The 'I' of Romans 7
The 'I' who cannot do the good he wills — Paul before conversion, the regenerate believer, or a rhetorical voice of anyone under the law.
Romans 7:14-25
14For we know that the law is spiritual, but I am fleshly, sold under sin.
15For I don’t know what I am doing. For I don’t practice what I desire to do; but what I hate, that I do.
16But if what I don’t desire, that I do, I consent to the law that it is good.
17So now it is no more I that do it, but sin which dwells in me.
18For I know that in me, that is, in my flesh, dwells no good thing. For desire is present with me, but I don’t find it doing that which is good.
19For the good which I desire, I don’t do; but the evil which I don’t desire, that I practice.
20But if what I don’t desire, that I do, it is no more I that do it, but sin which dwells in me.
21I find then the law that, to me, while I desire to do good, evil is present.
22For I delight in God’s law after the inward man,
23but I see a different law in my members, warring against the law of my mind, and bringing me into captivity under the law of sin which is in my members.
24What a wretched man I am! Who will deliver me out of the body of this death?
25I thank God through Jesus Christ, our Lord! So then with the mind, I myself serve God’s law, but with the flesh, sin’s law.
What each tradition says
Rabbinic / Midrashic
The Jewish Encyclopedia derives the idea from Genesis 8:21, where the imagination of man's heart is evil from his youth. Yet from the two yods in Genesis 2:7, the Rabbis deduced that man has two Yeẓarim, the good (Yeẓer Ṭob) and the evil, as in Berachot 61a.
Joseph Jacobs and the Executive Committee of the Editorial Board, The Jewish Encyclopedia, vol. 12, s.v. 'Yeẓer ha-Ra'' (New York: Funk & Wagnalls, 1901-1906) — Opening section (the two Yeẓarim)
Patristic
Chrysostom says that in the words "but I am carnal," we are given a sketch of man as comporting himself in the Law and before the Law. The "I" is thus presented as man in that condition.
John Chrysostom (c. 349-407), Homilies on the Epistle to the Romans, Homily XIII (trans. J. B. Morris, rev. W. H. Simcox; Oxford 1876), in Nicene and Post-Nicene Fathers, ser. 1, vol. 11 (ed. Philip Schaff, 1889) — Homily XIII, on Romans 7:14
Patristic
Augustine concludes that in that apostolic Scripture the apostle spoke not only in his own person but also of others established under grace with him. They were not yet established in that perfect peace in which death shall be swallowed up in victory.
Augustine of Hippo (354-430), Against Two Letters of the Pelagians, in St. Augustin: Anti-Pelagian Writings, Nicene and Post-Nicene Fathers, ser. 1, vol. 5 (ed. Philip Schaff; New York: Christian Literature Publishing Co., 1886) — Book I, ch. 24 (He Concludes that the Apostle Spoke in His Own Person, and that of Those Who are Under Grace)
Catholic
John Ming holds that freedom from concupiscence is not restored to man, just as immortality is not. Yet abundant grace is given, by which man may overcome rebellious sense and deserve life everlasting.
John Ming, The Catholic Encyclopedia, vol. 4, s.v. 'Concupiscence' (New York: Robert Appleton Company, 1908) — Section on the transmission of concupiscence (following the citation of Romans 7:21-25)
Orthodox
No sourced position found. Checked: John of Damascus, An Exact Exposition of the Orthodox Faith (NPNF ser. 2, vol. 9) — Romans is not expounded; The Acts and Decrees of the Synod of Jerusalem (1672, trans. J. N. W. B. Robertson, 1899; OCR of the archive.org scan) — searched 'concupiscence'/'carnal', no treatment of the passage; The Longer Catechism of Philaret (Blackmore, 1845) and the 1894 Moscow Catechism of the Orthodox Eastern Church — no treatment; The Orthodox Confession of Peter Mogila (English trans., 1898, archive.org) — searched 'carnal'/'chapter vii', no exposition; Theophylact's commentary on Romans exists in English only in modern copyrighted translations.
Reformed / Protestant
Calvin states that the passage sets before us an example in a regenerate man. In him, the remnants of the flesh are wholly contrary to the Lord’s law, while the spirit would gladly obey it.
John Calvin (1509-1564), Commentaries on the Epistle of Paul the Apostle to the Romans (trans. John Owen, Calvin Translation Society, 1849) — Commentary on Romans 7:14-17, on verse 14
Evangelical
Albert Barnes regards Romans 7:14-25 as describing the state of a man under the gospel. He takes it as describing the operations of Paul's mind after his conversion.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on Romans 7:14
Evangelical
Wesley reads Paul’s “I am carnal” as part of comparing believers’ past and present states, in the flesh and in the spirit, while answering objections about whether the law is sin or death. Paul interweaves the whole process of a man reasoning, groaning, striving, and escaping from the legal to the evangelical state.
John Wesley (1703-1791), Explanatory Notes upon the New Testament (1755); CCEL's 'Wesley's Notes on the Bible' — Note on Romans 7:14