'Baptized for the dead'
Vicarious baptism as some groups have practised it, the 'dead' read as a candidate's own mortal body (baptism in hope of the resurrection), or an unrecoverable reference to an early rite.
1 Corinthians 15:29
29Or else what will they do who are baptized for the dead? If the dead aren’t raised at all, why then are they baptized for the dead?
What each tradition says
Rabbinic / Midrashic
No sourced position found. Checked: full text of The Jewish Encyclopedia (1905), vols 2, 9, 10 and 11 (archive.org djvu scans) for 'baptized/baptism for the dead' and 1 Cor. xv. 29 — no article treats the verse, the Corinthian usage or any vicarious rite for the dead; no rabinic-midrashic reading of this Christian passage was found.
Patristic
Tertullian says being “baptized for the dead” means being baptized for the body, for it is the body that becomes dead. He asks what those who are baptized for the body will do if the body does not rise again.
Tertullian (c. 155-c. 220), The Five Books of Quintus Sept. Flor. Tertullianus Against Marcion (trans. Peter Holmes), in Ante-Nicene Fathers, vol. 3 (eds. Alexander Roberts and James Donaldson; Buffalo: Christian Literature Publishing Co., 1885) — Book V, ch. 10 (on 1 Cor 15:29)
Catholic
Fanning says there seems no question of conferring baptism on corpses, as later heretical sects practiced. He reports the conjecture that the Corinthians' unknown usage involved a living person receiving symbolic baptism as representing someone who died desiring Christian baptism but was prevented by unforeseen death.
William H. W. Fanning, The Catholic Encyclopedia, vol. 2, s.v. 'Baptism' (New York: Robert Appleton Company, 1907) — section 'Baptism of the dead'
Orthodox
Chrysostom takes Paul’s “baptized for the dead” to mean “for the dead bodies.” He says the one baptized is baptized with a view to the resurrection of his own dead body, believing that it no longer remains dead.
John Chrysostom (c. 349-407), Homilies on the Epistles of Paul to the Corinthians (trans. Talbot W. Chambers), in Nicene and Post-Nicene Fathers, ser. 1, vol. 12 (ed. Philip Schaff; New York: Christian Literature Publishing Co., 1889) — Homily XL, section 2 (on 1 Cor 15:29)
Reformed / Protestant
Calvin says those baptized for the dead are people looked upon as already dead, who have altogether despaired of life. He takes hyper here to have the force of the Latin pro, as in reckoning something as abandoned.
John Calvin (1509-1564), Commentary on the Epistles of Paul the Apostle to the Corinthians, vol. 2 (trans. John Pringle; Edinburgh: Calvin Translation Society, 1849; CCEL edition) — Commentary on 1 Corinthians 15:29
Evangelical
Albert Barnes holds that the apostle refers to baptism as administered to all believers. He calls this the most correct and simple view, best meeting the argument's design. It means believers were baptized with the hope and expectation of the resurrection of the dead.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on 1 Corinthians 15:29