The aspects of Erhard Weigel's Analysis Aristotelica ex Euclide restituta that foreshadowed and helped form some characteristics of symbolic logic are highlighted: first, the idea of a pure form of a logical syllogism or of a mathematical proof and, second, a tentative arithmetisation of some aspects of logic. Also, Weigel's emphasis on the role of symbols and figures in the process of mathematical proof is discussed.

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)