Much of the ice is on places lie Greenland and in mountains like mt Hood, which most summers nowadays only has very small glaciers.
But you are right, the
hysterics haven't read about Archimedes.
But, if the hysterics were right, given the supposed level of melting in Greenland and Antarctica ,most of florida should be underwater now.
However, most of the ice in the Arctic is floating on the ocean. The weight of the ice is the same as the water it displaces, so when the arctic ice melts, it is, as you say, like an ice cube melting in a cup of water. As it melts, the volume of water does not change.
If I fill a tumbler with ice cubes and add enough water to float them and then bring the water level to the very brim, then, as the ice melts, the water
doesn't over-flow BECAUSE that ice is floating. In that case, as YOU correctly noted, the ice displaces the same volume of water whether in its solid or in its liquid state. So intuitively, melting water in that case doesn't seem to pose a threat of raising sea levels.
However, if the ice isn't floating, but is "anchored" to the bottom or to dry land, when it melts and the water gets added to the sea-levels, the volume of water in the seas does increase.
I have a related question.
If the polar ice in the Arctic is getting smaller (i.e. global climate change is melting it), but the polar ice in the Antarctic is increasing (i.e., global climate change is adding to it), then isn't it possible that we could eventually see sea levels being REDUCED?