# Renormalization: Why is only a finite number of counter-terms allowed?

I have a question please about renormalization in QFT. Why a renormalizable theory requires only a finite number of counter-terms?

-
As Josh answered a theory is called renormalizable if it requires only a finite number of counter terms for canceling infinities. Initially it was thought that non-renormalizable theories are in some sense bad in that they have no predictive power. However nowadays such theories too are seen with respect and are studied as "effective field theories". But still most physicists believe that a fundamental theory of nature should have the property of renormalizability. Here by fundamental I mean a theory written in terms of fundamental entities i.e those which can not be broken into smaller ones. –  user10001 Mar 13 '13 at 19:42
Classical Electrodynamics of a point charge only needs one counter-term to get rid of the mass correction, but the reminder $\dddot{r}$ is still unphysical - it leads to runaway solutions. In this sense CED is non renormalizable. It needs further "development" - replacing the unknown radiation reaction term $\dddot{r}$ with a known function of time $f(t)$. –  Vladimir Kalitvianski Mar 14 '13 at 13:51