They understand that there can be only punishment or forgiveness, not both, realizing, e.g., that a child is either punished or forgiven, not forgiven after the punishment has been meted out. A spillover into Arminianism from Baptistic Calvinism is an opposition to infant baptism. It has been considered as the sacrament which helps prevenient grace to be implemented, restraining the child until such time as he becomes evangelically converted. Arminians believe that the several household baptisms mentioned in Acts 16 - 17 and 1 Cor. 1 imply that infants were baptized, and that this act is the NT counterpart of OT circumcision. But the untutored often feel that they should not baptize infants, because so many Baptist - type evangelicals do not.
Biblical inerrancy is another spillover.
The Arminian tradition has been a part of the long Protestant tradition which Fuller Seminary's Jack Rogers discusses in his Confessions of a Conservative Evangelical. It is interested in the Bible's authority and infallibility, and expresses confidence that Scripture is inerrant on matters of faith and practice, while remaining open on possible mathematical, historical, or geographical errors. Its scholars in general do not believe that Harold Lindsell correctly interprets the long Christian tradition on Scripture in such works as The Battle for the Bible, when he says that until about 150 years ago Christians in general believed in the total inerrancy of Scripture. Another spillover is in eschatological matters. But many lay Arminians have succumbed to such popular prophetic books as those of Hal Lindsey, which teach unequivocally that present political events and trends fulfill specific biblical prophecies.