Ice is filled with air. So how can it be that the water level is rising when the pole caps melt?

it's the ice that is above ground that is melting... so as that ice melts, water flows down into the ocean and causes the level to rise

Ice may be filled with air, but it is made of water. The ocean basins hold the water. When the ice melts, there is more water in the basins, and the water level rises along the sides.

You're right that ice has lots of air bubbles in it (dissolved air comes out of solution when the water freezes). But dissolved gasses don't significantly change the volume of water. And: ice is less dense than water, so it floats, and a proportion of it sticks *out* of the water. When the ice re-melts and flows into the seas, it will *all* be in the water - making a larger volume. Also, ice can stay on the land (not increasing sea levels), while water will flow into the seas.

Much of the polar ice caps is above sea level. If you melt a quantity of the ice (above sea level) and pour it into the sea, sea level must rise. Of course a great deal of ice must be melted for the effect to be detectable.

Ice is not "filled with air". It contains some air, but the proportion of air in the ice is not sufficient to cause the effect you describe. It's a matter of balance, isn't it?

ice stays above the water when it is hard (icebergs and glaciers), once it is melted it mixes with water it increases the amount of water.

Ice is a solid form of water. When the ice melts it turns back to a liquid thus raising the level of water on the earth. When enough ice has melted the earth's water will spill over on the land thus having less land for people to live on. That is why stopping global warming is so critical. The earth has a delicate balance. Raising the temperature too high or lowering it too low will ultimately destroy us all.

The amount of air in ice is insignificant; just enough to make it look cloudy. Since the ice caps on Greenland and Antarctica are above sea level, their melting would raise the average sea level by over 60 meters (according to the Wikipedia entry for Antarctica).

You have a misconception regarding ice which is mostly water, not air. In fact, polar ice is compacted by the weight of the ice levels and snow above it so there is no air and the water molecules are squished. The molecular makeup of water is H2O (two molecules Hydrogen to one of Oxygen). These are not easily separated by natural means so heated water becomes steam or water vapor, falls back to Earth as rain and can be frozen together as ice. Water levels will rise as the ice melts. All the scientists are acknowledging that, although they dispute how high and how soon. Politicians will tell you that it'll be about a foot in the next century because they don't want to do anything about it. The most conservative scientists agree with that. Those scientists who have studied the matter and have no political ties (very few) are more likely to say five to ten feet in the next century. Science fiction authors (a very informed group) have predicted the ultimate rise will be 120 feet. They tend to have very quick timetables because it makes for better fiction. Different factors must be taken into account. IF the ice melting in Greenland rejoins the oceans gradually, the sea level rise will be more gradual. If it suddenly gets released (like Al Gore has predicted), sea level rise will be dramatic. All I really know is I'm high and dry in Wyoming and the only thing that really concerns me is how property levels will rise as the coasters try to move here.