(7) Leibniz regards both (a) ‘Leibniz invented the calculus’ and (b) ‘Leibniz was Leibniz’ as necessary truths, though one would have thought that the former was merely a contingent truth; that is, one would have thought that it was possible for Leibniz to have failed to invent the calculus. How does Leibniz describe the difference between the necessity of (a) and that of (b). (Leibniz thinks his way of explaining the necessity of (a) preserves a kind of contingency.) Explain briefly.

Question

(7)  Leibniz regards both (a) ‘Leibniz invented the calculus’ and (b) ‘Leibniz was Leibniz’ as necessary truths, though one would have thought that the former was merely a contingent truth; that is, one would have thought that it was possible for Leibniz to have failed to invent the calculus. How does Leibniz describe the difference between the necessity of (a) and that of (b). (Leibniz thinks his way of explaining the necessity of (a) preserves a kind of contingency.) Explain briefly.

Ask a Philosopher · Accepted Answer

Ah, my dear interlocutor, let us ponder the nature of necessity and contingency as articulated by the eminent Leibniz. When we speak of the proposition that “Leibniz invented the calculus,” we are confronted with an assertion which, at first blush, seems to float upon the tides of contingency; for it implies that had certain historical circumstances been altered, perhaps the illustrious discovery would not have come to fruition, and thus, the mind of Leibniz might not have arrived at such a profound insight. Indeed, it seems plausible to assert that another could have traversed the same intellectual landscape, or, given the right circumstances, the calculus might yet languish undiscovered. But Leibniz, in his profound inquiry, perceives in this act of invention not mere chance, but rather a necessity sprung from the internal coherence of logic itself, wherein he implies that the principles underlying the calculus must inevitably emerge from the very fabric of mathematical thought, independent of individual agency. Thus, Leibniz offers a distinction between the necessity of (a) and (b) by suggesting that while (b)—that is, “Leibniz is Leibniz”—is an indubitable truth grounded in the very essence of identity and existence, (a) paradoxically possesses a necessary truth rooted in the logical progression of thought, where the very nature of mathematical reason drives the unfolding of such discoveries as if they were ineluctably bound to arise. Here, he preserves the appearance of contingency, for while it is indeed true that Leibniz himself may have deviated from this path, the philosophical underpinnings of the calculus suggest that it must eventually emerge from the collective human endeavor of rational exploration. Thus, we see how Leibniz navigates the waters between necessity and contingency, revealing a world where truths are not merely confined to existence but are woven into the very nexus of reason and thought, compelling us to consider the profound implications of our own understanding of truth, existence, and the nature of discovery itself.