You should also read, "How Can We Be Moved by the Fate of Anna Karenina?" by Colin Radford, and the literature that developed in response to it.
A mathematician might find his feelings engaged by certain questions. Sir Andrew Wiles was passionate about Fermat's Last Theorem from the age of about ten, I believe. (Say, by contrast, that he took little interest in statistics. Perhaps statistics even disgusts him.) Does any of this "corrupt the purity of the logic" of his (rather long) answer to the question how to prove Fermat's Theorem? No, it just powered his interest in mathematics. Besides, why isn't it possible to be inspired and motivated by a thought or an ideal? The ten-year old Wiles had the thought, 'I will prove the Theorem', and this motivated him and engaged his feelings - and the grown-up Wiles did prove the Theorem. The purity of his logic was perhaps even assisted by his passion.