4. The denial of common grace. The Protestant Reformed Churches (see #3 above) grew out of a controversy between Herman Hoeksema and the Christian Reformed Churches over the issue of common grace. Hoeksema denied that there is any such thing as common grace, and in the midst of the controversy, the PRC was founded.
The idea of common grace is implicit throughout Scripture. "The Lord is good to all: and his tender mercies are over all his works" (Ps. 145:9). "He doth execute the judgment of the fatherless and widow, and loveth the stranger, in giving him food and raiment. Love ye therefore the stranger: for ye were strangers in the land of Egypt" (Deut. 10:18-19). "Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you; that ye may be the children of your Father which is in heaven" (Matt. 5:44-45).
The distinction between common grace and special grace closely parallels the distinction between the general call and the effectual call. Common grace is extended to everyone. It is God's goodness to humanity in general whereby God graciously restrains the full expression of sin and mitigates sin's destructive effects in human society. Common grace imposes moral constraints on people's behavior, maintains a semblance of order in human affairs, enforces a sense of right and wrong through conscience and civil government, enables men and women to appreciate beauty and goodness, and imparts blessings of all kinds to elect and non-elect alike. God "causes His sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous" (Matt. 5:45). That is common grace.
The doctrine of common grace has a long history that goes all the way back to Calvin and even Augustine. But type-4 hyper-Calvinism denies the concept, insisting that God has no true goodwill toward the non-elect and therefore shows them no favor or "grace" of any kind.
Source:
http://www.spurgeon.org/~phil/articles/hypercal.htm