When it rains, water seeps up through my basement floor. Last year I had the property landscaped, so I know that that is not the problem. What could it be?
If landscaping did not solve the problem, then it sounds as if the water table under your house is naturally high. Even if the amount of water entering the basement is minor, it is still going to drastically raise the humidity level in the basement. The only way to solve this problem is to install a sump pump. It will turn on automatically when the water enters the basement. This will reduce the long-term damage to the floor itself, and more importantly it will keep the humidity level of the basement, and the entire house, down.