According to the received view (Bocheński, Kneale), from the end of the fourteenth to the second half of nineteenth century, logic enters a period of decadence. If one looks at this period, the richness of the topics and the complexity of the discussions that characterized medieval logic seem to belong to a completely different world: a simplified theory of the syllogism is the only surviving relic of a glorious past. Even though this negative appraisal is grounded on good reasons, it (...) overlooks, however, a remarkable innovation that imposes itself at the beginning of the sixteenth century: the attempt to connect the two previously separated disciplines of logic and mathematics. This happens along two opposite directions: the one aiming to base mathematical proofs on traditional (Aristotelian) logic; the other attempting to reduce logic to a mathematical (algebraical) calculus. This second trend was reinforced by the claim, mainly propagated by Hobbes, that the activity of thinking was the same as that of performing an arithmetical calculus. Thus, in the period of what Bocheński characterizes as ‘classical logic’, one may find the seeds of a process which was completed by Boole and Frege and opened the door to the contemporary, mathematical form of logic. (shrink)

This paper investigates the reason why, in the tradition of Western philosophy, a logic of relations was developed only in the second half of the nineteenth century. To this end, it moves along two different but interconnected paths: on the one hand, it attempts to reconstruct the main views concerning the ontology of relations during the middle ages; on the other, it focuses on the treatment of so-called oblique terms in the logical works of some preeminent authors belonging to the (...) scholastic and late-scholastic tradition. From the ontological point of view, realists and nominalist both denied that polyadic expressions of the language signify polyadic properties in the world extra. Some authors, such as Peter Auriol, claimed that polyadic expressions signify something merely mental, thus recognizing, even though in a limited ontological domain, the existence of full-fledged relations, that is, of ‘things’ simultaneousl... (shrink)

In a text written during his stay in Paris, Leibniz, to deny ontological reality to relations, employs an argument well known to the medieval thinkers and which later would be revived by Francis H. Bradley. If one assumes that relations are real and that a relation links any property to a subject – so runs the argument – then one falls prey to an infinite regress. Leibniz seems to be well aware of the consequences that this argument has for his (...) own metaphysical views, where the relation of inherence (‘inesse’) plays such a central role. Thus, he attempts first to interpret the relation of inherence as something ‘metaphoric’, originating from our ‘spatial way’ of looking at the surrounding world; and then he tries to reduce it to the part-whole relation which clearly he considers weaker, from the ontological point of view, than that of ‘being in’. (shrink)

A letter to The Times of London, May 9, 1992 protesting the Cambridge University proposal to award an honorary degree to M. Jacques Derrida.

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). This may be seen with sufficient clarity examining the last part, until now inedited, of the famous passage about Paris and Helen published by Couturat in his Opuscules. (shrink)

This book is a collection of essays published by the author in the long run of 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. 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. 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 to previous interpreters. Lenzen’s acquaintance with the entire corpus of Leibniz’s logical texts 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. (shrink)

MEDIEVAL LOGICS LAMBERT MARIE DE RIJK (ed.), Die mittelalterlichen Traktate De mod0 opponendiet respondendi, Einleitung und Ausgabe der einschlagigen Texte. (Beitrage zur Geschichte der Philosophie und Theologie des Mittelalters, Neue Folge Band 17.) Miinster: Aschendorff, 1980. 379 pp. No price stated. THE SEVENTEENTH CENTURY MARTA FATTORI, Lessico del Novum Organum di Francesco Bacone. Rome: Edizioni dell'Ateneo 1980. Two volumes, il + 543, 520 pp. Lire 65.000. VIVIAN SALMON, The study of language in 17th century England. (Amsterdam Studies in the Theory (...) and History of Linguistic Science, Series 111: Studies in theHistory of Linguistics, Volume 17.) Amsterdam: John Benjamins B.V., 1979.x + 218 pp. Dfl. 65. Theoria cum Praxi. Zum Verhaltnis von Theorie und Praxis im 17. und 18. Jahrhundert. (Akten des 111. Internationalen Leibnizkongress, Hannover, 12. bis 17.November 1977, Band 111: Logik, Erkenntnistheorie, Wissenschaftstheorie, Metaphysik, Theologie.) Wiesbaden: Franz Steiner Verlag, 1980. vii + 269 pp. DM 48. CLASSICAL AND NON-CLASSICAL LOGICS MICHAEL CLARK, The place of syllogistic in logical theory. Nottingham: University of Nottingham Press, 1980. ix + 151 pp. £3.00. A.F. PARKER-RHODES, The theory of indistinguishables. Dordrecht, Boston and London: D. Reidel Publishing Company, 1981. xvii + 216 pp. Dfl.90.00/$39.50. NICHOLAS RESCHER and ROBERT BRANDOM, The logic of inconsistency. Oxford:Basil Blackwell, 1980. x + 174 pp. f 11.50. MISCELLANEOUS J. ZELENY, The logic of Marx. Translated from the German by T. Carver. Oxford: Basil Blackwell, 1980. xcii + 247 pp. £12.50. FELIX KAUFMANN, The infinite in mathematics. Edited by Brian McGuinness. Introduction by E. Nagel. Translation from the German by Paul Foulkes. Dordrecht: Reidel, 1978. xvii + 235 pp. Dfl 85/$39.50 (cloth); Dfl 45/$19.95 (paper). PAMELA MCCORDUCK, Machines who think. San Francisco: W.H. Freeman and Company, 1979. xiv + 275 pp. $14.95. J. MITTELSTRASS (ed.), Enzyklopadie Philosophie und Wissenschaftstheorie Bd. 1 : A-G. Mannheim, Wien, Ziirich: Bibliographisches Institut, 1980. 835 pp. DM 128. (shrink)

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as (...) early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics. (shrink)

This book is a collection of essays published by the author in the long run of 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. 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. 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 to previous interpreters. Lenzen’s acquaintance with the entire corpus of Leibniz’s logical texts 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. (shrink)

Monades non sunt in loco nisi per harmoniam, id est per consensum cum phaenomenis loci, a nullo influxu sed sponte rerum ortum.