Naar het voorbeeld van de geometers
Dit citaat uit een essay dat ik acht jaar geleden afsloot. Het overweegt de invloed van Euclides op de filosofie van de Verlichting. Misschien heeft iemand er wat aan.
In seventeenth century Europe the Elements of Euclid of Alexandria, an African scientist living around 300 BCE, was portrayed as the work of a Greek genius, who only needed the definition of a point, a line and a circle to prove a vast geometrical universe of propositions, thus building up a fabulous construction of huge insight, created only by meticulous thinking, the power of the mind.
But even the most abstract mathematics can only be the application of trained procedures derived from experience, or of a search by trial-and-error for new procedures. The Elements of Euclid is a clever compilation of accidental and casual knowledge of engineers, architects and arms builders in Asia, Africa and Greece. The knowledge had been accumulated, directly or roundabout, during centuries of massive trials, experience and exchange of practice, accelerated first when Cyrus, and again when Alexander shattered the borders that separated civilizations and caused the emergence of a new meta-culture. Euclid himself named many of his sources and did never conceal that his famous work was a compilation. Fooled by this misrepresentation of Euclidean geometry as the pinnacle of the pure deductive mind, René Descartes interpreted the methodology of the Elements, derived from the handling of complex engineering projects, as a new and powerful method that would lead scientific speculation to its summit:
Those long chains of reasoning, very simple and easy, of which the geometricians use to arrive at the most difficult demonstrations, allowed me to imagine that all things knowable to men are linked in the same manner, and that, as long as nothing is taken for truth which is not and if the correct order of deductions is followed, nothing can be too difficult to be discovered.
A few years after Descartes, Benedict de Spinoza wrote his Ethics 'in detailed geometrical fashion', demonstrating the relation between God, man and universe by nothing but genuine brain work in the style of the Elements. The ten year younger Blaise Pascal – or his relatives – demonstrated to be fooled by the same neatly arranged deductions when claiming that he had discovered the first thirty-two propositions of the Elements at age twelve all by himself, without any preceding knowledge of mathematics. A century later Immanuel Kant geared up to cause a complete revolution in metaphysics ‘after the example of the geometricians’.