Such is our doctrine of punishment; and the inculcation of this doctrine turns many from their sins. But let us see, on the other hand, what is the response given on this subject by the priest of Jupiter or Apollo of whom Celsus speaks. It is this: “The mills of the gods grind slowly.” Another describes punishment as reaching “to children's children, and to those who came after them.” How much better are those words of Scripture: “The fathers shall not be put to death for the children, nor the children for the fathers.
Every man shall be put to death for his own sin.” And again, “Every man that eats the sour grape, his teeth shall be set on edge.” And, “The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.” If any shall say that the response, “To children's children, and to those who come after them,” corresponds with that passage, “Who visits the iniquity of the fathers upon the children unto the third and fourth generation of them that hate Me,” let him learn from Ezekiel that this language is not to be taken literally; for he reproves those who say, “Our fathers have eaten sour grapes, and the children's teeth are set on edge,” and then he adds, “As I live, says the Lord, every one shall die for his own sin.”
As to the proper meaning of the figurative language about sins being visited unto the third and fourth generation, we cannot at present stay to explain.
Source: Against Celsus (New Advent)