"In purpose" is your interpretation and addition. It is not in the text. Isaiah 9:6 says, "A child is born to us (the humanity of Jesus from Mary), a Son is given to us (the divinity of Jesus from the Father through the Spirit), and His name will be called...Eternal Father...The way this works is the tri-unity of God in the Spirit.
I did not say that the 3 are "one and the same." The 3 are distinct, but not separate. If They were physical, They could not be one. We would have to reason, as you said, that it must mean They are one in purpose. However, God is Spirit. All 3 are Spirit. It's like the oil that the ingredients of the compound ointment are compounded into to make one compounded ointment (Ex. 30). That is how God can be simultaneously 3 and 1, and we don't have to reason away that Jesus said, "I and the Father are one."
"In purpose" is your interpretation and addition. It is not in the text. Isaiah 9:6 says, "A child is born to us (the humanity of Jesus from Mary), a Son is given to us (the divinity of Jesus from the Father through the Spirit), and His name will be called...Eternal Father...The way this works is the tri-unity of God in the Spirit.
I did not say that the 3 are "one and the same." The 3 are distinct, but not separate. If They were physical, They could not be one. We would have to reason, as you said, that it must mean They are one in purpose. However, God is Spirit. All 3 are Spirit. It's like the oil that the ingredients of the compound ointment are compounded into to make one compounded ointment (Ex. 30). That is how God can be simultaneously 3 and 1, and we don't have to reason away that Jesus said, "I and the Father are one."