These three things are linked in a continuous process. The way they are used in the Lord’s Word are, in a way, like a legal contract. The covenant sets out the terms of the contract,, which the parties agree to. Reciprocation takes place as the two parties act in following the contract, and conjunction is the mutual satisfaction of the parties when the contract is fulfilled.
Our most important contract is the one between us and the Lord, because it brings us to heaven and it fulfills His end and purpose for us. The reciprocal action that we can take is played out in the struggle between our own will and our own understanding of the Lord’s law. That’s where we fight our battle with the temptations that come from hell. If we persist, we will find conjunction.
The same process - covenant, reciprocation, and conjunction - can be seen in our relationships with all other people, strangers, friends, family members, and especially spouses. It can be a very powerful process, as it was and is the process that took place between the Divine love and Divine wisdom when the Lord created the Universe.
Covenant
We will look at the term “Covenant” first, because it is the beginning of the process. The covenant is the outline of what the Lord requires of us; as he said to Abraham, “walk before me and be thou perfect”. Here, to walk means to live your life (Genesis 17:1). Later the Lord renewed His Covenant with Isaac and with Jacob, and later still with the whole of the children of Israel at Mt. Sinai. As is said in Isaiah, “… put away the evil of your doings from before My eyes; cease to do evil, learn to do well…” (Isaiah 1:7-8). The basic evils are more explicitly stated in the Ten Commandments given at Mt. Sinai on the two stone tables. And just as these tables were kept in the Ark of the Covenant, in the tabernacle which was in the center of the ordered camp of the children of Israel, so should these laws be in the center of an orderly human mind.
The Word of the Lord, or the Sacred Scriptures, are the only place where we are taught about the Lord and the only place where we can learn about His laws. The more we read them, the more light can be let into our minds so that we can realize that the whole of the Word is the Covenant. The same covenant that was with Abraham is active with us right now.
(References: Apocalypse Explained 701; Arcana Coelestia 666 [1-2], 1023, 1038 [1-2], Arcana Coelestia 2084, 4197 [9], Arcana Coelestia 6804 [5-6], Arcana Coelestia 8767)
Reciprocation
The word reciprocation means a give and take, back and forth - the sharing of a conversation or elements of a common task. As used in the doctrines for the New Church it can mean the working together of an individual’s wish to do something and the learning of how to do it, or the interaction of a couple working to build a marriage, and raise a family, or of a person striving, with the Lord’s help, to regenerate.
In this context, reciprocation is the actual day to day working out of the Covenant. For example, children and parents have a long slow time as children go from total dependence on the parents to the stage when they can make decisions on their own, and much of this time requires the parents to allow children more and more choice while still being in charge. Children learn in school the give and take of getting along with contemporaries. Husbands and wives must adjust from being individuals, to being half of a couple, and how to be dependent on each other in that couplehood.
At some point with every person, when they reach adulthood, the decision comes to accept or reject any covenant they will have with God. The basic covenant spelled out to Abraham is still in power and can be adopted by anyone. Then they will start to seek out ways to apply it, to see truth, see and admit to evils in themselves and try to shun them. The work of the Lord has been going on in the children, helping them to be happy in getting along with parents and friends, but now it moves to a deeper plane. The work of the adult natural person in shunning an evil, and the Lord’s work of helping, both as part of the covenant, are the reciprocation that can lead to the Lord’s implanting of good loves in place of the shunned evil ones. This work goes on and on a little bit at a time, addressing one evil after another.
(References: Arcana Coelestia 5365 [2], 5928, 5931, Arcana Coelestia 8691, Arcana Coelestia 9200, 9604; Divine Love and Wisdom 35, 57; Divine Providence 92; True Christian Religion 371)
Conjunction
Conjunction means a joining with. We join with the Lord in the project of making ourselves into an angel. He wants this so that we can be eternally happy and useful, and He created us so that we are able to do it. We can refuse if we want to - we’re free to do that - but we should realize that if we do we will be, in the long run, unhappy.
By ourselves we can’t change our loves from evil ones to good ones. Only the Lord can do that. But we can control our actions and the thoughts that we dwell on. This is why the Ten Commandments are mostly given as negatives and not positives. If we avoid evil actions, it creates room for the Lord to work in. Eventually He can move the evils off to the sides, and wall them off, and fill the center with better loves, slowly causing us to be reborn. But it is always up to us, because we are making the choice. And it doesn’t happen in an instant; the challenges from hell go on all through our natural lives.
Ultimately, in the spiritual world we will be joined to the Lord living freely in His Heaven, doing what we love to do without barriers, because our loves are aligned with the Lord’s order. Those who have chosen not to follow his covenant are continually frustrated because they are in their own order which has never aligned with His, and they can never do all that they want.
Other terms that might be of interest are Proprium, Regeneration, and Reformation.
(References: Apocalypse Revealed 937; Arcana Coelestia 2021, 2063 [2-3], Arcana Coelestia 4525, Arcana Coelestia 8495 [3-5], 8506, 8507, 8516 [2-3], Arcana Coelestia 8725, Arcana Coelestia 10143 [3], 10729; Divine Providence 28 [2-3]; Heaven and Hell 367)
