All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
There is no question as to whether it is permissible to omit the entity of the oath as long as the one swearing, or making an oath, does not intend to swear by other than Allaah. However, the scholars differed in opinion in regard to whether or not this formula is considered an oath in absolute terms, or whether it is considered an oath if someone intends thereby to make an oath.
The Kuwaiti Fiqh Encyclopedia reads: “If someone who swears does not mention the entity by which he swears but rather says, 'I swear,' 'I give oath,' 'I testify,' or 'I am determined' to do such and such,' or 'I swear not to do such and such,' then this is considered an oath by Abu Haneefah and his two companions.
The Maaliki School said: “If someone who swears omits saying (by Allaah) after saying I swear or I give oath or I testify, then it is considered an oath if he intended it, i.e. intended swearing by Allaah. In contrast, if he omits it after saying 'I am determined', it is not considered an oath even if he intends it. The difference between this verb and the three previous verbs is that in origin, 'to be determined' means 'to intend' and 'to be resolute', so it does not mean 'to swear' unless the entity by which one swears is mentioned, such as if one says 'by Allaah', for example. In contrast, the other three verbs are used for swearing; so with those verbs, it is enough to intend to swear by an entity without pronouncing it.
The Shaafi'i School said: “If the speaker omits the entity by which he swears, the formula will not be an oath, even if he intends to swear by Allaah, whether he mentions the verb of the oath or he omits it.”
The Hanbali School said: “If the one who swears omits saying 'by Allaah', for example, after having already uttered the verb or the noun that indicates swearing, then the formula is not an oath, unless he intended to swear by Allaah." [End quote]
Kashshaaf Al-Qinaa’ (a Hanbali book) reads: "If he did not mention the name of Allaah, such as if he said: 'I swear,' 'I have sworn,' 'I testify,' or 'I have testified,' and so on, such as 'I make oath' or 'I have made oath,' or 'I am determined,' or 'I have been determined,' or 'I am resolved to,' then it is not an oath because it might be an oath in Allaah's name or other than Allaah's name; so it is not an oath like other expressions which indicate this meaning unless he intends so because the intention turns it into swearing by Allaah, so it has to be considered an oath just as if he said it explicitly. This is established practice in both Islamic law and common usage.”
Allaah Knows best.