Seventeenth-century natural philosophers and mathematicians in France and Germany critiqued and then applied a disciplined reason to nature and mathematics. Descartes, Pascal, and Leibniz did not merely impose a disembodied pure reason onto nature, but, drawing on extant resources for civilizing and educating, attempted to apply the full range of human epistemic, physical, and social faculties to know nature. This chapter argues that in trying to understand and perfect the faculties, these seventeenth-century figures developed sundry innovations useful in scientific and mathematical work. Within their dour Christian conceptions of the fallen qualities of humankind, they worked to produce and to distribute intellectual, material, and social techniques appropriate to their wrongly universalized understanding of human greatness and wretchedness, techniques that they brought to the study of the natural world and mathematics. Instead of thinking humans divine, capable of knowing and changing the world easily, Descartes, Pascal, and Leibniz sought knowledge by humiliating humanity, and by critiquing and bracketing human ability. They sought knowledge of the world in knowing themselves. Fulfilling Socrates' old injunction required no small mathematical and natural-philosophical labor.
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