Gödel's Belief in a Leibnizian Conspiracy

Kurt Gödel's 1930s demonstration of the provability incompleteness of axiomatic arithmetic was a monumental achievement in mathematical logic and marked him as “one of the most significant logicians in history.” In the mid-1940s, Kurt Gödel embarked on a systematic study of Leibniz's logic which continued for at least another decade. During this time, I myself was writing my Princeton doctoral dissertation on Leibniz's Cosmology, and we had something of a tug-of-war over the Leibniz material in Firestone Library—each recalling for his own needs material out on loan to the other. (Unfortunately for me, we never made any direct contact.)

Gödel described himself as, unlike Einstein, “following Leibniz rather than Spinoza.” As Gödel studied Leibniz via Louis Couturat's classic La logique de leibniz, he became convinced that resistance to the logico-mathematical Platonic realism of his own position was prefigured in a conspiracy of suppression and silence that had kept Leibniz's similar insights from being properly understood and appreciated. And the more Gödel studied Leibniz, the more keenly he suspected that Leibniz might have anticipated parts of his own work—and especially his demonstration of arithmetic's provabilityincompleteness. Gödel came to this view because he saw Leibniz as a precursor and a kindred spirit whose problematic reception was a foreshadowing of his own difficulties.

But while there is little doubt that Gödel saw Leibniz as a precursor engaged in a kindred inquiry, there remained in his mind questions about the extent of anticipation about findings. Moreover, the matter of motivation remains somewhat obscure. Was he worried that he might have been fully anticipated? (After all, in mathematics all the credit goes to whoever gets there first.) Or was he hopeful of finding that he had succeeded where the great Leibniz had tried and failed? Perhaps we will never know. But either way, Leibniz's work on matters of provability and demonstrative systematization in mathematics was of deep concern to Gödel.

Curiously, Gödel saw Leibniz as a precursor not only in logic and the foundations and epistemology of mathematics but also in metaphysics, the general theory of reality.