God has shut up the whole world in sin (Ro 3:19), with no way out.
Man is helpless, powerless against sin, hopeless to change or fix it, lost and shut out from God.
This is the utter depravity of man.
"the Law"
In this context it must refer to the whole OT (cf. Rom. 3:21) because of the non-Pentateuch passages quoted in Rom. 3:10-18. Paul personifies "the law" as he did "the sin" inv. 9 (cf. Rom. 6:16-23).
"to those who are under the Law"
This refers uniquely to Jews and Gentile converts. Although it must be said that several of the OT quotes used refer to Gentiles in their original contexts.
All humans are sinful (cf. Rom. 3:23)!
NASB"that every mouth may be closed, and all the world may become accountable to God"
NKJV"that every mouth may be stopped, and all the world may become guilty before God"
NRSV"so that every mouth may be silenced, and the whole world may be held accountable to God "
TEV"in order to stop all human excuses and bring the whole world under God's judgment"
NJB"but it is meant to silence everyone and to lay the whole world open to God's judgment"
This is the major theme of Rom. 1:18-3:20 which is summarized in Rom. 3:23.
"every mouth" There are several phrases in Rom. 3:19-20 which denote all humanity.
1. "every mouth," Rom. 3:19
2. "all the world," Rom. 3:19
3. "no flesh," Rom. 3:20
3:20 "because by the works of the Law no flesh will be justified in His sight" This is an allusion to Ps. 143:2 (also note Job 4:17; 9:2; 25:4; Ps. 130:3; Pro. 20:9; Eccl. 7:20; 1 Kgs. 8:46; 2 Chr. 6:36), but with an added opening phrase. This was a major aspect of Paul's gospel (cf. Gal. 2:16; 3:11).
As a committed Pharisee, Paul uniquely knew the inability of religious enthusiasm and meticulous performance to provide inner peace.
For "flesh" see Special Topic at Rom. 1:3.
NASB, NRSV"through the Law comes the knowledge of sin"
NKJV"for by the law is the knowledge of sin"
TEV"what the Law does is to make man know that he has sinned"
NJB"all that law does is to tell us what is sinful"
This was one of the purposes of the OT. See Special Topic at Rom. 13:9. It was never meant to bring salvation to fallen mankind. Its purpose was to reveal sinfulness and drive all humans to the mercy of YHWH (cf. Rom. 4:15; 5:13,20; 7:7; Gal. 3:19-22, 23-29).
Utley