Herman Witsius on Romans 5:12

"By one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned." Romans 5:2

To illustrate the apostle’s meaning, we must observe these things: 

1st. It is very clear to any not under the power of prejudice, that when the apostle affirms that all have sinned, he speaks of an act of sinning, or of an actual sin; the very term, to sin, denoting an action. It is one thing to sin, another to be sinful, if I may so speak. 

2dly. When he affirms all to have sinned; he under that universality likewise includes those who have no actual, proper, and personal sin, and who, as he himself says, have not sinned after the similitude of Adam's transgression, verse 14. Consequently these are also guilty of some actual sin, as appears from their death; but that not being their own proper and personal sin, must be the sin of Adam, imputed to them by the just judgment of God. 

3dly. By these words  ἐφ' ᾧ πάντες ἥμαρτον for that all have sinned, he gives the reason why he had asserted that by the sin of one man death passed upon all. This, says he, ought not to astonish us, for all have sinned. If we must understand this of some personal sin of each, either actual or habitual, the reasoning would not have been just and worthy of the apostle, but mere trifling. For, his argument would be thus, that by the one sin of one all were become guilty of death, because each in particular had, besides that one and first sin, his own personal sin: which is inconsequential. 

4thly. The scope of the apostle is to illustrate the doctrine of justification he had before treated of. The substance of which consisted in this, that Christ, in virtue of the covenant of grace, accomplished all righteousness for his chosen covenant people, so that the obedience of Christ is placed to their charge, and they, on account thereof, are no less absolved from the guilt and dominion of sin, than if they themselves had done and suffered in their own person, what Christ did and suffered for them. He declares that in this respect, Adam was the type of Christ, namely, as answering to him. It is therefore necessary, that the sin of Adam, in virtue of the covenant of works, be so laid to the charge of his posterity, who were comprised with him in the same covenant that, on account of the demerit of his sin, they are born destitute of original righteousness, and obnoxious to every kind of death, as much as if they themselves, in their own persons, had done what Adam did. Unless we suppose this to be Paul’s doctrine, his words are nothing but mere empty sound. 

Herman Witsius, Economy of the Covenants  1.8.31