Greater love has no one than this, that any lay down his life for that his beloved (John 15:13)
The word beloved is φίλος (philos) meaning loved, dear; devoted; friend. Thus a friend; someone dearly loved. The word for brother love is philadelphía ,from phílos, "loving friend" and adelphós, "a brother." Love is something that is experiential, Jesus tells us to love one another as he loves us (John 13:34). And it is taught by God (1 Thessalonians 4:9). Love is something that increases as we increase in knowledge of God, it is knowing of a deep love of God that will not separate us from God, we will not fall away, be choked out... In other words what overcomes the thorns of persecution, affliction, hardships... is love. Faith without love is nothing, and love is greater than the gifts that God gives. Faith and hope and love abides, and the greatest of these is love.
... purifying your souls in obedience to truth to the extent a sincere brother love for another fervently from a pure heart (1 Peter 1:22)
What does purification, a pure heart produce? Brotherly Love. John writes love is a sign that we do not walk in darkness and that we are not liars without truth (1 John 2:11; 1 John 4:20). Judgemental people who look down on one another is a clear sign of a lack of love (1 Corinthians 6). If faith without love is nothing then what does genuine faith look like? If God is love, what does genuine love look like?
God so loved the world that he gave his only Son... (John 3:16)
Why did God give his Son? because he loved us. God was rich in mercy, through his great love which he loved us (Ephesians 2:4). So when we were dead in our trespasses and sin, God loved us and was merciful, giving us his Son, so to make us alive and raise and seat us in the heavenlies so to demonstrate the incomparable riches of his grace in kindness to us in Christ Jesus (Ephesians 2:4-8). Love motivated God to send his Son.
If God saved and reconciled the world because he loved then did he create the world because of love? God exists love. Surely love motivated God. We come to know him as our heavenly Father who loves and cares for us. How can we hallow his name if we do not know him? We might obey but would we honor and give glory to such a person without love? When we grow in grace and knowledge of Jesus we give him glory, and honor, and praise (2 Peter 3:18). How can we love him if we do not know him? We love him because he first loved us. Why is the greatest commandment to love God with all your heart, mind, soul, and strength? Because that is who God is and what he desires, love.
We receive encouragement as sons, in that those he loves he disciplines for our benefit. Earthly fathers discipline for their own benefit... it is less stress to have obedient children, but God does it for our benefit. God's love is pure. The blessings we have received in Christ are from the riches of his grace, his mercy, all through his great love for us. Paul goes on to pray that we might have strength through a proper foundation of faith and love and new birth of the Spirit so that we know more of the love of Christ that will bring us into the fullness of God (Ephesians 3:13-20). This type of love causes the church to grow in knowledge of Christ, Ephesians 4:9-16, who is the radiant image of the glory of God. What strengthens us is faith working through love (Galatians 5:6).
And let us consider how to spur one another on to love and good deeds (Hebrews 10:24)
Do we experience God's love and then move on to greater things, like serving? We serve one another in love. We are at first rooted and founded in love but it continues. Love is greater to the extent of all the virtues, it is the bond that leads to maturity (Colossians 3:12-14). Really are not all of these virtues the definition of love (1 Corinthians 13). Love never comes to an end, all else will be put aside, and when I know as I am fully known, I will know the incomparable love of Christ.
Brotherly love (philadelphia | φιλαδελφία) must continue (Hebrews 11:1)
What can we add to our faith that is greater than love? "For this very reason, make every effort to supplement your faith with virtue, and virtue with knowledge, and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, and godliness with brotherly affection, and brotherly affection with love. For if these qualities are yours and are increasing, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ" (2 Peter 1:5-15, ESV). No greater virtues, gifts, no greater way than love and if we do not have and are not increasing we are ineffective, unfruitful in the knowledge of Jesus.