Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected). We also prove the finitistic consistency of the extension of Heck’s theory to ${\Delta }_1^1$-comprehension and of Heck’s ramified predicative second-order system.