The Beatitudes are linked together. They do not stand separately.
The poor in spirit, those detached from the desire for worldly goods, must necessarily also be the pure in heart, since their heart is not split and set on many things of this world, but purely on the “one thing necessary”. They love God and therefore they shall see God. These pure in heart, in turn, are meek, the holy and harmless and humble, because that is the character of the God their hearts are set on. The meek, in turn, are persecuted by the world and made to mourn; they are taken advantage of. Yet by their very act of suffering persecution, they are peacemakers. They make peace by the same method Christ did on the Cross: by draining off the bloody mess of human history into their own broken hearts. The peacemakers are also the merciful, for war is caused by the insistence on justice almost as much as by injustice. The cure for war and the way to peace is not justice but mercy, forgiveness. Yet the merciful hunger and thirst for justice even as they go beyond it to mercy, for they realize that in God’s spiritual economic recovery program for our fallen world the only way to justice is not from below, from force, from something less than justice (like bombs), but from above, from something more than justice, from mercy, from the character of God himself as revealed in Christ. It is Christ’s mercy in dying for us that satisfies justice. Mercy and truth met together, righteousness and peace have kissed each other on the Cross.
— Peter Kreeft, Back to Virtue
There are, of course, other ways to string these pearls together. This is just one way.
Recently I read someone say that old secular mantra about Jesus—he was a wise and great teacher, but not God. I wonder how they explain, or even try to live, the Beatitudes? These people contradict themselves in the same sentence. Even though the Beatitudes are the exact opposite of the wisdom of the world, they are completely and totally dependent on Christ, on God.