The painting as non-object: Mark Rothko stated that art was communication on a spiritual level, outside of the confines of tangible form. His paintings were meant to transcend the category of "art" which he felt was too restrictive, decorative. He is quoted as saying that "flat forms destroy illusion and reveal truth". I would think that extending the painting around the sides would be contrary to this philosophy because it would draw attention to the object-ness of the art, something Rothko avoided.
The painting as an object: Donald Judd took his paintings to the level of object. But when he found the relationship between the painting support and the picture field too unspecified and difficult to reconcile, he began working in 3D.
In most instances, the sides of my support- not only the top- are part of the image. For support, I use either Blick Heavy Duty Stretcher Strips or Ampersand brand wood panels with deep cradled sides. Both offer a depth of between 1 1/2 and 2 inches. So then the painting could be deemed a three-dimensional object, although I hesistate to label them sculptures myself. Because of their three-dimensionality, one could argue that they are indeed sculptures, but I will leave this to critical debate.
It's obvious that paint and support- the actual materials, the matter- are tangible objects. But the painting, that is the picture field, may not be considered part of the object itself, even though it consists of matter. A critic or philosopher would probably say my current works are objects because the picture field encompasses four side planes and the top plane.
Artists, do you consider your paintings as objects or not, and why? And do you paint the sides of your work?