Kant, Kästner and the Distinction between Metaphysical and Geometric Space

Here is a recent paper co-authored by a top-notch Kantian scholar (and much more besides), a man with two PhDs (earned, not honorary); one in applied mathematics and the other in philosophy (and no, not philosophy of mathematics or science), a man who has transcended the often trivial aspects of academic analytical philosophy and the woolly “meaning of life” Continental approach. And I’m proud to say my occasional but vital collaborator.


It would be no exaggeration to claim that, by the end of the penultimate decade of the eighteenth century, Kant’s Critical philosophy, and his Critique of Pure Reason (henceforth CPR) in particular, had brought about a revolution in German intellectual life. Inevitably, such a change was bound to be resisted, and the resistance from the dominant Wolffian school of metaphysics in the Leibnizian tradition was chiefly led by Johann August Eberhard (1739–1809). Eberhard took it upon himself, after the publication of the second edition of Kant’s CPR in 1787, to organize a response to the spread of the new Critical philosophy. In 1788, he launched a new philosophical journal, the Philosophisches Magazin (PM), to which several Wolffians contributed. This journal was primarily designed to publish papers criticizing Kant’s Critical philosophy from a Wolffian angle, and specifically aimed at opposing the views published in the Allgemeine Literatur-Zeitung (ALZ). The latter was a journal started in 1785 by C. G. Schütz, which was committed to the propagation and defence of the new Critical philosophy. Among its contributors were some of Kant’s most prominent followers, especially Johann Friedrich Schultz (1739–1805) and Karl Leonhard Reinhold (1757–1823), who were keen to spare him the need to get involved in polemics, and thus allow him to concentrate fully upon the completion of the Critical system. They therefore took up the gauntlet, and assumed the responsibility of coordinating a Kantian response to the criticisms that were aimed at his philosophical system from various directions.

Over a short period of time, a number of papers were published in ALZ that, even if not written by Kant himself, expressed Kantian rejoinders to the criticisms published by the faction around Eberhard. Only once did Kant himself put pen to paper to respond to articles by Eberhard that were published in the first volume of PM (1788–9). Kant deemed that the author was not only fundamentally mistaken about the meaning of his writings, but also had been particularly dishonest in dealing with them. Kant’s response was published as a separate work titled On a Discovery According to which Any New Critique of Pure Reason Has Been Made Superfluous by an Earlier One (1790) (AA 8: 185–251). The main aim of this work was to counter Eberhard’s attacks on two fronts, namely on the issue of the limits of knowledge, with particular emphasis on the problem of synthetic a priori judgements, and on the very distinction these limits rest upon, namely that between analytic and synthetic judgements.

For Kant’s responses to other attacks from the Eberhard camp, we have to rely upon ALZ and Kant’s correspondence with Schultz and Reinhold in particular, which indicates to what extent Kant’s voice is speaking through them. One case in which the notes that Kant included as attachment in his reply to Schultz (2 August 1790; AA 11: 184) are, at Kant’s suggestion, reproduced practically verbatim by Schultz in the ALZ less than two months later, is in his discussion of three essays by the mathematician Abraham Gotthelf Kästner (1719–1800), professor of mathematics and physics in Göttingen, director of the old Göttingen observatory, and also a noted epigrammist (see Kästner 1797). These were published in the second volume of PM (1790) and bear the titles: ‘What is the Meaning of “Possible” in Euclid’s Geometry?’ (Kästner 1790a), ‘On the Mathematical Concept of Space’ (Kästner 1790b) and ‘On Geometric Axioms’ (Kästner 1790c).