Truth Empowers Binding Oaths
במדרש ונשבעת חי ה' באמת כו' אי אתה רשאי לישבע אלא אם יש בך מדות הללו ה' אלקיך תירא כאותן שנק' יראי ה' אברהם איוב יוסף
In the Midrash on the verse "And you shall swear, 'As Hashem lives,' in truth" (Yirmiyahu 4:2) — it is taught that you are not permitted to take an oath unless you possess these traits: "Hashem your God you shall fear" (Devarim 6:13), like those who are called the ones who fear Hashem — Avraham, Iyov, and Yosef.
The Midrash teaches that one may only take an oath in Hashem's name if he has refined himself with yiras Shamayim, like the tzaddikim who are called those who fear Hashem.
דנדרים ושבועות נמסרו לבנ"י בכח האמת שיש להם כדכ' תתן אמת ליעקב
For the power of vows and oaths was entrusted to Bnei Yisrael through the power of truth that is theirs, as it is written, "You give truth to Yaakov" (Michah 7:20).
The very ability of Bnei Yisrael to make binding vows and oaths flows from the trait of emes that Hashem granted to Yaakov and his descendants.
לכן תולין הנדר בו
Therefore one binds his vow to Him.
This is why a vow is tied to Hashem Himself.
נדר לאביר יעקב
"A vow to the Mighty One of Yaakov" (cf. Tehillim 132:2).
The Sfas Emes anchors this in the verse that calls Hashem "the Mighty One of Yaakov," linking the vow back to Yaakov's quality of truth.
כי אמת הפירוש שלא יוכל להשתנות וזה הכח א"א להשיג רק כשיש בו מדות הללו
For the meaning of truth is that which cannot change, and this power cannot be attained except when a person possesses these traits.
Truth by definition is unchanging, and only one who has these traits of yiras Shamayim can lay hold of this unchanging power.
ולכן אברהם יוסף ואיוב שנתנסו מן שמים זה הי' עדות שיש בהם זה הכח שלא להשתנות בשום אופן מזו האמונה שנקבע בהם
And therefore Avraham, Yosef, and Iyov — who were tested from Heaven — this testing was a testimony that they possessed this power, namely, not to change in any manner whatsoever from this emunah that was fixed within them.
The nisyonos that Avraham, Yosef, and Iyov withstood proved that their emunah was utterly unshakable — true emes that never wavers.
ולכן נקרא שבועת אמת
And therefore it is called an oath of truth.
Because their commitment was unchangeable, an oath sworn upon such steadfast truth is fittingly termed an oath of truth.
וזה הכח ניתן לבנ"י כמ"ש שארית ישראל כו' ולא ידברו כזב
And this power was given to Bnei Yisrael, as it is written, "The remnant of Yisrael... shall not speak falsehood" (Tzefaniah 3:13).
This same power of emes was implanted in all of Bnei Yisrael, as the navi promises that the remnant of Yisrael will speak no falsehood.
ואז שפת אמת תכון לעד ולפי שזה כח הדיבור נמסר לבנ"י מקפיד הכתוב שלא יחלל דברו שלא יחליש כח הדיבור שנטע הקב"ה באיש ישראל:
And then "the lip of truth shall be established forever" (Mishlei 12:19); and since this power of speech was entrusted to Bnei Yisrael, the verse is insistent that a person not profane his word — that he not weaken the power of speech that the Holy One, Blessed is He, implanted within the Jew.
When a person guards his word, the lip of truth endures forever; the Torah therefore warns him never to break his word, lest he weaken the holy power of speech that Hashem planted in every Jew.
Summary: The Sfas Emes explains that the power to make binding vows and oaths was entrusted to Bnei Yisrael specifically because of the trait of emes that Hashem gave to Yaakov. Truth, by its very nature, is that which never changes, and only one who possesses genuine yiras Shamayim can grasp this unchanging power. Avraham, Yosef, and Iyov are the model: their nisyonos proved that their emunah was fixed and unshakable, and an oath built on such steadfastness is rightly called an oath of truth. This same capacity for unwavering truth was implanted in every Jew, as the navi foretells that the remnant of Yisrael will speak no falsehood. For this reason the Torah is exacting that a person never profane his word, so as not to weaken the holy power of speech that the Holy One, Blessed is He, planted within him.