Dominique and Nef, Frédéric, 125-139. Paris: Vrin.

  48. Nelson, Alan. 2005. "Leibniz on Modality, Cognition, and Expression." In A Companion to Rationalism, edited by Nelson, Alan. Malden: Blackwell.

  49. Noordraven, Andreas. 2001. "Leibniz' onto-Logik Und Die Transzendentrale Logik Kants." In Kant Und Die Berliner Aufklarung. Akten Des 9. Internationalen Kant-Kongresses. Band V: Sektionen Xv-Xviii, edited by Gerhardt, Volker, Horstmann, Rolf-Peter and Schumacher, Ralph, 55-64. Berlin: de Gruyter.

  50. O'Briant, Walter H. 1967. "Leibniz's Preference for an Intensional Logic." Notre Dame Journal of Formal Logic no. 8:254-256.

    "G. H. R. Parkinson's contention that Leibniz was led to interpret his logic intensionally because of his desire to deny existential import to universal propositions is shown to be defective because (i) it disregards evidence such as that from 'General investigations' (1686) that Leibniz never adopted a definitive attitude on the issue of existential import and (ii) misinterprets Leibniz's statement that "concepts do not depend upon the existence of individuals". The author claims that Leibniz's preference is based primarily on his doctrine that the basic relation between concepts in a proposition is that of containment."

  51. Padilla-Gálvez, Jesús. 1991. "Las Lógicas Modales En Confrontación Con Los Conceptos Basicós De La Lógica Modal De G. W. Leibniz." Theoria.Revista de Teoria, Historia y Fundamentos de la Ciencia no. 6:115-127.

    "In the first section we examine Leibniz's "termini necesitas-possibilitas". In the second section we propose a minimal modal logic, L (subscript) LM, arises from the addition of modal principles. In the final section we examine his complex study towards the interpretation of modal language in the possible worlds. The resulting interplay between the minimal modal logic and the possible world perspective is one of the main charms of semantics."

  52. ———. 2001. "Modalisatoren Und Mögliche Welten in Den Logisch-Semantischen Untersuchungen Um 1686." In Nihil Sine Ratione. Mensch, Natur Und Technik Im Wirken Von G. W. Leibniz. Band 2, edited by Poser, Hans, Asmuth, Christoph, Goldenbaum, Ursula and Li, Wenchao, 926-933. Hannover: Gottfried-Wilhelm-Leibniz-Gesellschaft.

    Akten der VII. Internationaler Leibniz-Kongress (Berlin, 10. - 14. September 2001)

  53. Parkinson, George H. 1965. Logic and Reality in Leibniz's Metaphysics. Oxford: Clarendon Press.

    Reprint: New York, Garland 1985

  54. ———. 1995. "Philosophy and Logic." In The Cambridge Companion to Leibniz, edited by Jolley, Nicholas, 199-223. Cambridge: Cambridge University Press.

  55. Patzig, Günther. 1969. "Leibniz, Frege Und Die Sogennante 'Lingua Characteristica Universalis'." Studia Leibnitiana.Sonderheft:103-112.

    Akten des Internationale Leibniz-Kongresses Hannover 14-19 November 1966 - Vol. 3: Erkenntnislehre, Logik, Sprachphilosophie, Editionsberichte

  56. Peckhaus, Volker. 1997. Logik, Mathesis Universalis Und Allgemeine Wissenschaft. Leibniz Und Die Wiederentdeckung Der Formalen Logik Im 19. Jahrundert. Berlin: Akademie Verlag.

    Contents: Vorwort VII-VIII; 1. Einleitung 1; 2. Die Idee der mathesis universalis bei Leibniz 25; 3. Die frühe Rezeption Leibnizscher mathesis universalis und Logik 64; 4. Die "logische Frage" und die Entdeckung der Leibnizschen Logik 130; 5. Leibniz und die englische Algebra der Logik 185; 6. Ernst Schröder: "Absolute Algebra" und Leibnizprogramm 233; 7. Schluss 297; Verzeichnisse 309-412.

  57. ———. 2002. "Die Entdeckung Der Leibnizschen Logik." In Medium Mathematik. Anregungen Zu Einem Interdisziplinären Gedankenaustausch. Band 1, edited by Löffladt, Günter and Toepell, Michael, 149-169. Hildesheim: Franzbecker.

  58. ———. 2004. "Calculus Ratiocinator Versus Characteristica Universalis? The Two Traditions in Logic, Revisited." History and Philosophy of Logic no. 25:3-14.

  59. Peña, Lorenzo. 1991. "De La Logique Combinatoire Des 'Generales Inquisitiones' Aux Calculs Combinatoires Contemporains." Theoria.Revista de Teoria, Historia y Fundamentos de la Ciencia no. 6:129-159.

    "In his 1686 essay, Leibniz undertook to reduce sentences to noun-phrases, truth to being. Such a reduction arose from his equating proof with conceptual analysis. Within limits, Leibniz's logical calculus provides a reasonable way of surmounting the dichotomy, thus allowing a reduction of hypothetical to categorical statements. However it yields the disastrous result that whenever A is possible and so is B there can be an entity being both A and B. Yet, Leibniz was the forerunner of twentieth century combinatory logic, which (successfully!) practices -- sometimes for reasons not entirely unlike Leibniz's own grounds -- reductions of the same kinds he tried to carry out."

  60. Plaisted, Dennis. 2002. Leibniz on Purely Extrinsic Denominations. Rochester: University of Rochester Press.

  61. Pombo, Olga. 1987. Leibniz and the Problem of a Universal Language. Münster: Nodus Publikationen.

  62. ———. 1990. "The Leibnizian Theory of Representativity of the Sign." In History and Historiography of Linguistics. Vol. Ii, edited by Niederehe, Hans-Joseph and Koerner, Konrad, 447-459. Philadelphia: John Benjamins.

  63. ———. 1990. "Comparative Lines between Leibniz's Theory of Language and Spinoza's Reflexions on Language Themes." Studia Spinozana no. 6:147-177.

  64. ———. 1996. "Leibnizian Strategies for the Semantical Foundation of the Universal Language." In Im Spiegel Des Verstandes. Studien Zu Leibniz, edited by Dutz, Klaus D. and Gensini, Stefano, 161-171. Münster: Nodus Publikationen.

  65. ———. 1998. "La Théorie Leibnizienne De La Pensée Aveugle En Tant Que Perspective Sur Quelques-Unes Des Apories Linguistiques De La Modernité." Cahiers Ferdinand Saussure no. 51:63-75.

  66. Poser, Hans. 1969. "Zum Logischen Und Inhaltlichen Zusammenhang Der Modalbegriffe Bei Leibniz." Kant Studien no. 60:436-451.

  67. Rabouin, David. 2005. "Logique, Mathémathique Et Imagination Dans La Philosophie De Leibniz." Corpus.Revue de Philosophie no. 49:165-198.

  68. Rauzy, Jean-Baptiste. 1995. ""Quid Sit Natura Prius"? La Conception Leibnizienne De L'ordre." Revue de Métaphysique et de Morale no. 98:31-48.

    "It is well known that Leibniz's logic is grounded in the inherence of the predicate in the subject and in the compossibility of notions. It naturally stresses, therefore, relations of equivalence, rather than of order. Nevertheless, Leibniz provided a logical analysis of order, i.e., an account of the meaning of "prior", "subsequent", "concomitant". His account comprises three points: 1) Given two beings, the one that is more simple (i.e., the one whose analysis requires less operations of the mind) is prior by nature ("natura prius"); hence, concomitant ("simul") being. 2) The degree of composition of being corresponds to its degree of perfection. Hence, prior beings being simpler, subsequent beings are more perfect. 3) Given two beings such that one is simpler and the other more perfect, they differ temporally if they also contradict each other; conversely, two compossible beings contradict each other if, and only if, they are not simultaneous (i.e., if they do not belong to the same "state of the universe"). It will be shown that this relation makes it possible to characterize the axiomatic order of incomplete notions (in the field of the "mathesis universalis"). But the attempt to explain the terms prius, posterius and simul in a metaphysical manner, i.e., by laying the stress on the order among substances, raises grave philosophical problems."

  69. ———. 2001. La Doctrine Leibnizienne De La Verité. Aspects Logiques Et Ontologiques. Paris: Vrin.

    "Jean-Baptiste Rauzy writes here on Leibniz's theory of truth, construed broadly, mostly in Leibniz's earlier periods (to 1686). He focuses mostly on Leibniz's logical theory, particularly as given in the logical papers, published only with Couturat and others, in 1901 and following. Unlike a lot of the secondary literature, Rauzy's book gives much detail about how Leibniz's various logical models work out and apply to more general issues such as the reduction of relations, the ontological square (first given in Aristotle's Categories 2), haecceity, and the problem of universals.

    In addition to using the full opera of Leibniz, Rauzy incorporates a wide range of sources into his discussion: the secondary literature on Leibniz; Leibniz's contemporaries and predecessors, including not merely those like Malebranche and Hobbes, but also Marius Nizolius, Joachim Jungius, Francisco Suarez, and Thomas Aquinas. For he contends that, as in metaphysics, Leibniz in logic looks to the past, despite what some have thought (pp. 10, 14-16)." (from the review by Allan Bäck - Review of Metaphysics - March 2003)

  70. Rescher, Nicholas. 1954. "Leibniz's Interpretation of His Logical Calculi." Journal of Symbolic Logic no. 19:1-13.

    Reprinted in: N: Rescher - Nicholas Rescher collected papers. Vol. 10. Studies in the history of logic - Frankfurt, Ontos Verlag, 2006, 141-157

  71. Rijen, Jeroen van. 1989. "Some Misconceptions About Leibniz and the Calculi of 1679." Studia Leibnitiana no. 21:196-204.

    "In the April papers of 1679 Leibniz expounds an arithmetical model of the logic of categorical sentences. In later works one hardly finds any remaining trace of this project. This fact gave rise to the question why Leibniz abandoned his views of 1679. Several answers have been given. In this paper it is shown that all these answers are wrong and, moreover, that the question itself is pointless. It is argued that, although the arithmetical calculi are defective, Leibniz never abandoned them. Instead, he looked upon them as equivalent alternatives to his later deduction-theoretic representations of the same logic."

  72. Risse, Wilhelm. 1969. "Die Characteristica Universalis Bei Leibniz." Studi Internazionali di Filosofia no. 1:107-116.

  73. ———. 1969. "Zur Klassifiezierung Der Urteile Und Schlüsse Durch Leibniz." Studia Leibnitiana no. 1:23-53.

  74. Robinet, André. 2000. "Leibniz Et La Logique De Port-Royal." Revue des Sciences Philosophiques et Théologiques no. 84:69-81.

    "L'oeuvre de Leibniz comporte de multiples impacts, soit des circonstances historiques qui ont présidé à la composition de la Logique, soit au sujet des analyses de contenu. Au fond, l'œuvre combinatoire et la requête vers une mathesis divina commence (le De Arte combinatoria est de 1666) dès les premières éditions de l'Art de penser qui s'en tient à la mathesis universalis, faute de s'intéresser aux structures internes de l'incompréhensible que l'infinitisme permet d'aborder intelligiblement. Aussi le choc est-il constant à travers toutes les relations épistolaires entre Leibniz et Arnauld. "

  75. ———. 2002. "Lexicographie Et Caractéristique Universelle." In Neuzeitliches Denken. Festschrift Für Hans Poser Zum 65. Geburtstag, edited by Abel, Günter, Engfer, Hans-Jürgen and Hubig, Christoph, 163-172. Berlin: de Gruyter.

    "Les questions leibniziennes relatives à la 'caractéristique universelle' ont été amplement étudiées dans les travaux publiés par H. Poser. Est-ce que la lexicographie statistique, telle qu'elle s'est développée au cours de notre Informatikzeitalter, est susceptible de contribuer à l'édification du grand projet de Leibniz? Ces procédures linguistiques, hautement mathématiques et technologiques, sont survenues dans la lignée même des objectifs dégagés à partir du calcul binaire, des calculs statistiques et probabilitaires, dans la direction d'une simulation cybernétique des procédures pensantes. La machine à calculer en fonction de la table pythagoricienne des nombres ne pouvait être qu'une approximation de ce qui deviendrait réalisable à partir de la Dualzahltheorie. Mais une table combinatoire des concepts était d'une toute autre envergure et exigeait d'abord qu'on dominât la genèse et la composition des langues pour en venir à une logique des pensées. Il fallait, pour cela, résoudre d'abord le problème du signifiant, corollairement au problème des signes qui seraient mis en regard. La signification devenait ainsi l'étude du rapport possible entre un signifié de nature réelle ou conceptuelle et un signifiant naturel ou artificiel. Indépendamment des considérations concernant les langues vernaculaires et leurs éventuelles correspondances (cf. des opérations leibniziennes comme 'pater noster' ou 'langue commune'), Leibniz se meut à trois niveaux quand il approche la question de la caractéristique universelle: 1)inventer des procédures sémiotiques pour en rendre le contenu opérationnel; 2) dégager les notions-clés d'une sémantique générale; 3) examiner si, sur ce trajet constructif, intervient cette autre discipline scientifique leibnizienne qu'est la recherche d'une langue primitive. En un mot, est-ce que les procédures d'une caractéristique universelle convergent vers les fonctions qu'on peut observer dans la primitivité expressive du langage?"

  76. Rochhausen, Rudolf. 1997. "Leibniz Und Die Einheit Von Logik, Kombinatorik Und Erkenntnis." In Gottfried Wilhelm Leibniz. Wissenschaftliche Methoden Heute, edited by Heinz, Melitta and Reiprich, Kurt, 21-34. Leipzig: Rohrbacher Kreis.

  77. Roncaglia, Gino. 1988. "Modality in Leibniz' Essays on Logical Calculus of April 1679." Studia Leibnitiana no. 20:43-62.

  78. Ross, George MacDonald. 1981. "Logic and Ontology in Leibniz." Studia Leibnitiana.Sonderheft no. 9:20-26.

  79. Rossi, Jean-Gérard. 1997. "Sur Deux Types De Rapport Entre Sujets Et Prédicats Dans La Philosophie Leibnizienne." Studia Leibnitiana no. 29:103-111.

  80. Rossi, Paolo. 1989. "The Twisted Roots of Leibniz' Characteristic." In The Leibniz Renaissance, 271-289. Firenze: Olschki.

  81. ———. 2000. Logic and the Art of Memory. The Quest for a Universal Language. Chicago: University of Chicago Press.

    Translated from Italian with an introduction by Stephen Clucas.

    First edition: Clavis universalis. Arti mnemoniche e logica combinatoria da Lullo a Leibniz - Napoli, Ricciardi, 1960; Second revised edition: Bologna, Il Mulino, 1983.

    See in particular Chapter VII. The construction of a universal language pp. 145-175 and VIII. The sources of Leibni'z universal character pp. 176-193

  82. Royse, James R. 1980. "Leibniz and the Reducibility of Relations to Properties." Studia Leibnitiana no. 12:179-204.

    "On the basis of his remarks concerning metaphysics and logic, the thesis that relations are reducible to properties has often been ascribed to Leibniz. Russell and others have opposed this thesis, primarily by reference to asymmetrical relations and several precise formulations of the thesis prove in fact to be false. However, Leibniz's ontology may be seen as justifying a version of type theory, in which one form of reducibility can be demonstrated. The method used here shows also how two monads, each possible in itself, are not able to exist together, and thus how incompossibility can arise."

  83. Russell, Bertrand. 1900. A Critical Exposition of the Philosophy of Leibniz. With an Appendix of Leading Passages. London: Routledge.

    Second edition with a new preface 1937; reprint: New York, Cosimo Classics, 2008

  84. Rutherford, Donald. 1988. "Truth, Predication and Complete Concept of an Individual Substance." In Leibniz. Questions De Logique, edited by Heinekamp, Albert, 130-144. Stuttgart: Steiner Verlag.

  85. ———. 1995. "Philosophy and Language in Leibniz." In The Cambridge Companion to Leibniz, edited by Jolley, Nicholas, 224-269. Cambridge: Cambridge University Press.

  86. Sainati, Vittorio. 1970. "Sulla Logica Leibniziana." Filosofia no. 21:221-258.

  87. ———. 1986. "Leibniz E La Verità." Teoria no. 6:81-137.

  88. ———. 1989. "Verità E Modalità in Leibniz." In Le Teorie Delle Modalità. Atti Del Convegno Internazionale Di Storia Della Logica, edited by Corsi, Giovanni, Mangione, Corrado and Mugnai, Massimo, 113-120. Bologna: CLUEB.

  89. Sanchez-Maza, Miguel. 1991. "Actualisation, Developpement Et Perfectionnement Des Calculs Logiques Arithmetico-Intensionnels De Leibniz." Theoria.Revista de Teoria, Historia y Fundamentos de la Ciencia no. 6:175-259.

  90. Scheine, Erhard. 1990. "Calculemus! Das Problem Der Anwendung Von Logik Und Mathematik." In Leibniz' Auseinandersetzung Mit Vorgängern Und Zeitgenossen, edited by Heinekamp, Albert and Marchlewitz, Ingrid, 200-216. Stuttgart: F. Steiner.

    Studia Leibnitiana. Supplementa 27

  91. Schmidt, Franz. 1966. "Die Symbolisierten Elemente Der Leibnizschen Logik." Zeitschrift für Philosophische Forschung no. 20:595-605.

  92. Schneider, Martin. 1995. "Weltkonstitution Durch Logische Analyse: Kritische Uberlegungen Zu Leibniz Und Carnap." Studia Leibnitiana no. 27:67-84.

    "The question of the possibility of a world-constitution by logical analysis (i.e., as to the extent the ontological problem of the explanation of the structure of the real world by logical means can be achieved) is exemplarily investigated for two philosophers. Both of them try to the same extent to solve the problem in the context of a universal method (Einheitswissenschaft, scientia generalis') founded on the basis of formal logic, while each of them follows opposing aims: on the one hand the foundation (Leibniz), on the other the elimination (Carnap) of metaphysics by logical analysis of language."

  93. Schulz, Dietrich J. 1970. "Die Funktionen Analytischer Sätze in Leibniz's Frühen Entwürfen Zur Characteristik." Studia Leibnitiana no. 2:127-134.

  94. Schupp, Franz. 1982. "Einleitung." In Generales Inquisitiones De Analysi Notionum Et Veritatum / Allgemeine Untersuchungen Über Die Analyse Der Begriffe Und Wahrheiten, VII-XXXV. Hamburg: Meiner.

  95. ———. 2000. "Einleitung." In Die Grundlagen Des Logischen Kalkül, VII-LXXXIV. Hamburg: Meiner.

    See in particular 5. Grundprobleme pp. XX-LXXX and 6. Zur Geschichte der Leibniz-Programms LXXXI-LXXXIV.

  96. Shim, Michael. 2004. "Leibniz and Modal Realism." In Aufklärung Durch Kritik. Festschrift Für Manfred Baum Zum 65. Geburtstag, edited by Baum, Manfred, Hüning, Dieter, Michel, Karin and Thomas, Andreas, 95-111. Berlin: Duncker & Humblot.

  97. Skosnik, Jeffrey. 1980. "Leibniz and Russell on Existence and Quantification Theory." Canadian Journal of Philosophy no. 10:681-720.

  98. Sommers, Fred. 1976. "Leibniz's Program for the Development of Logic." In Essays in Memory of Imre Lakatos, edited by Cohen, Robert, Feyerabend, Paul and Wartofsky, Marx, 589-615. Dordrecht: Reidel Publishing Company.

    Boston studies in the philosophy of science Vol. 39

  99. ———. 1976. "Frege or Leibniz?" In Studies on Frege. Logic and Semantics, edited by Schirn, Matthias, 11-34. Stuttgart-Bad Cannstatt: Frommann-Holzboog.

    Volume III

  100. Sotirov, Vladimir. 1999. "Arithmetizations of Syllogistic À La Leibniz." Journal of Applied Non-Classical Logics no. 9:387-405.

  101. ———. 2001. "Leibniz's Logical Systems: A Contemporary View." In Nihil Sine Ratione. Mensch, Natur Und Technik Im Wirken Von G. W. Leibniz. Band 3, edited by Poser, Hans, Asmuth, Christoph, Goldenbaum, Ursula and Li, Wenchao, 1213-1220. Hannover: Gottfried-Wilhelm-Leibniz-Gesellschaft.

  102. Spruit, Leen. 1990. "Reasoning and Computation in Leibniz." History and Philosophy of Logic no. 11:1-14.

    "Leibniz's overall view of the relationship between reasoning and computation is discussed on the basis of two broad claims that one finds in his writings, concerning respectively the nature of human reasoning and the possibility of replacing human thinking by a mechanical procedure. A joint examination of these claims enables one to appreciate the wide scope of Leibniz's interests for mechanical procedures, concerning a variety of philosophical themes further developed both in later logical investigations and in methodological contributions to cognitive psychology."

  103. Swoyer, Chris. 1994. "Leibniz's Calculus of Real Addition." Studia Leibnitiana no. 26:1-30.

    "I examine what is probably Leibniz's most complete logical system and show that it is well- developed formal logic with a number of original and important features. Among other things, Leibniz discusses alternative interpretations of his system, provides detailed proofs of over twenty theorems about (what are now known as) semilattices and shows their relevance to logic, and he develops what is probably the first formal theory of the part- whole relation. I then show how Leibniz's system illuminates other aspects of his logic and philosophy, including his views on the structure of concepts and on infinite analysis."

  104. ———. 1995. "Leibniz on Intension and Extension." Noûs no. 29:96-114.

    "Leibniz is well-known for his intensional interpretation of logic, but he also discusses, and sometimes even employs, an extensional approach. I examine Leibniz's views on intension, extension, and the connections between them. I show that Leibnizian intensions and extensions share a common structure that explains the relationships among the various interpretations he proposes for his logics, that because of this common structure extensions express intensions in Leibniz's important, technical sense of expression, and that Leibniz's views on intension and extension (in conjunction with his views about truth) require that Leibnizian concepts be extensional."

  105. Thiel, Christian. 1982. "From Leibniz to Frege: Mathematical Logic between 1679 and 1879." In Logic, Methodology and Philosophy of Science, Vi, edited by Cohen, Jonathan L., 755-770. Amsterdam: North-Holland.

    Proceedings of the Sixth International Congress of logic. methodology and philosophy of science, Hannover 1979.

  106. Varani, Giovanna. 1995. "Ramistische Spuren in Leibniz' Gestaltung Der Begriffe ,Dialectica', ,Topica' Und ,Ars Inveniendi'." Studia Leibnitiana no. 27:135-156.

    "Vers la fin du XVIe siecle, le ramisme se repandit en Allemagne, gagna un grand nombre de proselytes et fit preuve d'une remarquable vitalite. L'histoire de ses effets constitue un interessant, neanmoins peu recherché chapitre de l'historiographie de la philosophie, et la question portant sur les "dettes" eventuelles de Leibniz envers le ramisme se tiend au coeur de cet essai. En premier lieu, quelques caractères théoriques du ramisme allemand et surtout du philippo-ramisme sont mis en évidence, aprés cela on analyse l'emploi de Leibniz (jusqu'au 1680) des notion "dialectica", "topica" et "ars inveniendi" et l'on decouvre une syntonisation conceptuelle entre cet emploi et la manière de penser des ramistes. Sans en tirer des conclusions hasardeuses, on peut comprendre le ramisme comme un ingrédient essentiel de l'univers leibnizien complèxe et comme un thème de plus en plus important pour Leibniz."

  107. ———. 1995. Leibniz E La "Topica" Aristotelica. Milano: IPL - Istituto di Propaganda Libraria.

  108. Velarde Lombraña, Julián. 2002. "Leibniz Y La Lógica." Themata.Revista de Filosofia no. 29:217-231.

    "This paper is a commented review of the studies about Leibniz's logic made in Spain during the last thirty years. In order to achieve a better treatment, I have divided the specific topics of Leibniz's logic in the following sections: (1) Characteristica; (2) Universal Language; (3) Calculi; (4) General Science (Encyclopaedia): Method of Analysis/Synthesis; (5) Truth; (6) Panlogism."

  109. Verburg, Pieter A. "The Idea of Linguistic System in Leibniz." In History of Linguistic Thought and Contemporary Linguistics, edited by Parret, Herman, 593-615. Berlin: Walter de Gruyter.

  110. Vezeanu, Ion. 2006. "Les Lois Fondamentales De La Théorie De L'identité Absolue." Logique et Analyse no. 49:169-190.

  111. Walker, Daniel P. 1972. "Leibniz and Language." Journal of the Warburg and Courtauld Institutes no. 35:294-307.

    Reprinted in: D. P. Walker - Music, Spirit and Language in the Renaissance - London, Variorum Reprints, 1985 and in: R. S. Woolhouse - Leibniz. Critical assessments - Vol. III - New York, Routledge, 1994, pp. 436-451

  112. Weizsäcker, Carl Friedrich von, and Rudolph, Enno, eds. 1989. Zeit Und Logik Bei Leibniz. Studien Zu Problemen Der Naturphilosophie, Mathematik, Logik Und Metaphysik. Stuttgart: Klett-Cotta.

  113. Wierzbicka, Anna. 2001. "Leibnizian Linguistics." In Perspectives on Semantics, Pragmatics, and Discourse. A Festschrift for Ferenc Kiefer, edited by Kenesei, István and Harnish, Robert M., 229-253. Amsterdam: John Benjamins.

  114. Wilson, Margaret. 1969. "On Leibniz's Explication of "Necessary Truth"." Studia Leibnitiana.Sonderheft:50-63.

    Akten des Internationale Leibniz-Kongresses Hannover 14-19 November 1966 - Vol. 3: Erkenntnislehre, Logik, Sprachphilosophie, Editionsberichte

  115. Woolhouse, Roger, ed. 1994. Philosophy of Science, Logic, and Language. New York: Routledge.

    Gottfried Wilhelm Leibniz. Critical assessments. Vol. III

  116. Zalta, Edward. 2000. "A (Leibnizian) Theory of Concepts." Logical Analysis and History of Philosophy no. 3:137-183.

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