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At the time of that letter from which I quoted, Lambert was a distinguished mathematician with a professorship in Berlin. Kant was in his pre-critical period. He had published some significant essays and was allowed to lecture at the University of Königsberg. Kant would become professor of logic and metaphysics in 1770. That was the year of his “Inaugural Dissertation,” which is traditionally taken to mark the beginning of his critical period. Lambert wrote Kant a letter on that dissertation, and problems raised in that letter are part of the reason Kant entered “the silent years,” molding his new philosophy past such problems. The silence broke with the Critique of Pure Reason in 1781. Lambert had died in 1777.
Lambert had initially written to Kant on November 13, 1765. Lambert had recently published a philosophy book (New Organon, or Thoughts on the Discovery and Designation of Truth and Its Differentiation from Error and Appearance), and he had another one in press (Outline of Architectonic, or Theory of the Simple and Primary Elements of Philosophical and Mathematical Knowledge). He had recently read Kant’s essay “Only Possible Argument in Support of a Demonstration of the Existence of God,” and he found it to be similar to some of his own ways of thinking. He had heard Kant was about to publish a book titled Proper Methods for Metaphysics, and he wondered how much Kant’s right methods would correspond to his own, as set out in his two recent books.
Kant replied to that initial letter on December 31, 1765. “I hold you to be the greatest genius in Germany. . . .” Kant tells Lambert that his envisioned book will be delayed. “What I am working on is mainly a book on the proper method of metaphysics (and thereby also the proper method for the whole of philosophy). . . . My problem is this: I noticed in my work that, though I had plenty of examples of erroneous judgments to illustrate my theses concerning mistaken procedures, I did not have examples to show in concreto what the proper procedure should be.” Kant reported that he had decided to create two other books first, one on the metaphysical foundations of natural philosophy, the other on metaphysical foundations of practical philosophy. Kant did in fact produce that first one (1786), but after the really big book (1781).
Now, at last, to come to Lambert’s letter of February 3, 1766. Lambert says that metaphysics is in need of “methodical reconstruction and cleansing.” Dealing with universals in that science leads us “to venture beyond the limits of possible human knowledge.” In “Only Possible” Kant had outlined the kind of argument to the existence of God he thought successful. He had then exposed the unsoundness of three of the four possible kinds of argument that had been put forth as establishing the existence of God. In the course of these assessments, Kant says a great deal about metaphysics and epistemology. In his letter, Lambert shares his own ideas related to some Kant had dealt with in the essay.
I see that the quotation I pulled from Lambert’s letter pertains to remarks of Kant’s in Section I of his essay, in the first subsection which is titled: “Of Existence in General.” Kant remarked that he will proceed as one looking for a definition of existence, but wants to determine first what can be said about the object of the definition, namely the object: existence. He says he doubts anyone has correctly defined what space is, yet “there is still a great deal which can be asserted with the highest degree of certainty about the object in question.” From such up-front certainties about subjects in metaphysics, too, we may be able “to infer with complete certainty that which is relevant to the purpose of the investigation. . . . The mania for method and the imitation of the mathematician who advances with a sure step along a well-surfaced road, have occasioned a large number of . . . mishaps on the slippery ground of metaphysics.”
The quotation from Lambert is in that portion of his letter responding to those remarks in Kant’s essay that I have just quoted. Lambert partly agrees. He agrees that Euclid did not have to define space or geometry. He adds that in mechanics we make little use of the definition of motion. But then he goes on to suggest how philosophy might well profit from method in mathematics. In geometry we begin with simple elements such as lines and angles. In mechanics we begin with simple elements that accompany motion, such as velocity and force. From a comparison of those elements, Lambert says, we are enabled to discover principles. Then follows the quote of Lambert’s that I posted.
Although Lambert intends what he writes in the quotation to apply to metaphysics—he sees metaphysics as more salvageable that Kant did at that time—I think that what Lambert has in mind as authority for his claims is the history of natural philosophy, that is, the history of mechanics. Galileo, Huygens, and Newton had to first clean up received concepts in natural philosophy, making them simpler and considering them in measureable characteristics. In this way, by comparisons, we have a chance to establish laws of free fall, collision, and so forth.
I quoted the passage from Lambert for its glint of Rand’s general measurement vision of the world of all concretes, which I share in my with-measurement extensions from Rand’s epistemology.* I should perhaps mention that my program would not be expected to yield anything along lines parallel relations such as that between length and frequency of a pendulum. But objects of one’s concepts can become clearer and more profoundly integrated with others if they are cashed in the right measurement terms. Learning how shape can be captured by the set of principal curvatures at the points over the surface of a body enhances one’s concept and definition of shape.
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Translations of the letters of Lambert and Kant are by Arnulf Zweig.*
The translation of “Only Possible” is by David Walford.*
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“I have been led to the conclusion that as long as a philosopher does not carry out his analysis of measurable objects to the point where the mathematician can find unities, measures, and dimensions he must surely still be hanging on to some confusion, or at least the predicates of his propositions do not apply uniformly to the subjects.” —J.H. Lambert to Kant (Feb. 3, 1766)
