He studied philosophy at the University of Königsberg, where he was influenced by Johann Friedrich Herbart, and continued his studies at the University of Leipzig. In 1845, he became professor of philosophy at the University of Dorpat, and after 1872 he held a similar position at the University of Leipzig.
He became known as a prominent representative of Herbart's philosophy and published Erläuterungen zu Herbarts Philosophie (Explanations of Herbarts philosophy, 1834), Die Hauptpunkte der Herbartschen Metaphysik kritisch beleuchtet (The main points of Herbart's metaphysics critically illustrated, 1840), Gedanken über Religion und religiöse Probleme (Thoughts on religion and religious problems, 1888), Abhandlungen zur Geschichte der Metaphysik, Psychologie und Religionsphilosophie (Treatise on the history of metaphysics, psychology and the philosophy of religion, 1896), and Vermischte Ahhandlungen aus der theoretischen und praktischen Philosophie (Miscellaneous treatise on topics from theoretical and practical philosophy, 1897).
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- Wilhelm Kahl. (1908), "Strümpell, Ludwig", Allgemeine Deutsche Biographie (ADB) (in German) 54, Leipzig: Duncker & Humblot, pp. 623–630
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