BUT IF OUR (in context primarily JEWISH) UNRIGHTEOUSNESS DEMONSTRATES THE RIGHTEOUSNESS OF GOD:ei de e adikia hemon theou dikaiosunen sunisthesin (3SPAI): (Ro 3:7,25,26; 8:20,21)

As you study this somewhat complex section, keep the context of Paul's purpose in mind. From the chart above, note that Paul is building his case for the deadliness of sin and the need for righteousness. So far, he has dealt first with the lost pagan's utterly depraved state and then he turned to the religious man (including the pious Jew), proving that the entire human race is guilty before God and preparing them to hear only answer to human sin and guilt, the gospel of Jesus Christ. Whether one is pagan or pious, both must come and receive the good news of salvation by grace through faith.

The New Living Translation has a helpful paraphrase rendering Romans 3:5-6...

“But,” some might say, “our sinfulness serves a good purpose, for it helps people see how righteous God is. Isn’t it unfair, then, for Him to punish us?” (This is merely a human point of view.) 6 Of course not! If God were not entirely fair, how would He be qualified to judge the world? (NLT - Tyndale House)

In other words, the imaginary Objector's question is that if people’s unrighteousness is an occasion for the righteousness of God to be shown, is it not unfair for God to execute His wrath upon unrighteousness?

Unrighteousness (93) (adikia from a = without + díke = what is right) is a condition of not being right, whether with God, according to the standard of His holiness and righteousness, or with man, according to the standard of what man knows to be right by his conscience.

If our unrighteousness causes the righteousness of God to shine more gloriously, how can God visit us with wrath?

Righteousness (1343) (dikaiosune from díkaios = , being proper or right in the sense of being fully justified being in accordance with what God requires) conveys the idea of conforming to a standard or norm. In Biblical terms it is that which is acceptable to God and in keeping with what God is in His holy character.

The word “righteousness” comes from a root word that means “straightness.” It refers to a state that conforms to an authoritative standard. Righteousness is a moral concept. God’s character is the definition and source of all righteousness and this is exactly what Paul is referring to in the context of the present verse.

God is totally righteous because He is totally as He should be. The righteousness of God could be succinctly stated as that which is all that God is, all that He commands, all that He demands, all that He approves, all that He provides (through Christ).

Demonstrates (4921) (sunistao from sún = together with + hístemi = set, place, stand) means literally to set together. It was used of setting one person with another by way of introducing or presenting him, hence, “to commend.” (commend = recommend as worthy of confidence or notice).

Here in (Romans 3:5) sunistao is used in the sense of putting together with a view to showing, proving, or establishing. Human sin is a foil by which God’s righteousness is seen all the more clearly. It establishes the fact of God’s righteousness, proves it by its very contrast with that sin.

The idea of "demonstrates" is that man's unrighteousness presents a dramatic contrast with God's righteousness -- it's like a jeweler who displays a diamond on black velvet to make the stone appear even more beautiful. It is true that God’s judgment of sin shows His righteousness and brings Him glory, but this does not mean that God is unfair.

The question is whether, considering that human unrighteousness demonstrates God’s righteousness it is right that He should punish man for what makes for His glory. The answer is that God is judge and therefore must punish sin. If this were not the case He could not be God.

What was their "Jewish Righteousness?" William Newell (Romans 3: Devotional and Expositional) has the following suggestions...

1. National disobedience to God’s oracles from Sinai onward.

2. Such neglect of these oracles, that at times (as in Josiah’s day), a single copy of the Law was a rarity!

3. Pride, however, over their position as the possessors of these oracles, even to the despising of nations that had them not, instead of ministering them to others (as Ps 67 shows was Israel’s real business).

4. Appalling ignorance of the spiritual meaning of the Divine oracles, and of the "voices of their prophets, " so they even killed the Righteous One! (Acts 13:27).

In context it is quite likely that this imaginary antagonist is making an appeal to David's unrighteousness that Paul had just used to show that God is righteous when He judges sin. But this valid observation may be twisted and perverted to serve the purpose of the apostolic antagonists. If this is true, the objector says, then our unrighteousness is the means of the commendation of God's righteousness and, if that be true, then what shall we say? Is it not man who thereby makes God's righteousness more conspicuous? Is he not to be commended for this rather than to be judged for sin by the infliction of divine wrath? Should not God be grateful rather than vindictive?

S. Lewis Johnson comments on "the righteousness of God" as

"not a reference to the righteousness of God that is given in justification to men who believe (cf. Ro 1:17 ; 3:21, 22 ; 10:3 ), but to the divine attribute of righteousness in its comprehensive sense, inclusive of His faithfulness (cf. v3) and truth (cf. v4, v7) .

WHAT SHALL WE SAY? THE GOD WHO INFLICTS WRATH IS NOT UNRIGHTEOUS, IS HE?: ti eroumen (1PFAI) me adikos o theos o epipheron (PAPMSN) ten orgen: (Ro 4:1; 6:1; 7:7; 9:13,14) (Ro 2:5; 3:19; 9:18-20; 12:19; Dt 32:39-43; Ps 58:10,11; 94:1,2; Nah 1:2,6-8; 2Thes 1:6-9; Rev 15:3; 16:5-7; 18:20)

This is clearly a rhetorical question, which Paul is asking for effect. The question is accompanied by the Greek negative particle me, which expects a negative answer.

Paul anticipates and answers the objection that his teaching actually impugned the very holiness and purity of God’s character

The KJV Bible Commentary says that ...

This is a clever but illogical argument. It is twisting Scripture to make what is inherently evil appear to be ultimately good. Paul anticipates someone saying, “If my unfaithfulness causes God’s faithfulness to be more apparent, is not my sin by contrast enhancing the world’s concept of the absolute holiness and faithfulness of God?” (Dobson, E G, Charles Feinberg, E Hindson, Woodrow Kroll, H L. Wilmington: KJV Bible Commentary: Nelson)

Inflicts (2018) (epiphero from epí = upon, to + phéro = to bring) is literally to bear upon, and in the present context means to bring upon or to inflict wrath or vengeance. Note the present tense indicating that this is a continual attitude of God.

Wrath (3709) (orge from orgaô = to teem, to swell) (Click word study of orge) is based on the root idea of a gradual swelling which eventually bursts, and thus describes an anger that proceeds from one’s settled nature. It is a deep, inner resentment that seethes and smolders. God's orge in short is His constant, controlled and settled indignation and opposition toward sin. God's settled indignation means that His holiness cannot and will not coexist with sin in any form whatsoever. God’s wrath is His holy hatred of all that is unholy and everything that is unrighteous. 

Note that God's orge does not refer to sudden, explosive, uncontrollable outbursts of anger and rage to which men are so prone. 

Orge is not God's uncontrollable rage, vindictive bitterness or losing of His temper, but the wrath of righteous reason and holy law.

Unrighteous (94) (adikos) pertains to  not being right or just and thus means unjust, wicked, treacherous,  unrighteous, crooked, characterized by lack of integrity. Adikos pertains to acting in a way that is contrary to what is right.

I AM SPEAKING IN HUMAN TERMS: kata anthropon lego (1SPAI): (Ro 6:19; 1Cor 9:8; Gal 3:15)

Human (444) (anthropos from aner = man + ops = countenance) is a human being, this generic name standing in distinction from gods and the animals.

Paul is simply paraphrasing the weak, unbiblical logic of his opponents—the product of their natural, unregenerate minds. Again lest his readers conclude that he was expressing his own thinking, Paul immediately adds the parenthetical explanation that he was speaking in human terms, that is, according to the human logic of the natural mind, arguing the way fallen man would argue. He was saying, in effect,

“Don’t think for a minute that I believe such perverted nonsense. I am only paraphrasing the charges that are often made against me.”

Paul, in even bringing up such a question as God’s acting unrighteously in visiting disobedient Israelites with wrath, instantly puts in the reverent parenthesis: "I speak after the manner of men"; as, "putting himself in the place of the generality of men, and using an argument such as they would use."

The KJV Bible Commentary adds a helpful note reminding us that "speaking in human terms"...

should not be understood as an absence of divine inspiration in recording these questions, but rather that Paul is using the form of human reasoning to express this inspired truth about God. Since God’s justice is not something that may be called into question, Paul indicates that only foolish human reasoning would attempt to do so. (Ibid)

Morison aptly paraphrases,

When I ask a question, ‘Is God unjust who inflicts wrath?’ I am deeply conscious that I am using language which is intrinsically improper when applied to God. But in condescension to human weakness I transfer to Him language which is customary for men to employ when referring to human relationships.”

S. Lewis Johnson writes:

May it never be (me genoito) is translated in both AV and RV "God forbid" but  Greek does not contain the name "God" so it should not be so translated.

Literally it reads "Be it not so!" or "Let it not be conceived of!" It is like saying "Banish the thought!" Paul uses this interjection frequently in Romans to denote an instant, even horrified rejection of a conception.

It's as he shouts out in the court of law "Objection" ... "Far be such a thought! for then (if God should be unrighteous in visiting a Jew with wrath) how shall God judge the world?"

FOR OTHERWISE HOW WILL GOD JUDGE THE WORLD: epei pos krinei (3SFAI) o theos ton kosmon: (Job 8:3; 34:17-19; Ps 9:8; 11:5-7; 50:6; 96:13; 98:9)

Newell comments that...

Paul assumes, and so do even these cavilers (Ed note: those who might be objecting and arguing), that there will be a day of judgment: "God Who visits with wrath." What the apostle is attacking is the false hopes of men to evade that judgment. Christ has been judged and smitten in our stead. But, alas, how a man hates to come to the cross as one "to whom that stroke was due" (Isa 53:8). But if you manage to escape conviction of sin, and thus miss personal faith in the Crucified One, you will go to hell forever. (Romans 3: Devotional and Expositional)

Abraham attests to God as Judge of the world just before He destroyed Sodom and Gomorrah...

"Far be it from Thee to do such a thing, to slay the righteous with the wicked, so that the righteous and the wicked are treated alike. Far be it from Thee! Shall not the Judge of all the earth deal justly?" (Ge 18:25)

David declares that...

He will judge the world in righteousness; He will execute judgment for the peoples with equity. (Ps 9:8)

Paul alludes to this psalm in Acts declaring that...

He (God the Father) has fixed a day in which He will judge the world in righteousness through a Man (the Lord Jesus Christ) Whom He has appointed, having furnished proof to all men by raising Him from the dead." (Acts 17:31)

For otherwise (1893) (epei) means since, if that were so.

Judge (2919) (krino) primarily signifies to distinguish, separate or discriminate; then, to distinguish between good and evil, right and wrong.

The Nelson Study Bible comments that...

Paul answers his own question (in Ro 3:5) with another question. If God does not punish unrighteousness, then He is not just and there will be no Day of Judgment. The flaw in logic is evident: God’s justice demands that He judge unrighteousness. To claim that God is unjust because He judges is a ludicrous argument. (Radmacher, E. D., Allen, R. B., & House, H. W. The Nelson Study Bible: NKJV.  Nashville: Thomas Nelson)

World (2889) (Kosmos) refers to this present evil man-centered (humanistic) world-system ruled and directed by Satan and in general living apart from God and opposed to Him.

Judgment of the world is a major theme of Scripture (Ge 18:25; Ps 50:6; 58:11; 94:2) and here the phrase "judge the world" probably refers to the great future day of judgment (see Ro 2:5, Rev 20:11-15).

In Romans 2 Paul wrote that

because of your stubbornness and unrepentant heart you are storing up wrath for yourself in the day of wrath and revelation of the righteous judgment of God (see note Romans 2:5)

John describes the final judgment of the world in Revelation recording that...

I saw a great white throne and Him who sat upon it, from whose presence earth and heaven fled away, and no place was found for them. And I saw the dead, the great and the small, standing before the throne, and books were opened; and another book was opened, which is the book of life; and the dead were judged from the things which were written in the books, according to their deeds. And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them; and they were judged, every one of them according to their deeds. And death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. And if anyone's name was not found written in the book of life, he was thrown into the lake of fire. (Revelation 20:11-15)

Paul’s point is that if God condoned sin, He would have no equitable, righteous basis for judgment. He shall judge the world, and in His judgment the ancient question, “Shall not the Judge of all the earth judge justly?” (Ge 18:25), shall have a resounding affirmative answer.

To summarize -  If there were any possibility of God’s being unrighteous, then how could He be fit to judge the world? Yet we all admit that He will judge the world.

The Wycliffe Bible Commentary adds that...

The New Living Translation renders it this way...

“But,” someone might still argue, “how can God condemn me as a sinner if my dishonesty highlights His truthfulness and brings him more glory?” (NLT - Tyndale House)

Lie (5582) (pseúsma from pseúdomai = to lie) is found only in  this verse and not in the Septuagint (LXX) and describes  the content of a false utterance, a falsehood or an untrue statement.

It is true that human sin does provide God the opportunity to show the truth about His character, specifically His great mercy and lovingkindness. Indeed, in response to mans' sin, God does not obliterate mankind but provides the way of salvation and reveals more about His own righteousness. Sinners (and this imaginary objector in Paul's illustration) argue therefore that mankind's sin serves a good purpose! Ridiculous! Such fallacious reasoning says we should go on sinning so God can go on proving how true and faithful He is. Sin is evil and is never justified and those who think this receive just condemnation. Sin is against God, not for Him. God does good because of who He is, not because of our evil

S. Lewis Johnson writes:

"With a different emphasis Paul, offering arguments an objector might pose to his doctrine of God’s determination to fulfill His promises even in the face of human sin and disobedience, continues the discussion. Putting words in the sinner’s mouth he asks, “If God’s truth is increased and God’s glory advanced by means of my lying, then why am I brought to judgment, Why may I not just do evil that good may come?” The apostle has inserted a parenthesis in the last question, asserting that this is the very charge brought against him and his followers, namely, that