The abomination of desolation
What the abomination names — Antiochus, Rome's armies, or a last desecration.
Matthew 24:15-22
15“When, therefore, you see the abomination of desolation, which was spoken of through Daniel the prophet, standing in the holy place (let the reader understand),
16then let those who are in Judea flee to the mountains.
17Let him who is on the housetop not go down to take out the things that are in his house.
18Let him who is in the field not return back to get his clothes.
19But woe to those who are with child and to nursing mothers in those days!
20Pray that your flight will not be in the winter, nor on a Sabbath,
21for then there will be great suffering, such as has not been from the beginning of the world until now, no, nor ever will be.
22Unless those days had been shortened, no flesh would have been saved. But for the sake of the chosen ones, those days will be shortened.
What each tradition says
Rabbinic / Midrashic
Louis Ginzberg writes that the rabbis as a whole consider the expression to refer to the desecration of the Temple. Specifically, they understand it as the erection of a Zeus statue in the Temple's sacred precincts by Antiochus Epiphanes.
Louis Ginzberg, Abomination of Desolation (The Jewish Encyclopedia, 1901-1906) — In Rabbinical Literature
Patristic
Irenaeus says the enemy will sit in the temple, endeavoring to show himself as Christ. He connects this with the Lord’s declaration that the abomination of desolation spoken by Daniel will stand in the holy place, and let the reader understand.
Irenaeus, Against Heresies, Book V (ANF vol. 1, ed. Roberts & Donaldson) — Book V, ch. 25, §2 (Antichrist and the abomination of desolation)
Catholic
Haydock says the abomination of desolation was first partly fulfilled by various profanations of the temple: Pilate setting up Caesar’s image, Adrian’s statue in the holy of holies, and the removal of sacrifices. It will be more completely fulfilled by Antichrist and his precursors when they try to abolish the holy sacrifice of the Mass.
George Haydock, George Haydock's Catholic Bible Commentary (1859) — Comment on Matthew 24:15
Orthodox
Chrysostom says Christ referred his hearers to Daniel. According to Chrysostom, by “abomination” Christ means the statue of the one who then took the city, placed in the temple by the one who desolated the city and temple. Therefore Christ calls it “of desolation.”
John Chrysostom, Homilies on the Gospel of St. Matthew (NPNF ser. 1, vol. 10) — Homily LXXV on Matt. xxiv. 1, 2 (the abomination = the statue of the conqueror)
Reformed / Protestant
Calvin considers the natural meaning to be that the angel declares: after the temple has been once purified from Antiochus's pollutions and idols, another period will arrive when it is exposed to a new profanation. Then all its sacredness and majesty will be forever lost.
John Calvin, Commentary on Matthew, Mark, Luke, vol. 3 (Calvin Translation Society) — Comment on Matthew 24:15 (on Daniel ix. and xii.)
Evangelical
Wesley identifies the abomination of desolation as Daniel’s term, “the abomination that maketh desolate” (Dan 11:31). He explains it as the standards of the desolating legions, on which they bear the abominable images of their idols.
John Wesley, Wesley's Notes on the Bible, Matthew (Wesley Center Online) — Notes on Matthew 24:15