Suppose classical "pure matter" as you describe it existed and suppose a spherical volume $V$ of $1\,\text{m}^3$ of this stuff has mass $M$. Since it exists of pure matter only, one expects a uniform mass density $\rho$.
Now you can zoom in on that volume forever and never would you reach a point where you see 'bubbles' or any space between things. Just the same old impenetrable stuff, forever. So $M$ can't go to zero as you take $V$ down to zero, which would mean an infinite mass density. Therefore $1\,\text{m}^3$ of it would have infinite mass.