Striving for Truth, the Importance of Seeing for Understanding and the Ideal of a »universal character«
Mathematical understanding begins with seeing. The modern view that understanding and the advancement of learning require (visual) signs or forms of expression can be traced to Leibniz. Leibniz’s insight is that language is a human creation that does not merely record our thought but is instead an embodiment of understanding, an insight that can be found also in the German mathematician-philosopher G. Frege, inventor of a two-dimensional form of writing for »the expression of pure thought« (1879). On Leibniz’s mature views there is no abstract human thought that does not require something sensible. He describes his notion of character in visual terms: just as in mathematical symbolic writing, his symbols or characters are to provide us with the »tangible« thread necessary to develop and fix our thoughts. Taking advantage of recently published material, as well as more recent scholarship, Professor Goethe takes a fresh look at some of Leibniz’s most striking insights concerning »tangible« signs, the ideal of a »universal character«, and his view of the essence of science and the growth of knowledge. It is her aim to understand how and why seeing, and in particular, the seeing that is enabled by a Leibnizian universal character, is essential to understanding.