Daughter, mother, sister analogy is modalism. But how is solid-liquid-gas analogy modalism? In the former, there is only one person in three functions. In the latter, there are three distinct states with one essence; that's similar to three distinct persons with one essence, namely the trinity.
But you see, water cannot be solid, liquid and gas
all at once. You freeze water, it becomes ice. You heat it up, it melts into liquid. You heat it up more, it becomes steam. Everything in between is not "co-existing," but one bit of matter going from one form (aka "mode") into another. These "states" are also "modes." Therein lies the error. The Trinity is not One Person within the Being of God going through three different "states." That, again, falls into Modalism.
Qyöt27;55339310 said:
I had explicitly noted that it was not based on the amount of water in the glass, but the essence of what all three are - H2O. That doesn't change at all among them, but yet all three states of it can exist in one place at one time. No more reading into it after that. Which is why I called it rather insufficient.
Personally, I prefer the Eastern Orthodox approach to these sorts of matters, trying to rationalize stuff like this is one of the problems in the worldview of the Western church.
In regards to your metaphor, the problem is, once again, you had to
add to that amount (dropping the ice cube into the water). Aside from the fact that it seems to turn the analogy from Modalism into Arianism, it also, as I said before, falls into the trap that Muslims see coming and will use. In any case, if you have to add a solid ice cube, then that isn't the Trinity, which is the Three Persons of the One Being of God being co-eternal and co-existent since the beginning of time - nobody had to drop the Son into a class of the Father and Holy Spirit.
In regards to rationalization, the Muslim
is going to rationalize, however. He's going to pick apart every goofy (forgive the wording) analogy of the Trinity. This is why many of us have suggested to simply turn to the Word of God and verify it as a scriptural truth. It also helps, instead of knocking our brains over what metaphor works more than others, having a good, firm definition of what the Trinity is. Half the struggle will be making the Muslim understand the correct definition of the Trinity. The other half will be helping him see that the Trinity is not made up, but a revealed truth of God. You won't get that by comparing it to ice cubes.
On a separate note, I was reminded earlier today of a story told by Fulton Sheen. He was explaining to an old woman what the Trinity was. At the end of his explanation, the woman said, "Oh! I understand it fully now!" Sheen replied, "Then I didn't explain it to you well enough."