In Romans 5:1
Therefore being justified by faith, we have peace with God through our Lord Jesus Christ
What is this peace?
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In Aristotelian terms peace is per definition that for the reason of which wars are waged. Thus, peace is causa finalis, or final cause of war. Now, the peace that a Christian will gain in God is the outcome of his war against the reign of sin and Satan, who acts in and through the sin and foments it. When a Christian fights against sin and Satan through the power/grace of Christ working powerfully in him (Col. 1:29), defeats them in this valiant and violent fight and grabs the Kingdom (Luke 16:16), then a Godly peace will be established in his heart, for there will be nothing to block coming of the Father and the Son to dwell in it (John 14:30), together with the Holy Spirit, of whom this heart will become an eternal temple (1 Cor. 6:19). This indwelling of the Holy Trinity in a Christian victor's heart, is called "Peace".
This peace was announced by the angel to the shepherds when Jesus was born.
Luke 2:11 Today in the town of David a Savior has been born to you; he is the Messiah, the Lord. 12This will be a sign to you: You will find a baby wrapped in cloths and lying in a manger.”
13Suddenly a great company of the heavenly host appeared with the angel, praising God and saying,
14“Glory to God in the highest heaven,
and on earth peace to those on whom his favor rests.”
This same peace was confirmed by Jesus before he went to the Cross.
John 14:26 But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you. 27Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid.
It is the peace of Jesus enabled by the Holy Spirit. It is an inner peace free from the wrath of God and evils of the world.
eiréné: one, peace, quietness, rest.
Original Word: εἰρήνη, ης, ἡ
Part of Speech: Noun, Feminine
Phonetic Spelling: (i-ray'-nay)
Definition: one, peace, quietness, rest
Usage: peace, peace of mind; invocation of peace a common Jewish farewell, in the Hebraistic sense of the health (welfare) of an individual.
Thayer's Greek Lexicon
In sum, it is the perfect peace of Christ undisturbed by anything in this world or out of this world.
Peace / Shalom (שָׁלֽוֹם) is living in Compliance with unchanging moral principles (Torah, תוֹרָה).
Jesus explains Peace is achieved by maintaining purity & healthy relationships [Mark 9:50] : “Salt is good, but if it loses its saltiness, how can you make it salty again? Have salt among yourselves, and be at peace with each other.”
By fulfilling the Torah, Yeshua Ha-Meshiach demonstrates Peace for Yisrael as “Sar-Shalom” ( שַׂר־שָׁלֽוֹם ) = Prince [of] Peace.
Through Jesus of Nazareth’s ministry, nations were not given peace with God [Matthew 10:34] - But nations were shown how to have peace with God by establishing a kingdom built on the Word [of] the Lord / Devar-YHVH (דְבַר־יְהֹוָ֖ה).
This peace is the reconciliation with God that we can have because of Christ's propitiatory work for us.
Paul goes on to say in this chapter:
Romans 5:6-11: You see, at just the right time, when we were still powerless, Christ died for the ungodly. Very rarely will anyone die for a righteous person, though for a good person someone might possibly dare to die. But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
Since we have now been justified by his blood, how much more shall we be saved from God’s wrath through him! For if, while we were God’s enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life! Not only is this so, but we also boast in God through our Lord Jesus Christ, through whom we have now received reconciliation.
Before Christ we were not just sinners, breaking an abstract impersonal law, but we were cut off from God, even to the extent that we are called his enemies (verse 10). We needed to be reconciled, not just because in our ignorance and blindness we opposed ourselves to God, but because God's righteous wrath at sin means he cannot tolerate those who stand in unrepentant opposition to him. But while we may struggle to love those we are enraged at, God does not. His love was stronger, and he sent his son Jesus to deal with our sin, cleansing and justifying us, bearing the wrath we deserve, and reconciling us back to him. Christ is the mediator who brings together the two sides of God and humanity who were divided by sin. If we have faith in Christ our conflict with God has been resolved and now we have peace.