This article compares and contrasts the reception of Comte’s positivism in the works of William Whewell, John Stuart Mill and (to a lesser extent) Franz Brentano. It is argued that Whewell’s rejection of positivism derives from his endorsement of (what I shall call) a constructivist account of the inductive sciences, while Mill and Brentano’s sympathies for positivism are connected to their endorsement of an empiricist account. The mandate of the article is to spell out the chief differences between these two rival accounts. In the last, conclusive section, Whewell’s anti-positivist argument is briefly assessed and rebutted.