Poeta Calculans: Harsdorffer, Leibniz, and the mathesis universalis
- Poeta Calculans: Harsdörffer, Leibniz, and the mathesis universalis
This paper seeks to indicate some connections between a major philosophical project of the seventeenth century, the conception of a mathesis universalis, and the practice of baroque poetry. I shall argue that these connections consist in a peculiar view of language and systems of notation which was particularly common in European baroque culture and which provided the necessary conceptual background for both poetry and the mathesis universalis. 1
Because such a work, especially when attempted within the scope of a paper, needs a clearly determined focal point, I shall concentrate on the works of two baroque savants, Gottfried Wilhelm Leibniz and Georg Philipp Harsdörffer. The reason for the choice of Leibniz is obvious: there is no single philosopher whose entire intellectual career, from his earliest youth to his death-bed, was so deeply connected with the idea of a mathesis universalis. Harsdörffer has the advantage of being not only a poet but also a language-theorist and scientist, and this informs the conceptual background of his poetry. In order to explain that background I shall also rely to some extent on the works of Justus Georg Schottel, a fellow language theorist and personal acquaintance of Harsdörffer’s.
Three of Harsdörffer’s works will be at the center of our attention, the Frauenzimmer Gesprächsspiele, 2 an eight-volume series of dialogues about social, poetic, and scientific matters, which incorporates much of Harsdörffer’s [End Page 449] own poetry and even entire plays; the Delitiae Mathematicae et Physicae, 3 a three-volume scientific work, of which Harsdörffer edited the last two volumes and which deal with a number of sciences in question-and-answer form; and the Poetischer Trichter, Harsdörffer’s magnum opus on the theory of poetry. 4
The Idea of the mathesis universalis
The Leibnizian project of the mathesis universalis took off from the idea of finding a method of deciding all questions, whether they belonged to physics, 5 to metaphysics, 6 or to any other science, 7 with mathematical certainty. This should be brought about by inventing a universal system of notation, which would allow the detection of errors of thinking as purely grammatical or syntactical errors. 8 This system should consist of two parts, the lingua characteristica and the calculus ratiocinator. 9
The lingua characteristica 10 was supposed to act as a system of notation for “the alphabet of human thoughts,” 11 i.e., for the primitive concepts. 12 For Leibniz all conceptual complexity arises as the result of a combination of simple concepts. 13 By combining the primitive concepts one can produce more complex ones and thus gain new knowledge. Similarly, every concept can be resolved into [End Page 450] the most simple concepts that constitute it in a unique way. 14 The lingua characteristica was supposed to make this conceptual constitution obvious, so that there could not possibly be any doubt left about what a given concept entailed. Furthermore, it should be a means of visualizing proofs, to enable people to check the correctness of a derivation at a glance. 15
The aim of the calculus ratiocinator 16 was to provide a means of systematic work with the notational system of the lingua universalis, i.e., the recombination of the primitive signs according to specific rules. 17 The latter was intended as a means of obtaining a clear expression of concepts, the former as an auxiliary for their transformation, i.e., the process of reasoning and thinking. The idea of the calculus ratiocinator thus comes quite close to the modern idea of formal logic.
Leibniz tried to design this calculus similar to those of arithmetic so that it would literally be possible to “calculate” the correctness of an inference in a purely mechanical way without needing any ingenuity. 18 His most famous design was based on the idea of assigning prime numbers to the simple concepts and to represent complex concepts as products of these. Because every number can be uniquely reduced to its prime factors, the “characteristic number” of each concept could be uniquely resolved into the primitive concepts which compose it. 19 Leibniz also...
