A pot of boiling water that one removed [from the fire]-one should not put cold water in so that it will be warmed up. But one may put such water in it, or into a cup to cool it down
Talmud Bavli Shabbat 41b
Abbaye said, this is what it means: with regard to a pot that one removed, which has hot water in it, one may not put a small amount of cold water in it to be heated up, but one may put a large amount in it, to cool it down.
As we have seen, cooking is one of the thirty-nine Torah-prohibited Shabbat labors (avot melakha). It seems clear to us that bringing water to a boil is cooking. But there's a gray area. Under what circumstances may we put cold water into a container of water that has already been brought to boiling? This question is relevant because many ways in which one might heat water on Shabbat (including bringing it into contact with other hot objects) are considered "cooking."
The Mishnah's standard seems, at first, to be based entirely on intention: the physical reality matters little so long as it is my intention to cool water down, rather than heat it up. But Abbaye dislikes such a reading of the Mishnah. For him the intention does not matter—only the amounts and the resulting physical reaction. If we add a little cold water to a lot of hot water, the net effect is that the hot water is cooled slightly, but the cold water is heated much more, and brought close to the temperature of the hot water. On the other hand, if we add a lot of cold water, the net effect will be to bring the hot water and the cold water to a lukewarm temperature.