This is a challenging passage--I've endeavored to approach it with what historians call charity: I won't immediately assume contradiction on the part of the writer when the message is unclear, but will first explore what non-contradictory interpretations are available.
This is a long post, so I broke it up into pieces to create the illusion that it isn't as long.
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Spirit
The Greek word πνεῦμα (“pneuma”) and the English word spirit are not exact equivalents. Lexicons provide a variety of meanings/usages of pneuma; a useful electronic resource is found here, focusing on 3 principal English words to capture the essence of what is meant by pneuma: wind, breath, spirit.
The Greco-Roman writers did not have a concept of the element oxygen, nor a solid handle on the relationships among the states of matter. But they knew that pneuma was necessary to life and without it a person would die very quickly. This may have facilitated the mythology (in some places) that a less compassionate deity ruled the waters—there was no pneuma there (as far as they knew).
The Hebrew scriptures have a very similar concept of spirit (rûach). Genesis speaks of the breath of life; multiple families of religion believe that a spirit was supplied to flesh to make a living human being. Without the pneuma supplied by God, the body was just inanimate clay.
In English we now have several words to convey what is supplied by a single word in Hebrew & Greek. In addition to accepting that oxygen is necessary for life, many believers in the Bible hold that God supplied a spirit—which conveys the idea of the essence of one’s person but is never explicitly defined in the Bible. That individuals have their own spirit is stated by Paul himself (e.g. 2 Cor. 2:13, 7:13).
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The Holy Spirit
In addition to pneuma representing “the breath or essence of life”, Jesus, Paul, and others speak of one very specific pneuma, the pneuma that is ἅγιον (holy). One of the best descriptions of this specific use of pneuma is John 14:26
But the Comforter, which is the Holy Ghost, whom the Father will send
in my name, he shall teach you all things, and bring all things to
your remembrance, whatsoever I have said unto you.
Since Paul uses pneuma in multiple ways in his writings, he frequently (but not always!) disambiguates what spirit he is referring to (several examples cited above). When he refers to the Spirit of the Lord, the Spirit of God, or the Holy Spirit, it is possible to consistently interpret these as references to the Holy Ghost without running into hermeneutic difficulties.
But when he doesn’t disambiguate, we’re left to resolve the referent from context. In fairness to Paul, I find that he usually makes this pretty clear. I’ve acknowledged in a separate post that the first usage of pneuma in 2 Cor. 3:17 is less clear…and I’ll expand upon my thoughts there based on my latest reflections.
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The Spirit gives life
That pneuma gives life, in Paul’s world, is a tautology—its like saying that electricity powers electronics or pie is delicious. Of course pneuma gives life, that’s precisely what Genesis 2:7 teaches. But in 2 Corinthians 3 what is being given life?
Paul is contrasting covenants. In the law given to Moses there were numerous outward actions, and it won’t do to say they were unimportant—they were commanded by God—but they were no more an end in themselves than was the clay of Adam without rûach/pneuma. Paul compares the Law to the clay of man and the new covenant through Christ to the pneuma that brought life to the clay. Except in this case the creation is not of mortal life, but eternal life (see below).
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Process vs. Purpose
It is important to note what the old & new covenants have in common.
the law was our schoolmaster to bring us unto Christ (Galatians 3:24)
Come unto me, all ye that labour and are heavy laden (Matthew 11:28)
The jots & tittles of how to get there may have been updated, but the destination--and the overarching purpose God has for His children--remains exactly the same.
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The Lord is that Spirit
What then does Paul mean by “the Lord is [that] Spirit” in verse 17?
- “The Lord” is a reference to Christ (see here)
- The pneuma is not disambiguated
- Paul is contrasting covenants
- Paul has already told the Corinthians quite definitively that Jesus has a body (see discussion here)
I conclude that Paul is saying that it is Christ that brings life to the laws and ordinances of God’s covenants. Without the Lord, everything Paul talked about in verses 3-16 would be dead clay. Or to use Paul’s own words, without Christ we are left with “dead works”.
Because in the latter part of verse 17 Paul uses pneuma in a different way, he must now disambiguate it from the previous usage, and he specifies that he’s talking about the Holy Ghost—something he hasn’t done in the last 3 uses of pneuma.
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Letter vs. Spirit in verses 6-8
Circling back to verse 6-8, Paul talks about what we today colloquially refer to as “the letter of the law” and “the spirit of the law”. I believe the Shakespearean (and indeed the modern) use of these ideas does reflect Paul’s teaching here…but may not fully capture in cultural context what Paul is saying.
The letter of the law—the jots & tittles, the detailed instructions in the Torah—are not an end in themselves. On their own they are dead clay. The broader purpose God has in mind explains why the Torah was given, and not the other way around. This is what is meant by “the spirit of the law”, and I submit it is why Jesus focused so much more on who we are becoming inside than what is visible outside.
But Paul goes further than that--the new testament he’s teaching, centered on the atoning sacrifice of Jesus Christ, breaths life into the law, the ordinances, the plan, and the people who are transformed by it—past, present, and future.
The letter of the law is what’s visible on the outside. The spirit of the law is what one is becoming inside. The new covenant is giving life through the changes that are happening on the inside. These changes are the intent of the covenants.
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Disambiguating verse 17
Jesus gives life to the Law—many of the faithful obeyed the Law for generations. Jesus gives life to the covenants, old and new; He gives life to the ordinances, He gives life to the plan.
Thus it is entirely appropriate, after discussing how the new testament breathes life into humanity, to affirm that it is ultimately the Lord Jesus Christ—through whom the new covenant is given—that is that breath of life.
I do not believe Paul is stating that Jesus is spirit (see here); nor do verses 6, 8, or 17a refer to the specific Holy Spirit (17b & 18 do), but Paul is using pneuma in the entirely culturally appropriate sense of the word—it is that which gives life.
(I won’t attempt to disambiguate Romans 8 here but concede that very similar questions could be asked of it)
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What is Life
God wants to grant life. If Paul has in mind here just ordinary, mortal life, his statement is bland to the point of irrelevance—we noted above that “pneuma gives life” is a tautology.
Paul isn’t telling people how to live long, healthy mortal lives; he’s teaching people what leads to eternal life.
I conclude therefore that Paul is speaking not of mortal life, but everlasting life. Jesus granted another chance at mortal life to a few who had died (such as Lazarus); but He grants the opportunity of eternal life to all who accept His covenants.
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Conclusion
The pneuma that gives life in verse 6 is the new covenant in Christ, whose intent/focus is not on outward appearances but on inner transformation.
By life Paul is not referring to mortal life, but to eternal life, which is the intended result of that transformation.