The meaning of Oneness is that He is not a Self composed of pieces. So there is no self like His Self, and no one other than Him has an attribute like His Attribute, or a doing like His Doing. The oneness of number is not meant by His Oneness. The one who is one by number has a half, and parts as well. Instead, the meaning is that He has no similar.
The proof for His Oneness is that it is necessary that the Maker would be Living, Powerful, Knowledgeable, Willful, and Choosing. So if the Attribute of the Maker is confirmed as we have mentioned, then we say that had the world had two makers, it would be necessary for each of them to be alive, powerful, knowledgeable, willing, and choosing. If there are two choosers, then it is valid that they would differ in the choice, because each of them is not forced to comply with the other in his choice; or else both of them would be forced, and the one who is forced would not be God.
If this is valid, then if one of them willed for what opposes the will of the other in something—like for one of them to will a person to be alive, and for the other to will his death—then it must be that either both of their wills are fulfilled, or neither of their wills is fulfilled, or one of their wills is fulfilled and the other’s is not. It is impossible that both wills would be fulfilled, because of their opposition. That is, if one of them willed a person’s life and the other willed his death, it is impossible that this person would be alive and dead at the same time. If both of their wills are unfulfilled, they are both weak; the one who is weak would not be God. If the will of one of them were fulfilled and the will of the other were not, then surely the one whose will was unfulfilled is weak, and the weak one would not be God and would not be Eternal. This evidence is known to those who believe in the Oneness; it is called the proof of mutual exclusivity.
Allah the Exalted Said:
﴿لَو كَانَ فِيهِمَا ءَالهَةٌ إِلا اللهُ لَفَسَدَتَا﴾
[which means] “Had there been for the Heavens and Earth gods other than Allah, they would have been in ruins.”