Is intention a condition for a vow to be valid and binding? To clarify, when a person inattentively says: "I make a vow," without having the intention to make a vow, is the vow binding?

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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

When one inadvertently utters the word 'vow', he either does so without actually meaning it, as when he wants to say something but his tongue says the words of a vow by mistake, in which case he is not liable for anything, or he may intend the word, but not the meaning, i.e. he intends to say the words of a vow but without intention to make it binding, such as when one says this playfully. In this case, the vow is binding, as he said the word while intending it. So, as the cause (the vow's statement) is present, its consequence necessarily ensues even if it is against his will. It was narrated on the authority of Ibn ‘Umar that he said: "Four are binding in all cases: emancipation of slaves, divorce, marriage, and a vow." [Ibn Abi Shaybah]

Allaah Knows best.