BigH, your last paragraph was very nice and it makes much more easier to understand/remember this concept.
Also, from my school notes, my understanding of "half space" is that it can be defined as the space to the boundaries of a specific soil model in which solutions are not affected, so for simplicity it can be assumed as infinite, but for practical purposes, not necessarily it needs to be infinite.
For example, not sure if it is possible to adjust the extent of the soil model in geotechnical software for calculating settlements, but, if you analyze the settlement for a footing with a "space" of 2B (which B is the width of the footing) you will get larger settlements than if you analyze for a model with a "space" of 1B. However, then, if you analyze for "spaces" of 4B, 5B, 6B, etc, you will see that the settlement will converge to a given value. So, the "half space" in this case may be 5B-6B. That is how I understood "half space".
hi hokie66, your post reminded me that I saw an article in the Geostrata magazine from ASCE some time ago about why for geotechnical engineers soils are not just "dirt"... I will try to locate that article and post it here....