Adam Clarke on Hebrews 12:8

Then are ye bastards - This proceeds on the general fact, that bastards are neglected in their manners and education; the fathers of such, feeling little affection for, or obligation to regard, their spurious issue. But all that are legitimate children are partakers of chastisement or discipline; for the original word παιδεια does not imply stripes and punishments, but the whole discipline of a child, both at home and at school.