Mathematical type of teaching

The method of mathematical teaching , characterized by strict rationality, aimed at giving an account of the formal structure of each sentence when composing an orally presented or written text, comparable to mathematics, in which each individual calculation step must be logically based on the preceding one. In the early German Enlightenment, this method was considered the only accepted way to obtain reliable scientific knowledge and was an important methodological tool, the focus of which was on the philosopher Christian Wolff . With this critical method, the Wolffians wanted to expose the logical weakness of the “dogmatic type of teaching”, in which “the teaching is written in short sayings; but as it were randomly put through each other. ”It was hoped that the application of this method, which was also described as“ demonstrative ”, would lead to the dawn of a new age. In his preface to the 19th and 20th volumes of the Zedler Lexicon, Carl Günther Ludovici called the present century a "Seculum demonstrativum" and emphasized that Wolff's method was now used by numerous authors. This method, which is characterized by the thoroughness of the scientific work and which serves the purpose of driving away superstition, has many enemies. Ludovici hit the heart of the conflict by demanding that theology should submit to philosophy.

At the beginning of his beginnings in all mathematical sciences, Christian Wolff gave a "Kurtzen course of the mathematical teaching method". The influential Leipzig Wolffian Johann Christoph Gottsched adopted this method in the first volume of his work First Reasons for the Whole World of Wisdom , which is considered a compendium of Wolff's philosophy. Here he presented the mathematical teaching method in detail:

“Of the differences in the sentences with regard to the mathematical teaching method.

68th §. In mathematics one has for a long time distinguished the propositions most precisely: and thereby one has reached a greater degree of thoroughness than in other sciences: that is why we want to explain this difference here recently. Now the sentences either stop in the mere consideration, or they go into action: those are called contemplative sentences, but these are called exercise sentences. ZE God is infinite; this is a reflection sentence: One must worship God, this is a practice sentence. Again, the propositions of consideration are either those which deal with all things of one kind; z. E. All circles are round: or they only talk about a single thing; z. E. The moon is waning every now and then. They are called dogmatic; but this historically. The latter are often used in the midst of the others to be interspersed as comments. "

Gottsched carried out the mathematical method with additional sentence categories and examples and, with this representation, compared the statements made by his role model Christian Wolff and some of his followers.

literature

Johann Christoph Gottsched: First reasons of the entire world wisdom , Vol. 1, Leipzig 1756.
Large complete Universal Lexicon of All Sciences and Arts , Vol. 19/20, Leipzig 1738 [Zedler].
Christian Wolff : Beginnings of all mathematical sciences , Leipzig and Halle, [first edition 1710] 1728.

Individual evidence

↑ Zedler-Lexikon, Vol. 20., Col. 1296.
↑ Ludovici 1739, preface p. 1f.
↑ Detlef Döring : Gottfried Wilhelm Leibniz's Philosophy and the Leipzig Enlightenment in the first half of the 18th century (= Saxon Academy of Sciences in Leipzig Philological-Historical Class, vol. 75, no. 4), Leipzig 1999, p. 95 .
^ Christian Wolff, Beginnings of all Mathematical Sciences, Leipzig and Halle, [first edition 1710] 1728, pp. 5–23.
↑ The first edition appeared in Leipzig in 1733. Johann Gottfried Gottsched: First reasons of the entire world wisdom, vol. 1, Leipzig 1756, p. 126.
↑ cf. z. B. the mathematical teaching of the Wolffian Lorenz Christoph Mizler in: Lutz Felbick : Lorenz Christoph Mizler de Kolof - student of Bach and Pythagorean "apostle of Wolffian philosophy". Georg-Olms-Verlag, Hildesheim 2012, ISBN 978-3-487-14675-1 (University of Music and Theater "Felix Mendelssohn Bartholdy" Leipzig - Writings; 5), pp. 486–489.

[1] Zedler-Lexikon, Vol. 20., Col. 1296.

[2] Ludovici 1739, preface p. 1f.

[3] Detlef Döring : Gottfried Wilhelm Leibniz's Philosophy and the Leipzig Enlightenment in the first half of the 18th century (= Saxon Academy of Sciences in Leipzig Philological-Historical Class, vol. 75, no. 4), Leipzig 1999, p. 95 .

[4] Christian Wolff, Beginnings of all Mathematical Sciences, Leipzig and Halle, [first edition 1710] 1728, pp. 5–23.

[5] The first edition appeared in Leipzig in 1733. Johann Gottfried Gottsched: First reasons of the entire world wisdom, vol. 1, Leipzig 1756, p. 126.

[6] . z. B. the mathematical teaching of the Wolffian Lorenz Christoph Mizler in: Lutz Felbick : Lorenz Christoph Mizler de Kolof - student of Bach and Pythagorean "apostle of Wolffian philosophy". Georg-Olms-Verlag, Hildesheim 2012, ISBN 978-3-487-14675-1 (University of Music and Theater "Felix Mendelssohn Bartholdy" Leipzig - Writings; 5), pp. 486–489.