Modern philosophy opened with a man trying to doubt absolutely everything
In six short meditations, René Descartes set out to throw away every belief he could, from physical objects to mathematics. The one thing left standing was the fact that he was doubting. From that foothold he rebuilt knowledge, and in doing so turned his back on the scholastic tradition that had dominated European thought.
Modern philosophy is not a single doctrine but an era, roughly from the 17th century to the early 20th. Its edges are disputed: how much of the Renaissance belongs to it, and whether postmodernity has replaced it. Renaissance humanists had already challenged scholastic dogma, seeing nature as mathematically ordered rather than driven by purposes, and Machiavelli's The Prince opened a new path in political thought. Leonardo da Vinci jotted that knowledge begins in perception but certainty needs mathematics, two ideas that would split philosophers into camps.
Those camps became the rationalists and the empiricists, labels largely applied afterwards by Kant. Rationalists, mostly French and German, such as Spinoza and Leibniz, held that knowledge starts from innate ideas. Empiricists including Locke, Berkeley and Hume insisted it begins with sense experience. Descartes, working from certainty of his own thinking, concluded that some of his ideas could only come from God, and that God would not deceive him wholesale, which rescued ordinary science as fallible but trustworthy.
Late in the 18th century Kant proposed a system meant to unify both sides. It did not end the arguments but triggered German idealism, which culminated in Hegel's declaration that the real is rational and the rational real. His heirs scattered. Marx recast Hegel in materialist form; Kierkegaard rejected systems as useless guides to living; Schopenhauer drew a bleak, atheist picture of endless desire. Nietzsche took that pessimism and proclaimed the death of God, yet saw in it a new kind of freedom.
By the 20th century the field had fragmented. In Britain, Bertrand Russell and G. E. Moore reacted against British idealism and, drawing on Gottlob Frege's logic, launched analytic philosophy, now dominant in English-speaking universities. Edmund Husserl founded phenomenology, the study of experience's structure, which spread from Göttingen and Munich to France and America. Charles Sanders Peirce, followed by William James and John Dewey, built pragmatism around the traffic between theory and practice, while existentialists made the individual's experience the starting point.
Source: Modern philosophy