Full Idea
Sensations and mental pictures, formed from the amalgamated traces of earlier sense-impressions, are absolutely no concern of arithmetic; they are characteristically fluctuating and indefinite, in contrast to the concepts and objects of mathematics.
Gist of Idea
Mental states are irrelevant to mathematics, because they are vague and fluctuating
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro)
Book Reference
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.-7
A Reaction
Sounds very like Plato's distinction between the worlds of opinion and knowledge (Ideas 1170 and 2133). This view is fine amidst the implicit dualism of all nineteenth century thought, but how does abstract mathematics link to the soggy brain?
Related Ideas
Idea 2133 Knowledge must be of the permanent unchanging nature of things [Plato]