Well, we could, say, look at the FSF's definition of free software:
http://www.gnu.org/philosophy/free-sw.html- The freedom to run the program, for any purpose (freedom 0).
- The freedom to study how the program works, and change it so it does your computing as you wish (freedom 1). Access to the source code is a precondition for this.
- The freedom to redistribute copies so you can help your neighbor (freedom 2).
- The freedom to distribute copies of your modified versions to others (freedom 3). By doing this you can give the whole community a chance to benefit from your changes. Access to the source code is a precondition for this.
It's arguable that the ability to install/uninstall a program isn't direction mentioned among these freedoms, but the ability, say, to run the software deletion program for any purpose would fall under that cateogory, and Android fails in this regard.
The Android platform as a whole is most certainly NOT FSF Free Software. There's some free software at the core. I consider my Android phone to be a proprietary product, and one I trust little with my privacy, confidentiality, and/or data integrity.
Unfortunately, it's best-of-breed and "most free" of generally available smartphone software presently, though Meego (or whatever it's being called today) and the Nokia 900 series might be a superior option (I've got my eye on both).