Genesis 4:26 Began vs. Profane
Genesis 4:26 Seth also had a son, and he named him Enosh. At that time men began to call on the name of the LORD.
First, I believe the more correct interpretation of Genesis 4:26 would be to use the term 'begin' as opposed to 'profane.' Note that the BDB translates the word 'begin' as: H2490 chlal - 1) to profane, defile, pollute, desecrate, begin.
So, as one can see both definitions 'profane' or 'begin' are possible and context would advise of which to use.
If one looks at some of the ancient Jewish writings (the Targums of Onkelos and Jonathan) they translate the term as 'profane.' I believe Adam Clarke also has a side note on this issue in his commentary. However, the LXX uses epikaleisthai from, kalew which means 'call.' Certain families did 'call' upon the Lord; a progression of 'calling' happened. However, the flood came because many 'profaned' the Lord. So, either definition could work.
However, though both could work, and neither damages the overall meaning of Scripture, I lean toward 'begin' as opposed to 'profane;' as Seth's line (in the context of the verse) is seen as the seed of the woman as opposed to the seed of the serpent - Genesis 3:15. Seth's line would be more prone to begin 'calling' as opposed to 'profaning.'
The meaning:
The covenant family by making its petition and voicing its praise in the name of the Lord, glorified God, not man (Gen. 4:26). This practice later distinguished Israel from all other nations (Gen. 12:8; 13:4, etc.). Thus, Moses' original audience would rightly have identified themselves with Seth and his descendents. In addition, I see a correlation between this and The Law (Sinai Decalogue was attested to before Moses, etc.): 'You shall not take the name of the Lord your God in vain' (Exod. 20:7) and 'calling' on the 'name of the Lord" (Gen. 4:26).

Dr. Joseph R. Nally, Jr., D.D., M.Div. is the Theological Editor at Third Millennium Ministries (Thirdmill).