Full Idea
The metaphysical inquiry into the nature and composition of what have been called Abstract Ideas, or in other words, of the notions which answer in the mind to classes and to general names, belongs not to Logic, but to a different science.
Gist of Idea
The study of the nature of Abstract Ideas does not belong to logic, but to a different science
Source
John Stuart Mill (System of Logic [1843], 4.2.1)
Book Reference
Mill,John Stuart: 'System of Logic (9th ed, 2 vols)' [Longmans, Green etc 1875], p.195
A Reaction
He doesn't name the science, but the point here seems to be precisely what Frege so vigorously disagreed with. I would say that the state of being 'abstract' has logical aspects, and can be partly described by logic, but that Mill is basically right.