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Rh according to Hamilton (like Cusanus), philosophy ends in a docta ignorantia. Its value consists in its constant seeking, by means of which the energies of the mind are exercised.

Hamilton is nevertheless convinced that faith in the unconditioned is necessary in order to establish our spiritual existence. The more refined definitions of unconditioned being can only be secured by analogy with human personality.—This argument was applied to the defense of the orthodox faith by Hamilton's disciple, Henry Mansel (Limits of Religious Thought, 1858).

William Whewell (1795-1866), professor at Cambridge, demonstrated the principles of the critical philosophy from another point of view. He endeavored to verify Kant's fundamental principles as the necessary presuppositions of the inductive sciences (History of the Inductive Sciences, 1837; Philosophy of the Inductive Sciences, founded on their History, 1840). Induction signifies not only a collection of facts, but their arrangement according to some governing principle. The organization of the facts is possible only in case the investigator brings such a principle with him (as e.g. Kepler brought the idea of the ellipse to his studies of the planets). We must finally go back to the fundamental concepts which express the very principles of our cognitive faculty, principles which form the basis of all sense perception and all induction. Such fundamental concepts are: time, space, cause (in mechanics), end (in biology), and duty (in ethics). These cannot be analyzed into simpler concepts.

John Stuart Mill, the son of James Mill, was trained in the ideas of the radical enlightenment, as they had been developed by his father and Bentham, and he accepted