following, and xvii. 4.) In the Fourth Book it is body alone that has real existence, an existence revealed by actually present sensation, while all mathematical ideas, the ideas of the circle and the square, have ‘barely an ideal existence’ (Book IV. chap. iv. sec. 6); and this means nothing else than the reduction of the primary qualities of body to a nominal essence. Our ideas of them are general (Book IV. chap. iii. sec. 24), or merely in the mind. ‘There is no individual parcel of matter, to which any of these qualities are so annexed as to be essential to it or inseparable from it.’ (Book III. chap. vi. sec. 6.) How should there be, when the ‘individual parcel’ means that which copies itself by impact in the present sensation, while the qualities in question are relations which cannot be so copied? Yet, except as attaching to such a parcel, they have no ‘real existence;’ and, conversely, the ‘body,’ from which they _are_ inseparable, not being an individual parcel of matter in the above sense, must itself be unreal and belong merely to the mind. The ‘body’ which is real has for us no qualities, and that reference to it of the ‘actually present sensation’ by which such sensation is distinguished from other feeling, is a reference to something of which nothing can be said. It is a reference which cannot be stated in any proposition _really_ true; and the difference which it constitutes between ‘bare vision’ and the feeling to which reality corresponds, must be either itself unreal or unintelligible. Summary view of Locke’s difficulties in regard to the real.