Émile Boutroux was born on 21 July 1845 in Montrouge near Paris. He received his secondary education at lycée Napoléon (now lycée Henri IV), where in 1865 he graduated to the École Normale Supérieure. While engaged in tertiary education, Boutroux was influenced by the philosophy of Maine de Biran, whose work in the early nineteenth century laid the metaphysical foundations for modern French psychology. Here also Boutroux encountered Biran's follower J. Lachelier, whose writings in logic and the philosophy of science proved particularly important to Boutroux's own work in the same. From 1869 to 1870, Boutroux continued his studies at Heidelberg University where he was introduced to German philosophy by his teacher Hermann von Helmholtz.
While completing the two dissertations required by his doctorate at Heidelberg (De veritatibus aeternis apud Carthesium and De la contingence des lois de nature), Boutroux took the post of philosophy instructor at the lycée (secondary school) in Caen. Also in 1874, De la Contingence was published, and Boutroux took up a lectureship at the University of Montpelier. Directly after he secured tenure at Montpelier, Boutroux was offered and accepted a two-year appointment as Lecturer in Philosophy in the Faculty of Letters at the University of Nancy. While at Nancy, he married Aline Poincaré, the sister of scientist and mathematician Henri Poincaré. In 1880 Aline gave birth to their son, Pierre Boutroux, who himself became a distinguished mathematician and historian of science. From 1877 to 1885 Boutroux lectured in philosophy at École Normale Supérieure, and in 1888 he was made professor of history of modern philosophy at the Sorbonne in Paris.
Among his other honours, Boutroux was elected a member of the Academy of the Moral and Political Sciences in 1898 and in 1902 he became Director of the Thiers Foundation. In 1912 he was elected to the Académie française, where he was a member from 1914. Boutroux died in Paris on 22 November 1921.
As is reflected in his Gifford Lectures, Boutroux's work can be situated in a branch of philosophy known as French spiritualism, a school that reacted against the nineteenth century left-Hegelian philosophies of Materialism. Spiritualism aspired to preserve metaphysics and religion while simultaneously affirming the ongoing work of the natural sciences. In Boutroux this is reflected most prominently in his De la Contingence, which suggests that physical determinism is only valid on the macro-physical scale whereas on the micro-physical scale there exists an indeterminacy that is too small to be detected by instrumentation. As such, science cannot always discover the necessary connections that exist in nature. His argument against absolute necessity implied that science could exist alongside religion and ethics. Whereas science uncovered information about certain lower domains of life, religion appealed to the highest manifestations of nature, namely the human spirit. Spirit, for Boutroux, transcends the possibilities of science, thus making metaphysics and the religious dimension indispensable facets of existence.
His published works include: Pascal (1900); Science and Religion in Contemporary Philosophy, trans. Jonathan Nield (1909); Historical Studies in Philosophy, trans. Fred Rothwell (1912); William James, trans. Archibald and Barbara Henderson (1912); La philosophie de Kant (1926); Morale et Religion (1925); De la Contingence des Lois de la Nature (1929). For further information about Boutroux's life and work, see Alexandre F. Baillot, Emile Boutroux et la Pensée Religieuse (1957); Lucy Shepard Crawford, The Philosophy of Emile Boutroux, as Representative of French Idealism in the Nineteenth Century (1924).