Abstract

L.E.J. Brouwer made a mistake in the formulation of his famous bar theorem, as was pointed out by S.C. Kleene. By repeating this mistake several times, Brouwer has caused confusion. We consider the assumption underlying his bar theorem, calling it Brouwer’s Thesis. This assumption is not refuted by Kleene’s example and we use it to obtain a conclusion different from Brouwer’s. Thus we come to support a view first expressed and defended by E. Martino and P. Giaretta in [Martino 1981]. We also indicate that Brouwer’s Thesis has many more applications than Brouwer dreamt of.