Does an oath take effect by uttering it in the heart without verbalization, and by merely uttering the object of the oath without uttering the condition of the oath?

An oath is not constituted by mere intention of the heart. Rather, it must be uttered verbally, such as saying "By God," and be accompanied by an action, such as saying "I will certainly do such-and-such." Uttering only one of them is not sufficient. The utterance must also be audible to the person himself, as stated in the Hadith (definition): "Indeed, Allah has forgiven my Ummah for what their souls whisper – or what they speak to themselves – as long as they do not act upon it or utter it." Therefore, merely thinking about an oath is not considered an oath until it is verbally expressed.