The mathematicians have a careful definition of dimension which would say that every physical object is three dimensional. In physics and engineering it is often useful to consider something to have a different dimensionality, but that will be an approximation. Your example of a piece of paper is a good one. When I am drawing on it, the useful concept is that it is two dimensional. If I look at it under a microscope, the surface is no longer flat and it is clearly three dimensional. Which view is useful depends on the problem. An example that is used a lot is a garden hose. When you are close, it is clearly three dimensional. Step back a ways and it looks like a line, 1 dimension. Flow problems will often use this approximation. Step back further and it is a mass point, 0 dimensions. If you put it in orbit around the earth, this will be useful.