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Here in Philippians 3:3-21, the FLESH is connected to these OUTER factors like race, nationality, organization, birth/genes etc. See also Galatians 3:26-29 and Romans chapter 8.
And those are connected to the LAW (That is; the old law, covenant and order). As in Legalism. Rather than by faith = law by faith = the new, mature law, covenant and order.
The law of the letter, walking by sight, by the spirit of the world (law in the outer, law of the flesh. The law and spirit of the flesh, world, self.)
VERSUS
The law of faith, walking by faith, by the spirit of God (the law and spirit of God and Christ, written on the inner man: heart and mind, by grace through faith)
...
PAUL SAYS:
"If someone else thinks they have reasons to put confidence in the FLESH, I have more: circumcised on the eighth day, of the people of Israel, of the TRIBE OF BENJAMIN of Benjamin, a Hebrew of Hebrews; in regard to the law, a PHARISEE; as for zeal, persecuting the church; as for righteousness based on the law, faultless.
But whatever were gains to me I now consider loss for the sake of Christ. What is more, I consider everything a loss because of the surpassing worth of knowing Christ Jesus my Lord, for whose sake I have lost all things. I consider them garbage, that I may gain Christ and be found in him, *not having a righteousness of my own that comes from the law*, but that which is through faith in Christ—*the righteousness that comes from God on the basis of faith*. I want to know Christ—yes, to know the power of his resurrection and participation in his sufferings, becoming like him in his death, and so, somehow, attaining to the resurrection from the dead.
Not that I have already obtained all this, or have already arrived at my goal, but I press on to take hold of that for which Christ Jesus took hold of me. Brothers and sisters, I do not consider myself yet to have taken hold of it. But one thing I do: Forgetting what is behind and straining toward what is ahead, I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus. All of us, then, who are mature should take such a view of things. And if on some point you think differently, that too God will make clear to you. Only let us live up to what we have already attained.
Join together in following my example, brothers and sisters, and just as you have us as a model, keep your eyes on those who live as we do. For, as I have often told you before and now tell you again even with tears, many live as enemies of the cross of Christ. Their destiny is destruction, their god is their stomach, and their glory is in their shame. Their mind is set on earthly things. But our citizenship is in heaven. And we eagerly await a Savior from there, the Lord Jesus Christ, who, by the power that enables him to bring everything under his control, will transform our lowly bodies so that they will be like his glorious body.”
Philippians 3: 3-21
So...
The Law of the flesh, self, world = to be under the old, immature law, covenant, order
= Self righteousness
The Law of faith, by the spirit of God = to be under the new, mature, everlasting law, covenant, order.
= Righteousness by faith in Christ.
"That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit" -Romans 8:4
EGW says toward the end of the Christian dispensation, there will be an end to self righteousness. Hebrews 12:26-29 call it an end to the created. We can also read in Hebrews 8:13 that there will be a falling away of the old law and covenant. I believe this include also to judge by health and organization. Which are also outer, external, fleshly factors. Read Galatians 3:26-29.
"By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will soon disappear." -Hebrews 8:13 Entire series: "The Old vs. New Law, Covenant and Order"