the first discovery of infinite ideals and of infinite tasks was accomplished simultaneously

The historical process of development is definitively marked out through this focus on the environing world. Even the hastiest glance at the corporeality present in the environing world shows that nature is a homogeneous, unified totality, a world for itself, so to speak, surrounded by a homogeneous spatiotemporality and divided into individual things, all similar in being res extensae and each determining the other causally. Very quickly comes a first and greatest step in the process of discovery: overcoming the finitude of nature that has been thought of as objective-in-itself, finitude in spite of the open infinity of it. Infinity is discovered, and first of all in form of idealized quantities, masses, numbers, figures, straight lines, poles, surfaces, etc. Nature, space and time become capable of stretching ideally into infinity and also of being infinitely divided ideally. From the art of surveying develops geometry; from counting, arithmetic; from everyday mechanics, mathematical mechanics; etc. Now, without anyone forming a hypothesis in this regard, the world of perceived nature is changed into a mathematical world, the world of mathematical natural sciences. As ancient times moved forward, with the mathematics proper to that stage, the first discovery of infinite ideals and of infinite tasks was accomplished simultaneously. That discovery becomes for all subsequent times the guiding star of the sciences.

EDMUND HUSSERL: Philosophy and the Crisis of European Man


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