Commentary on the Bible, by Adam Clarke, [1831], at sacred-texts.com
Of false prophets and their lying signs, Deu 13:1-6. Of those who endeavor to entice and seduce people to idolatry, Deu 13:7-8. The punishment of such, Deu 13:9-11. Of cities perverted from the pure worship of God, Deu 13:12-14. How that city is to be treated, Deu 13:15. All the spoil of it to be destroyed, Deu 13:16. Promises to them who obey these directions, Deu 13:17, Deu 13:18.
If there arise among you a prophet - Any pretending to have a Divine influence, so as to be able perfectly to direct others in the way of salvation; or a dreamer of dreams - one who pretends that some deity has spoken to him in the night-season; and giveth thee a sign, אות oth, what appears to be a miraculous proof of his mission; or a wonder, מופת mopheth, some type or representation of what he wishes to bring you over to: as some have pretended to have received a consecrated image from heaven; hence the origin of the Palladium, Numa's Shields, and many of the deities among the Hindoos. But here the word seems to mean some portentous sign, such as an eclipse, which he who knew when it would take place might predict to the people who knew nothing of the matter, and thereby accredit his pretensions.
The Lord your God proveth you - God permits such impostors to arise to try the faith of his followers, and to put their religious experience to the test; for he who experimentally knows God cannot be drawn away after idols. He who has no experimental knowledge of God, may believe any thing. Experience of the truths contained in the word of God can alone preserve any man from Deism, or a false religion. They who have not this are a prey to the pretended prophet, and to the dreamer of dreams.
If thy brother - or thy son - The teacher of idolatry was to be put to death; and so strict was this order that a man must neither spare nor conceal his brother, son, daughter, wife, nor friend, because this was the highest offense that could be committed against God, and the most destructive to society; hence the severest laws were enacted against it.
Children of Belial - בליעל, from בל bal, not, and יעל yaal, profit; - Sept. ανδρες παρανομοι, lawless men; - persons good for nothing to themselves or others, and capable of nothing but mischief.
Thou shalt surely smite the inhabitants - If one city were permitted to practice idolatry, the evil would soon spread, therefore the contagion must be destroyed in its birth.
And there shall cleave naught of the cursed thing - As God did not permit them to take the spoils of these idolatrous cities, they could be under no temptation to make war upon them. It could only be done through a merely religious motive, in obedience to the command of God, as they could have no profit by the subversion of such places. How few religious wars would there ever have been in the world had they been regulated by this principle: "Thou shalt neither extend thy territory, nor take any spoils!"