Deuteronomy 19:18

18. shall make diligent inquisition] See Deu_13:14 (15), Deu_17:4; Deu_17:9; Sg.

false, falsely] Heb. sheḳer: so in Exo_20:16, but Deu_5:20 has shav, vain.

brother] here and next v.: the usual term in Sg. passages for fellow-Israelite.

The Cambridge Bible for Schools and Colleges (gen. ed. J. J. S. Perowne; Cambridge University Press, 1878–1918) — public domain. Text from a community e-Sword module.

Then shall ye do unto him as he had thought to have done unto his brother,.... Inflict the same fine or punishment on him he thought to have brought his brother under by his false testimony of him; whether any pecuniary fine, or whipping and scourging, or the loss of a member, or the value of it, or death itself; whether stoning, strangling, burning, or killing with the sword: though, in the case of accusing a priest's daughter of adultery, as Jarchi observes, such were not to be burnt, as would have been her case if proved, but strangled:

so shalt thou put the evil away from among you; the evil man that bears a false testimony of his brother, or the guilt of sin which would be incurred by conniving at him.

John Gill's Exposition of the Whole Bible (1746–1763) — public domain (CC PDM 1.0). Text via the HelloAO Bible API.

ודרשו השפטים היטב AND THE JUDGES SHALL DILIGENTLY ENQUIRE concerning the statement of those who assert them (the first witnesses) to be “plotting witnesses”, in that they investigate and crossexamine those who assert them to be “plotting witnesses” by diligent enquiry and scrutiny.

והנה עד שקר העד AND, BEHOLD, IF THE WITNESS BE A FALSE WITNESS — Wherever עד is written, [except if the numeral אחד, “one” is added (cf. Rashi on v. 15)], Scripture is speaking of two witnesses (Sanhedrin 30a).

Rashi on the Tanakh — English translations: “The Judaica Press complete Tanach with Rashi, translated by A. J. Rosenberg” (CC BY 4.0); “Pentateuch with Rashi's commentary by M. Rosenbaum and A.M. Silbermann, 1929-1934” (public domain); “The Metsudah Tanach series, Lakewood, N.J” (CC BY 4.0); and “The Book of Joshua, Metsudah Publications, 1997” (CC BY 4.0). Text via Sefaria.

AND THE JUDGES SHALL INQUIRE DILIGENTLY; AND, BEHOLD, IF THE WITNESS BE A FALSE WITNESS. Scripture has not explained how it became known that he is a false witness, for, since the testimony was presented by two witnesses, even if a hundred witnesses were to come and contradict them it would still not be established that they testified falsely [because the testimony of two witnesses carries the same weight as that of a hundred]. Nor can we say that the alleged murder-victim walked [into court], for, in that case Scripture would not say and the judges shall inquire diligently [for an investigation of testimony is incongruous when it is so demonstratively false]. Therefore, trustworthy tradition came and explained that the refutation, and thus nullified, and testimony that is merely contradicted. Ramban holds that if the second pair says, “How can you testify so, when at the same time you say Reuben killed Shimon you yourselves were with us in another place, far removed from that scene,” the first witnesses stand totally refuted and nullified. On the other hand, if the second pair merely contradicts the first pair by claiming that the alleged crime did not take place, we have a case of contradictory witnesses — two against two. If refutation is established and the person on trial has not yet been executed, then the plotting witnesses are subject to the same penalty they wanted to inflict upon their brother. If the verdict has already been executed, see Ramban further in Verse 19. But in the case of contradictory evidence, none of the witnesses is punished since we do not know which one is the false pair (Mishneh Torah, Hilchoth Eiduth 18:2). of witnesses takes place when they [the second pair of witnesses] say to the first “But you were with us on that day [and hour in such a place — away from the alleged scene of the crime].” The reason [that such testimony of the second pair of witnesses is accepted as conclusive] is because their testimony refers to the first witnesses themselves [rather than to their testimony, and the first pair, in order to defend itself, would therefore have to testify as to its own whereabouts at the time of the alleged crime]. Witnesses, however, are not given credence when testifying about themselves saying, “We have not done so,” and the second pair could say of the first pair that they killed someone or that they profaned the Sabbath.

Ramban (Nachmanides) on the Tanakh — English translation: “Commentary on the Torah by Ramban (Nachmanides). Translated and annotated by Charles B. Chavel. New York, Shilo Pub. House, 1971-1976” (CC BY 4.0). Text via Sefaria.