IN THE SAME WAY THEN: houtos oun kai:

This relates to the previous statement that "I have kept for myself" (v4) which reflects God's gracious choice ~ God's Sovereignty in salvation.

THERE HAS ALSO COME TO BE AT THE PRESENT TIME A REMNANT: en to nun kairo leimma kat ekloghen charitos gegonen (3SRAI): (6,7; 9:27) (28; 9:11; Ephesians 1:5,6)

Come to be (1096) (ginomai) means to cause to be ("gen"-erate), to become or to come into existence. The verb "come to be" is in the perfect tense which means that this remnant has come into existence at a point in time in the past and is a permanent part of the great host of the saved. (just another small "jot or tittle" supporting the great truth that one cannot lose his or her salvation).

"Remnant" (3005) (leimma from leípo = to leave or to lack) (See study on remnant) describes that which is left or that which remains.

Paul uses leimma in this verse to describe that group of Jews in national Israel which was left (so to speak) out of the general apostasy (abandonment of a previous loyalty) of most of Israel. Yes, most of the "chosen people" chose not to bow down to Jehovah, the great "I Am" but to bow down and kiss Baal, the pitiful "is not" (i.e., an idol is nothing). This remnant of Jews who placed their faith in the Messiah were "left" because God graciously elected them. Remember that "elect" is from ekloge which means to select or pick out some from a larger number.

Time (2540) (kairos) (Click for an in depth study of kairos)

Trench describes as

“the seasons...the critical epoch-making periods foreordained of God … when all that has been slowly, and often without observation, ripening through long ages is mature and comes to the birth in grand decisive events which constitute at once the close of one period and the commencement of another”.

The time to which Paul had reference was a strategic one, one marked by the inclusion of the Gentiles together with the Jew in the one Body of Christ, a time at which, while the Gentiles gladly received the Word, Israel was apostate, a time at which in spite of Israel’s apostasy, there was a remnant in Israel saved in the sovereign grace of God.

Although the nation had rejected Jesus, thousands of individual Jews had come to faith in Him (Acts 2:41 4:4; 6:1).

ACCORDING TO GOD'S GRACIOUS CHOICE (lit = choice of grace): kat ekloghen charitos:

Grace: (5485) (charis) (Click for in depth word study of charis) 

Grace is genitive of description. The ground or motivating factor in this choice of certain in Israel who were to be the objects of the sovereign choice of God for salvation, was grace, the spontaneous overflowing love of God bestowing the gift of salvation upon one who does not only not deserve that gift, but deserves appropriate punishment for his sins (compare a vessel of wrath otherwise prepared for destruction).

God did not choose this remnant because of its natural or racial descent or their "good works" (for as Jesus says "apart from Me you can do nothing"), but solely because of His grace, His unmerited favor (Dt 7:7-8 Ep 2:8-9 2 Ti 1:9).

Remnant Summary (Click study on remnant):

Note that the remnant is saved by grace and not by works (cf Ro 4:4-5) which parallels the truth Paul taught in [Ro 9:30-33]. It is impossible to mix grace and works, for the one cancels the other. Israel’s main concern had always been in trying to please God with good works (Ro 9:30-10:4). The nation refused to submit to Christ’s righteousness (Ro 10:4-5), just as religious, self-righteous people refuse to submit today.

This truth is found in a parallel verse in Deuteronomy where Moses warns the nation of Israel...

"Do not say in your heart when the LORD your God has driven them out before you, 'Because of my righteousness the LORD has brought me in to possess this land,' but it is because of the wickedness of these nations that the LORD is dispossessing them before you. It is not for your righteousness or for the uprightness of your heart that you are going to possess their land, but it is because of the wickedness of these nations that the LORD your God is driving them out before you, in order to confirm the oath which the LORD swore to your fathers, to Abraham, Isaac and Jacob. Know, then, it is not because of your righteousness that the LORD your God is giving you this good land to possess, for you are a stubborn people. (Deuteronomy 9:4-6)

OTHERWISE GRACE IS NO LONGER GRACE: epei e charis ouketi ginetai (3SPMI) charis:

If it were on the basis of works God's grace would not be what it really is -- free and undeserved. Human effort and God’s grace are therefore mutually exclusive ways to salvation.

Writing to the Galatian churches Paul stated that...

If you seek to be justified and declared righteous and to be given a right standing with God through the Law, you are brought to nothing and so separated (severed) from Christ. You have fallen away from grace (from God’s gracious favor and unmerited blessing). (Galatians 2:21, Amplified)

Paul understood grace as shown by his testimony to the Corinthians that...

by the grace of God I am what I am, and His grace toward me did not prove vain; but I labored even more than all of them, yet not I, but the grace of God with me. (1 Corinthians 15:10)

Henry Alford, commenting on the contents of verse six, says;

What was Israel “so earnestly” seeking? The answer can be found in [Ro 9:30-10:3] -- They were pursuing righteousness, a right standing before God. The situation was ironic. The Jews zealously sought to be accepted by God on the basis of works and the righteousness of the Law (cf. Romans 10:2-3). However, they were not accepted by God; only the elect were, because of God’s sovereign choice by grace.

So this is the situation: Most of the Jews have not found the favor of God they are looking for so earnestly. Why? [Ro 9:32] Because it is obtained only by faith and they were stubborn and rebellious.

The writer of Hebrews (4:2) says that...

(NASB) indeed we have had good news (gospel) preached to us, just as they also; but the word they heard did not profit them, because it was not united by faith in those who heard."

(Amplified " For indeed we have had the glad tidings [Gospel of God] proclaimed to us just as truly as they [the Israelites of old did when the good news of deliverance from bondage came to them]; but the message they heard did not benefit them, because it was not mixed with faith (with the leaning of the entire personality on God in absolute trust and confidence in His power, wisdom, and goodness) by those who heard it; neither were they united in faith with the ones [Joshua and Caleb] who heard (did believe)." (Hebrews 4:2)

BUT THOSE WHO WERE CHOSEN OBTAINED IT AND THE REST WERE HARDENED: e de ekloge epetuchen (3SAAI) oi de loipoi eporothesan (3PAPI):  (5; Ro 8:28-30; 9:23; Ephesians 1:4; 2 Thessalonians 2:13,14; 1 Peter 1:2)

"The Chosen" (1589) (ekloge from eklegomai in turn from ek = out + légo = select, choose, eklegomai meaning to choose or select for oneself, but not necessarily implying rejection of what is not chosen) means literally a choosing out and in Scripture speaks of election, the benevolent purpose of God by which any are chosen unto salvation so that they are led to embrace and persevere in Christ’s bestowed grace and the enjoyment of its privileges and blessings here and hereafter. Although not used in this way in the present context, ekloge, can describe election which is vocational. The Lord called out the tribe of Levi to be His priests, but Levites were not thereby guaranteed salvation. Jesus called twelve men to be apostles but only eleven of them to salvation. After Paul came to Christ because of God’s election to salvation, God then chose him in another way to be His special apostle to the Gentiles (Acts 9:15; Rom. 1:5).

Obtained (2013) (epitugchano from epí = intensifier + tugcháno = obtain, meet by chance, meet with, fall in with a person, hit the mark, to attain) means to hit, especially hit a mark with an arrow, to chance upon, and to to attain or obtain. The idea is to obtain or gain what is sought after.

Hardened (4456) (poroo from poros = small piece of stone broken off from a larger one) means to make hard like a stone, and so to make callous or insensitive to touch. Here as elsewhere in the New Testament, poroo is used only figuratively and specifically only in a spiritual sense referring to the effect on one's heart and mind. Poroo is used in this verse (and the noun form, porosis, is used in Romans 11:25) with a meaning similar to the verb skleruno in Ro 9:18 ("So then He has mercy on whom He desires, and He hardens whom He desires").

Some versions translate poroo in this verse as "blinded".

NIDNTT has the following note on poroo...

(from Hippocrates on) is derived from poros, tufa or tuff (porous stone), and means to harden, to form a callus (when broken bones heal), and thus to petrify, to become hard. (Colin Brown: New International Dictionary of NT Theology)

Kenneth Wuest comments that poroo means...

to cover with a thick skin, to harden by covering with a callous,” metaphorically, “to make the heart dull” (John 12:40). (Wuest's Word Studies in the New Testament)

William Barclay has a lengthy comment

Those chosen and the rest hardened equate with the "vessels of wrath" prepared for destruction and "vessels of mercy" prepared beforehand for glory (Ro 9:22,23) You say if He Hardened it's "not fair" -- don't take God to court Oh man. God is fair and just. Who are we to question His justice. That any are shown mercy should cause us to give Him glory in the highest for none deserved or earned His mercy. We must look at salvation from God's viewpoint not from man's where we think we can earn His favor or since we are so good in serving Him He owes us something. Modern day Christianity has a "small" God made in man's image and needs a fresh infusion of His divine perspective on life & eternity that he might simply bow in reverential awe at so great a salvation and so wonderful a Savior!

THE REST WERE HARDENED: oi de loipoi eporothesan (3PAPI): (Isaiah 6:10; 44:18; Matthew 13:14,15; John 12:40; 2 Corinthians 3:14; 4:4; 2 Thessalonians 2:10-12)

They were "covered with a thick skin" or "hardened by covering with a callous" which was a metaphor meaning to make the heart dull as in (Jn 12:40). (Lk 8:10) perfectly illustrates the elect remnant & the rest being hardened to not be able to understand what He was saying.

The Lord says to Isaiah after he cries "Send me" to...

"Go, and tell this people: 'Keep on listening, but do not perceive; Keep on looking, but do not understand.' 10 "Render the hearts of this people insensitive, their ears dull, and their eyes dim, lest they see with their eyes, hear with their ears, understand with their hearts, and return and be healed." 11 Then I said, "Lord, how long?" And He answered, "Until cities are devastated and without inhabitant, Houses are without people, And the land is utterly desolate... (Isaiah 6:9-11) (Comment: Isaiah’s preaching would not be that the people would repent but that they would harden their hearts against his messages. Isaiah’s message was to be God’s instrument for hiding the truth from an unreceptive people. Centuries later, Jesus’ parables were to do the same)

Note in the passage in Isaiah, the prophet asks "How Long?" and God explains that Israel's spiritual hardening will not be forever thus implying that there would be a remnant of believing Israel (see Isaiah 6:13).

Why are they hardened? It is in essence a judicial act of God for Israel's refusal to heed the Word of God (cf God's hardening in Ex 4:21 7:3 9:12 10:20, 27 11:10 14:4, 8, 17; Dt 2:30 Jn 12:40) and in response to them first hardening their hearts (Ex 8:15, 32 9:34 10:1 2Ch 36:13 Ps 95:8 Pr 28:14 Mt 19:8 Mk 3:5 Ep 4:18 Heb 3:8, 15 4:7).

Let us be very clear on what Paul is not saying. He is not saying that divine hardening is the cause of Israel's rejection of the gospel, but a punishment for it. Their hardening was the result of their resisting the truth, just as Pharaoh’s heart was hardened because he first resisted the truth and thus first hardened his own heart. It is not surprising to see Pharaoh, a pagan idol worshipping despot, harden himself against the Lord, but it might come as a surprise that most of God’s "chosen people" would do the same thing! Indeed, most of Israel was hardened because they deserved it and it was a just recompense (v9) for their sin against so great a light.

The noted Christian scholar Charles Feinberg, like Paul a believing Jew, tells the following story that gives contemporary evidence that God will never be without a believing remnant of His chosen people Israel.

Over a quarter of a century ago a Russian Jew of great learning named Joseph Rabbinowitz was sent to Palestine by the Jews to buy land for them. He went to Jerusalem. One day he went up on the Mount of Olives to rest. Someone had told him to take a New Testament as the best guidebook about Jerusalem. The Christ He had known was the Christ of the Greek and Roman churches, who were his persecutors and the persecutors of his people. But as he read the New Testament he became acquainted with the real Christ of whom the Old Testament Scriptures had foretold, and his heart grew warm. He looked off toward Calvary and thought: Why is it that my people are persecuted and cast out? And his conviction gave the answer: It must be because we have put to death our Messiah. He lifted his eyes to that Messiah and said: “My Lord and my God.” He came down from the mount a disciple of the Lord Jesus Christ. He went home to Russia and erected a synagogue for the Jews, over the door of which was written: “Let all the house of Israel know that God hath made that same Jesus whom ye have crucified, both Lord and Christ” [Ac2:36]. He was one of the many present remnant of Israel, which proves conclusively and better than words that God has not cast away His people.