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**Leibniz’s science of the rational.**
*(English)*
Zbl 0971.01003

Studia Leibnitiana. Sonderheft. 26. Stuttgart: Franz Steiner Verlag Wiesbaden. 107 p. (1998).

This essay investigates Leibniz’s notions of intelligibility, truth, and analysis, furthermore his use of principles and his account of method in logic and in the philosophy of mathematics. It is Leibniz’s (in most cases) intensional approach to logic which the authors regard as principal tool for maintaining his “general project” of searching for conditions of intelligibility (p. 10).

In the introduction the authors stress the close connection between the principles of contradiction and of sufficient reason which jointly govern all knowledge (p. 16). In the first part the authors present “Elements of a Leibnizian theory of predication” discussing among other topics the subject-predicate distinction and the intensional interpretation of logic. They then present the theory of predication as given in the Generales Inquisitiones and the Discours de MÃ©taphysique, both written at almost the same time (1686).

The third part is devoted to Leibniz’s analysis of arithmetic. The authors attempt to show that Leibniz’s analysis is not purely deductive and that it does not reduce arithmetic to logic, nor integers to the unit. “Rather, it embeds arithmetic open-endedly in systematic analogies motivated by the demands of reason” (p.75). The authors finally compare Leibnizian analysis with positions in 19th century philosophy. In order to support their interpretations they present two hitherto unpublished manuscripts, “Mathesis generalis est scientia magnitudinis” (pp.89-98), and “Numerus integer est totum ex unitatibus collectum” (pp.99-102).

In the introduction the authors stress the close connection between the principles of contradiction and of sufficient reason which jointly govern all knowledge (p. 16). In the first part the authors present “Elements of a Leibnizian theory of predication” discussing among other topics the subject-predicate distinction and the intensional interpretation of logic. They then present the theory of predication as given in the Generales Inquisitiones and the Discours de MÃ©taphysique, both written at almost the same time (1686).

The third part is devoted to Leibniz’s analysis of arithmetic. The authors attempt to show that Leibniz’s analysis is not purely deductive and that it does not reduce arithmetic to logic, nor integers to the unit. “Rather, it embeds arithmetic open-endedly in systematic analogies motivated by the demands of reason” (p.75). The authors finally compare Leibnizian analysis with positions in 19th century philosophy. In order to support their interpretations they present two hitherto unpublished manuscripts, “Mathesis generalis est scientia magnitudinis” (pp.89-98), and “Numerus integer est totum ex unitatibus collectum” (pp.99-102).

Reviewer: Volker Peckhaus (Erlangen)

### MSC:

01A45 | History of mathematics in the 17th century |

00A30 | Philosophy of mathematics |

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |