Dedekind shares Frege’s aim of substituting logical standards of rigour for intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic. But sharing this aim does not mean having the same fundamental goal nor using or inventing the same tools. I will highlight the basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. Let us not be misguided by words: a contextual and comparative analysis shows indeed that Dedekind gives to the terms ‘logic’, ‘number’, ‘thought’, ‘pure thought’, ‘laws of thought, ‘concept’, ‘object’, ‘function’ a radically different meaning from that which Frege’s work made familiar to most of us. In the light of his semantic and practical background, Dedekind’s famous assertion that arithmetic is “a part of logic”, which has been taken as an expression of something close to Frege’s logicism, does not mean, in my reading, that arithmetic is reducible to logic, but on the contrary, that arithmetic, intrinsically, constitutes a purely rational (logical in a pre-Fregean sense) norm of thinking. The Dedekidian “logic of the mind” is arithmetic generalized to undetermined elements.