The book discusses some basic building blocks which, according to Lambert, are at the roots of Euclid’s strategy, lying upon the constructive contributions of “postulates” and “problems” without which the whole Euclidean machine would not have started. Genetic procedures and construction are heuristics which, well beyond the principle of non-contradiction, aim to offer a more positive notion of possibility, excluding such chimeras as a “dreamed” triangle with “equal sides and unequal angles”.
Lambert draws from Euclid’s tool-box a fundamental geometrical notion, that of “figuerlich”, a sort of diagrammatic, graphical, knowledge, distinct from mere words, made of signs and lines, exclusively at the level of syntactic relations and not of semantic references. His goal are “figures transformed into signs” thanks to the metaphorical shift of logical relations into spatial connections: in this way, drawing inferences geometrically is a non-discursive cognitive resource. Lambert’s research programme implied joining together a visual logic and a pure algorithmic method. It was indeed a very demanding endeavour.