וְנִשְׁבַּ֙עְתָּ֙ חַי־יְהוָ֔ה בֶּאֱמֶ֖ת בְּמִשְׁפָּ֣ט וּבִצְדָקָ֑ה וְהִתְבָּ֥רְכוּ ב֛וֹ גּוֹיִ֖ם וּב֥וֹ יִתְהַלָּֽלוּ׃ (ס)
און װעסט שװערן: ”אַזױ װי גאָט לעבט“. מיט אמת, מיט רעכט, און מיט גערעכטיקײט, װעלן זיך בענטשן מיט אים פֿעלקער, און מיט אים װעלן זײ זיך רימען.
Rabbeinu Bahya
A Midrashic approach based on Tanchuma Mattot 1. On the words: איש כי ידור נדר לה' the Midrash quotes G’d as saying to the Israelites: ‘be careful before making a vow not to violate it, as if someone violates a vow he will eventually violate his oaths also.’ If that were to happen he is as if he had denied G’d and all aspects of the Jewish religion and there is no forgiveness for this as the Torah has told us in Exodus 20,7 that G’d will not completely exonerate anyone who has used His name in vain. We have another verse on this subject in Jeremiah 4,2: “and swear ‘as the Lord lives;’” G’d said to the people: “do not think that it is permissible to utter such a kind of oath as the prophet quotes.” There is a general prohibition of swearing an oath involving the name of G’d unless the people doing so possess the following characteristics: described in Deut. 10,20 as: “you shall revere the Lord your G’d to serve Him and to cling to Him--and to swear in His name.” Only when you have fulfilled the conditions set out in the first half of this verse are you allowed to swear an oath using the name of the Lord.
Radak
The clean of hand and pure of heart, who hath not lifted up his soul unto vanity, And hath not sworn deceitfully: – Notice that he indicates in this verse three dispositions in man, action, thought, and speech; and in the three of them the man will be perfect who shall be clean in his actions, pure in his heart, and trustworthy in his speech. (The marginal reading) is נפשׁי (written) with yodh (= my soul), and is the utterance of God, as (in the verses) (Exod. 20:7; Deut. 5:11), “Thou shalt not take the name of the Lord thy God in vain”; and נפשׁו (His soul, essence, being) is (equivalent to) His Name. And so it says (in the verse) (Amos. 6:8), “The Lord God hath sworn by Himself (בנפשׁו).” And the word as written, נפשׁו, i.e. with waw, means his soul, viz. the swearer's; a man shall not lift up unto vanity nor swear deceitfully, but in truth and righteousness. And such swearing is a mitzvah to the fearers of the Name, as is said (in the text) (Deut. 6:13), “And shalt swear by His Name”; and another verse says (ibid. 10:20), “The Lord thy God shalt thou fear, Him shalt thou serve, and to Him shalt thou cleave, and by His Name shalt thou swear.” When these attributes (i.e. service, fear, adhesion) are thine, then by His Name shalt thou swear. And so it says (Jer. 4:2), “And thou shalt swear ‘As the Lord liveth,’ in truth, in judgment, and in righteousness.”