G.W. Leibniz: From the “Symbolic Revolution” in Mathematics to the Concept of Suppositive Cognition

Abstract

The transition from the exclusive use of words to the predominant use of symbols in mathematics continued for centuries, but by the seventeenth century it turned out to be explosive. This phenomenon became known as the “symbolic revolution” in mathematics. One of its main outcomes was the discovery of mathematical analysis almost simultaneously and independently by Isaac Newton and Gottfried Wilhelm Leibniz. To both scientists their discovery served as the basis for far-reaching philosophical generalizations. For Leibniz, it led to the concept of suppositive cognition, the opposite of the prevailing notions at that time. He was the first to argue that the criterion of clarity and distinctness in cognition is impossible, because it relies on intuition about primary concepts, but these are in fact confuse and undistinct, and the foundation of such cognition is shaky. Using the successful use of symbols in mathematics as a model, Leibniz arrives at the concept of blind or symbolic cognition, cognitio caeca, which makes it possible to achieve validity and verifiability of results without reliance on intuition or primary concepts. The truthfulness of the result is found to depend more on grammar, which determines the substitution rules of some signs, or characters, for others, than on the connection between signs and the signified. Leibniz’s opening debate served as a prologue to the fundamental modernization of scientific discourse in the early Modern Time. Although he failed to achieve entirely his philosophical goals, the concept itself turned out to be extremely productive and modern, effectively decoupling the progress of natural science from its philosophical foundations. This innovative cognitive ideology opened up enormous prospects for the formation and accumulation of new knowledge, closed by the rigid requirements of the Cartesian paradigm of science still dominant in Leibniz’s time.