Kosta Došen and Zoran Petrić. Proof-net categories . Polymetrica International Scientific Publisher, Monza, Italy, 2007, viii + 147 pp.

Abstract

also suggests a non-standard syllogistics with restricted quantifiers, using a symbolism like “C 2 is B” standing for “I know only with half certainty that C is B”. The central piece is the famous “Sammlung der Schriften, welche den logischen Calcul Herrn Prof. Ploucquet’s betreffen, mit neuen Zusätzen” (Collection of writings concerning Professor Ploucquet’s logical calculus, with new additions) (pp. 37–316), first published by August Friedrich Bök in 1766. It contains the documents of an argument about the qualities of Lambert’s line calculus in comparison with the geometrical calculus of Gottfried Ploucquet, professor of philosophy in Tübingen, who used rectangulars on the basis of an identity theory of judgements. Further contributions by Heinrich Wilhelm Clemm and Georg Jonathan Holland are included in this collection. A short tract “De universaliori calculi idea disquisitio una cum adnexo specimine” (pp. 327–359) first published in Nova acta eruditorum (1765) explicitly extends the Leibnizian idea of a universal calculus. Lambert suggests a calculus of properties and qualities using algebraic symbols for logical operations and relations. It is Lambert’s only publication on calculi of intensions. His “Sechs Versuche einer Zeichenkunst in der Vernunftlehre” (Six attempts of an art of characters in a theory of reason) appeared posthumously (see vol. VI of the Philosophische Schriften). Considerations on a characteristic art and its application to different fields are taken up in other papers like “In algebram philosophicam cl. Richeri breves adnotationes” (pp. 361– 372) or “Observations sur quelques dimensions du monde intellectuel” (pp. 373–390) with an application to esthetics. Partial volume 2 is devoted to Lambert’s reviews published in the Allgemeine Deutsche Bibliothek between 1768 and 1777, among them several comments on works on logic. An index of the books reviewed makes access easier. This edition provides facsimile reprints of the texts. A comprehensive introduction gives useful information on the background and summaries of the material edited. This important edition of Lambert’s philosophical works will be finished in 2008 with volume X, containing further philosophical writings, drafts and reviews with new material from the Nachlass. The edition provides a reliable textual basis for investigating the philosophical ideas of this major figure in European enlightenment who wrote in Leibnizian spirit. Volker Peckhaus Universität Paderborn, Institut für Humanwissenschaften: Philosophie, Warburger Str. 100, D-33098 Paderborn, Germany. volker.peckhaus@upb.de.