The influence of William James on Ludwig Wittgenstein has been widely studied, as well as the criticism that the latter addresses to the former, but one aspect that has only rarely been focused on is the two philosophers’ use of the image of the flux, stream, or river. The analysis of some notes belonging to Wittgenstein’s Nachlass support the possibility of a comparison between James’ stream of thought, as outlined in the Principles of Psychology, and Wittgenstein’s river-bed of thoughts, presented (...) in On Certainty. After an introduction which offers a general frame for the following work, the first section of the paper examines all the Nachlass entries that directly mention James’ stream. Section 2 focuses on two remarks in which Wittgenstein explicitly criticizes James’ concept and implicitly anticipates his own way of dealing with this matter. These remarks, belonging to Manuscripts 165 and 129, both dating 1944, have not been published in any of Wittgenstein’s edited books, nor is it possible to find the same argument elsewhere. Wittgenstein’s critique concerns James’ lack of distinction between what is grammatical, or a priori, and what is empirical, or a posteriori, a distinction which the image of the stream should have suggested: a stream flows in a stream-bed and within banks. This is exactly the meaning that Wittgenstein’s own metaphor of the river-bed of thoughts is intended to convey. Section 3 analyses James’ concept of the stream and its corollaries, in order to clarify whether Wittgenstein’s critique is justified or not. James in effect draws a separation between a priori and a posteriori, but this separation is conceived from within the framework of empirical science. This analysis leads to the theme of the relations among science, philosophy and metaphysics, which is the subject of section 4. The conclusion is that Wittgenstein did appreciate James for his intuitions and for the power of his imagination: in a sense he even developed them; but he could not agree on the explicit formulation of his ideas. (shrink)