Hegel's dominance of German philosophy in the 1820s through the 1840s ended the first wave of Kantianism, but the version of Kantianism propounded by Arthur Schopenhauer (1788–1860) in the Fourfold Root of the Principle of Sufficient Reason (1813) and The World as Will and Representation (1818) became influential after 1848 and prepared the way for a tremendous resurgence in the influence of Kant in German philosophy beginning in the 1860s. The "neo-Kantian" movement begun at that time dominated German philosophy until the 1920s. This movement took many forms. The scientist Hermann Helmholtz (1821–1894) gave a psychological interpretation of Kant's conception that the mind brings its own innate structure to perception, which influenced research into perception well into the twentieth century. But within academic philosophy, the two main forms of neo-Kantianism were the Marburg and Heidelberg schools.
The main representatives of the Marburg school were Hermann Cohen (1842–1918), Paul Natorp (1854–1924), and Ernst Cassirer (1874–1945). Cohen made his reputation with a series of commentaries on Kant's three critiques, published between 1871 and 1889, and then with his own system of philosophy, published between 1902 and 1912. He also published The Religion of Reason out of the Sources of Judaism (1919), an influential work on Judaism modeled on Kant's Religion. Cassirer's main work was the three-volume Philosophy of Symbolic Forms (1923–1929; trans. 1953–1957 with a fourth volume posthumously published in 1996). The Marburg school developed Kant's idea that we bring to both ordinary experience and more formalized science presuppositions reflecting the structure of our own thought; but especially by the time of Cassirer the school also recognized that we bring a multiplicity of such principles to our experience and that they may change over time. Cassirer's views were to some extent paralleled by those developed by the British philosopher Robin George Collingwood (1889–1943) in his Essay on Philosophical Method (1933) and Essay on Metaphysics (1940), although Collingwood did not call himself a neo-Kantian.
The chief representatives of Heidelberg neo-Kantianism were Wilhelm Windelband (1848–1915) and Heinrich Rickert (1863–1936). They stressed Kant's distinction between the principles of theoretical and practical reason and focused attention on our projections of values as well as knowledge into our experiences. Rickert developed the philosophical views of the school in The Limits of Concept Formation in Natural Science (1896–1902; trans. 1986) and Science and History (1899; trans. 1962). Both Windelband and Rickert also stressed the difference between the methods of natural science and history and thereby greatly influenced the methodological thought of the sociologist Max Weber (1864–1920), especially his theory of "ideal types" and his distinction between fact and value in the practice of social science.
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