Let me put it this way. Matter is composed of quarks, which form into protons and neutrons, and of electrons. Compress matter enough, such as in a neutron star, and you get a superdense material known as neutronium. Compress it even more and the end result is what appears to be a singularity, a region of space where matter is compressed into infinite density. It is unknown whether singularities actually exist or if they are simply artifacts of an incomplete theory. "Pure matter" seems to me to be the infinitely compressed type, which cannot occupy a set volume of space, as it is compressed infinitely small.