And after that men began to be multiplied upon the earth, and daughters were born to them, The sons of God seeing the daughters of men, that they were fair, took to themselves wives of all which they chose. And God said: My spirit shall not remain in man for ever, because he is flesh, and his days shall be a hundred and twenty years. Now giants were upon the earth in those days. For after the sons of God went in to the daughters of men, and they brought forth children, these are the mighty men of old, men of renown.
(Genesis 6:1-4)
Why does the term 'giants' appear in this translation of the above scriptural passage? The word γίγαντες is used in the Septuagint to translate the Hebrew 'Nephilim.' In Greek Mythology, the γίγαντες were a savage race, children of Gaia, who fought and were defeated by the Olympian gods. The word Nephilim seems to come from the Hebrew root n-p-l (נ־פ־ל) - 'fall.' Therefore, the proselyte Aquila of Sinope translated Nephilim as 'the fallen ones.' Others, however, take it to mean that they cause others to fall, or are ones who fall upon their enemies. The translater Symmachus translated Nephilim as 'the violent ones.'
The word Nephilim re-appears later on in the Old Testament, such as in Numbers 13, where the term is used to refer to the hugely tall inhabitants of Canaan - the Anakim, descendants of a giant man named Anak. There is also the giant race of the Repha'im in the Old Testament.
When the Anakim are called Nephilim, they aren't being identified as a race. Their race has already been identified: they are Anakim. Rather, the term Nephilim is being used to describe them as giants. So they are not to be read as being the same race of people mentioned in Genesis 6. Rather, both are called Nephilim by analogy - because they were both giant groups of people.
Nephilim come up again in Judith 16, which celebrates how the Assyrian enemy was not defeated by tall and powerful giants; but by one woman, Judith.
In Ecclesiasticus 16:8, in the context of discussing the punishments of sinners, the inspired author writes that "the ancient giants [nephilim] did not obtain pardon for their sins, who were destroyed trusting to their own strength." He gives other biblical examples of divine punishment, such as the destruction of Sodom.
Consider also Baruch 3:24-28:
O Israel, how great is the house of God, and how vast is the place of his possession! It is great, and hath no end: it is high and immense. There were the giants, those renowned men that were from the beginning, of great stature, expert in war. The Lord chose not them, neither did they find the way of knowledge: therefore did they perish. And because they had not wisdom, they perished through their folly.
Then in Wisdom 14, there is an explicit link made to the Flood and Noe's ark:
But that the works of thy wisdom might not be idle: therefore men also trust their lives even to a little wood, and passing over the sea by ship are saved. And from the beginning also when the proud giants perished, the hope of the world fleeing to a vessel, which was governed by thy hand, left to the world seed of generation. For blessed is the wood, by which justice cometh.
Of course, the text at the beginning of Genesis 6 comes just before the Flood Narrative. The Nephilim, then, in Genesis 6 seem to be giant men of old who were destroyed in the flood. Were they a particular group of antediluvian men? As you will see, I think not.
In apocryphal writings that come under a 'book of Enoch', there can been be found an explanation that describes how the Nephilim were sons of fallen angels mingling with human women. Now, it is true that the biblical Enoch did give prophecies, as St Jude tells us, but the 'book of Enoch' as we have it is not to be taken as an unchanged extant text written by Enoch.
Nevertheless, the fallen angel interpretation was picked up by a lot of Jews and endorsed by significant Church Fathers, including St Irenaeus and St Ambrose. However, St Augustine realised a problem with this. In City of God 15.23, he explains that this is impossible because Angels have a spiritual substance. They do not have bodies. If they appear with bodies, this is in the manner of an apparition, not the assumption of a real body (consider what the Archangel Raphael reveals in Tobit, when he explains who he is).
Augustine then deals with the supposed testimony of the Book of Enoch and gives his own interpretation:
Let us omit, then, the fables of those scriptures which are called apocryphal, because their obscure origin was unknown to the fathers from whom the authority of the true Scriptures has been transmitted to us by a most certain and well-ascertained succession. For though there is some truth in these apocryphal writings, yet they contain so many false statements, that they have no canonical authority. We cannot deny that Enoch, the seventh from Adam, left some divine writings, for this is asserted by the Apostle Jude in his canonical epistle. But it is not without reason that these writings have no place in that canon of Scripture which was preserved in the temple of the Hebrew people by the diligence of successive priests; for their antiquity brought them under suspicion, and it was impossible to ascertain whether these were his genuine writings, and they were not brought forward as genuine by the persons who were found to have carefully preserved the canonical books by a successive transmission. So that the writings which are produced under his name, and which contain these fables about the giants, saying that their fathers were not men, are properly judged by prudent men to be not genuine; just as many writings are produced by heretics under the names both of other prophets, and more recently, under the names of the apostles, all of which, after careful examination, have been set apart from canonical authority under the title of Apocrypha. There is therefore no doubt that, according to the Hebrew and Christian canonical Scriptures, there were many giants before the deluge, and that these were citizens of the earthly society of men, and that the sons of God, who were according to the flesh the sons of Seth, sunk into this community when they forsook righteousness.
In the previous chapter, he had also given this view and used it as an example of his theme of the two cities. He presents us with a spiritual and pastoral exegesis:
When the human race, in the exercise of this freedom of will, increased and advanced, there arose a mixture and confusion of the two cities by their participation in a common iniquity. And this calamity, as well as the first, was occasioned by woman, though not in the same way; for these women were not themselves betrayed, neither did they persuade the men to sin, but having belonged to the earthly city and society of the earthly, they had been of corrupt manners from the first, and were loved for their bodily beauty by the sons of God, or the citizens of the other city which sojourns in this world. Beauty is indeed a good gift of God; but that the good may not think it a great good, God dispenses it even to the wicked. And thus, when the good that is great and proper to the good was abandoned by the sons of God, they fell to a paltry good which is not peculiar to the good, but common to the good and the evil; and when they were captivated by the daughters of men, they adopted the manners of the earthly to win them as their brides, and forsook the godly ways they had followed in their own holy society. And thus beauty, which is indeed God's handiwork, but only a temporal, carnal, and lower kind of good, is not fitly loved in preference to God, the eternal, spiritual, and unchangeable good. When the miser prefers his gold to justice, it is through no fault of the gold, but of the man; and so with every created thing. For though it be good, it may be loved with an evil as well as with a good love: it is loved rightly when it is loved ordinately; evilly, when inordinately. It is this which some one has briefly said in these verses in praise of the Creator: These are Yours, they are good, because You are good who created them. There is in them nothing of ours, unless the sin we commit when we forget the order of things, and instead of You love that which You have made.
St Augustine is surely right that fallen angels did not mingle with human women. Furthermore, Angels, being pure spirits (pure in the sense of physically simple ie. without physical parts and without matter), are not capable of lust. They are capable of pride, spiritual envy, and spiritual anger of the will, the rational appetite. But they do not possess sensible appetites or bodily passions (eg. lust, gluttony, the passion of sensible anger). And how could they assume bodies? They would have to be given them by God. Why would God give human bodies to fallen angels? He does not incarnate Angels but only His Eternal Word. But, they would have to have human bodies to copulate with humans. Only humans and humans can reproduce humans.
So then, were the sons of God the descendants of Seth and the daughters of men descendants of Cain? Perhaps. And this would certainly fit well with St Augustine's model of the heavenly city and the earthly city.
However, I propose here an alternative interpretation. This is that 'Nephilim' simply refers to men before the flood simpliciter, and that the 'sons of God' are just human men simpliciter, and that the 'daughters of men' are just human women simpliciter.
Are Angels sons of God? They are not sons in the sense of the Only Begotten Eternal Word of God. Angels are contingent beings created ex nihilo by the free decision of God. They are 'sons of God' in the sense of being created by God. But what about humans? Human beings are also children of God in the sense of being created by God. So, 'sons of God' can be interpreted just as much as referring to human men than as referring to immaterial Angels. Since we know that immaterial Angels cannot copulate, 'sons of God' must refer to human men.
But which human men? A particular group or generally? St Augustine's interpretation that it refers to a particular group has merit. Humans are also children of God in the sense of being created by God, but those that are in a covenant of grace with God are children of God in a higher sense. So, it is plausible that if there was a special covenant with Seth but not Cain, then the former could be called 'sons of God' in a special sense. However, I would like to propose an alternative interpretation. This is that 'sons of God' refers to human men generally.
But why would men be described as 'sons of God' while women be described as 'children of men'? Well, perhaps it is a semi-poetic way of describing men and women in a way that recalls their respective creation. Remember that Adam was created directly out of dust by God, whereas Eve was created out of a rib of Adam. So, in this sense, Adam was more directly a 'son of God,' while Eve came from Adam - from man.
St Augustine thinks that 'Nephilim' does not even refer to all the children of sons of Seth and daughters of Cain, but to only some of those. However, I want to go the other way and suggest that it refers to all humans before the flood. We know that before the flood, humans had greater longaevity. They lived longer. Methuselah only got the high score; but he wasn't otherwise exceptional. Others also lived into their 900s. It is also plausible that humans before the flood were of greater stature, hence 'giants.' They were taller, stronger, and more powerful, as the text of Genesis 6 suggests. As Wisdom says, these more powerful men were sinners and were destroyed by the flood. After the flood, men's years declined, and their stature and physical ability seem to have done so as well. When post-diluvian men are analogically called giants, these refer to men who were of greater than average stature, and so can be compared to 'the mighty men of old.'