Gen 18:1 The LORD appeared to Abraham by the oaks of Mamre while he was sitting at the entrance to his tent during the hottest time of the day. 18:2 Abraham looked up and saw three men standing across from him. When he saw them he ran from the entrance of the tent to meet them and bowed low to the ground.

Who were these ‘three men’?

Some writers, both ancient and modern, have seen the three persons of the Trinity here.

According to Caesarius of Arles, cited in ACCS:

‘[Abraham] received the three men and served them loaves out of three measures. Why is this, brothers, unless it means the mystery of the Trinity? He also served a calf; not a tough one, but a “good, tender one.” Now what is so good and tender as he who humbled himself for us even unto death? He himself is that fatted calf which the father killed upon receiving his repentant son. “For God so loved the world that he gave his only-begotten Son.” For this reason Abraham went to meet the three men and adored them as one. In the fact that he saw three, as was already said, he understood the mystery of the Trinity; but since he adored them as one, he recognized that there is one God in the three persons.’

However, the relevant article in Wikipedia goes beyond any evidence that I am aware of (and does not cite any of its own) when it asserts that within the last 100-200 years the scholarly consensus has been that the three angels represent the Christian Trinity.

In the 15th century Andrei Rublev produced his famous icon.  Three figures are seated on three sides of a square table.  The fourth side is left open, and this seen by some as an invitation to the viewer to join the three at the table (or, it could just be that as in da Vinci’s The Last Supper and many other depictions of table scenes, the front is left open so that the picture is not dominated by the backs of its subjects’ heads!).

Carole Crumley writes:

‘As one gazes on this image, one is aware of the vast silence that surrounds the three figures. They seem to be looking into each other with an unqualified dignity, respect, and loving gaze—three distinct persons, three yet one. The fourth side to the table is left open intentionally by Rublev, signaling an invitation for the person viewing the image to draw near, even to sit at the table and join in the intimate conversation taking place. In a profound sense the person viewing the icon completes the image by joining the divine circle of the Sacred Three.’ (Feasting on the Word, Vol 3)

Rublev’s icon plays a key role in Richard Rohr’s recent (2016) book The Divine Dance: The Trinity and Your Transformation.  Rohr argues as follows:-

‘The scene is set up as “the Lord” appearing to Abraham, but in the realm of discernable form, those appearing to him are seen as “three men.”’

Rohr then notes that in the centuries of ‘reflection, theology, and storytelling’ that following the original biblical story the three men often came to be regarded as angels, ‘and perhaps something more’.  Then, following Rublev, Rohr makes the assumption that these three men are, or represent, the Trinity.  The evidence for this imaginative leap is, of course, flimsy, but then Rohr seems to have more confidence in knowledge that is derived from intuition, rather than that which is based on evidence.  Rohr’s next move is away from the biblical text altogether, and towards the icon.  He follows one unlikely assumption (that the story in Genesis tells of the Trinity) with another vague possibility: that ‘there was perhaps once a mirror glued to the front of the table!’  Much then is made of this, as indicating that the icon (not the biblical text, mind, but the icon) invites the observer into the fellowship of the Trinity.

It’s difficult to know what to do with such imaginings, because Rohr’s approach, relying on it does on intuition rather than on evidence, cannot be challenged on its own grounds.  What we can do is examine the biblical text itself, and seek to follow where it leads.

It should be noted, however, that Rohr is by no means alone.  Some writers with a firmer grounding in Scripture seem also to find this approach irresistable.  One such is Glynn Harrison, in his (otherwise) excellent book A better story: God, sex and human flourishing, chapter 13.

The passage distinguishes between the Lord and the two others, Gen 18:22; 19:1.  The latter text actually defines the two others as ‘angels’.  It is better, then, to regard the three as being the Lord (the ‘angel of the Lord’ / the preincarnate Christ?) accompanied by two angels.  Heb 13:2 alludes to this story when it says that ‘some have entertained angels unawares’.

Wenham (WBC) writes:

‘Throughout these chapters, the relationships between “the LORD,” “the men,” and “the angels” are shrouded in mystery. Initially it is said that “The LORD appeared” (v 1), but Abraham sees three men (v 2); there is also the strange alternation between singular and plural address in vv 3–4, as though Abraham regarded one as the leader. The supernatural nature of the visitors becomes evident in their conversation, and the promise of a son seems to prove that at least one of them speaks for the LORD. Nevertheless, the exact relationship between them is again blurred in vv 16–17 when “the men stood up … But the LORD thought.” Here at last the identity of the visitors is clarified: one is or represents the LORD; the other two are angelic companions. When they arrive in Sodom, they are called angels (19:1)…Gunkel, Westermann, and Haag see the variation in description of the visitors and the alternation of singular and plural address as proof of the composite nature of the narrative. With Delitzsch, Dillmann, and Jacob, I see these confusions as deliberate: they express the difficulty of human comprehension of the divine world.’

Gill observes that

‘the Father and the Holy Spirit are never said to appear in an human form, see Jn 5:37; or are ever called angels, as these are, Gen 19:1.’

Ellicott:

‘Jewish commentators explain the number by saying that, as no angel might execute more than one commission at a time, one of the three came to heal Abraham, the second to bear the message to Sarah, and the third to destroy Sodom. More correctly one was “the angel of Jehovah,” who came as the manifestation of Deity to Abraham, and the other two were his companions, commissioned by him afterwards to execute judgment on the cities of the plain, The number three pointed also to the Trinity of Persons in the Godhead, and is therefore read by our Church as one of the lessons for Trinity Sunday. But we must be careful not to use it as a proof of this doctrine, lest the inference should be drawn of a personal appearance of the Father and of the Holy Ghost, which would savour of heretical impiety.’

The Orthodox Study Bible is more careful that many, in noting that the text itself identifies at least two of Abraham’s visitors as angels:

‘The Holy Spirit says through the prophet Moses that God appeared to Abraham. This is another personal appearance of the Son of God to him. He saw three men standing before him, but he worshiped only one of them as Lord, for He is Lord and God. The other two are called “angels” (19:1). The Son of God is the Lord of all the angels.’